Linear Regression With a Sparse Parameter Vector

We consider linear regression under a model where the parameter vector is known to be sparse. Using a Bayesian framework, we derive the minimum mean-square error (MMSE) estimate of the parameter vector and a computationally efficient approximation of it. We also derive an empirical-Bayesian version of the estimator, which does not need any a priori information, nor does it need the selection of any user parameters. As a byproduct, we obtain a powerful model ("basis") selection tool for sparse models. The performance and robustness of our new estimators are illustrated via numerical examples     

Tomlinson-Harashima precoding with partial channel knowledge

We consider minimum mean-square error Tomlinson-Harashima (MMSE-TH) precoding for time-varying frequency-selective channels. We assume that the receiver estimates the channel and sends the channel state information (CSI) estimate to the transmitter through a lossless feedback channel that introduces a certain delay. Thus, the CSI mismatch at the receiver is due to estimation errors, while the CSI mismatch at the transmitter is due to both estimation errors and channel time variations. We exploit a priori statistical channel knowledge, and we derive an optimal TH precoder, adopting a Bayesian approach. We use simulations to compare the performance of the so-derived TH precoder with that of the same-complexity MMSE decision-feedback equalizer (DFE). We observe that for low signal-to-noise ratios (SNRs) and sufficiently slow channel time variations, the optimal TH precoder outperforms the DFE, while at high SNR, the opposite happens.     

Adaptive Bayesian multiuser detection for synchronous CDMA withGaussian and impulsive noise

We consider the problem of simultaneous parameter estimation and data restoration in a synchronous CDMA system in the presence of either additive Gaussian or additive impulsive white noise with unknown parameters. The impulsive noise is modeled by a two-term Gaussian mixture distribution. Bayesian inference of all unknown quantities is made from the superimposed and noisy received signals. The Gibbs sampler (a Markov chain Monte Carlo procedure) is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities. Adaptive Bayesian multiuser detectors based on the Gibbs sampler are derived for both the Gaussian noise synchronous CDMA channel and the impulsive noise synchronous CDMA channel. A salient feature of the proposed adaptive Bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities, and they produce as output the a posteriori symbol probabilities. (That is, they are “soft-input soft-output” algorithms.) Hence, these methods are well suited for iterative processing in a coded system, which allows the adaptive Bayesian multiuser detector to refine its processing based on the information from the decoding stage, and vice versa-a receiver structure termed the adaptive turbo multiuser detector     

Achieving near-optimum asymptotic efficiency and fading resistanceover the time-varying Rayleigh-faded CDMA channel

We study multiuser receiver design and analysis for synchronous code-division multiple-access (CDMA) channels with time-varying Rayleigh fading. Starting from an error probability criterion, we first derive a near-optimum receiver for this channel that admits a detector-estimator decomposition, has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval. The performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time-invariant (or static) CDMA Rayleigh-fading channel when it is implemented over the time-varying channel. Notable among our conclusions is the fact that, unlike the static channel multiuser detector, the time-varying channel detector is able to withstand not only the estimated interference from the other system users, but also, the residual interference (that cannot be estimated) arising out of imperfect estimation of the interferer fading parameters. Using estimation error covariance information, this detector shows flexibility in accommodating a wide range of interferer fading conditions     

Soft output interference suppression in TDMA wireless communications

We present a novel symbol-by-symbol Bayesian multiuser detector for cochannel interference cancellation in TDMA cellular communications. To begin with, we present the usual composite signal model consisting of the desired signal, interferer, channel parameters and channel noise. Then, we derive the soft output interference cancellation algorithm (SICA) to compute fixed-lag maximum a posteriori (MAP) estimates of the data symbols of the desired user, using a fixed lookahead of D observations. In the process, the interferer symbols are treated as nuisance parameters and averaged out. The complexity of the SICA is exponential in the length of the combined channel at the receiver. Subsequently, we present a simple, yet effective, technique for complexity reduction without significant performance degradation. We apply the algorithm to some typical scenarios, using the IS-136 TDMA standard, to demonstrate its interference suppression capabilities. In this paper, we assume that all relevant channel parameters are known. Hence, our results should be viewed as representing the best possible performance that can be obtained with the SICA in the scenarios considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Linear Differentially Coherent Multiuser Detection for Multipath Channels

