IEEE Transactions on Signal Processing

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TOC Alert for Publication# 78
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An Online Algorithm for Separating Sparse and Low-Dimensional Signal Sequences From Their Sum

Fri, 15/08/2014 - 00:00
This paper designs and extensively evaluates an online algorithm, called practical recursive projected compressive sensing (Prac-ReProCS), for recovering a time sequence of sparse vectors $S_{t}$ and a time sequence of dense vectors $L_{t}$ from their sum, $M_{t}:=S_{t}+L_{t}$, when the $L_{t}$ 's lie in a slowly changing low-dimensional subspace of the full space. A key application where this problem occurs is in real-time video layering where the goal is to separate a video sequence into a slowly changing background sequence and a sparse foreground sequence that consists of one or more moving regions/objects on-the-fly. Prac-ReProCS is a practical modification of its theoretical counterpart which was analyzed in our recent work. Extension to the undersampled case is also developed. Extensive experimental comparisons demonstrating the advantage of the approach for both simulated and real videos, over existing batch and recursive methods, are shown.

Kernel Additive Models for Source Separation

Fri, 15/08/2014 - 00:00
Source separation consists of separating a signal into additive components. It is a topic of considerable interest with many applications that has gathered much attention recently. Here, we introduce a new framework for source separation called Kernel Additive Modelling, which is based on local regression and permits efficient separation of multidimensional and/or nonnegative and/or non-regularly sampled signals. The main idea of the method is to assume that a source at some location can be estimated using its values at other locations nearby, where nearness is defined through a source-specific proximity kernel. Such a kernel provides an efficient way to account for features like periodicity, continuity, smoothness, stability over time or frequency, and self-similarity. In many cases, such local dynamics are indeed much more natural to assess than any global model such as a tensor factorization. This framework permits one to use different proximity kernels for different sources and to separate them using the iterative kernel backfitting algorithm we describe. As we show, kernel additive modelling generalizes many recent and efficient techniques for source separation and opens the path to creating and combining source models in a principled way. Experimental results on the separation of synthetic and audio signals demonstrate the effectiveness of the approach.

Outage-Constrained Coordinated Beamforming With Opportunistic Interference Cancellation

Fri, 15/08/2014 - 00:00
In this paper, interference management is considered for the K-user multiple-input single-output (MISO) block-faded interference channel. It is assumed that perfect channel state information (CSI) can be obtained at the receivers, whereas only channel distribution information (CDI) is available to the transmitters. Furthermore, the receivers are assumed to be capable of implementing opportunistic interference cancellation (OIC). Based on these assumptions, the beamforming design problem for the MISO interference channel under consideration is formulated as a rate utility maximization problem under outage constraints and individual power constraints. By implementing OIC at the receivers, the outage probability is expected to be reduced, leading to a potential improvement on the utility value. However, this flexibility complicates the outage constraint, resulting in an optimization problem that is non-convex and difficult to handle. We propose a successive convex approximation (SCA) method that employs first-order approximation techniques and semi-definite relaxation (SDR) to efficiently obtain an approximate beamforming solution to this problem. Our proposed SCA algorithm has been shown to yield solutions that are stationary points of the original beamforming design problem. Furthermore, a decentralized version of the SCA algorithm is proposed, in which only local CDI and a limited amount of information exchange between transmitters are required. Our simulation results demonstrate that both of our proposed algorithms achieve near-optimal performance for the two-user case, and that enabling the receivers to implement OIC indeed improves the system performance by as large as 260% at high signal-to-noise ratios when user fairness is considered.

Towards the Asymptotic Sum Capacity of the MIMO Cellular Two-Way Relay Channel

Fri, 15/08/2014 - 00:00
In this paper, we consider the transceiver and relay design for the multiple-input multiple-output (MIMO) cellular two-way relay channel (cTWRC), where a multi-antenna base station (BS) exchanges information with multiple multiantenna mobile stations via a multi-antenna relay station (RS). We propose a novel two-way relaying scheme to approach the sum capacity of the MIMO cTWRC. A key contribution of this work is a new nonlinear lattice-based precoding technique to precompensate the interstream interference, so as to achieve efficient interference-free lattice decoding at the relay. We derive sufficient conditions for the proposed scheme to asymptotically achieve the sum capacity of the MIMO cTWRC in the high signal-to-noise ratio (SNR) regime. To fully exploit the potential of the proposed scheme, we also investigate the optimal power allocation at the BS and the RS to maximize the weighted sum-rate of the MIMO cTWRC in the general SNR regime. It is shown that the problem can be formulated as a monotonic program, and a polyblock outer approximation algorithm is developed to find the globally optimal solution with guaranteed convergence. We demonstrate by numerical results that the proposed scheme significantly outperforms the existing schemes and closely approaches the sum capacity of the MIMO cTWRC in the high SNR regime.

