IEEE Transactions on Signal Processing

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Performance Metrics, Sampling Schemes, and Detection Algorithms for Wideband Spectrum Sensing

Wed, 01/10/2014 - 00:00
In this paper, we study the problem of wideband spectrum sensing for cognitive radio networks by partitioning it into four fundamental elements: system modeling, performance metrics, sampling schemes, and detection algorithms. Each element can potentially couple the individual channels so that designs for wideband spectrum sensing should consider the four elements jointly. We propose the $p$-sparse model for the primary occupancies and study three uniform sampling schemes for wideband spectrum sensing, specifically, partial-band Nyquist sampling, sequential narrowband Nyquist sampling, and integer undersampling. We suggest new performance metrics more appropriate for wideband spectrum sensing, specifically, the probability of insufficient spectrum opportunity and the probability of excessive interference opportunity. We also develop detection algorithms that effectively tradeoff these metrics. Our results indicate that for performance metrics that couple the individual channels, multichannel detection algorithms have a significant advantage over channel-by-channel detection algorithms even for wideband Nyquist sampling. Furthermore, integer undersampling, which corresponds to the simplest sub-Nyquist sampling scheme, along with suitable detection algorithms exhibits appealing detection performance in the regime that better protects the primary system.

Convergence Analysis of the Variance in Gaussian Belief Propagation

Wed, 01/10/2014 - 00:00
It is known that Gaussian belief propagation (BP) is a low-complexity algorithm for (approximately) computing the marginal distribution of a high dimensional Gaussian distribution. However, in loopy factor graph, it is important to determine whether Gaussian BP converges. In general, the convergence conditions for Gaussian BP variances and means are not necessarily the same, and this paper focuses on the convergence condition of Gaussian BP variances. In particular, by describing the message-passing process of Gaussian BP as a set of updating functions, the necessary and sufficient convergence conditions of Gaussian BP variances are derived under both synchronous and asynchronous schedulings, with the converged variances proved to be independent of the initialization as long as it is chosen from the proposed set. The necessary and sufficient convergence condition is further expressed in the form of a semi-definite programming (SDP) optimization problem, thus can be verified more efficiently compared to the existing convergence condition based on computation tree. The relationship between the proposed convergence condition and the existing one based on computation tree is also established analytically. Numerical examples are presented to corroborate the established theories.

Weighted Fair Multicast Multigroup Beamforming Under Per-antenna Power Constraints

Wed, 01/10/2014 - 00:00
A multiantenna transmitter that conveys independent sets of common data to distinct groups of users is considered. This model is known as physical layer multicasting to multiple cochannel groups. In this context, the practical constraint of a maximum permitted power level radiated by each antenna is addressed. The per-antenna power constrained system is optimized in a maximum fairness sense with respect to predetermined quality of service weights. In other words, the worst scaled user is boosted by maximizing its weighted signal-to-interference plus noise ratio. A detailed solution to tackle the weighted max-min fair multigroup multicast problem under per-antenna power constraints is therefore derived. The implications of the novel constraints are investigated via prominent applications and paradigms. What is more, robust per-antenna constrained multigroup multicast beamforming solutions are proposed. Finally, an extensive performance evaluation quantifies the gains of the proposed algorithm over existing solutions and exhibits its accuracy over per-antenna power constrained systems.

Joint Interference Mitigation and Data Recovery in Compressive Domain: A Sparse MLE Approach

Wed, 01/10/2014 - 00:00
We consider the problem where a receiver acquires information (data) corrupted by interference and noise. Both the information and interference are assumed to have a sparse structure. This problem occurs in many applications such as data demodulation in cellular systems. The joint interference mitigation and data recovery is formulated as a sparse maximum likelihood estimation (MLE) problem which maximizes the associated likelihood function under individual sparsity levels (ISLs) constraints. This sparse MLE framework can fully exploit the individual sparse structure of the information and interference to improve the data recovery performance at the receiver. We propose an alternating optimization (AO) recovery algorithm to solve the non-convex sparse MLE problem. To analyze the performance of the proposed AO algorithm, we introduce a new kind of restricted isometry property (RIP) called the ISLs-RIP. Under the ISLs-RIP conditions, we show that the proposed AO algorithm converges to the optimal solution of the sparse MLE problem. We also derive an upper bound of the corresponding estimation error for the information. Finally, we extend the above results and algorithms to the case when the receiver only has statistical knowledge of the ISLs. Simulations show that the proposed solution achieves significant gain over various baselines.

