ALBERT

Description: It is known that if the objective of a wireless sensor network is not to reconstruct individual sensor readings at a fusion center but rather to compute a linear function of them, then the interference property of the wireless channel can be beneficially harnessed by letting nodes transmit simultaneously. Recently, an analog computation scheme was proposed to show that it is possible to take the advantage of the interference property even if nonlinear functions are to be computed. The scheme involves some pre-processing on the sensor readings and post-processing on the superimposed signals observed by the fusion center. Correspondingly, this paper provides a thorough base for a theory of analog-computing functions over wireless channels by specifying what is the maximum achievable. This means it is determined for networks of arbitrary topology which functions are generally analog-computable over the channel and how many wireless resources are needed. It turns out that the considerations are closely related to the famous 13th Hilbert problem and that analog-computations can be universally performed in the sense that the pre-processing at sensor nodes is independent of the function to be computed. Universality reduces the complexity of transmitters and the signaling overhead, and it is shown that this property is preserved if nodes leave or join the network. Analog-computability is therefore of high practical relevance as it allows for an efficient computation of functions in sensor networks.

Description: We study the application of matrix completion in the process of calibrating physical devices. In particular we propose an algorithm together with reconstruction bounds for calibrating circular ultrasound tomography devices. We use the time-of-flight (ToF) measurements between sensor pairs in a homogeneous medium to calibrate the system. The calibration process consists of a low-rank matrix completion algorithm to de-noise and estimate random and structured missing ToFs, and the classic multi-dimensional scaling method to estimate the sensor positions from the ToF measurements. We provide theoretical bounds on the calibration error. Several simulations are conducted to evaluate the theoretical results presented in this paper.

Description: We propose a particle filtering technique to track multiple maneuvering targets in the presence of clutter. We treat data association and state estimation, which are the two important sub-problems in tracking, as separate problems. We develop a game-theoretic framework to solve the data association, in which we model each tracker as a player and the set of measurements as strategies. We develop utility functions for each player, and then use a regret-based learning algorithm to find the equilibrium of this game. The game-theoretic approach allows us to associate measurements to all the targets simultaneously. Further, in contrast to the traditional Monte-Carlo data association algorithms that use samples of the association vector obtained from a proposal distribution, our method finds the association in a deterministic fashion. We then use Monte-Carlo sampling on the reduced dimensional state of each target, independently, and thereby mitigate the curse-of-dimensionality problem that is known to occur in particle filtering. We provide a number of numerical results to demonstrate the performance of our proposed filtering algorithm.

Description: In this paper we deal with the problem of detecting an extended target embedded in homogeneous Gaussian interference with unknown but structured covariance matrix. We model the possible target echo, from each range bin under test, as a deterministic signal with an unknown scaling factor accounting for the target response. At the design stage, we exploit some a-priori knowledge about the operating environment enforcing the inverse interference plus noise covariance matrix to belong to a set described via unitary invariant continuous functions. Hence, we derive the constrained Maximum Likelihood (ML) estimates of the unknown parameters, under both the $H_{0}$ and $H_{1}$ hypotheses, and design the Generalized Likelihood Ratio Test (GLRT) for the considered decision problem. At the analysis stage, we assess the performance of the devised GLRT for some covariance matrix uncertainty sets of practical relevance both for spatial and Doppler processing. The results highlight that correct use of the a-priori knowledge can lead to a detection performance quite close to the optimum receiver which supposes the perfect knowledge of the interference plus noise covariance matrix.

Description: In this paper, we present a novel memory-efficient high-throughput scalable architecture for multi-level 2-D DWT. We studied the existing DWT architectures and observed that data scanning method has a significant impact on the memory efficiency of DWT architecture. We propose a novel parallel stripe-based scanning method based on the analysis of the dependency graph of the lifting scheme. With the new scanning method for multi-level 2D DWT, a high memory efficient scalable parallel pipelined architecture is developed. The proposed architecture requires no frame memory and a temporal memory of size only $3 N +682$ for the 3-level DWT decomposition with an image of size $N times N$ pixels with 32 pixels processed concurrently. The elimination of frame memory and the small temporal memory lead to significant reduction in overall size. The proposed architecture has a regular structure and achieves 100% hardware utilization. The synthesis results in 90 nm CMOS process show that the proposed architecture achieves a better area-delay product by 60% and higher throughput by 97% when compared to the best existing design for the CDF (Cohen-Daubechies-Favreau) 9/7 2-D DWT.

Description: We consider a multiple-input multiple-output (MIMO) interference channel (IC), where a single data stream per user is transmitted and each receiver treats interference as noise. The paper focuses on the open problem of computing the outermost boundary (so-called Pareto boundary-PB) of the achievable rate region under linear transceiver design. The Pareto boundary consists of the strict PB and non-strict PB. For the two user case, we compute the non-strict PB and the two ending points of the strict PB exactly. For the strict PB, we formulate the problem to maximize one rate while the other rate is fixed such that a strict PB point is reached. To solve this non-convex optimization problem which results from the hard-coupled two transmit beamformers, we propose an alternating optimization algorithm. Furthermore, we extend the algorithm to the multi-user scenario and show convergence. Numerical simulations illustrate that the proposed algorithm computes a sequence of well-distributed operating points that serve as a reasonable and complete inner bound of the strict PB compared with existing methods.

Description: This paper studies secrecy rate optimization in a wireless network with a single-antenna source, a multi-antenna destination and a multi-antenna eavesdropper. This is an unfavorable scenario for secrecy performance as the system is interference-limited. In the literature, assuming that the receiver operates in half duplex (HD) mode, the aforementioned problem has been addressed via use of cooperating nodes who act as jammers to confound the eavesdropper. This paper investigates an alternative solution, which assumes the availability of a full duplex (FD) receiver. In particular, while receiving data, the receiver transmits jamming noise to degrade the eavesdropper channel. The proposed self-protection scheme eliminates the need for external helpers and provides system robustness. For the case in which global channel state information is available, we aim to design the optimal jamming covariance matrix that maximizes the secrecy rate and mitigates loop interference associated with the FD operation. We consider both fixed and optimal linear receiver design at the destination, and show that the optimal jamming covariance matrix is rank-1, and can be found via an efficient 1-D search. For the case in which only statistical information on the eavesdropper channel is available, the optimal power allocation is studied in terms of ergodic and outage secrecy rates. Simulation results verify the analysis and demonstrate substantial performance gain over conventional HD operation at the destination.

Description: A novel filter for nonlinear and non-Gaussian systems is proposed in this paper. The unscented Kalman filter is designed to give a preliminary estimation of the state. An additional RBF-network is added to the UKF innovation term to compensate for the non-Gaussianity of the whole system. The Renyi's entropy of the innovation is introduced and parameters of the RBF-network are updated using minimum entropy criterion at each time step. It has been shown that the proposed algorithm has a high accuracy in estimation because entropy can characterize all the randomness of the residual while UKF only cares for the mean and the covariance. It has been proved that with properly chosen bandwidth $Sigma$ , the minimum entropy problem of the innovation is convex. Therefore, the proposed adaptive nonlinear filter will be globally convergent and the misadjustment will be proportional to the step size $mu$ . The effectiveness of the proposed method is shown by simulation.

Description: In this paper, we explore a sequential Bayesian bound for state-space models focusing on hybrid continuous and discrete random states. We provide an analytic recursion for the sequential Weiss–Weinstein (SWW) bound for linear state-space models with solutions for Gaussian, uniform, and exponential distributions as derived, as well as for a combination of these. We compare the SWW bound for discretized states with the corresponding bound for the continuous states. The SWW bound is contrasted with the sequential Cramér–Rao bound for Gaussian distributions. Practical issues of SWW bounds are discussed and numerical simulation results provide insights into their behavior.

Description: Achieving better imaging of weak sources in the presence of strong interfering sources is a major challenge in various fields of signal processing, such as radio astronomy, SAR imaging, SONAR and wideband signal processing. We present a new algorithm for parameter estimation that can be implemented when a moving array is used. This adaptive beamformer can be employed in a variety of applications, such as radio astronomy with synthetic aperture arrays, SAR imaging, DOA estimation in towed array SONAR and wideband DOA estimation. Analytic performance analysis is provided together with simulations and tests on a new radio astronomy array. All these indicate a significant improvement compared to currently used filterbank techniques such as the MVDR, when strong interference is present, either inside or outside the field of view of the array. The latter case is especially important when directional antennas are used.

Description: This paper addresses the problem of adaptive waveform design for estimation of parameters of linear systems. This problem arises in several applications such as radar, sonar, or tomography. In the proposed technique, the transmit/input signal waveform is optimally determined at each step based on the observations in the previous steps. The waveform is determined to minimize the Bayesian Cramér-Rao bound (BCRB) or the Reuven-Messer bound (RMB) for estimation of the unknown system parameters at each step. The algorithms are tested for spatial transmit waveform design in multiple-input multiple-output radar target angle estimation at very low signal-to-noise ratio. The proposed techniques allow to automatically focusing the transmit beam toward the target direction. The simulations show that the proposed adaptive waveform design methods achieve significantly higher rate of performance improvement as a function of the pulse index, compared to other signal transmission methods, in terms of estimation accuracy.