Distributed Hybrid Power State Estimation Under PMU Sampling Phase Errors

Fri, 15/08/2014 - 00:00
Phasor measurement units (PMUs) have the advantage of providing direct measurements of power states. However, as the number of PMUs in a power system is limited, the traditional supervisory control and data acquisition (SCADA) system cannot be replaced by the PMU-based system overnight. Therefore, hybrid power state estimation taking advantage of both systems is important. As experiments show that sampling phase errors among PMUs are inevitable in practical deployment, this paper proposes a distributed power state estimation algorithm under PMU phase errors. The proposed distributed algorithm only involves local computations and limited information exchange between neighboring areas, thus alleviating the heavy communication burden compared to the centralized approach. Simulation results show that the performance of the proposed algorithm is very close to that of centralized optimal hybrid state estimates without sampling phase error.

Table of Contents

Fri, 01/08/2014 - 00:00

Table of Contents

Fri, 01/08/2014 - 00:00

Superfast Tikhonov Regularization of Toeplitz Systems

Fri, 01/08/2014 - 00:00
Toeplitz-structured linear systems arise often in practical engineering problems. Correspondingly, a number of algorithms have been developed that exploit Toeplitz structure to gain computational efficiency when solving these systems. Early “fast” algorithms required $ {cal O}(n^{2})$ operations, but recent “superfast” algorithms are more efficient. In this work, we present a superfast algorithm for Tikhonov regularization of Toeplitz systems. Using an “extension-and-transformation” technique, our algorithm translates a Tikhonov-regularized Toeplitz system into a type of specialized polynomial problem known as tangential interpolation. Under this formulation, we can compute the solution in only $ {cal O}(KNlog ^{2} N)$ operations, where $K$ is the number of regularizers and $N$ is on the order of the number of parameters defining the system matrix. Our algorithm is further improved with displacement structure, which reduces the complexity when solving the system for multiple input vectors. We use numerical simulations to demonstrate our algorithm's complexity and accuracy.

Adaptive Radar Detection Algorithm Based on an Autoregressive GARCH-2D Clutter Model

Fri, 01/08/2014 - 00:00
We propose a model for radar clutter that combines an autoregressive (AR) process with a two-dimensional generalized autoregressive conditional heteroscedastic (GARCH-2D) process. Based on this model, we derive an adaptive detection test, called AR-GARCH-2D detector, for a target with known Doppler frequency and unknown complex amplitude. Using real radar data, we evaluate its performance for different model orders, and we use a model selection criteria to choose the best fit to the data. The resulting detector is not the constant false alarm rate (CFAR) with respect to the process coefficients, but we show that in practical situations it is very robust. Finally, we compare the AR-GARCH-2D detector performance with the performance of the generalized likelihood ratio test (GLRT), the adaptive linear-quadratic (ALQ), and the autoregressive generalized likelihood ratio (ARGLR) detectors by processing the real radar data. We show that the proposed detector offers a higher probability of detection than the other tests, for a given probability of false alarm.

A Distributed Reflector Localization Approach to Ultrasonic Array Imaging in Non-Destructive Testing Applications

Fri, 01/08/2014 - 00:00
In array-based immersion ultrasonic non-destructive testing (NDT), an ultrasonic array and a solid test sample are immersed in water for the purpose of imaging and flaw detection inside the test sample. In such a test scenario, the upper surface of the test sample has two effects: i) it produces a strong interference signal in the backscattered received signal, and ii) its shape determines the array spatial signature of every point inside the material under test. Hence, in immersion NDT, to achieve a precise localization of a crack inside a test sample, the knowledge of the shape of the upper surface of the test sample is required. In this paper, we propose a distributed reflector modeling approach to characterize the interface between water and a solid test sample as well as any crack inside the solid test sample. This approach relies on the so-called incoherently distributed reflector modeling, where a distributed reflector can be modeled as infinitely many point sources located close to each other. Using such an approach, we present a model for the array data, and then develop a covariance fitting based technique to estimate the parameters of the shape of the interface between the two media and those of the shape of a crack inside the test material. Our numerical experiments show that our proposed approach yields a lower root mean squared error for the parameter estimates, compared to a state-of-the-art method, called root mean squared velocity technique.