By combining multipath processing, differential signal detection, and multiuser detection techniques, we develop a class of near-far resistant linear detectors for differentially coherent multipath signals. We derive and establish performance relationships among the following detectors: an optimally near-far resistant detector, a suboptimum detector which does not require knowledge of the signal coordinates, and a minimum mean square error (MMSE) detector which achieves near-optimum asymptotic efficiency. We present an adaptive multiuser detector which converges to the MMSE detector without training sequences and which requires less information than the conventional single user rake receiver.     

Autocorrelation-based blind spreading-factor detection for CDMA

Spreading factor (SF) in code-division multiple-access (CDMA) systems depends on the data rate of the user, and is, therefore, unknown a priori for a communication receiver. In this letter, the blind SF-detection problem in an additive white Gaussian noise channel is studied, and a novel one-step autocorrelation-based SF detector is proposed. Three decision rules are derived to find simple and robust SF detectors for practical communication receivers. Performance of the detectors is studied and compared with the optimal detector via Monte Carlo computer simulations. The autocorrelation-based SF detector appears to give performance close to the optimal detector, assuming perfect knowledge of signal-to-noise ratio (SNR). It is also found to be significantly more robust to SNR estimation errors than the optimal detector.     

A flexible receiver for CDMA multiuser communications

Code division multiple access (CDMA) capacity is limited by interference amongst users. The effect of this interference on receiver outputs depends on the users' signatures and the actual detector used in the receiver. A matched filter receiver is particularly sensitive to interference, whereas an optimum multiuser receiver is less sensitive but infeasible due to its exponential complexity. We propose a receiver structure that trades detection performance for reduced complexity. It can interpolate between the performances and complexities of these two receivers. Our detector uses a tree structure, and some of its special cases are the decision feedback detector, the decorrelating detector, and the optimal linear detector. We show that at equal complexity levels, a particular implementation of our detector outperforms these detectors. We also show that our approach can be used with a minimum-mean-square-error design criterion and coded CDMA transmission     

Differential Detection Based on Space-Time Block Codes

In this paper we consider the use of differential detection when there aremultiple transmitter and receiver antennas. Our differential scheme is based on the theory ofSpace-Time Block Codes that are used to achieve space-time diversity. Compared to the existingdifferential schemes for multiple antennas our scheme has a much smaller computationalcomplexity. It has the same encoding and decoding complexities as the coherent detection based on space-time block codes and achieves the same rate for up-to 8 transmitterantennas. The performance of the differential detector (which assumes no knowledge of the flat fading channel) is 3 dB less than that of the coherent detector (which uses exact channelstate information for reception). We also show that the proposed receiver is a Maximum Likelihood detector.     

Blind turbo multiuser detection for long-code multipath CDMA

We consider the problem of demodulating and decoding multiuser information symbols in an uplink asynchronous coded code-division multiple-access (CDMA) system employing long (aperiodic) spreading sequences, in the presence of unknown multipath channels, out-cell multiple-access interference (OMAI), and narrow-band interference (NBI). A blind turbo multiuser receiver, consisting of a novel blind Bayesian multiuser detector and a bank of MAP decoders, is developed for such a system. The effect of OMAI and NBI is modeled as colored Gaussian noise with some unknown covariance matrix. The main contribution of this paper is to develop blind Bayesian multiuser detectors for long-code multipath CDMA systems under both white and colored Gaussian noise. Such detectors are based on the Bayesian inference of all unknown quantities. The Gibbs sampler, a Markov chain Monte Carlo procedure, is then used to calculate the Bayesian estimates of the unknowns. The blind Bayesian multiuser detector computes the a posteriori probabilities of the channel coded symbols, which are differentially encoded before being sent to the channel. Being soft-input soft-output in nature, the proposed blind Bayesian multiuser detectors and the MAP decoders can iteratively exchange the extrinsic information to successively refine the performance, leading to the so-called blind turbo multiuser receiver     