Table of contents

Mon, 15/09/2014 - 00:00
Presents the table of contents for this issue of the periodical.

Table of contents

Mon, 15/09/2014 - 00:00
Presents the table of contents for this issue of the periodical.

Resource Optimization of Non-Additive Utility Functions in Localized SC-FDMA Systems

Mon, 15/09/2014 - 00:00
In this paper, we study the problem of resource allocation in SC-FDMA systems. A sum-utility maximization is considered where the utility of each user may be neither additive nor super additive. Unlike OFDMA, in addition to the restriction of allocating a subchannel to at most one user, the multiple subchannels allocated to a user in SC-FDMA must be consecutive. This makes the resource allocation problem prohibitively difficult and challenging. We provide a fundamental complexity analysis of the optimization problem for general non-additive utility functions and show that not only the problem is NP-hard but also approximating it within a factor better than $ {{2011}over {2012}}$ is not possible unless ${rm P}={rm NP}$. An efficient cutting plane algorithm is presented and five suboptimal heuristics are also presented that achieve near optimal solution in different scenarios. Computational results of the cutting plane and heuristic algorithms are reported and a comparison between these heuristics is provided as well.

Rigid Body Localization Using Sensor Networks

Mon, 15/09/2014 - 00:00
A framework for joint position and orientation estimation of a rigid body using range measurements is proposed. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body is not known. However, we know how the sensors are mounted on the rigid body, i.e., the sensor topology is known. The rigid body is localized using noisy range measurements between the sensors and a few anchors (nodes with known absolute positions), and without using any inertial measurements. We propose a least-squares (LS), and a number of constrained LS estimators, where the constrained estimators solve an optimization problem on the Stiefel manifold. As a benchmark, we derive a unitarily constrained Cramér–Rao bound. Finally, the known topology of the sensors can be perturbed during fabrication or if the body is not entirely rigid. To take these perturbations into account, constrained total-least-squares estimators are also proposed.

Multiuser MISO Beamforming for Simultaneous Wireless Information and Power Transfer

Mon, 15/09/2014 - 00:00
This paper studies a multiuser multiple-input single-output (MISO) broadcast simultaneous wireless information and power transfer (SWIPT) system, where a multi-antenna access point (AP) sends wireless information and energy simultaneously via spatial multiplexing to multiple single-antenna receivers each of which implements information decoding (ID) or energy harvesting (EH). We aim to maximize the weighted sum-power transferred to all EH receivers subject to given minimum signal-to-interference-and-noise ratio (SINR) constraints at different ID receivers. In particular, we consider two types of ID receivers (referred to as Type I and Type II, respectively) without or with the capability of cancelling the interference from (a priori known) energy signals. For each type of ID receivers, we formulate the joint information and energy transmit beamforming design as a nonconvex quadratically constrained quadratic program (QCQP). First, we obtain the globally optimal solutions for our formulated QCQPs by applying an optimization technique so-called semidefinite relaxation (SDR). It is shown via SDR that under the condition of independently distributed user channels, no dedicated energy beam is used for the case of Type I ID receivers to achieve the optimal solution; while for the case of Type II ID receivers, employing no more than one energy beam is optimal. Next, we establish a new form of the celebrated uplink–downlink duality for our studied downlink beamforming problems, and thereby develop alternative algorithms to obtain the same optimal solutions as by SDR. Finally, numerical results are provided to evaluate the performance of proposed optimal beamforming designs for MISO SWIPT systems.

Theory, Design and Application of Arbitrary Order Arbitrary Delay Filterbanks

Mon, 15/09/2014 - 00:00
Classical design of filterbanks results in equal order inverses, thus resulting in filterbanks with equal analysis and synthesis filter length. While it is known that filterbanks may have unequal orders, there does not exist a simple, systematic method to design a $p$th-order analysis and $q$th-order synthesis filterbank where $p ne q$. Also, the design criteria of the $p$ th-order analysis having $q$ th-order synthesis filters ($p ne q$) with a flexibility to control the system delay has never been addressed concomitantly. In this work, we propose the use of unit non-diagonal matrix polynomials to design such filterbanks for given orders $p$, $q$ with arbitrary delay. We demonstrate how these orders depend on the sequence of unit matrices. Not only the achievable ranges of $p$ , $q$ are found, but construction methods for all such cases are also suggested. The proposed design has several desirable properties such as structural perfect reconstruction in its factorized form, completeness, and ability to control the resulting system delay of the filterbank. Several design examples and an application example for audio illustrate the flexibility and usefulness of the proposed design.