Achievable Rates of Full-Duplex MIMO Radios in Fast Fading Channels With Imperfect Channel Estimation

Fri, 01/08/2014 - 00:00
We study the theoretical performance of two full-duplex multiple-input multiple-output (MIMO) radio systems: a full-duplex bi-directional communication system and a full-duplex relay system. We focus on the effect of a (digitally manageable) residual self-interference due to imperfect channel estimation (with independent and identically distributed (i.i.d.) Gaussian channel estimation error) and transmitter noise. We assume that the instantaneous channel state information (CSI) is not available the transmitters. To maximize the system ergodic mutual information, which is a nonconvex function of power allocation vectors at the nodes, a gradient projection algorithm is developed to optimize the power allocation vectors. This algorithm exploits both spatial and temporal freedoms of the source covariance matrices of the MIMO links between transmitters and receivers to achieve higher sum ergodic mutual information. It is observed through simulations that the full-duplex mode is optimal when the nominal self-interference is low, and the half-duplex mode is optimal when the nominal self-interference is high. In addition to an exact closed-form ergodic mutual information expression, we introduce a much simpler asymptotic closed-form ergodic mutual information expression, which in turn simplifies the computation of the power allocation vectors.

Data Assimilation by Conditioning of Driving Noise on Future Observations

Fri, 01/08/2014 - 00:00
Conventional recursive filtering approaches, designed for quantifying the state of an evolving stochastic dynamical system with intermittent observations, use a sequence of i) an uncertainty propagation step followed by ii) a step where the associated data is assimilated using Bayes' rule. Alternatively, the order of the steps can be switched to i) one step ahead data assimilation followed by ii) uncertainty propagation. In this paper, we apply this smoothing-based sequential filter to systems driven by random noise, however with the conditioning on future observation not only to the system variable but to the driving noise. Our research reveals that, for the nonlinear filtering problem, the conditioned driving noise is biased by a nonzero mean and in turn pushes forward the filtering solution in time closer to the true state when it drives the system. As a result our proposed method can yield a more accurate approximate solution for the state estimation problem.

Sub-Nyquist Sampling for Power Spectrum Sensing in Cognitive Radios: A Unified Approach

Fri, 01/08/2014 - 00:00
In light of the ever-increasing demand for new spectral bands and the underutilization of those already allocated, the concept of Cognitive Radio (CR) has emerged. Opportunistic users could exploit temporarily vacant bands after detecting the absence of activity of their owners. One of the crucial tasks in the CR cycle is therefore spectrum sensing and detection which has to be precise and efficient. Yet, CRs typically deal with wideband signals whose Nyquist rates are very high. In this paper, we propose to reconstruct the power spectrum of such signals from sub-Nyquist samples, rather than the signal itself as done in previous work, in order to perform detection. We consider both sparse and non sparse signals as well as blind and non blind detection in the sparse case. For each one of those scenarios, we derive the minimal sampling rate allowing perfect reconstruction of the signal's power spectrum in a noise-free environment and provide power spectrum recovery techniques that achieve those rates. The analysis is performed for two different signal models considered in the literature, which we refer to as the analog and digital models, and shows that both lead to similar results. Simulations demonstrate power spectrum recovery at the minimal rate in noise-free settings and the impact of several parameters on the detector performance, including signal-to-noise ratio, sensing time and sampling rate.

State Estimation Over a Lossy Network in Spatially Distributed Cyber-Physical Systems

Fri, 01/08/2014 - 00:00
In this paper, we analyze stochastic stability of Kalman filter (KF) based state estimation over a lossy network in spatially distributed cyber-physical systems. We study a practical scenario in which sensors are arbitrarily deployed over an area to jointly sense the state of underlying physical system. The sensors directly communicate observations to a central state estimation unit over a network resulting in random loss in measurements and partial observation updates in KF. We analyzed stability of state estimation process in this scenario by establishing conditions under which steady state error covariance matrix is bounded. In contrast to previous work on gathered measurement scenario with intermittent loss, we considered a dispersed measurement scenario and established bounds on critical probability of receiving measurements over individual sensor communication links. Our analysis later exploited possible existence of spatial correlation among states in the filtering process and characterized its impact on the bounds. We further extended our analysis by considering correlated loss among sensor measurements. The overall analysis quantifies the trade-off between state estimation accuracy and the quality of underlying communication network. In addition, our analysis demonstrates that by exploiting spatial correlation among states, a higher degree of information loss (or lower network quality) can be tolerated to achieve a certain estimation accuracy. Since estimation accuracy directly impacts the stability of control operation, this analysis is critical for architecture and network planing design of cyber-physical systems.

Adaptive Penalty-Based Distributed Stochastic Convex Optimization

Fri, 01/08/2014 - 00:00
In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a fully distributed adaptive diffusion algorithm based on penalty methods that allows the network to cooperatively optimize the global cost function, which is defined as the sum of the individual costs over the network, subject to all constraints. We show that when small constant step-sizes are employed, the expected distance between the optimal solution vector and that obtained at each node in the network can be made arbitrarily small. Two distinguishing features of the proposed solution relative to other approaches is that the developed strategy does not require the use of projections and is able to track drifts in the location of the minimizer due to changes in the constraints or in the aggregate cost itself. The proposed strategy is able to cope with changing network topology, is robust to network disruptions, and does not require global information or rely on central processors.