Description: In this paper, we investigate the robust beamforming schemes for a multi-user multiple-input-single-output (MU-MISO) system with per-antenna power constraints and quantized channel direction information (CDI) feedback. Our design objective is to maximize the expectation of the weighted sum-rate performance by means of controlling the interference leakage and properly allocating the power among user equipments (UEs). First, we prove the optimality of the non-robust zero-forcing (ZF) beamforming scheme in the sense of generating the minimum amount of average inter-UE interference under quantized CDI. Then we derive closed-form expressions of the cumulative density function (CDF) of the interference leakage power for the non-robust ZF beamforming scheme, based on which we adjust the leakage thresholds and propose two robust beamforming schemes under per-antenna power constraints with an iterative process to update the per-UE power allocations using the geometric programming (GP). Simulation results show the superiority of the proposed robust beamforming schemes compared with the existing schemes in terms of the average weighted sum-rate performance.

Description: Delta-sigma $(Delta Sigma)$ A/D conversion is a popular technique used to achieve high resolution data conversion for low to moderate bandwidth applications. It is commonly accepted that the digital circuitry of the $Delta Sigma$ A/D converters should perform a linear time-invariant (LTI) filtering on the output of the $Delta Sigma$ modulator in order to reconstruct the input signal. However, it has been shown that, when higher order $Delta Sigma$ A/D converters are operated at higher oversampling ratios (OSRs), non-linear reconstruction algorithms extract more information about the input signal than LTI methods. Still, use of non-linear algorithms has been limited due to their complexity and stability issues. Two practical non-linear methods presented in the literature are fast projection onto convex sets (POCS) and direct projection (DP). In this work, we show that the non-linear reconstruction process for $Delta Sigma$ modulated sequences can be treated as a linear feasibility problem (LFP). We then show that if the reconstruction process is defined as an LFP, its implementation is less complex than in the case of the DP method. We further describe how the LFP can be well-conditioned and demonstrate the reconstruction process by using the surrogate constraint algorithm with random constraint selection. The described algorithm considers a small number of constraints at a time, which makes it suitable for serial implementation.

Description: Cognitive radio (CR) systems require awareness of spectrum occupancy in order to operate without causing harmful interference to primary users (PUs). Cyclostationary feature detection (CFD) is a preferred method for spectrum sensing under low signal-to-noise ratio (SNR) or/and noise uncertainty scenarios. To determine the presence, or otherwise, of PU signals, conventional CFD schemes tend to use test statistics over, either, multiple cycle frequencies for a fixed lag set, or, multiple lags for a fixed cycle frequency. This paper proposes a new method that jointly utilizes cycle frequencies and lags to produce more reliable test statistics. As the optimal way to apply this joint utilization requires prior knowledge of the 4th-order cyclic cumulant, which can be challenging to obtain, an alternative sub-optimal scheme independent of this cumulant knowledge will also be provided. It will be shown that, in the low SNR region, where it is most critical for CR applications, the proposed sub-optimal scheme can lead to similar detection performances as the optimal maximum likelihood technique. It will also be demonstrated that, compared to multi-cycle-frequency detection with selection combining, equal gain combining, or maximum ratio combining, the proposed provide superior performance.

Description: In this paper, we study the problem of code design to improve the detection performance of multi-static radar in the presence of clutter (i.e., a signal-dependent interference). To this end, we briefly present a discrete-time formulation of the problem as well as the optimal detector in the presence of Gaussian clutter. Due to the lack of analytical expression for receiver operation characteristic (ROC), code design based on ROC is not feasible. Therefore, we consider several popular information-theoretic criteria including Bhattacharyya distance, Kullback-Leibler (KL) divergence, J-divergence, and mutual information (MI) as design metrics. The code optimization problems associated with different information-theoretic criteria are obtained and cast under a unified framework. We propose two general methods based on Majorization-Minimization to tackle the optimization problems in the framework. The first method provides optimal solutions via successive majorizations whereas the second one consists of a majorization step, a relaxation, and a synthesis stage. Moreover, derivations of the proposed methods are extended to tackle the code design problems with a peak-to-average ratio power (PAR) constraint. Using numerical investigations, a general analysis of the coded system performance, computational efficiency of the proposed methods, and the behavior of the information-theoretic criteria is provided.

Description: Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework is defined and studied, that permits the formal definition of random vectors and time series whose desired joint distributions are a priori prescribed. Its key feature consists of preserving the writing of the joint distribution as the simple product structure it has under independence, while inputing controlled dependencies amongst components: This is obtained by replacing the product of probability densities by a product of matrices of probability densities. It is first shown that this matrix product model can be remapped onto the framework of Hidden Markov Models. Second, combining this dual perspective enables us both to study the statistical properties of this model in terms of marginal distributions and dependencies (a stationarity condition is notably devised) and to devise an efficient and accurate numerical synthesis procedure. A design procedure is also described that permits the tuning of model parameters to attain targeted statistical properties. Pedagogical well-chosen examples of times series and multivariate vectors aim at illustrating the power and versatility of the proposed approach and at showing how targeted statistical properties can actually be prescribed.

Description: Flow-induced Molecular Communication (FMC), where molecular transport is performed via flow, is utilized in microfluidic channels to enhance diffusion-based molecular communication. The incorporation of the microfluidic channel and the transport of molecules by flow, i.e., convection, require a rigorous analysis to develop an end-to-end concentration propagation model and a design for microfluidic channels. To the best of our knowledge, this is the first attempt to analyze concentration propagation in microfluidic channels from FMC perspective and devise them specifically to enhance the FMC. In this paper, a system-theoretic analysis of molecular transport is presented first. The system-theoretic model incorporates the solution of flow velocity in microfluidic channels and yields an end-to-end transfer function for concentration propagation based on building blocks of microfluidic channels. Then, the design of microfluidic channels is performed based on the least-squares Finite Impulse Response (FIR) filtering to achieve the desired end-to-end transfer function in FMC. According to the desired pass and stop bands, the required length and aspect-ratio parameters of the microfluidic channels are obtained for FIR filtering. The transfer functions for FMC is elaborated via numerical results. Furthermore, two example designs of microfluidic channels are presented for least-squares FIR band-pass and band-stop filtering in FMC.

Description: We study the problem of linear filter optimization with finite sample size, which has wide applications such as beamformer design in wireless communications and portfolio optimization in finance. Traditional methods in both fields are not robust against the imprecise channel vector and the noise covariance matrix (or the mean return and the covariance of assets in finance) due to finite sample size. We consider estimation errors both in the channel vector and the noise covariance matrix (or the mean return and the covariance) simultaneously. We resort to high-dimensional asymptotics to account for the fact that the observation dimension is of the same order of magnitude as the number of samples, and use the diagonal loading method (or the shrinkage estimator) to improve the robustness. The channel vector (or mean return) and the noise covariance matrix are estimated from the training data, and then corrected under several widely-used criteria. In an asymptotic setting where the number of samples is comparable to the observation dimension, we obtain linear filters that are as good as the optimal filters with a shrinkage structure and a perfect channel vector (or mean return) under different criteria. Monte Carlo simulations show the advantage of our linear filters in the finite sample size regime.

Description: The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space on a subgroup. Most of the literature focuses on separable subgroups, in this paper we will survey existing methods for a generalization to arbitrary groups, as well as present an improvement on existing methods. Comparisons are made with respect to the computational complexity, and the running time of optimized implementations in the C programming language. The new algorithms have the lowest known computational complexity for nonseparable lattices and the implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis.

Description: This study devotes to uncertainty principles under the linear canonical transform (LCT) of a complex signal. A lower-bound for the uncertainty product of a signal in the two LCT domains is proposed that is sharper than those in the existing literature. We also deduce the conditions that give rise to the equal relation of the new uncertainty principle. The uncertainty principle for the fractional Fourier transform is a particular case of the general result for LCT. Examples, including simulations, are provided to show that the new uncertainty principle is truly sharper than the latest one in the literature, and illustrate when the new and old lower bounds are the same and when different.

Description: This paper proposes a new relay selection method based on local channel state information (CSI) for a system consisting of a source, a destination and an arbitrary number of amplify-and-forward relay nodes. A set of candidate relays, whose source-relay (S-R) links are not in outage, is formed. An S-R link is in outage if its signal-to-noise ratio (SNR) is below the predefined threshold value of the destination SNR plus some adjustable margin. The candidate relay that yields the maximum second-hop SNR is then selected at the destination. Unlike the opportunistic relaying (OR) based on full CSI (F-CSI), the proposed method requires to equip the destination node with the instantaneous CSI of the S-R channel corresponding to only the selected relay. It is qualitatively shown that the training overhead of the proposed relay selection is less than or comparable to that of the partial relay selection (PRS) but can be much smaller than that of the OR with F-CSI. However, the proposed scheme requires to estimate a higher number of single-input single-output (SISO) channels than in the PRS scheme. The exact and asymptotic expressions of outage probability are derived and it is shown that the proposed method achieves full diversity. Simulation results verify theoretical analysis, and show that, for the optimized margin, the proposed scheme provides performance which is comparable to the method having F-CSI. The results also show that the proposed method significantly outperforms PRS, which may justify the linear order of the computational complexity associated with the estimation of the additional SISO channels and the low-cost one-dimensional line search used for optimizing the margin.