<formula formulatype="inline"><tex Notation="TeX">$R$</tex> </formula>-Dimensional ESPRIT-Type Algorithms for Strictly Second-Order Non-Circular Sources and Their Performance Analysis

Mon, 15/09/2014 - 00:00
High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) noncircular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the $R$ ${mathchar"702D}{rm D}$ NC Standard ESPRIT and the $R$ ${mathchar"702D}{rm D}$ NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant $R$ ${mathchar"702D}{rm D}$ antenna arrays and do not require a centro-symmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both $R$ ${mathchar"702D}{rm D}$ NC ESPRIT-type algorithms is identical in the high-effective SNR regime. Finally, - case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.

<formula formulatype="inline"><tex Notation="TeX">${cal H}_2$</tex></formula> Sampled&#x2014;Data Filtering of Linear Systems

Mon, 15/09/2014 - 00:00
This paper addresses the ${cal H}_2$ state estimation problem in the context of sampled-data systems, which is closely related to ${cal H}_2$ filtering design under limited bandwidth constraints. Our first approach considers a fixed data-rate setting, for which a discrete-time equivalent system is devised and, based on this concept, sufficient conditions for the ${cal H}_2$ filtering design are yielded. These results are then generalized to obtain a robust filter that is able to cope with uneven data-rates. Academical examples illustrate the theoretical results and point out the main characteristics of the design techniques devised in this paper.

Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity

Mon, 15/09/2014 - 00:00
We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially i) gains with different amplitude and the same phase, ii) gains with the same amplitude and different phase and iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided.

Superoscillations With Optimum Energy Concentration

Mon, 15/09/2014 - 00:00
Oscillations of a bandlimited signal at a rate faster than the bandlimit are called “superoscillations” and have applications e.g. in superresolution and superdirectivity. The synthesis of superoscillating signals is a numerically difficult problem. Minimum energy superoscillatory signals seem attractive for applications because (i) the minimum-energy solution is unique (ii) it has the smallest energy cost (iii) it may yield a signal of the smallest possible amplitude. On the negative side, superoscillating functions of minimum-energy depend heavily on cancellation and give rise to expressions that have very large coefficients. Furthermore, these coefficients have to be found by solving equations that are very ill-conditioned. Surprisingly, we show that by dropping the minimum energy requirement practicality can be gained rather than lost. We give a method of constructing superoscillating signals that leads to coefficients and condition numbers that are smaller by several orders of magnitude than the minimum-energy solution, yet yields energies close to the minimum. In contrast with the minimum-energy method, which builds superoscillations by linearly combining functions with an ill-conditioned Gram matrix, our method combines orthonormal functions, the Gram matrix of which is obviously the identity. Another feature of the method is that it yields the superoscillatory signal that maximises the energy concentration in a given set, which may or may not include the superoscillatory segment.

Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility

Mon, 15/09/2014 - 00:00
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this work we consider elementary methods based on projections for solving a sparse feasibility problem without employing convex heuristics. It has been shown recently that, locally, the fundamental method of alternating projections must converge linearly to a solution to the sparse feasibility problem with an affine constraint. In this paper we apply different analytical tools that allow us to show global linear convergence of alternating projections under familiar constraint qualifications. These analytical tools can also be applied to other algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm where we establish local linear convergence of this method applied to the sparse affine feasibility problem.

Low-Sampling-Rate Ultra-Wideband Channel Estimation Using Equivalent-Time Sampling

Mon, 15/09/2014 - 00:00
In this paper, a low-sampling-rate scheme for ultra-wideband channel estimation is proposed. The scheme exploits multiple observations generated by transmitting multiple pulses. In the proposed scheme, $P$ pulses are transmitted to produce channel impulse response estimates at a desired sampling rate, while the ADC samples at a rate that is $P$ times slower. To avoid loss of fidelity, the number of sampling periods (based on the desired rate) in the inter-pulse interval is restricted to be co-prime with $P$ . This condition is affected when clock drift is present and the transmitted pulse locations change. To handle this case, and to achieve an overall good channel estimation performance, without using prior information, we derive an improved estimator based on the bounded data uncertainty (BDU) model. It is shown that this estimator is related to the Bayesian linear minimum mean squared error (LMMSE) estimator. Channel estimation performance of the proposed sub-sampling scheme combined with the new estimator is assessed in simulation. The results show that high reduction in sampling rate can be achieved. The proposed estimator outperforms the least squares estimator in almost all cases, while in the high SNR regime it also outperforms the LMMSE estimator. In addition to channel estimation, a synchronization method is also proposed that utilizes the same pulse sequence used for channel estimation.

