Data-record size requirements for adaptive space-time DS-CDMA signal detection

We investigate the data-record size requirements of sample-matrix-inversion-based minimum-variance-distortionless response and maximum-signal-to-interference-plus-noise-ratio adaptive algorithms to meet a given performance objective in joint space-time signal-detection problems for direct-sequence code-division multiple-access systems. We derive closed-form expressions that provide the data-record size that is necessary to achieve a given performance confidence level in a neighborhood of the optimal performance point, as well as expressions that identify the performance level that can be reached for a given data-record size. This is done by using close approximations of the involved probability density functions. The practical significance of the derived expressions lies in the fact that the expressions are functions of the number of antenna elements, the number of multipaths, and the system spreading gain only, while they depend neither on the ideal input covariance matrix, which is not known in most realistic applications, nor on the exact ideal performance value.     

Design and Analysis of Supervised and Decision-Directed Estimators of the MMSE/LCMV Filter in Data Limited Environments

We consider sample-matrix-inversion (SMI)-type estimates of the minimum-mean-square-error (MMSE) and the linearly constrained-minimum-variance (LCMV) linear filters obtained from data records of limited size. We quantify theoretically the (detrimental) effect of the desired-signal energy level on the mean square (MS) filter estimation error and the normalized output signal-to-interference-plus-noise ratio (SINR) by deriving a new exact analytical expression and a lower bound, respectively. For cases where accumulation of pure disturbance observations is not possible, we show theoretically how certain intuitive, pilot-assisted, and decision-directed adaptive filter implementations that utilize desired-signal-present data/observations perform close to their desired-signal-absent counterparts. Simulation studies illustrate our theoretical developments in the context of spread-spectrum communications over multipath fading channels under perfect and nonperfect synchronization.     

BER performance of BPSK transmissions over multipath channels

A new closed form expression for the bit error rate (BER) performance of binary phase shift keying (BPSK) transmissions over frequency selective channels is presented. The expression is obtained through a novel approximation of the Gaussian Q(middot) function by a fixed series of sinusoids with exponentially decreasing amplitudes. Numerical results demonstrate the accuracy of the derived expression     

Recursive short-data-record estimation of AV and MMSE/MVDR linear filters for DS-CDMA antenna array systems

The presence of the desired signal during estimation of the minimum mean-square error (MMSE)/minimum-variance distortionless-response (MVDR) and auxiliary-vector (AV) filters under limited data support leads to significant signal-to-interference-plus-noise ratio (SINR) performance degradation. We quantify this observation in the context of direct-sequence code-division multiple-access (DS-CDMA) communications by deriving close approximations for the mean-square filter estimation error, the probability density function of the output SINR, and the probability density function of the symbol-error rate (SER) of the sample matrix inversion (SMI) receiver evaluated using both a desired-signal-"present" and desired-signal-"absent" input covariance matrix. To avoid such performance degradation, we propose a DS-CDMA receiver that utilizes a simple pilot-assisted algorithm that estimates and then subtracts the desired signal component from the received signal prior to filter estimation. Then, to accommodate decision-directed operation, we develop two recursive algorithms for the on-line estimation of the AV and MMSE/MVDR filter and we study their convergence properties. Finally, simulation studies illustrate the SER performance of the overall receiver structures.     

Performance of blind channel estimation algorithms for space-frequency block coded multi-carrier code division multiple access systems

The problem of blind channel estimation for downlink space-frequency block coded multi-carrier code division multiple access (SFBC MC-CDMA) schemes is considered. For these schemes, the authors first develop a system model for complex modulated signals, which reduces the multichannel estimation problem to a single-input single-output problem. Then, they present an intuitive subspace-based channel estimation method along with the corresponding necessary and sufficient conditions under which the channel estimate is unique (within a complex scalar). Their studies highlight two interesting properties of SFBC MC-CDMA systems: (i) there is no antenna order ambiguity (also known as permutation ambiguity) even though only one spreading code is assigned to each user; (ii) channel identifiability is guaranteed, regardless of the channel zeros location. They also establish the unbiasedness of the channel estimates and derive closed-form expressions for the mean-square-error of the estimates as well as the corresponding Cramer-Rao bound (CRB). In the derivation of the CRB, they suggest a novel approach which assumes the knowledge of only the spreading code of desired user. This approach results in a tighter bound than the CRB derived based on the knowledge of all users' signatures.     