Description: Pulse-coupled synchronization is attracting increased attention in the sensor network community. Yet its properties have not been fully investigated. Using statistical analysis, we prove analytically that by controlling the number of connections at each node, synchronization can be guaranteed for generally pulse-coupled oscillators even in the presence of a refractory period. The approach does not require the initial phases to reside in half an oscillation cycle, which improves existing results. We also find that a refractory period can be strategically included to reduce idle listening at nearly no sacrifice to the synchronization probability. Given that reduced idle listening leads to higher energy efficiency in the synchronization process, the strategically added refractory period makes the synchronization scheme appealing to cheap sensor nodes, for which energy is a precious system resource. We also analyzed the pulse-coupled synchronization in the presence of unreliable communication links and obtained similar results. QualNet experimental results are given to confirm the effectiveness of the theoretical predictions.

Description: The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares (NLLS) problems. In this paper, a multi-agent distributed version of this algorithm is proposed to solve general NLLS problems in a network, named Gossip-based Gauss-Newton (GGN) algorithm. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

Description: Recently, various methods have emerged for sub- Nyquist sampling and reconstruction of signals with finite rate of innovation (FRI). These methods seek to sample parametric signals at close to their information rate and later reconstruct the parameters of interest. Some proposed reconstruction algorithms are based on annihilating filters and root-finding. Stochastic methods based on Gibbs sampling were subsequently proposed with the intent of improving robustness to noise, but these may run too slowly for some real-time applications. We present a fast maximum-likelihood-based deterministic greedy algorithm, IterML, for reconstructing FRI signals from noisy samples. We show in simulation that it achieves comparable or better performance than previous algorithms at a much lower computational cost. We also uncover a fundamental flaw in the application of MMSE (minimum mean squared error) estimation, a technique employed by some existing methods, to the problem in question.

Description: This paper addresses the problem of sampling non-bandlimited signals within the Finite Rate of Innovation (FRI) setting. We had previously shown that, by using sampling kernels whose integer span contains specific exponentials (generalized Strang-Fix conditions), it is possible to devise non-iterative, fast reconstruction algorithms from very low-rate samples. Yet, the accuracy and sensitivity to noise of these algorithms is highly dependent on these exponential reproducing kernels — actually, on the exponentials that they reproduce. Hence, our first contribution here is to provide clear guidelines on how to choose the sampling kernels optimally, in such a way that the reconstruction quality is maximized in the presence of noise. The optimality of these kernels is validated by comparing with Cramér-Rao's lower bounds (CRB). Our second contribution is to relax the exact exponential reproduction requirement. Instead, we demonstrate that arbitrary sampling kernels can reproduce the “best” exponentials within quite a high accuracy in general, and that applying the exact FRI algorithms in this approximate context results in near-optimal reconstruction accuracy for practical noise levels. Essentially, we propose a universal extension of the FRI approach to arbitrary sampling kernels. Numerical results checked against the CRB validate the various contributions of the paper and in particular outline the ability of arbitrary sampling kernels to be used in FRI algorithms.

Description: This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity. For covariance matrices of low separation rank, our results establish that PRLS has significantly faster convergence than the standard sample covariance matrix (SCM) estimator. The convergence rate captures a fundamental tradeoff between estimation error and approximation error, thus providing a scalable covariance estimation framework in terms of separation rank, similar to low rank approximation of covariance matrices . The MSE convergence rates generalize the high dimensional rates recently obtained for the ML Flip-flop algorithm , for Kronecker product covariance estimation. We show that a class of block Toeplitz covariance matrices is approximatable by low separation rank and give bounds on the minimal separation rank $r$ that ensures a given level of bias. Simulations are presented to validate the theoretical bounds. As a real world application, we illustrate the utility of the proposed Kronecker covariance estimator for spatio-temporal linear least squares prediction of multivariate wind speed measurements.

Description: Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper develops algorithms for decentralized sparsity-regularized rank minimization over networks, when the nuclear- and $ell_1$ -norm are used as surrogates to the rank and nonzero entry counts of the sought matrices, respectively. While nuclear-norm minimization has well-documented merits when centralized processing is viable, non-separability of the singular-value sum challenges its decentralized minimization. To overcome this limitation, leveraging an alternative characterization of the nuclear norm yields a separable, yet non-convex cost minimized via the alternating-direction method of multipliers. Interestingly, if the decentralized (non-convex) estimator converges, under certain conditions it provably attains the global optimum of its centralized counterpart. As a result, this paper bridges the performance gap between centralized and in-network decentralized, sparsity-regularized rank minimization. This, in turn, facilitates (stable) recovery of the low rank and sparse model matrices through reduced-complexity per-node computations, and affordable message passing among single-hop neighbors. Several application domains are outlined to highlight the generality and impact of the proposed framework. These include unveiling traffic anomalies in backbone networks, and predicting networkwide path latencies. Simulations with synthetic and real network data confirm the convergence of the novel decentralized algorithm, and its centralized performance guarantees.

Description: Multiple-input multiple-output (MIMO) radar utilizes orthogonal waveforms on each transmit element to achieve virtual aperture extension. Compared to a directed beam radar, MIMO radar has increased Doppler resolution due to the longer integration times required to maintain the same energy on target. However, the requirement for longer integration times can also cause target returns to be spread over multiple range-Doppler bins, which decreases probability of detection. This paper derives an analytical expression for probability of detection that explicitly accounts for range-Doppler migration. The effect of target velocity, target acceleration and integration time on range-Doppler migration is analyzed. A framework for velocity and acceleration compensation and step sizes for full and partial compensation are proposed. Single-target track completeness and track accuracy are compared for directed beam radar, MIMO radar with full compensation, MIMO radar with partial compensation, and uncompensated MIMO radar. Results indicate that compensation is required to prevent degraded probability of detection and track completeness as target velocity and acceleration increase. Full compensation mitigates the effects of range-Doppler migration but requires additional computational complexity. The use of partial compensation reduces computational complexity requirements but has diminished tracking performance due to coasting over missed measurements.

Description: In this paper we address the problem of sparse signal reconstruction. We propose a new algorithm that determines the signal support applying statistical thresholding to accept the active components of the model. This adaptive decision test is integrated into the sparse Bayesian learning method, improving its accuracy and reducing convergence time. Moreover, we extend the formulation to accept multiple measurement sequences of signal contaminated by structured noise in addition to white noise. We also develop analytical expressions to evaluate the algorithm estimation error as a function of the problem sparsity and indeterminacy. By simulations, we compare the performance of the proposed algorithm with respect to other existing methods. We show a practical application processing real data of a polarimetric radar to separate the target signal from the clutter.

Description: In wireless communications, increased spectral efficiency and low error rates can be achieved by means of space- time-frequency coded MIMO-OFDM systems. In this work, we consider a MIMO-OFDM transmit signal design combining space-frequency modulation with a time-varying linear precoding technique which allows spreading and multiplexing the transmitted symbols, in both space, time and frequency domains. For this system, we propose two closed-form semi-blind receivers that exploit differently the multilinear structure of the received signal, which is formulated as a nested PARAllel FACtor (PARAFAC) model. First, we devise a least squares Khatri-Rao factorization (LS-KRF) based receiver for joint channel and symbol estimation by making an efficient use of a short frame of pilot symbols. The LS-KRF receiver provides the same performance at a lower computational complexity compared to the alternating least squares (ALS) based receiver. For further reducing pilot overhead, we develop a simplified closed-form PARAFAC (S-CFP) receiver coupled with a pairing algorithm that yields an unambiguous estimation of the transmitted symbols without the need of a pilot frame. The uniqueness conditions, spectral efficiency and computational complexity of the LS-KRF and S-CFP with pairing receivers are analyzed and compared with the ALS receiver. It is shown that the S-CFP with pairing receiver has the same order of computational complexity as the ALS receiver. Meanwhile, simulation results show that our S-CFP with pairing receiver achieves the same or very similar performance of the competing receivers with extra pilot overhead at sufficiently high signal-to-noise ratio (SNR) conditions. On the other hand, it is slightly inferior to them in terms of channel estimation accuracy and bit error rate at lower SNRs.

Description: In this paper, we consider robust optimization of amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay precoders in presence of deterministic imperfect channel state information (CSI), when the CSI uncertainty lies in a norm bounded region. Two widely used performance metrics, mutual information (MI) and mean square error (MSE), are adopted as design objectives. According to the philosophy of worst-case robustness, the robust optimization problems with respect to maximizing the worst-case MI and minimizing the worst-case MSE are formulated as maximin and minimax problems, respectively. Due to the fact that these two problems do not have a concave-convex or convex-concave structure, we cannot rely on the conventional saddle point theory to find the robust solutions. Nevertheless, by exploiting majorization theory, we show that the formulated maximin and minimax problems both admit saddle points. We further analytically characterize the saddle points, and provide closed-form solutions to robust relay precoder designs. Interestingly, we find that, under both MI and MSE metrics, the robust relay optimization leads to a channel-diagonalizing structure, meaning that eigenmode transmission is optimal from the worst-case robustness perspective. The proposed robust designs can improve the spectral efficiency and reliability of AF MIMO relaying against CSI uncertainties at the similar cost of computational complexity as the existing non-robust schemes.

