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Signal Processing, IEEE Transactions on

Issue 8 • Date Aug. 2009

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Displaying Results 1 - 25 of 46
  • Table of contents

    Page(s): C1 - C4
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    Freely Available from IEEE
  • IEEE Transactions on Signal Processing publication information

    Page(s): C2
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    Freely Available from IEEE
  • Consistent Reduced-Rank LMMSE Estimation With a Limited Number of Samples per Observation Dimension

    Page(s): 2889 - 2902
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (881 KB) |  | HTML iconHTML  

    An improved construction of the optimal reduced- rank linear minimum mean-square error (MMSE) estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree-of-freedom. The new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate, and being consistent when all dimensions in the model but the number of samples remain bounded. Our solution not only generalizes the conventional estimator, but also turns out to appropriately characterize model mismatch constraints due to finite sample-size limitations of fundamental importance in practical situations. The proposed implementation results from a generalized consistent estimation of the set of MMSE filter subspace coefficients on the reduced-dimensional subspace. Results are based on the theory of the spectral analysis of large-dimensional random matrices. In particular, we build on the analytical description of the asymptotic spectrum of sample-covariance-type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate. As a result, the proposed MMSE signal waveform estimator is shown to present a superior mean-square error performance under a finite sample-size by avoiding the breakdown experienced as the selected rank increases. View full abstract»

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  • Prediction of the SINR RMS in the IEEE 802.16 OFDMA System

    Page(s): 2903 - 2907
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB) |  | HTML iconHTML  

    In this paper, we perform the prediction of the signal-to-interference-plus-noise ratio (SINR) root mean square (RMS) in the IEEE 802.16 system. We obtain the time series of the SINR RMS using system-level simulations. The SINR RMS is a heteroscedastic stochastic process. We propose a nonlinear transform of the SINR RMS that generates a linear homoscedastic stochastic process, which may be considered Gaussian in practice. We construct the prediction model of this Gaussian stochastic process using the linear autoregressive process. We propose three predictions of the SINR RMS, that is, the minimum mean square, the median, and the maximum-likelihood predictions, using the prediction of the linear autoregressive process. Our minimum mean-square error (MMSE) prediction of the SINR RMS is more reliable than the prediction based on averaging of the SINR RMS. View full abstract»

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  • Jump Function Kolmogorov for Audio Classification in Noise-Mismatch Conditions

    Page(s): 2908 - 2918
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1219 KB) |  | HTML iconHTML  

    We present jump function Kolmogorov (JFK), a novel signal representation, which is (a) additive, thus the sum of signal and noise yields the sum of their JFKs; (b) sparse, therefore the signal and noise are separable in this domain. In this paper, the proposed signal representation is used in developing a classification system under noise-mismatch conditions. In this framework, we estimate JFKs from noisy signals in wavelet domain and compare them with the templates trained in clean condition. As the JFK is additive and sparse, the noise is simply eliminated by limiting JFKs only within the confidence intervals. The experiments show that the JFK-driven method significantly outperforms the conventional ones in three different classification tasks. The proposed method is further improved by adopting a discriminative feature selection for the classification. View full abstract»

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  • Fast LMS/Newton Algorithms for Stereophonic Acoustic Echo Cancelation

    Page(s): 2919 - 2930
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (943 KB) |  | HTML iconHTML  

    This paper presents a new class of adaptive filtering algorithms to solve the stereophonic acoustic echo cancelation (AEC) problem in teleconferencing systems. While stereophonic AEC may be seen as a simple generalization of the well-known single-channel AEC, it is a fundamentally far more complex and challenging problem to solve. The main reason being the strong cross correlation that exists between the two input audio channels. In the past, nonlinearities have been introduced to reduce this correlation. However, nonlinearities bring with it additional harmonics that are undesirable. We propose an elegant linear technique to decorrelate the two-channel input signals and thus avoid the undesirable nonlinear distortions. We derive two low complexity adaptive algorithms based on the two-channel gradient lattice algorithm. The models assume the input sequences to the adaptive filters to be autoregressive (AR) processes whose orders are much lower than the lengths of the adaptive filters. This results in an algorithm, whose complexity is only slightly higher than the normalized least-mean-square (NLMS) algorithm; the simplest adaptive filtering method. Simulation results show that the proposed algorithms perform favorably when compared with the state-of-the-art algorithms. View full abstract»