Base Station Activation and Linear Transceiver Design for Optimal Resource Management in Heterogeneous Networks

Fri, 01/08/2014 - 00:00
In a densely deployed heterogeneous network (HetNet), the number of pico/micro base stations (BS) can be comparable with the number of the users. To reduce the operational overhead of the HetNet, proper identification of the set of serving BSs becomes an important design issue. In this work, we show that by jointly optimizing the transceivers and determining the active set of BSs, high system resource utilization can be achieved with only a small number of BSs. In particular, we provide formulations and efficient algorithms for such joint optimization problem, under the following two common design criteria: i) minimization of the total power consumption at the BSs, and ii) maximization of the system spectrum efficiency. In both cases, we introduce a nonsmooth regularizer to facilitate the activation of the most appropriate BSs. We illustrate the efficiency and the efficacy of the proposed algorithms via extensive numerical simulations.

A Particle Marginal Metropolis-Hastings Multi-Target Tracker

Fri, 01/08/2014 - 00:00
We propose a Bayesian multi-target batch processing algorithm capable of tracking an unknown number of targets that move close and/or cross each other in a dense clutter environment. The optimal Bayes multitarget tracking problem is formulated in the random finite set framework and a particle marginal Metropolis–Hastings (PMMH) technique which is a combination of the Metropolis–Hastings (MH) algorithm and sequential Monte Carlo methods is applied to compute the multi-target posterior distribution. The PMMH technique is used to design a high-dimensional proposal distributions for the MH algorithm and allows the proposed batch process multi-target tracker to handle a large number of tracks in a computationally feasible manner. Our simulations show that the proposed tracker reliably estimates the number of tracks and their trajectories in scenarios with a large number of closely spaced tracks in a dense clutter environment albeit, more expensive than online methods.

VLSI Implementation of a Non-Binary Decoder Based on the Analog Digital Belief Propagation

Fri, 01/08/2014 - 00:00
This work presents the VLSI hardware implementation of a novel Belief Propagation (BP) algorithm introduced in [G. Montorsi, “Analog digital belief propagation,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1106–1109, 2012] and named as Analog Digital Belief Propagation (ADBP). The ADBP algorithm works on factor graphs over linear models and uses messages in the form of Gaussian like probability distributions by tracking their parameters. In particular, ADBP can deal with system variables that are discrete and/or wrapped. A variant of ADBP can then be applied for the iterative decoding of a particular class of non binary codes and yields decoders with complexity independent of alphabet size $M$ , thus allowing to construct efficient decoders for digital transmission systems with unbounded spectral efficiency. In this work, we propose some simplifications to the updating rules for ADBP algorithm that are suitable for hardware implementation. In addition, we analyze the effect of finite precision on the decoding performance of the algorithm. A careful selection of quantization scheme for input, output and intermediate variables allows us to construct a complete ADBP decoding architecture that performs close to the double precision implementation and shows a promising complexity for large values of $M$. Finally, synthesis results of the main processing elements of ADBP are reported for 45 nm standard cell ASIC technology.

Carrier Phase and Amplitude Estimation for Phase Shift Keying Using Pilots and Data

Fri, 01/08/2014 - 00:00
We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., $M$-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is asymptotically biased and converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. This appears to be the first time that the statistical properties of a non-data-aided estimator for carrier amplitude have been analyzed theoretically. The results of Monte Carlo simulations are provided and these agree with the theoretical results.

Variants of Non-Negative Least-Mean-Square Algorithm and Convergence Analysis

Fri, 01/08/2014 - 00:00
Due to the inherent physical characteristics of systems under investigation, non-negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate. The Non-Negative Least-Mean-Square algorithm (NNLMS) was proposed to adaptively find solutions of a typical Wiener filtering problem but with the side constraint that the resulting weights need to be non-negative. It has been shown to have good convergence properties. Nevertheless, certain practical applications may benefit from the use of modified versions of this algorithm. In this paper, we derive three variants of NNLMS. Each variant aims at improving the NNLMS performance regarding one of the following aspects: sensitivity of input power, unbalance of convergence rates for different weights and computational cost. We study the stochastic behavior of the adaptive weights for these three new algorithms for non-stationary environments. This study leads to analytical models to predict the first and second order moment behaviors of the weights for Gaussian inputs. Simulation results are presented to illustrate the performance of the new algorithms and the accuracy of the derived models.