Bayesian Monte Carlo multiuser receiver for space-time codedmulticarrier CDMA systems

We consider the design of optimal multiuser receivers for space-time block coded (STBC) multicarrier code-division multiple-access (MC-CDMA) systems in unknown frequency-selective fading channels. Under a Bayesian framework, the proposed multiuser receiver is based on the Gibbs sampler, a Markov chain Monte Carlo (MCMC) method for numerically computing the marginal a posteriori probabilities of different users' data symbols. By exploiting the orthogonality property of the STBC and the multicarrier modulation, the computational complexity of the receiver is significantly reduced. Furthermore, being a soft-input soft-output algorithm, the Bayesian Monte Carlo multiuser detector is capable of exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel code decoders of all users, and successively improving the overall receiver performance. Several practical issues, such as testing the convergence of the Gibbs sampler in fading channel applications, resolving the phase ambiguity as well as the antenna ambiguity, and adapting the proposed receiver to multirate MC-CDMA systems, are also discussed. Finally, the performance of the Bayesian Monte Carlo multiuser receiver is demonstrated through computer simulations     

A blind adaptive decorrelating detector for CDMA systems

The decorrelating detector is known to eliminate multiaccess interference when the signature sequences of the users are linearly independent, at the cost of enhancing the Gaussian receiver noise. We present a blind adaptive decorrelating detector which is based on the observation of readily available statistics. The algorithm recursively updates the filter coefficients of a desired user by using the output of the current filter. Due to the randomness of the information bits transmitted and the ambient Gaussian channel noise, the filter coefficients evolve stochastically. We prove the convergence of the filter coefficients to a decorrelating detector in the mean squared error (MSE) sense. We develop lower and upper bounds on the MSE of the receiver filter from the convergence point and show that with a fixed step size sequence, the MSE can be made arbitrarily small by choosing a small enough step size. With a time-varying step size sequence, the MSE converges to zero implying an exact convergence. The proposed algorithm is distributed, in the sense that no information about the interfering users such as their signature sequences or power levels is needed. The algorithm requires the knowledge of only two parameters for the construction of the receiver filter of a desired user: the desired user's signature sequence and the variance of the additive white Gaussian (AWG) receiver noise. This detector, for an asynchronous code division multiple access (CDMA) channel, converges to the one-shot decorrelating detector     

Bayesian wavelet shrinkage with edge detection for SAR image despeckling

In this paper, we present a wavelet-based despeckling method for synthetic aperture radar images and derive a Bayesian wavelet shrinkage factor to estimate noise-free wavelet coefficients. To preserve edges during despeckling, we apply a modified ratio edge detector to the original image and use the obtained edge information in our despeckling framework. Experimental results demonstrate that our method compares favorably to several other despeckling methods on test images.     

Space-time iterative and multistage receiver structures for CDMAmobile communication systems

We propose novel space-time multistage and iterative receiver structures and examine their application in code division multiple access (CDMA) mobile communication systems. In particular we derive an expression for weighting coefficients in parallel interference cancellers (PICs) in a system with a large number of users, where decision statistics bias is pronounced. We further examine the parameters in this expression and show how to obtain a practical partial cancellation method that allows on-line estimation of the weighting coefficients. In the proposed multistage PIC, the coefficients are calculated by using only the variances of the detector outputs. We also examine an iterative PIC and observe that this receiver has similar limitations as the multistage PIC. The application of the novel parallel interference cancellation strategy in the iterative receiver structure results in a spectacular system capacity improvement with a negligible complexity increase relative to the standard iterative receiver. The performance of the proposed receivers is further enhanced by receiver adaptive array antennas and space-time processing     