Rapid combined synchronization/demodulation structures for DS-CDMA systems. I. Algorithmic developments

Blind adaptive linear receivers are considered for the demodulation of direct-sequence code-division multiple-access signals in asynchronous transmissions. The proposed structures are self-synchronized in the sense that adaptive synchronization and demodulation are viewed and treated as an integrated receiver operation. Two computationally efficient combined synchronization/demodulation schemes are proposed, developed, and analyzed. The first scheme is based on the principles of minimum-variance distortionless-response processing, while the second scheme follows the principles of auxiliary-vector filtering and exhibits enhanced performance in short data-record scenarios. In both cases, the resulting receiver is a linear structure of order exactly equal to the system processing gain. Simulation studies included in this paper demonstrate the coarse synchronization as well as the bit-error rate performance of the proposed strategies.     

Fast converging minimum probability of error neural network receivers for DS-CDMA communications

We consider a multilayer perceptron neural network (NN) receiver architecture for the recovery of the information bits of a direct-sequence code-division-multiple-access (DS-CDMA) user. We develop a fast converging adaptive training algorithm that minimizes the bit-error rate (BER) at the output of the receiver. The adaptive algorithm has three key features: i) it incorporates the BER, i.e., the ultimate performance evaluation measure, directly into the learning process, ii) it utilizes constraints that are derived from the properties of the optimum single-user decision boundary for additive white Gaussian noise (AWGN) multiple-access channels, and iii) it embeds importance sampling (IS) principles directly into the receiver optimization process. Simulation studies illustrate the BER performance of the proposed scheme.     

Adaptive robust spread-spectrum receivers

We consider the problem of robust detection of a spread-spectrum (SS) signal in the presence of unknown correlated SS interference and additive non-Gaussian noise. The proposed general SS receiver structure is comprised by a vector of adaptive chip-based nonlinearities followed by an adaptive linear tap-weight filter and combines the relative merits of both nonlinear and linear signal processing. The novel characteristics of our approach are as follows. First, the nonlinear receiver front-end adapts itself to the unknown prevailing noise environment providing robust performance for a wide range of underlying noise distributions. Second, the adaptive linear tap-weight filter that follows the nonlinearly processed chip samples results in a receiver that is proven to be effective in combating SS interference as well. To determine the receiver parameters, we propose, develop, and study three adaptive schemes under a joint mean-square error (MSE), or a joint bit-error-rate (BER), or a joint MSE-BER optimization criterion. As a side result, we derive the optimum decision fusion filter for receivers that utilize hard-limiting (sign) chip nonlinearities. Numerical and simulation results demonstrate the performance of the proposed schemes and offer comparisons with the conventional matched-filter (MF), the decorrelator, the conventional minimum-variance-distortionless-response (MVDR) filter, and the sign-majority vote receiver     

On the Chandra–Poram–Bose symbol error probability expression for coherent orthogonal M‐ary frequency shift keying

An expression for the average symbol error probability of coherent orthogonal M‐ary frequency shift keying in generalized fading was recently reported by Chandra, Poram, and Bose. We show that the expression is only exact for M = 2; it does, however, provide an accurate approximation for M > 2. By modifying the derivation of the reported expression, we derive a lower bound for M ?5 that has the same complexity as the reported expression, and we illustrate that, for M > 2, the expression of the derived bound provides an approximation that is also more accurate.Copyright © 2012 John Wiley & Sons, Ltd.     

On adaptive minimum probability of error linear filter receiversfor DS-CDMA channels

Receiver architectures in the form of a linear filter front-end followed by a hard-limiting decision maker are considered for DS-CDMA communication systems. Based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front-end in the minimum BER sense. The recursive form is decision driven and distribution free. For additive white Gaussian noise (AWGN) channels, theoretical analysis of the BER surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a formal proof of guaranteed global optimization with probability one for the two-user case. To the extent that the output of a linear DS-CDMA filter can be approximated by a Gaussian random variable, a minimum-mean-square-error optimized linear filter approximates the minimum BER solution. Numerical and simulation results indicate that for realistic AWGN DS-CDMA systems with reasonably low signature cross-correlations the linear minimum BER filter and the MMSE filter exhibit approximately the same performance. The linear minimum BER receiver is superior, however, when either the signature cross-correlation is high or the background noise is non-Gaussian