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  • Properties of FXLMS-Based Narrowband Active Noise Control With Online Secondary-Path Modeling

    Page(s): 2931 - 2949
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    Rotating machines such as diesel engines, cutting machines, fans, motors, etc., generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control (ANC) systems. In this paper, a typical filtered-X LMS (FXLMS) based narrowband ANC system equipped with an online secondary-path modeling subsystem is analyzed in detail. First, difference equations governing the dynamics of the FXLMS algorithm for secondary source synthesis and the LMS algorithm for secondary-path estimation are derived in terms of convergence in both mean and mean square. Steady-state expressions for mean-square error (MSE) as well as the residual noise power are then developed in closed form. Extensive simulations are performed to demonstrate the validity of the analytical results. View full abstract»

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  • Maxflat Fractional Delay IIR Filter Design

    Page(s): 2950 - 2956
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (244 KB) |  | HTML iconHTML  

    Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters. View full abstract»

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  • Frequency-Domain Design of Overcomplete Rational-Dilation Wavelet Transforms

    Page(s): 2957 - 2972
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (609 KB) |  | HTML iconHTML  

    The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Q-factor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Q-factors (desirable for processing oscillatory signals) or the same low Q-factor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible 'constant-Q' discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2(R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the time-frequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform's redundancy and the flexibility allowed by frequency-domain filter design. View full abstract»

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  • Time-Frequency Characterization and Receiver Waveform Design for Shallow Water Environments

    Page(s): 2973 - 2985
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1514 KB) |  | HTML iconHTML  

    We investigate a frequency-domain characterization of shallow water environments based on normal-mode models of acoustic mediums. The shallow water environment can be considered as a time-dispersive system whose time-varying impulse response can be expressed as a superposition of time-frequency components with dispersive characteristics. After studying the dispersive characteristics, a blind time-frequency processing technique is employed to separate the normal-mode components without knowledge of the environment parameters. This technique is based on first approximating the time-frequency structure of the received signal and then designing time-frequency separation filters based on warping techniques. Following this method, we develop two types of receivers to exploit the diversity inherent in the shallow water environment model and to improve underwater communication performance. Numerical results demonstrate the dispersive system characterization and the improved processing performance of the receiver structures. View full abstract»

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  • Compressed Sensing of Analog Signals in Shift-Invariant Spaces

    Page(s): 2986 - 2997
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (410 KB) |  | HTML iconHTML  

    A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in which the signal occupies the entire available bandwidth. In practice, many signals are sparse so that only part of the bandwidth is used. In this paper, we develop methods for low-rate sampling of continuous-time sparse signals in shift-invariant (SI) spaces, generated by m kernels with period T . We model sparsity by treating the case in which only k out of the m generators are active, however, we do not know which k are chosen. We show how to sample such signals at a rate much lower than m/T, which is the minimal sampling rate without exploiting sparsity. Our approach combines ideas from analog sampling in a subspace with a recently developed block diagram that converts an infinite set of sparse equations to a finite counterpart. Using these two components we formulate our problem within the framework of finite compressed sensing (CS) and then rely on algorithms developed in that context. The distinguishing feature of our results is that in contrast to standard CS, which treats finite-length vectors, we consider sampling of analog signals for which no underlying finite-dimensional model exists. The proposed framework allows to extend much of the recent literature on CS to the analog domain. View full abstract»

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  • Chromatic Derivatives and Local Approximations

    Page(s): 2998 - 3007
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (596 KB) |  | HTML iconHTML  

