Dimitrios A. Pados

An iterative algorithm for the computation of the MVDR filter

Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation.

New bounds on the total squared correlation and optimum design of DS-CDMA binary signature sets

The Welch lower bound (see Welch, R.L., IEEE Trans. Inform. Theory, vol.IT-20, p.397-9, 1974) on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. We derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L. Then, for almost all K, L in {1,2,...,256}, we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.

Joint space-time auxiliary-vector filtering for DS/CDMA systems with antenna arrays

Direct-sequence/code-division multiple-access (DS/CDMA) communication systems equipped with adaptive antenna arrays offer the opportunity for jointly effective spatial and temporal (code) multiple-access interference (MAI) and channel noise suppression. This work focuses on the development of fast joint space-time (S-T) adaptive optimization procedures that may keep up with the fluctuation rates of multipath fading channels. Along these lines, the familiar S-T RAKE processor is equipped with a single orthogonal S-T auxiliary vector (AV) selected under a maximum magnitude cross-correlation criterion. Then, blind joint spatial/temporal MAI and noise suppression with one complex S-T degree of freedom can be performed. This approach is readily extended to cover blind processing with multiple AVs and any desired number of complex degrees of freedom below the S-T product. A sequential procedure for conditional AV weight optimization is shown to lead to superior bit-error-rate (BER) performance when rapid system adaptation with limited input data is sought. Numerical studies for adaptive antenna array reception of multiuser multipath Rayleigh-faded DS/CDMA signals illustrate these theoretical developments. The studies show that the induced BER can be improved by orders of magnitude, while at the same time significantly lower computational optimization complexity is required in comparison with joint S-T minimum-variance distortionless response or equivalent minimum mean-square-error conventional filtering means.

An integrated cross-layer study of wireless CDMA sensor networks

In this paper, we characterize analytically the multiaccess interference in wireless code-division multiple-access sensor networks with uniformly random distributed nodes and study the tradeoff between interference and connectivity. To provide a guideline for improving system behavior, three competitive deterministic topologies are evaluated along with the random topology in terms of link-level and network-level (routing) performance. The impact of signature code length and receiver design on the network performance for different topologies is also studied.

On overfitting, generalization, and randomly expanded training sets

An algorithmic procedure is developed for the random expansion of a given training set to combat overfitting and improve the generalization ability of backpropagation trained multilayer perceptrons (MLPs). The training set is K-means clustered and locally most entropic colored Gaussian joint input-output probability density function (pdf) estimates are formed per cluster. The number of clusters is chosen such that the resulting overall colored Gaussian mixture exhibits minimum differential entropy upon global cross-validated shaping. Numerical studies on real data and synthetic data examples drawn from the literature illustrate and support these theoretical developments.

On adaptive minimum probability of error linear filter receivers for 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.

Adaptive maximum SINR RAKE filtering for DS-CDMA multipath fading channels

The conventional signature-matched RAKE processor for multipath direct-sequence code division multiple access channels is viewed as a regular linear tap-weight filter of length equal to the sum of the system processing gain and the user channel memory. In this paper, performance improvements are sought in the context of adaptive filtering under maximum signal-to-interference-plus-noise-ratio criteria. The minimum-variance-distortionless-response RAKE (RAKE-MVDR) filter and the lower complexity scalar optimized auxiliary-vector RAKE (RAKE-AUX) filter are developed. Bit error rate (BER) comparisons with the conventional RAKE signature-matched filter are carried out for training sets of reasonably small size, perfectly known, and mismatched/estimated channel coefficients, and extreme near-far system configurations.

A decoding algorithm for finite-geometry LDPC codes

In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low-cost, yet effective, decoding of (high-rate) finite-geometry (FG) LDPC codes. The decoding procedure updates iteratively the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.

Low-complexity blind detection of DS/CDMA signals: auxiliary-vector receivers

A fresh look on the design of practical low-complexity direct-sequence code-division multiple-access (DS/CDMA) receivers is proposed from the Wiener reconstruction-filter point of view. The natural outcome is the emergence of a new class of linear scalar-parameterized auxiliary-vector receivers (filters). Then, the blind optimization of these receivers in the maximum signal-to-interference-plus-noise-ratio (SINR) sense becomes a straightforward procedure. The conceptual and computational simplicity of this general approach promises immediate practical utility. This new generation of receivers exhibits minimal optimization requirements and near-matched-filter (MF) operational complexity. Yet, theoretical arguments supported by numerical and simulation results included in this work suggest that the blind auxiliary-vector receiver compares favorably, both complexity-wise and performance-wise, to multiuser (MU) detectors such as the minimum output energy (MOE) and the decorrelating receiver (although the latter utilizes the assumed known spreading codes of all interfering users).

Optimal Algorithms for L 1 -subspace Signal Processing

We describe ways to define and calculate L1-norm signal subspaces that are less sensitive to outlying data than L2-calculated subspaces. We start with the computation of the L1 maximum-projection principal component of a data matrix containing N signal samples of dimension D. We show that while the general problem is formally NP-hard in asymptotically large N, D, the case of engineering interest of fixed dimension D and asymptotically large sample size N is not. In particular, for the case where the sample size is less than the fixed dimension , we present in explicit form an optimal algorithm of computational cost 2N. For the case N ≥ D, we present an optimal algorithm of complexity O(ND). We generalize to multiple L1-max-projection components and present an explicit optimal L1 subspace calculation algorithm of complexity O(NDK-K+1) where K is the desired number of L1 principal components (subspace rank). We conclude with illustrations of L1-subspace signal processing in the fields of data dimensionality reduction, direction-of-arrival estimation, and image conditioning/restoration.