Elliptic Localization: Performance Study and Optimum Receiver Placement

Mon, 15/09/2014 - 00:00
Range based localization often relies on TOA that creates a circular contour or TDOA that yields hyperbolic surface to determine the position of an emitting object. Another approach that has gained attention recently is elliptic localization. Elliptic localization uses an active transmitter to send out a signal and several receivers to acquire the reflected or relayed signal from an object to obtain its location. This paper performs a fundamental investigation on the performance of elliptic localization, for both the synchronous and asynchronous cases between the transmitter and the receivers. Their performance is also characterized with respect to the hyperbolic localization. The study is based on the Cramér–Rao lower bound (CRLB) for the object location under Gaussian measurement noise as well as Gaussian errors in the transmitter and receiver positions. When the receiver positions are controllable, we derive the optimum receiver placement for elliptic positioning to improve the localization accuracy. We conclude the study with simulation results to demonstrate the elliptic localization performance using the CRLBs and the Maximum Likelihood estimators.

An Empirical-Bayes Approach to Recovering Linearly Constrained Non-Negative Sparse Signals

Mon, 15/09/2014 - 00:00
We propose two novel approaches for the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as a simplex signal. This problem arises in, e.g., hyperspectral imaging, portfolio optimization, density estimation, and certain cases of compressive imaging. Our first approach solves a linearly constrained non-negative version of LASSO using the max-sum version of the generalized approximate message passing (GAMP) algorithm, where we consider both quadratic and absolute loss, and where we propose a novel approach to tuning the LASSO regularization parameter via the expectation maximization (EM) algorithm. Our second approach is based on the sum–product version of the GAMP algorithm, where we propose the use of a Bernoulli non-negative Gaussian-mixture signal prior and a Laplacian likelihood and propose an EM-based approach to learning the underlying statistical parameters. In both approaches, the linear equality constraints are enforced by augmenting GAMP's generalized-linear observation model with noiseless pseudo-measurements. Extensive numerical experiments demonstrate the state-of-the-art performance of our proposed approaches.

Construction of Doppler Resilient Complete Complementary Code in MIMO Radar

Mon, 15/09/2014 - 00:00
Orthogonal waveform design has become an important research topic in recent years due to the performance advantages of MIMO radar incorporating orthogonal transmitted signals. Complete complementary code (CCC) has ideal ambiguity along the zero Doppler axis, which is desirable in MIMO radar. However, the main obstacle for the extensive usage of CCC is its sensitivity to nonzero Doppler shift. In this paper, we introduce a systematic method of constructing Doppler resilient CCC in MIMO radar, where the range sidelobes can vanish at modest Doppler shifts. In the construction of Doppler resilient waveforms, the generalized Prouhet–Thue–Morse (GPTM) sequence plays a key role. Numerical results are presented to demonstrate the effectiveness of the proposed method.

Knowledge-Aided Parametric Adaptive Matched Filter With Automatic Combining for Covariance Estimation

Mon, 15/09/2014 - 00:00
In this paper, a knowledge-aided parametric adaptive matched filter (KA-PAMF) is proposed that utilizing both observations (including the test and training signals) and a priori knowledge of the spatial covariance matrix. Unlike existing KA-PAMF methods, the proposed KA-PAMF is able to automatically adjust the combining weight of a priori covariance matrix, thus gaining enhanced robustness against uncertainty in the prior knowledge. Meanwhile, the proposed KA-PAMF is significantly more efficient than its KA nonparametric counterparts when the amount of training signals is limited. One distinct feature of the proposed KA-PAMF is the inclusion of both the test and training signals for automatic determination of the combining weights for the prior spatial covariance matrix and observations. Numerical results are presented to demonstrate the effectiveness of the proposed KA-PAMF, especially in the limited training scenarios.