    We present a detailed motivation for the notions of chromatic derivatives and chromatic expansions. Chromatic derivatives are special, numerically robust linear differential operators; chromatic expansions are the associated local expansions, which possess the best features of both the Taylor and the Nyquist expansions. We give a simplified treatment of some of the basic properties of chromatic derivatives and chromatic expansions which are relevant for applications. We also consider some signal spaces with a scalar product defined by a Cesaro-type sum of products of chromatic derivatives, as well as an approximation of such a scalar product which is relevant for signal processing. We also introduce a new kind of local approximations based on trigonometric functions. View full abstract»

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  • Design of Robust D-Stable IIR Filters Using Genetic Algorithms With Embedded Stability Criterion

    Page(s): 3008 - 3016
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (965 KB) |  | HTML iconHTML  

    This paper proposes a novel evolution strategy for a genetic algorithm (GA). This new algorithm is then applied to design robust D(alpha,r)-stable infinite-impulse-response (IIR) filters. Unlike existing research on designing IIR filters by using GA, in which the stability of IIR filters is tested by trial and error after the evolution of each generation of a GA, the stability criterion in this paper is embedded within the evolution of each generation. Consequently, the stability of this system can be guaranteed without the need for any other checks of the stability criterion in the evolution of each generation. Numerical experimental results are discussed to illustrate the soundness of the proposed evolution strategy. The robustness of the IIR filters is achieved by ensuring that all poles of the filters are located inside a disk D(alpha,r) contained in the unit circle, in which alpha is the center, r is the radius of the disk and IalphaI +r < 1 . So, in this paper, a D(alpha,r)-stability criterion will be first derived and then embedded in the GA for the design of robust IIR filters. Finally, two examples will be presented to show that the designed filters remain D(alpha,r)-stable during the evolution of the GA and will provide satisfactory results. View full abstract»

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  • Blind Maximum-Likelihood Identification of Wiener Systems

    Page(s): 3017 - 3029
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (908 KB) |  | HTML iconHTML  

    This paper is about the identification of discrete-time Wiener systems from output measurements only (blind identification). Assuming that the unobserved input is white Gaussian noise, that the static nonlinearity is invertible, and that the output is observed without errors, a Gaussian maximum-likelihood estimator is constructed. Its asymptotic properties are analyzed and the Cramer-Rao lower bound is calculated. A two-step procedure for generating high-quality initial estimates is presented as well. The paper includes the illustration of the method on a simulation example. View full abstract»

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  • Intra-Predictive Transforms for Block-Based Image Coding

    Page(s): 3030 - 3040
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (684 KB) |  | HTML iconHTML  

    This paper presents the theory and the design of intra-predictive transforms, which unify the inter-block prediction and block-based transforms in block-based image coding. Motivated by interpreting inter-block prediction as a transform with a larger size, we derive the concept of intra-predictive transforms. Conventional predictions and transforms can be viewed as special cases of intra-predictive transforms. Intra-predictive transforms are able to exploit both inter and intra-block correlations. We derive the tight upper bound of the coding gain of intra-predictive transforms for stationary Gaussian sources. It turns out that the coding gain can be greater than that of conventional transforms. The optimal intra-predictive transform that achieves the upper bound is also derived. We also design a practical intra-predictive transform using frequency-domain prediction that can achieve better performance in image coding while exhibiting low computational complexity. Experimental results confirm the effectiveness of the proposed intra-predictive transforms in block-based image coding systems and show the improvements over the current design. View full abstract»

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  • Circular Acoustic Vector-Sensor Array for Mode Beamforming

    Page(s): 3041 - 3052
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1434 KB) |  | HTML iconHTML  