Blind turbo equalization in Gaussian and impulsive noise

We consider the problem of simultaneous parameter estimation and restoration of finite-alphabet symbols that are blurred by an unknown linear intersymbol interference (ISI) channel and contaminated by additive Gaussian or non-Gaussian white noise with unknown parameters. Non-Gaussian noise is found in many wireless channels due to the impulsive phenomena of radio-frequency interference. Bayesian inference of all unknown quantities is made from the blurred and noisy observations. The Gibbs sampler, a Markov chain Monte Carlo procedure, is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknowns and then to average the appropriate samples to obtain the estimates of the unknown quantities. Blind Bayesian equalizers based on the Gibbs sampler are derived for both Gaussian ISI channel and impulsive ISI channel. A salient feature of the proposed blind Bayesian equalizers is that they can incorporate the a priori symbol probabilities, and they produce as output the a posteriori symbol probabilities. (That is, they are “soft-input soft-output” algorithms.) Hence, these methods are well suited for iterative processing in a coded system, which allows the blind Bayesian equalizer to refine its processing based on the information from the decoding stage and vice versa-a receiver structure termed as blind turbo equalizer     

Nonparametric multiuser detection in non-Gaussian channels

Existing multiuser detection techniques in wireless systems are based on the assumption that some information on the parameters of the probability density function (pdf) of ambient noise is available. Such information may not be available in all cases, particularly for non-Gaussian and impulsive noises, or may change depending on circumstances. In this paper, we present a technique for multiuser detection that does not require any a priori knowledge about the noise parameters. This method is based on using pseudo norms for linear nonparametric regression. Analytical and simulation results show that the proposed method offers an improved, or at least comparable, performance over existing robust techniques in the absence of any information on the nature of noise in the environment. The increased computational complexity is marginal compared to existing parametric detectors. In addition, the proposed nonparametric detector is portable in the sense that it does not need to be tuned for different noise models without any considerable degradation of performance. We also show that in non-Gaussian noise, the performance of blind adaptive nonparametric multiuser detectors is better than that of robust multiuser detectors.     

Large system performance of second-order linear multistage CDMA receivers

We analyze the performance of a second-order linear multistage multiuser code-division multiple-access receiver. The receiver's filtered output is designed to converge to that of the linear minimum mean-squared error solution as the number of stages increase. Our analysis is based on a related second-order stationary iterative solution method. We derive the large system output signal to interference-plus-noise ratio for each stage. We use this result to perform a numerical optimization with respect to the two second-order parameters of our receiver. Within this iterative framework, we can achieve performance extremely close to the optimal linear multistage multiuser receiver.     

A sequential Monte Carlo blind receiver for OFDM systems infrequency-selective fading channels

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. Bayesian inference of the unknown data symbols in the presence of an unknown multipath fading channel is made only from the observations over one OFDM symbol duration. A novel blind SMC detector built on the techniques of importance sampling and resampling is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied. Furthermore, being soft-input and soft-output in nature, the proposed SMC detector is employed as the first-stage demodulator in a turbo receiver for a coded OFDM system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations     

Blind Channel Identifiability for Generic Linear Space-Time Block Codes

Linear space-time block codes (STBCs) have proven their effectiveness in performance improvement of wireless multiple-input multiple-output communication systems. Their successful decoding, however, requires reliable channel knowledge at the receiver. In this paper, we present a semiblind channel estimation method for linear STBC without the usual code orthogonality condition. We provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration. We also present a simple channel estimation algorithm. Finally, we provide simulation results that illustrate the performance of the proposed scheme     

Impact of the mapping strategy on the performance of APP decoded space-time block codes

In this paper, we propose a "turbo" coding scheme consisting of the serially concatenation of a channel code and OSTBC with iterative processing at the receiver. We analyze the impact of different mapping strategies on the information transfer of the space-time detector with EXIT-charts and derive some criteria for the optimum mapping strategy.