Description: We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function, we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when significant speed-ups over the standard gradient method are obtained. Furthermore, we quantify how uncertainty in problem data at design-time affects the run-time performance of the gradient method and its multi-step counterpart, and conclude that in most cases the multi-step method outperforms gradient descent. Finally, we apply the proposed technique to three engineering problems: resource allocation under network-wide budget constraint, distributed averaging, and Internet congestion control. In all cases, our proposed algorithms converge significantly faster than the state-of-the art.

Description: This paper presents a new computationally efficient method for direction-of-arrival (DOA) estimation with arbitrary arrays. The total angular field-of-view is first divided into several small sectors and the original noise subspace exploited by the multiple signal classification (MUSIC) algorithm is mapped from one sector to the other sectors by a Hadarmard product transformation. This transformation gives a new noise-like subspace cluster (NLSC), whose intersection is found to be simultaneously orthogonal to the steering vectors associated with the true DOAs and several virtual DOAs. Based on such a multiple orthogonality, a novel compressed MUSIC (C-MUSIC) spatial spectrum at hand is derived. Unlike MUSIC with tremendous spectral search, C-MUSIC involves a limited search over only one sector, and hence it is computationally very attractive. To obtain the intersection of NLSC for more than two sectors, a low-complexity method is also proposed in the present work, which shows advantages over the existing alternative projection method (APM) and singular value decomposition (SVD) techniques. Furthermore, the mean square errors (MSEs) of the proposed estimator is derived. Simulation results illustrate that C-MUSIC trades-off MSEs by complexity and resolution as compared to the standard MUSIC efficiently.

Description: We analyze the performance of a matched subspace detector (MSD) where the test signal vector is assumed to reside in an unknown, low-rank $k$ subspace that must be estimated from finite, noisy, signal-bearing training data. Under both a stochastic and deterministic model for the test vector, subspace estimation errors due to limited training data degrade the performance of the standard plug-in detector, relative to that of an oracle detector. To avoid some of this performance loss, we utilize and extend recent results from random matrix theory (RMT) that precisely quantify the quality of the subspace estimate as a function of the eigen-SNR, dimensionality of the system, and the number of training samples. We exploit this knowledge of the subspace estimation accuracy to derive from first-principles a new RMT detector and to characterize the associated ROC performance curves of the RMT and plug-in detectors. Using more than the a critical number of informative components, which depends on the training sample size and eigen-SNR parameters of training data, will result in a performance loss that our analysis quantifies in the large system limit. We validate our asymptotic predictions with simulations on moderately sized systems.

Description: Standard spatial time-frequency distribution (STFD) estimators, derived based on the Gaussian noise assumption, are known to have poor performance in the case of impulsive noise. Recently, different STFD estimators have been proposed, which, based on simulations, are claimed to be robust. In this paper, we provide an influence function robustness analysis of STFD estimators. We derive the influence functions for the asymptotic and for the finite-sample case and study robustness of the standard, as well as for some recently proposed robust STFD estimators. The empirical influence function gives practitioners a simple way to pre-select STFD estimators for their scenario. Our analysis confirms that, unlike for the standard estimator, the proposed robust estimators yield a bounded influence function and are robust over a broad class of distributions. Future research on STFD estimation will allow for the design of robust and efficient estimators based on the influence function.

Description: In cognitive radio (CR), the soft decision fusion (SDF) rule plays a critical role in cooperative spectrum sensing (CSS). However, the computational cost on obtaining efficient SDF rule becomes infeasible even with a small number of cooperative users. In this paper, the efficiency of SDF rule in inhomogeneous background is studied from the perspective of quantization theory. We formulate the calculation of sensing performance including the probabilities of detection and false alarm when regarding both i) the quantization impact and ii) the inhomogeneous background, and then conclude a condition under which the sensing performance can be calculated by the fast Fourier transform (FFT). Based on this condition, two novel quantization schemes with two optimization methods are proposed to guarantee both the quantizer and decision threshold of SDF rule can be obtained efficiently, at the same time, the SDF can achieve high sensing performance.

Description: We examine the recovery of block sparse signals and extend the recovery framework in two important directions; one by exploiting the signals' intra-block correlation and the other by generalizing the signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One family, directly derived from the BSBL framework, require knowledge of the block structure. Another family, derived from an expanded BSBL framework, are based on a weaker assumption on the block structure, and can be used when the block structure is completely unknown. Using these algorithms, we show that exploiting intra-block correlation is very helpful in improving recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation and improve performance.

Description: In this paper, we first propose a generalized fourth-order PARATUCK2 tensor model for multiple-input multiple-output (MIMO) communication systems with space-time-frequency (STF) spreading-multiplexing. The core of the proposed PARATUCK2 model is composed of two third-order interaction tensors that define a joint time and frequency allocation of the data streams to the transmit antennas, thus allowing to adjust the multiplexing degree and spreading redundancy in three domains: space (transmit antennas), time (blocks) and frequency (subcarriers). Then, we investigate the identifiability of the PARATUCK2-STF MIMO system by deriving sufficient conditions which are translated into design recommendations for the STF allocation structure. In particular, essential uniqueness is discussed by interpreting the generalized fourth-order PARATUCK2 model as an equivalent third-order constrained factor (CONFAC) model with two fixed constraint matrices and one variable constraint matrix that depends on the stream-to-antenna allocation structure. We also present a blind receiver using the Levenberg-Marquardt (LM) algorithm based on the generalized fourth-order PARATUCK2 model. Numerical results are provided for a bit-error-rate performance evaluation and a comparison with some competing algorithms.

Description: The standard Capon beamformer (SCB) achieves the maximum output signal-to-interference-plus-noise ratio in the error-free case. However, estimation errors of the signal steering vector and the array covariance matrix can result in severe performance deteriorations of the SCB, especially if the training data contains the desired signal component. A popular technique to improve the robustness against model errors is to compute the Capon beamformer with the maximum output power, considering an uncertainty set for the signal steering vector. However, maximizing the total beamformer output power may result in an insufficient suppression of interferers and noise. As an alternative approach to mitigate the detrimental effect of model errors, we propose to compute the Capon beamformer with the minimum sensitivity, considering the uncertainty set for the signal steering vector. The proposed maximally robust Capon beamformer (MRCB) is at least as robust as the maximum output power Capon beamformer with the same uncertainty set for the signal steering vector. We show that the MRCB can be implemented efficiently using Lagrange duality. Simulation results demonstrate that the MRCB outperforms state-of-the-art robust adaptive beamformers in many scenarios.

Description: The possibility to accurately localize tags by using wireless techniques is of great importance for several emerging applications in the Internet of Things. Precise ranging can be obtained with ultra wideband (UWB) impulse radio (IR) systems, where short impulses are transmitted, and their time-of-arrival (ToA) is estimated at the receiver. Due to the presence of noise and multipath, the estimator has the difficult task of discriminating the time intervals where the received waveform is due to noise only, by those where there are also signal components. Common low-complexity methods use an energy detector (ED), whose output is compared with a threshold, to discriminate the time intervals containing noise only from those containing signal plus noise. Optimal threshold design for these methods requires knowledge of the channel impulse response and of the receiver noise power. We propose a different approach, where ToA estimation is based on model selection by information theoretic criteria (ITC). The resulting ToA algorithms do not use thresholds, and do not require any information about the channel or the noise power level. These blind, universal ToA estimators show, for completely unknown multipath channels and in the presence of noise with unknown power, excellent performance when compared with ideal genie-aided schemes.

Description: Detection of cyclostationary primary user (PU) signals in colored Gaussian noise for cognitive radio systems is considered based on looking for single or multiple cycle frequencies at single or multiple time lags in the cyclic autocorrelation function (CAF) of the noisy PU signal. We explicitly exploit the knowledge that under the null hypothesis of PU signal absent, the measurements originate from possible colored Gaussian noise with unknown correlation function. Our formulation allows us to simplify the spectrum sensing detector and obviates the need for estimating an unwieldy covariance matrix needed in some prior works. We consider both single and multiple antenna receivers, and both nonconjugate and conjugate CAFs. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided to demonstrate the efficacy of the proposed approaches and to compare them with some existing approaches. Our proposed approaches are computationally cheaper than the Dandawate- Giannakis and related approaches while having quite similar detection performance for a given false alarm rate.

Description: This paper presents a Cramér-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a random Gaussian i.i.d. tensor). A novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor of an arbitrary dimension. The expression needs less operations for computing the bound, $O(NR^{6})$ , than the best existing state-of-the art algorithm, $O(N^{3}R^{6})$ operations, where $N$ and $R$ are the tensor order and the tensor rank. Insightful expressions are derived for tensors of rank 1 and rank 2 of arbitrary dimension and for tensors of arbitrary dimension and rank, where two factor matrices have orthogonal columns.

Description: Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition coincides with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

Description: This paper introduces the novel class of modulated cyclostationary processes, a class of nonstationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also exhibit frequency correlation but have Loève spectra whose support lies only on parallel lines in the dual-frequency plane. Such extremely sparse structure does not adequately represent many biological processes. Thus, we propose a model that, in the time domain, modulates the covariance of cyclostationary processes and consequently broadens their frequency support in the dual-frequency plane. The spectra and the cross-coherence of the proposed modulated cyclostationary process are first estimated using multitaper methods. A shrinkage procedure is then applied to each trial-specific estimate to reduce the estimation risk.