    Undersea warfare relies heavily on acoustic means to detect a submerged vessel. The frequency of the acoustic signal radiated by the vessel is typically very low, thus requires a large array aperture to achieve acceptable angular resolution. In this paper, we present a novel approach for low-frequency direction-of-arrival (DOA) estimation using miniature circular vector-sensor array mounted on the perimeter of a cylinder. Under this approach, we conduct beamforming using decomposition in the acoustic mode domain rather than frequency domain, to avoid the long wavelength constraints. We first introduce a multi-layer acoustic gradient scattering model to provide a guideline and performance predication tool for the mode beamformer design and algorithm. We optimize the array gain and frequency response with this model. We further develop the adaptive DOA estimation algorithm based on this model. We formulate the Capon spectra of the mode beamformer which is independent of the frequency band after the mode decomposition. Numerical simulations are conducted to quantify the performance and evaluate the theoretical results developed in this study. View full abstract»

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  • Multiple Peer-to-Peer Communications Using a Network of Relays

    Page(s): 3053 - 3062
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (615 KB) |  | HTML iconHTML  

    We consider an ad hoc wireless network consisting of d source-destination pairs communicating, in a pairwise manner, via R relaying nodes. The relay nodes wish to cooperate, through a decentralized beamforming algorithm, in order to establish all the communication links from each source to its respective destination. Our communication strategy consists of two steps. In the first step, all sources transmit their signals simultaneously. As a result, each relay receives a noisy faded mixture of all source signals. In the second step, each relay transmits an amplitude- and phase-adjusted version of its received signal. That is each relay multiply its received signal by a complex coefficient and retransmits the so-obtained signal. Our goal is to obtain these complex coefficients (beamforming weights) through minimization of the total relay transmit power while the signal-to-interference-plus-noise ratio (SINR) at the destinations are guaranteed to be above certain predefined thresholds. Although such a power minimization problem is not convex, we use semidefinite relaxation to turn this problem into a semidefinite programming (SDP) problem. Therefore, we can efficiently solve the SDP problem using interior point methods. Our numerical examples reveal that for high network data rates, our space division multiplexing scheme requires significantly less total relay transmit power compared to other orthogonal multiplexing schemes, such as time-division multiple access schemes. View full abstract»

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  • Orthogonalizing Beams to Train Unscheduled Terminals

    Page(s): 3063 - 3074
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (669 KB) |  | HTML iconHTML  

    Recent work on wireless beamforming has focused on multiuser diversity effects, where terminals in a cellular system are chosen opportunistically from a pool of terminals based on their responses to test beams. Orthogonality between the test beams is typically chosen to aid subsequent interference-free transmission to the corresponding terminals. However, much of this work assumes that i) the pool of terminals on a given time-frequency resource is large enough that a subset of terminals can be found whose spatial signatures match the orthogonal test beams; ii) the responses to the test beams of the entire pool are known to the base station; iii) beamforming considerations can drive traffic scheduling and resource allocation. These conditions are not always met. Rather, we examine orthogonalizing a given set of data-carrying beams for terminals that are scheduled on distinct time-frequency resources. The scheduled terminals are not chosen for their spatial signatures, but rather for their need to receive data. Our orthogonalization is chosen to maximize the beamforming gain to the scheduled terminals, whose channels are generally not spatially orthogonal. Unscheduled terminals may then ldquoeavesdroprdquo on pilots embedded in the orthogonal beams and thereby learn their own channel state information. This process eliminates the need for separate dedicated orthogonal training signals. We show how this scheme may be deployed in frequency-division duplex and time-division duplex systems. We quantify the price in beamforming gain paid for orthogonalizing a set of beams. One result analytically shows that the average price is at most 1.4 dB in SNR. View full abstract»

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  • On the Reconstruction of Block-Sparse Signals With an Optimal Number of Measurements

    Page(s): 3075 - 3085
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (703 KB) |  | HTML iconHTML  

    Let A be an M by N matrix (M < N) which is an instance of a real random Gaussian ensemble. In compressed sensing we are interested in finding the sparsest solution to the system of equations A x = y for a given y. In general, whenever the sparsity of x is smaller than half the dimension of y then with overwhelming probability over A the sparsest solution is unique and can be found by an exhaustive search over x with an exponential time complexity for any y. The recent work of Candes, Donoho, and Tao shows that minimization of the lscr 1 norm of x subject to Ax = y results in the sparsest solution provided the sparsity of x, say K, is smaller than a certain threshold for a given number of measurements. Specifically, if the dimension of y approaches the dimension of x , the sparsity of x should be K < 0.239 N. Here, we consider the case where x is block sparse, i.e., x consists of n = N /d blocks where each block is of length d and is either a zero vector or a nonzero vector (under nonzero vector we consider a vector that can have both, zero and nonzero components). Instead of lscr1 -norm relaxation, we consider the following relaxation: times min ||X 1||2 + ||X 2||2 + ldrldrldr + ||X n ||2, subject to A x = y (*) where X i = (x ( i-1)d+1, x ( i-1)d+2, ldrldrldr , x i d)T for i = 1, 2, ldrldrldr , N. Our main result is that as n rarr infin, (*) finds the sparsest solution to A=x = y, with overwhelming probability in A, for any x whose sparsity is k/n < (1/2) - O (isi- - n), provided m /n > 1 - 1/d, and d = Omega(log(1/isin)/isin3) . The relaxation given in (*) can be solved in polynomial time using semi-definite programming. View full abstract»

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  • Worst-Case Robust MIMO Transmission With Imperfect Channel Knowledge

    Page(s): 3086 - 3100
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (712 KB) |  | HTML iconHTML  

    In this paper, we consider robust transmit strategies, against the imperfectness of the channel state information at the transmitter (CSIT), for multi-input multi-output (MIMO) communication systems. Following a worst-case deterministic model, the actual channel is assumed to be inside an ellipsoid centered at a nominal channel. The objective is to maximize the worst-case received signal-to-noise ratio (SNR), or to minimize the worst-case Chernoff bound of the error probability, thus leading to a maximin problem. Moreover, we also consider the QoS problem, as a complement of the maximin design, which minimizes the transmit power consumption and meanwhile keeps the received SNR above a given threshold for any channel realization in the ellipsoid. It is shown that, for a general class of power constraints, both the maximin and QoS problems can be equivalently transformed into convex problems, or even further into semidefinite programs (SDPs), thus efficiently solvable by the numerical methods. The most interesting result is that the optimal transmit directions, i.e., the eigenvectors of the transmit covariance, are just the right singular vectors of the nominal channel under some mild conditions. This result leads to a channel-diagonalizing structure, as in the cases of perfect CSIT and statistical CSIT with mean or covariance feedback, and reduces the complicated matrix-valued problem to a scalar power allocation problem. Then we provide the closed-form solution to the resulting power allocation problem. View full abstract»

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  • Minimum Symbol Error Rate Carrier Phase Recovery of QPSK

    Page(s): 3101 - 3107
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (839 KB) |  | HTML iconHTML  

    This paper considers the problem of phase recovery of QPSK signals with phase-locked loops (PLL) using two new phase error detectors (PEDs) which are designed to minimize the probability of making a symbol decision error. The new PEDs resemble the PED derived from the maximum likelihood criterion. However, the new PEDs penalize matched filter outputs that are close to decision region boundaries. This penalty gives rise to faster converging PLLs relative to PLLs using the maximum likelihood PED, as shown in simulation results. The S-curves for the PEDs are used as a tool to gain insight into the behavior of the new PEDs. View full abstract»

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  • Stochastic Modeling and Particle Filtering Algorithms for Tracking a Frequency-Hopped Signal

    Page(s): 3108 - 3118
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1140 KB) |  | HTML iconHTML  