Description: Using an infinite sample, the contrast function and the FastICA algorithm are deterministic. In the practical case, we have only a finite sample. Then the contrast function and the FastICA algorithm become estimators of the deterministic case. This paper provides a unified study of the deflation FastICA algorithm assuming a finite or an infinite sample. We consider four random probability distributions based on the finite sample, and construct four FastICA estimators. We show that under mild conditions, each of these estimators are equal to a local minimizer of the contrast function with respect to the underlying random probability distribution. Making use of the existing results of M-estimators, we give a rigorous analysis of the asymptotic errors of FastICA estimators. We derive five criteria for the optimal choice of the nonlinearity function.

Description: The Delsarte-Goethals frame (DGF) has been proposed for deterministic compressive sensing of sparse and compressible signals. Results in compressive sensing theory show that the DGF enables successful recovery of an overwhelming majority of sufficiently sparse signals. However, these results do not give a characterization of the sparse vectors for which the recovery procedure fails. In this paper, we present a formal analysis of the DGF that highlights the presence of clustered sparse vectors within its null space. This in turn implies that sparse recovery performance is diminished for sparse vectors that have their nonzero entries clustered together. Such clustered structure is present in compressive imaging applications, where commonly-used raster scannings of 2-D discrete wavelet transform representations yield clustered sparse representations for natural images. Prior work leverages this structure by proposing specially tailored sparse recovery algorithms that partition the recovery of the input vector into known clustered and unclustered portions. Alternatively, we propose new randomized and deterministic raster scannings for clustered coefficient vectors that improve recovery performance. Experimental results verify the aforementioned analysis and confirm the predicted improvements for both noiseless and noisy measurement regimes.

Description: This article deals with learning dictionaries for sparse approximation whose atoms are both adapted to a training set of signals and mutually incoherent. To meet this objective, we employ a dictionary learning scheme consisting of sparse approximation followed by dictionary update and we add to the latter a decorrelation step in order to reach a target mutual coherence level. This step is accomplished by an iterative projection method complemented by a rotation of the dictionary. Experiments on musical audio data and a comparison with the method of optimal coherence-constrained directions (mocod) and the incoherent k-svd (ink-svd) illustrate that the proposed algorithm can learn dictionaries that exhibit a low mutual coherence while providing a sparse approximation with better signal-to-noise ratio (snr) than the benchmark techniques.

Description: In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle estimator, whose performance has been shown to act as a benchmark to the performance of standard sparse recovery algorithms, we use the fact that a Parseval tight frame is the closest design - in the Frobenius norm sense - to the solution of a convex relaxation of the optimization problem that relates to the minimization of the MSE of the oracleestimator with respect to the equivalent sensing matrix, subject to sensing energy constraints. Based on this result, we then propose two sensing matrix designs that exhibit two key properties: i) the designs are closed form rather than iterative; ii) the designs exhibit superior performance in relation to other designs in the literature, which is revealed by our numerical investigation in various scenarios with different sparse recovery algorithms including basis pursuit de-noise (BPDN), the Dantzig selector and orthogonal matching pursuit (OMP).

Description: In this paper we consider adaptive detection of a signal embedded in additive disturbance whose multivariate distribution belongs to a very general class, including many statistical models commonly adopted for radar disturbance. We introduce the concept of generalized Constant False Alarm Rate (CFAR) and show that a class of receivers sharing some invariances complies with the quoted property. Then, we devise the Generalized Likelihood Ratio Test (GLRT) and prove that, under some mild technical conditions, it coincides with that obtained under the Gaussian assumption for the observations. We also deal with the existence of the Uniformly Most Powerful Invariant (UMPI) detector either using the Wijsman theorem or directly computing the maximal invariant Likelihood Ratio (LR). At the analysis stage, we focus on a compound matrix variate model for the disturbance component, which is a natural generalization of the Spherically Invariant Random Vector (SIRV). In this context, we assess the performance of some well known invariant decision rules also in comparison with the Most Powerful Invariant (MPI) detector. The results highlight that some among the analyzed receivers exhibit a performance level very close to the MPI test.

Description: This Special Issue seeks to review progress in synthetic aperture radar imaging which has been made possible through new algorithms and enabling hardware. It serves to capture the approaches propelling recent cutting-edge research and scholarly activities in SAR Imagery. SAR has become a valuable tool for civilian remote sensing applications as well as for military surveillance and reconnaissance. SAR operations can take place in all weather and times. SAR data can provide key information about the scene which can be extracted e.g. from the polarimetric features, the phase variation over time, and the reflectivity dependency on frequency. A wide variety of air- and space based sensors for long and short range operation has been realized, operating at frequencies extending from VHF to the upper millimeter wave region. Spectacular missions I ike the Shuttle Radar Topographic Mission, the TanDEM-X satellite pair and the COSMO/SkyMed constellation have underscored the unique and important role of SAR. In addition to the basic SAR modes, across- and along track interferometry have been established. Multi-band operations and the full polarimetric scattering matrix have been effectively utilized. We encourage paper submissions that highlight recent trends and applications of SAR imaging. We welcome contributions showing the marked improvements in SAR imaging and the attributes of efficient data acquisition, fast image computations, high image resolution, and effective image segmentations. This Special Issue aims to present the new developments in radar imaging related to polarimetry, bi- and multi-static sensors including MIMO architectures, novel focusing techniques and algorithms, compressive sensing and sparse imaging reconstructions, and other forthcoming radar imaging techniques. Air- and spaceborne SAR systems and techniques will also be considered.

Description: The robustness and integrity of IP networks require efficient tools for traffic monitoring and analysis, which scale well with traffic volume and network size. We address the problem of optimal large-scale monitoring of computer networks under resource constraints. Specifically, we consider the task of selecting the “best” subset of at most $K$ links to monitor, so as to optimally predict the traffic load at the remaining ones. Our notion of optimality is quantified in terms of the statistical error of network traffic predictors. The optimal monitoring problem at hand is akin to certain combinatorial constraints, which render the algorithms seeking the exact solution impractical. We develop a number of fast algorithms that improve upon existing algorithms in terms of computational complexity and accuracy. Our algorithms exploit the geometry of principal component analysis, which also leads us to new types of theoretical bounds on the prediction error. Finally, these algorithms are amenable to randomization, where the best of several parallel independent instances often yields the exact optimal solution. Their performance is illustrated and evaluated on simulated and real-network traces.

Description: This paper provides a detailed overview of the Digital Video Broadcasting Terrestrial (DVB-T) signal structure and the implications for passive radar systems that use these signals as illuminators of opportunity. In particular, we analyze the ambiguity function and explain its delay and Doppler properties in terms of the underlying structure of the DVB-T signal. Of particular concern for radar range-Doppler processing are ambiguities consistent in range and Doppler with targets of interest. In this paper we adopt a mismatched filtering approach for range-Doppler processing. We also recognize that while the structure of the DVB-T signal introduces ambiguities, the structure can also be exploited to better estimate the transmitted signal and channel, as well as any mismatch between transmitter and receiver (e.g., clock offsets). This study presents a scheme for pre-processing both the reference and surveillance signals obtained by the passive radar to mitigate the effects of the ambiguities and the clutter in range-Doppler processing. The effectiveness of our proposed scheme in enhancing target detection is demonstrated using real-world data from an (Australian) 8k-mode DVB-T system. A 29 dB reduction in residual ambiguity levels over existing techniques is observed, and a 36 dB reduction over standard matched filtering; with only a 1 dB reduction in the zero-delay, zero-Doppler peak.

Description: This paper presents a novel nonparametric Bayesian estimator for signal and image denoising in the wavelet domain. This approach uses a prior model of the wavelet coefficients designed to capture the sparseness of the wavelet expansion. A new family of Bessel K Form (BKF) densities are designed to fit the observed histograms, so as to provide a probabilistic model for the marginal densities of the wavelet coefficients. This paper first shows how the BKF prior can characterize images belonging to Besov spaces. Then, a new hyper-parameters estimator based on EM algorithm is designed to estimate the parameters of the BKF density; and, it is compared with a cumulants-based estimator. Exploiting this prior model, another novel contribution is to design a Bayesian denoiser based on the Maximum A Posteriori (MAP) estimation under the 0–1 loss function, for which we formally establish the mathematical properties and derive a closed-form expression. Finally, a comparative study on a digitized database of natural images and biomedical signals shows the effectiveness of this new Bayesian denoiser compared to other classical and Bayesian denoising approaches. Results on biomedical data illustrate the method in the temporal as well as the time-frequency domain.

Description: A conventional multilateration is a two-step process where, in the first step the time difference of arrivals (TDOA) of a signal at multiple sensors are estimated, and in the second step, these TDOAs are used in some position fixing technique to estimate the location of an emitter. Several estimators have been proposed over the years for the estimation of the TDOAs. Many techniques have been proposed for position fixing as well. Much of the research on position fixing has been focused on obtaining a simplified closed form solution. For the unknown deterministic signal model, Stein had derived the maximum-likelihood estimator (MLE) for the TDOA between two sensors, which is the peak location of the cross-correlation function. Since the asymptotic variance of an MLE approaches the Cramer-Rao lower bound (CRLB), which is the inverse of the negative of the expected value of the curvature of the log-likelihood function, using this as a motivation, we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log-likelihood function.

Description: Evaluation of the convergence bound in the frequency domain for Volterra series expansion of nonlinear systems described by NARX models is studied. This provides new convergence criteria under which the nonlinear system of interest has a convergent Volterra series expansion, and the new criteria are expressed explicitly in terms of the input magnitude, model parameters, and frequency variable. The new convergence criteria are firstly developed for harmonic inputs and then extended to multi-tone and general input cases. Based on the theoretical analysis, a general procedure for calculating the convergence bound is provided. The results provide a fundamental basis for nonlinear signal processing using the Volterra series theory.

Description: The distributed beamforming problem for amplify-and-forward relay networks is studied. Maximizing output SNR (signal-to-noise ratio) for distributed beamforming can be considered as a generalized eigenvector problem (GEP) and the principal eigenvector and its eigenvalue can be derived with a standard closed-form solution. In this paper, four classes of beamforming algorithms are derived based on different design criteria and constraints, including maximizing output SNR subject to a constraint on the total transmitted signal power, minimizing the total transmitted signal power subject to certain level of output SNR, minimizing the relay node number subject to constraints on the total signal power and output SNR, and a robust algorithm to deal with channel estimation errors. All of the algorithms have a low computational complexity due to the proposed real-valued implementation.

Description: In this paper, we study the design and analysis of optimal detection scheme for sensors that are deployed to monitor the change in the environment and are powered by energy harvested from the environment. In this type of applications, detection delay is of paramount importance. We model this problem as quickest change detection problem with stochastic energy constraints. In particular, a wireless sensor powered by renewable energy takes observations from a random sequence, whose distribution will change at an unknown time. Such a change implies events of interest. The energy in the sensor is consumed by taking observations and is replenished randomly. The sensor cannot take observations if there is no energy left in the battery. Our goal is to design optimal power allocation and detection schemes to minimize the worst case detection delay, which is the difference between the time when the change occurs and the time when an alarm is raised. Two types of average run length (ARL) constraints, namely an algorithm level ARL constraint and a system level ARL constraint, are considered. We propose a low complexity scheme in which the energy allocation rule is to spend energy to take observations as long as the battery is not empty and the detection scheme is the Cumulative Sum test. We show that this scheme is optimal for the formulation with the algorithm level ARL constraint and is asymptotically optimal for the formulations with the system level ARL constraint.

Description: This paper considers a transmit strategy for an AWGN MIMO bidirectional broadcast channel in the wideband regime. In order to characterize the boundaries of the wideband capacity and energy per bit regions, the transmit strategy at the relay is designed to maximize the weighted wideband rate sum. A closed form of the optimal transmit covariance matrix is derived, which shows that a single beam transmit strategy is optimal. The transmit strategies for some special cases are also analyzed. The fairness versus energy efficiency tradeoff is then discussed. In addition, an extension to multipair MIMO bidirectional broadcast channel is studied in which we show that serving a certain pair with full power is optimal in the sense of maximizing the achievable weighted wideband rate sum. Finally, a discussion on the conjecture of the minimum energy per bit for multi-pair systems is provided.

Description: In this paper, we present and evaluate dynamic dictionary-based estimation methods for joint model order and parameter estimation. In dictionary-based estimation, a continuous parameter space is discretized, and vector-valued dictionary elements are formed for specific parameter values. A linear combination of a subset of dictionary elements is used to represent the model, where the number of elements used is the estimated model order, and the parameters corresponding to the selected elements are the parameter estimates. In static-based methods, the dictionary is fixed; while in the dynamic methods proposed here, the parameter sampling, and hence the dictionary, adapt to the data. We propose two dynamic dictionary-based estimation algorithms in which the dictionary elements are dynamically adjusted to improve parameter estimation performance. We examine the performance of both static and dynamic algorithms in terms of probability of correct model order selection and the root mean-squared error of parameter estimates. We show that dynamic dictionary methods overcome the problem of estimation bias induced by quantization effects in static dictionary-based estimation, and we demonstrate that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramér-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.

Description: The problem of distributed learning in wireless sensor networks is addressed, with the perspective of implementing nearest-neighbor (NN) regression in a decentralized way, with communication constraints. Elaborating on the ordered-transmission idea of Blum and Sadler , a universal channel access policy is designed that, without inter-sensor coordination, enables the fusion center to recover exactly the training-set labels it needs, while less informative labels are not delivered at all. Exploiting the aforementioned access policy, two different paradigms are then considered. In the first one, a constraint is imposed on the number of channel accesses, and a distributed regression algorithm is proposed reaching an asymptotic performance of twice the minimum achievable mean-squared error, while requiring just a single channel access. In the second one, a constraint is imposed on the number of quantization bits, and the focus is on devising consistent $k_{n}$ -NN regression rules. The noiseless case with quantized data is preliminarily addressed. Then, the role of the channel is explicitly taken into account, and a scheme with one-bit quantizers is proposed, reaching consistency over binary symmetric channels. Finally, it is argued that the inference task can be naturally suited to uncoded communications. Accordingly, two schemes are proposed, ensuring consistency over coherent and noncoherent channels, respectively; possible gains over the coded schemes are discussed.

Description: In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.

Description: Suppose a linear model ${bf y}={bf H}{bf x}+{bf n}$ , where inputs ${bf x,n}$ are independent Gaussian mixtures. The problem is to design the transfer matrix ${bf H}$ so as to minimize the mean square error (MSE) when estimating ${bf x}$ from ${bf y}$ . This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed ${bf H}$ , the minimum MSE (MMSE) has no analytical form. Secondly, the MMSE is generally not convex in ${bf H}$ . Thirdly, derivatives of the MMSE w.r.t. ${bf H}$ are hard to obtain. This paper casts the problem as a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy—markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why.

Description: Complex-valued vector time series occur in diverse fields such as oceanography and meteorology, and scientifically interpretable parameters may be estimated from them. We show that it is possible to make inference such as confidence intervals on these parameters using a vector-valued circulant embedding simulation method, combined with bootstrapping. We apply the methodology to three parameters of interest in oceanography, and compare the resulting simulated confidence intervals with those computed using analytic results. We conclude that the simulation scheme offers an inference approach either in the absence of theoretical distributional results, or to check the effect of nuisance parameters where theoretical results are available.

Description: We introduce an iterative linear estimator (ILE) for estimating a signal from samples having location errors and additive noise. We assume that the signals lie in the span of a finite basis and the location errors and noise are mutually independent and normally distributed. The parameter estimation problem is formulated as obtaining a maximum likelihood (ML) estimate given the observations and an observation model. Using a linearized observation model we derive an approximation to the likelihood function. We then adopt an iterative strategy to develop a computationally efficient estimator, which captures the first order effect of sample location errors on signal estimation. Through numerical simulations we establish the efficacy of the proposed estimator for one-dimensional and two-dimensional parametric signals, comparing the mean squared estimation error against a basic linear estimator. We develop a numerical approximation of the Cramér-Rao lower bound (CRB) and the Expectation-Maximization (EM) algorithm, and for a one-dimensional signal compare our algorithm against them. We show that for high location error variance and small noise variance the mean squared error (MSE) with ILE is significantly lower when compared to the baseline linear estimator. When compared to EM, our algorithm provides comparable MSE with a significant reduction in computational time.

Description: A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator.

Description: Three-dimensional ultrasound imaging is a promising medical imaging technology because of its ease of use and improved accuracy in diagnosis. However, its high computational complexity and resulting high power consumption has precluded its use in hand-held applications. In this paper, we present a separable beamforming method that greatly reduces computational complexity. Our method is based on decomposing the delay term in a way that minimizes the root-mean-square error caused by the decomposition. We analyze tradeoffs between the approximation error caused by the decomposition and computational complexity. Then, we present enhancements to the Sonic Millip3De hardware accelerator for ultrasound beamforming to implement separable beamforming. Using hardware synthesis targeting standard cells in 45 nm, we show that the proposed method allows us to boost the Sonic Millip3De frame rate from 1–2 Hz to 32 Hz while maintaining power consumption at 15 W. We validate image quality of our method using cyst phantom simulations in Field II. Our evaluation demonstrates that the proposed separable beamforming method can produce 3-D images with high quality that are comparable to those generated by non-separable beamforming.

Description: For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables, e.g., precoders, equalizers, and training sequences, are usually matrices. It is well known that matrix operations are usually more complicated compared with their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper, we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then, exploiting the framework of matrix-monotonic optimization the optimal structures of the considered matrix variables can be derived first. Based on the optimal structure, the matrix-variate optimization problems can be greatly simplified into the ones with only vector variables. In particular, the dimension of the new vector variable is equal to the minimum number of columns and rows of the original matrix variable. Finally, we also extend our work to some more general cases with multiple matrix variables.

Description: RES, a regularized stochastic version of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method, is proposed to solve strongly convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second-order methods, on the other hand, is impracticable because the computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost, RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian eigenvalues of the sample functions are sufficient to guarantee almost sure convergence of a subsequence generated by RES and convergence of the sequence in expectation to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

Description: This paper presents an optimized software implementation of a Successive Cancellation (SC) decoder for polar codes. Despite the strong data dependencies in SC decoding, a highly parallel software polar decoder is devised for x86 processor target. A high level of performance is achieved by exploiting the parallelism inherent in today's processor architectures (SIMD, multicore, etc.). Some optimizations that were originally thought for hardware implementation (memory reduction techniques and algorithmic simplifications) were also applied to enhance the throughput of the software implementation. Finally, some low level optimizations such as explicit assembly description or data packing are used to improve the throughput even more. The resulting decoder description is implemented on different x86 processor targets. An analysis of the decoder in terms of latency and throughput is proposed. The influence of several parameters on the throughput and the latency is investigated: the selected target, the code rate, the code length, the SIMD mode (SSE/AVX), the multithreading mode, etc. The energy per decoded bit is also estimated. The proposed software decoder compares favorably with state of the art software polar decoders. Extensive experimentations demonstrate that the proposed software polar decoder exceeds 1 Gb/s for code lengths $Nleq 2^{17}$ on a single core and reaches multi-Gb/s throughputs when using four cores in parallel in AVX mode.

Description: This paper deals with the two-dimensional (2-D) direction-of-arrival (DOA) estimation of a mixture of noncoherent (including uncorrelated and partially correlated) and coherent (i.e., fully correlated) narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays (ULAs). An oblique projection based approach for 2-D direction estimation (OPADE) is proposed by using some cross-correlations between the received array data. In the proposed OPADE, the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated, while the computationally intensive eigendecomposition is avoided, and the estimated elevation and azimuth angles are paired automatically. Further, an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the DOAs of coherent signals. The Cramér–Rao lower bound (CRB) for the mixture of noncoherent and coherent signals is also derived explicitly, where the prior knowledge of the signal correlation is incorporated into the 2-D DOA estimation of noncoherent signals. Finally the effectiveness of the OPADE and the theoretical analysis are substantiated through numerical examples.

Description: Bounded Component Analysis (BCA) is a recent framework which enables development of methods for the separation of dependent as well as independent sources from their mixtures. This paper extends a recent geometric BCA approach introduced for the instantaneous mixing problem to the convolutive mixing problem. The paper proposes novel deterministic convolutive BCA frameworks for the blind source extraction and blind source separation of convolutive mixtures of sources which allows the sources to be potentially nonstationary. The global maximizers of the proposed deterministic BCA optimization settings are proved to be perfect separators. The paper also illustrates that the iterative algorithms corresponding to these frameworks are capable of extracting/separating convolutive mixtures of not only independent sources but also dependent (even correlated) sources in both component (space) and sample (time) dimensions through simulations based on a Copula distributed source system. In addition, even when the sources are independent, it is shown that the proposed BCA approach have the potential to provide improvement in separation performance especially for short data records based on the setups involving convolutive mixtures of digital communication sources.

Description: This paper investigates the problem of frequency-specific (FS) model approximation of transfer functions using a min-max approach. The objective is to find an approximation model for a transfer function such that the maximum error gain over a specific frequency range is minimized. First, a linear matrix inequality condition characterizing the FS gain of a transfer function is derived by using the generalized Kalman-Yakubovich-Popov lemma, and then a simple iterative approach is proposed to optimize the approximation model. Numerical experiments show that the proposed approach can produce better approximation models over a specific frequency range than some existing approaches. Moreover, it is indicated how to apply the proposed approximation approach to the design problem of infinite impulsive response digital filters, and design examples clearly illustrate that the proposed design flow can generate filters comparable with the latest design method.

Description: We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramér–Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise.

Description: In this paper, shrinkage linear complex-valued least mean squares (SL-CLMS) and shrinkage widely linear complex-valued least mean squares (SWL-CLMS) algorithms are devised for adaptive beamforming. By exploiting the relationship between the noise-free a posteriori and a priori error signals, the SL-CLMS method is able to provide a variable step size to update the weight vector for the adaptive beamformer, significantly enhancing the convergence speed and decreasing the steady-state misadjustment. On the other hand, besides adopting a variable step size determined by minimizing the square of the augmented noise-free a posteriori errors, the SWL-CLMS approach exploits the noncircular properties of the signal of interest, which considerably improves the steady-state performance. Simulation results are presented to illustrate their superiority over the CLMS, complex-valued normalized LMS, variable step size, recursive least squares (RLS) algorithms and their corresponding widely linear-based schemes. Additionally, our proposed algorithms are more computationally efficient than the RLS solutions though they may have a slightly slower convergence rate.

Description: Downsampling of signals living on a general weighted graph is not as trivial as of regular signals where we can simply keep every other samples. In this paper we propose a simple, yet effective downsampling scheme in which the underlying graph is approximated by a maximum spanning tree (MST) that naturally defines a graph multiresolution. This MST-based method significantly outperforms the two previous downsampling schemes, coloring-based and SVD-based, on both random and specific graphs in terms of computations and partition efficiency quantified by the graph cuts. The benefit of using MST-based downsampling for recently developed critical-sampling graph wavelet transforms in compression of graph signals is demonstrated.

Description: We consider mesh networks composed of groups of relaying nodes which operate in decode-and-forward mode. Each node from a group relays information to all the nodes in the next group. We study these networks in two setups, one where the nodes have complete state information about the channels through which they receive the signals, and another when they only have the statistics of the channels. We derive recursive expressions for the probabilities of errors of the nodes and present several implementations of detectors used in these networks. We compare the mesh networks with multihop networks formed by a set of parallel sections of multiple relaying nodes. We demonstrate with numerous simulations that there are significant improvements in performance of mesh over multihop networks in various scenarios.

Description: The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage, while maintaining the theoretical convergence of the sampler. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost per effective sample. The connection between this algorithm and some existing strategies is given and its performance is illustrated on a linear inverse problem of image resolution enhancement.

Description: In this paper, we develop verifiable sufficient conditions and computable performance bounds of $ell_{1}$ -minimization based sparse recovery algorithms in both the noise-free and noisy cases. We define a family of quality measures for arbitrary sensing matrices as a set of optimization problems, and design polynomial-time algorithms with theoretical global convergence guarantees to compute these quality measures. The proposed algorithms solve a series of second-order cone programs, or linear programs. We derive performance bounds on the recovery errors in terms of these quality measures. We also analytically demonstrate that the developed quality measures are non-degenerate for a large class of random sensing matrices, as long as the number of measurements is relatively large. Numerical experiments show that, compared with the restricted isometry based performance bounds, our error bounds apply to a wider range of problems and are tighter, when the sparsity levels of the signals are relatively low.

Description: A novel method enabling single-site localization of wireless emitters in a rich multipath environment is presented. The localization is based on a novel fingerprinting technique exploiting the spatial-temporal characteristics of the multipath signals received by the base station antenna array. The fingerprint is based on a lower dimensional signal subspace of the spatial-temporal covariance matrix, capturing the dominant multipath signals. The performance is validated with both simulated and real data, demonstrating localization accuracy of about 1 m in typical indoor environments.

Description: Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid.

Description: This paper investigates reliable and covert transmission strategies in a multiple-input multiple-output (MIMO) wiretap channel with a transmitter, receiver and an adversarial wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper possesses a novel capability to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data, or broadcasting artificial interference along with the information signal in an attempt to jam the eavesdropper (assuming its instantaneous channel state is unknown). To examine the resulting trade-offs for the legitimate transmitter and the adversary, we model their interactions as a two-person zero-sum game with the ergodic MIMO secrecy rate as the payoff function. We first examine conditions for the existence of pure-strategy Nash equilibria (NE) and the structure of mixed-strategy NE for the strategic form of the game. We then derive equilibrium strategies for the extensive form of the game where players move sequentially under scenarios of perfect and imperfect information. Finally, numerical simulations are presented to examine the equilibrium outcomes of the various scenarios considered.

Description: We propose a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly-moving target using an orthogonal frequency division multiplexing (OFDM) radar. We observe that the target and interference spectra are inherently sparse in the spatio-temporal domain. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data and produces an equivalent performance as the other existing STAP techniques. In addition, the use of an OFDM signal increases the frequency diversity of our system, as different scattering centers of a target resonate at different frequencies, and thus improves the target detectability. First, we formulate a realistic sparse-measurement model for an OFDM radar considering both the clutter and jammer as the interfering sources. Then, we apply a residual sparse-recovery technique based on the LASSO estimator to estimate the target and interference covariance matrices, and subsequently compute the optimal STAP-filter weights. Our numerical results demonstrate a comparative performance analysis of the proposed sparse-STAP algorithm with four other existing STAP methods. Furthermore, we discover that the OFDM-STAP filter-weights are adaptable to the frequency-variabilities of the target and interference responses, in addition to the spatio-temporal variabilities. Hence, by better utilizing the frequency variabilities, we propose an adaptive OFDM-waveform design technique, and consequently gain a significant amount of STAP-performance improvement.

Description: Mixed-scaling-rotation (MSR) coordinate rotation digital computer (CORDIC) is an attractive approach to synthesizing complex rotators. This paper presents the fixed-point error analysis and parameter selections of MSR-CORDIC with applications to the fast Fourier transform (FFT). First, the fixed-point mean squared error of the MSR-CORDIC is analyzed by considering both the angle approximation error and signal round-off error incurred in the finite precision arithmetic. The signal to quantization noise ratio (SQNR) of the output of the FFT synthesized using MSR-CORDIC is thereafter estimated. Based on these analyses, two different parameter selection algorithms of MSR-CORDIC are proposed for general and dedicated MSR-CORDIC structures. The proposed algorithms minimize the number of adders and word-length when the SQNR of the FFT output is constrained. Design examples show that the FFT designed by the proposed method exhibits a lower hardware complexity than existing methods.

Description: Three-dimensional (3-D) digital filters find applications in a variety of image and video signal processing problems. This paper presents a coefficient-sensitivity analysis for a wide class of 3-D digital filters with separable denominators in local state space that leads to an analytic formulation for sensitivity minimization, and to present two solution techniques for the sensitivity minimization problem at hand. To this end, a vector-matrix-vector decomposition of a given 3-D transfer function that separates the three variables and leads to a state-space realization in a form convenient for subsequent analysis. An $l_2$ -sensitivity analysis is then performed. The result is a computationally tractable formula of the overall $l_2$ -sensitivity for 3-D digital filters. The $l_2$ -sensitivity is minimized subject to $l_2$ -scaling constraints by using one of the two solution methods proposed—one relaxes the constraints into a single trace constraint and solves the relaxed problem with an effective matrix iteration scheme; while the other converts the contained optimization problem at hand into an unconstrained problem and solves it using a quasi-Newton algorithm. A case study is presented to illustrate the validity and effectiveness of the proposed techniques.

Description: Channel state information (CSI) in the interference channel can be used to reduce the dimension of received interference and helps achieve the channel's maximum multiplexing gain through what is known as interference alignment (IA). Most interference alignment algorithms require knowledge of all the interfering channels to compute the alignment precoders. CSI, considered available at the receivers, can be shared with the transmitters via limited feedback. When IA is done by coding over frequency extensions in a single antenna system, the required CSI lies on the Grassmannian manifold and its structure can be exploited in feedback. Unfortunately, the number of channels to be shared grows with the square of the number of users, creating too much overhead with conventional feedback methods. This paper proposes Grassmannian differential feedback to reduce feedback overhead by exploiting both the channel's temporal correlation and Grassmannian structure. The performance of the proposed algorithm is characterized both analytically and numerically as a function of channel length, mobility, and the number of feedback bits. The main conclusions are that the proposed feedback strategy allows IA to perform well over a wide range of Doppler spreads, and to approach perfect CSI performance in slowly varying channels. Numerical results highlight the trade-off between the frequency of feedback and the accuracy of individual feedback updates.

Description: In this paper, we investigate the challenging problem of joint source and relay optimization for two-way linear non-regenerative multiple-input multiple-output (MIMO) relay communication systems. We derive the optimal structure of the source and relay precoding matrices when linear minimal mean-squared error (MMSE) receivers are used at both destinations in the relay system. We show that for a broad class of frequently used objective functions for MIMO communications such as the MMSE, the maximal mutual information (MMI), and the minimax MSE, the optimal relay and source matrices have a general beamforming structure. This result includes existing works as special cases. Based on this optimal structure, a new iterative algorithm is developed to jointly optimize the relay and source matrices. We also propose a novel suboptimal relay precoding matrix design which significantly reduces the computational complexity of the optimal design with only a marginal performance degradation. Interestingly, we show that this suboptimal relay matrix is indeed optimal for some special cases. The performance of the proposed algorithms are demonstrated by numerical simulations. It is shown that the novel minimax MSE-based two-way relay system has a better bit-error-rate (BER) performance compared with existing two-way relay systems using the MMSE and the MMI criteria.

Description: Hybrid automatic repeat request (ARQ) protocols have become common in many packet transmission systems due to their incorporation in various standards. Hybrid-ARQ combines the normal ARQ method with forward error correction (FEC) codes to increase reliability and throughput. In this paper, we look at improving upon this performance using feedback information from the destination, in particular, using a powerful FEC code in conjunction with a proposed linear feedback code for the Rayleigh block fading channels. The new hybrid-ARQ scheme is initially developed for full received packet feedback in a point-to-point link. It is then extended to various multiple-antenna scenarios [e.g., multiple-input single-output (MISO), multiple-input multiple-output (MIMO), etc.] with varying amounts of packet feedback information. Simulations illustrate gains in throughput.

Description: This paper studies the MIMO applicability to filter bank based multicarrier (FBMC) modulations for low coherence bandwidth channels. Under these conditions the channel frequency response cannot be modeled flat at a subcarrier level. This implies that the techniques originally devised for OFDM do not restore the orthogonality between subcarriers when they are directly applied to FBMC. Aiming at circumventing this problem we propose the design of two MIMO FBMC schemes, which are based on a new subband processing. The figures of merit that govern the design of the first and second scheme are the signal to leakage plus noise ratio (SLNR) and the signal to interference plus noise ratio (SINR), respectively. However, we do not restrict the analysis to the design of a new subband processing but we also carry out an asymptotic analysis of the complexity as well as tackle the problem of estimating the channel. Simulation-based results have demonstrated that the addressed solutions clearly outperform previous MIMO FBMC schemes in terms of BER. In comparison to OFDM, the devised techniques are able to remain competitive even if the knowledge of the channel state information is not perfect. In those scenarios where the cyclic prefix (CP) length is not sufficiently large to avoid inter block interference, the proposed designs are able to reduce the BER. However, the price that should be paid is the increase of the complexity.

Description: This paper deals with optimal joint user power control and relay distributed beamforming for two-way relay networks, where two end-users exchange information through multiple relays, each of which is assumed to have its own power constraint. The problem includes the design of the distributed beamformer at the relays and the power control scheme for the two end-users to optimize the network performance. Considering the overall two-way network performance, we maximize the lower signal-to-noise ratio (SNR) of the two communication links. For single-relay networks, this maximization problem is solved analytically. For multi-relay networks, we propose an iterative numerical algorithm to find the optimal solution. While the complexity of the optimal algorithm is too high for large networks, two sub-optimal algorithms with low complexity are also proposed, which are numerically shown to perform close to the optimal technique. It is also shown via simulation that for two-way networks with both single relay and multiple relays, proper user power control and relay distributed beamforming can significantly improve the network performance, especially when the power constraints of the two end-users in the networks are unbalanced. Our approach also improves the power efficiency of the network largely.

Description: Full-diversity full-rate (FDFR) space-time codes achieve both high data rate and good reliability at the cost of high decoding complexity. In this paper, we propose a low-complexity MIMO scheme that achieves both full diversity and full rate over flat fading channels for a sufficiently large number of transmit and receive antennas. The proposed scheme is constructed by applying energy spreading transforms (EST's) to multiple data streams and spatially multiplexing the streams to multiple transmit antennas. Simulation results show that the proposed FDFR scheme outperforms the threaded algebraic space-time (TAST) code, which is a FDFR code based on maximum likelihood (ML) detection, when the number of transmit antennas (with the same number of receive antennas) are three and four. However, its detection complexity is only that of a decision-feedback detector.

Description: The coherence spectrum is of notable interest as a bivariate spectral measure in a variety of application, and the topic has lately attracted interest with the recent formulation of several high-resolution data adaptive estimators. In this work, we further this development with the presentation of computationally efficient implementations of the Capon- and APES-based MSC estimators. The presented implementations furthers the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices to include also the required cross-correlation covariance matrices for the mentioned coherence algorithms. Numerical simulations together with theoretical complexity measures illustrate the performance of the proposed implementations.

Description: A linearly-constrained recursive least-squares adaptive filtering algorithm based on the method of weighting and the dichotomous coordinate descent (DCD) iterations is proposed. The method of weighting is employed to incorporate the linear constraints into the least-squares problem. The normal equations of the resultant unconstrained least-squares problem are then solved using the DCD iterations. The proposed algorithm has a significantly smaller computational complexity than the previously proposed constrained recursive least square (CRLS) algorithm while delivering convergence performance on par with CRLS. The effectiveness of the proposed algorithm is demonstrated by simulation examples.

Description: This paper considers the average-consensus problem in a network with arbitrary (but finite) communication delays. A novel Distributed-Averaging (DA) algorithm is presented and shown to achieve average-consensus if at any time $t$ there exists a finite time interval $[t, T_{t}]$ over which each node can communicate (via a time-respecting path) with all other nodes. For consensus variables with dimensions on the order of the network size, the DA algorithm requires an order of magnitude less data to be communicated and stored at each node as compared to an idealized algorithm that floods the initial data. In the companion paper , practical applications of the DA algorithm are provided along with numerical examples.

Description: In this correspondence, we present a new and fast design algorithm for perfect-reconstruction (PR), maximally decimated, uniform, cosine-modulated filter banks. Perfect reconstruction is obtained within arithmetic machine precision. The new design does not need numerical optimization routines and is significantly faster than a competing method based on second-order cone programming (SOCP). The proposed design algorithm finds the optimum solution by iteratively solving a quadratic programming problem with linear equality constraints. By a special modification of the basic algorithm, we obtain PR filter banks with high stopband attenuations. In addition, fast convergence is verified by designing PR filter banks with up to 128 channels.