    The problem of tracking a frequency-hopped signal without knowledge of its hopping pattern is considered. The problem is of interest in military communications, where, in addition to frequency, hop timing can also be randomly shifted to guard against unauthorized reception and jamming. A conceptually simple nonlinear and non-Gaussian stochastic state-space model is proposed to capture the randomness in carrier frequency and hop timing. This model is well-suited for the application of particle filtering tools: it is possible to compute the optimal (weight variance-minimizing) importance function in closed-form. A convenient mixture representation of the latter is employed together with Rao-Blackwellization to derive a very simple optimal sampling procedure. This is representative of the state-of-art in terms of systematic design of particle filters. A heuristic design approach is also developed, using the mode of the spectrogram to localize hop particles. Performance is assessed in a range of experiments using both simulated and measured data. Interestingly, the results indicate that the heuristic design approach can outperform the systematic one, and both are robust to model assumptions. View full abstract»

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  • Analysis and Compensation of Transmitter IQ Imbalances in OFDMA and SC-FDMA Systems

    Page(s): 3119 - 3129
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (912 KB) |  | HTML iconHTML  

    One limiting issue in implementing high-speed wireless systems is the impairment associated with analog processing due to component imperfections. In uplink transmission of multiuser systems, a major source of such impairment is in-phase/quadrature-phase imbalance (IQI) introduced at multiple transmitters. In this paper, we deal with orthogonal-frequency-division multiple access (OFDMA) and single-carrier frequency-division multiple access (SC-FDMA) which have received attention in recent years as physical layer protocol in WiMAX and 3GPP Long Term Evolution (LTE) and analyze the effect of the transmitter (Tx) IQIs on OFDMA and SC-FDMA receivers. To cope with the interuser interference problem due to Tx IQIs, we propose a widely linear receiver for OFDMA and SC-FDMA systems and also propose a novel subcarrier allocation scheme, which has high tolerance to such Tx IQ distortion. View full abstract»

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  • Robust Collaborative-Relay Beamforming

    Page(s): 3130 - 3143
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (805 KB) |  | HTML iconHTML  

    Relay communications is a promising technique to extend the range of wireless communications by forwarding the message from the sender to the intended destination. While fixed or variable-power relays have been previously investigated, this paper addresses the collaborative use of variable-phase variable-power amplify-and-forward (AF) relays for robust beamforming, with the aid of imperfect channel state information (CSI) at the sender. In particular, the maximization of the worst-case signal-to-noise ratio (SNR) at the destination terminal is studied under a bounded spherical region for the norm of the CSI error vector from the relays to the destination. Our main contribution is that we prove, under a condition on the quality of the estimated CSI, the robust-optimal collaborative-relay beamforming (CRBF) can be obtained by S-procedure and rank relaxation techniques. In addition, a distributed algorithm is developed by examining the structure of the optimal CRBF solution. Results demonstrate a significant gain of CRBF over non-robust approaches. View full abstract»

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  • Optimal Training Sequence for MIMO Wireless Systems in Colored Environments

    Page(s): 3144 - 3153
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (747 KB) |  | HTML iconHTML  

    In this paper, we design the training signal for a multi-input multi-output (MIMO) communication system in a colored medium. We assume that the known channel covariance matrix (CM) is a Kronecker product of a transmit channel CM and a receive channel CM. Similarly, the CM of the additive Gaussian noise is modeled by a Kronecker product of a temporal CM and a spatial CM. We maximize the differential entropy gained by receiver for a limited energy budget for training at the transmitter. Using, singular value decomposition of the involved CMs, we turn this problem into a convex optimization problem. We prove that the left and right singular vectors of the optimal training matrix are eigenvectors of the channel transmit CM and the noise temporal CM. In general case, this problem can be solved numerically using efficient methods. The impact of the optimal training is more significant in environments with larger eigenvalue spread. The expression of the optimal solution is interesting for some specific cases. For uncorrelated receive channel, the optimal training looks like water filling, i.e., more training power must be invested on the directions which have more impact. For high signal-to-noise ratios (SNRs), any orthogonal training is optimal; this means that if large amount of energy is available, it must be invested uniformly in all directions. In low SNR scenarios where low amount of energy is available for channel training, all the energy must be allocated to the best mode of channel (which has the highest ratio of the received channel variance to the received noise power). View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota