Supervised Phase Correction of Blind Space–Time DS-CDMA Channel Estimates

Blind channel-estimation algorithms return phase-ambiguous estimates. From a receiver design point of view, the phase-ambiguity problem can be by-passed by differential modulation and detection at the expense of a well-known performance loss, in comparison with direct modulation and coherent detection schemes. An alternative approach is followed in this paper. A theoretical minimum mean-square error phase-estimation criterion leads to a supervised phase-recovery procedure that directly corrects the phase of arbitrary linear filter receivers through a simple closed-form projection operation. Conveniently, any known blind channel-estimation algorithm can be used to provide the initial phase-ambiguous estimate. The presentation is given in the context of adaptive space-time receiver designs for binary phase-shift keying direct-sequence code-division-multiple-access antenna array systems. Numerical and simulation studies support the theoretical developments and show that effective phase correction and multiple-access interference suppression can be achieved with about 2% pilot signaling     

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.     

Rank-2-Optimal Adaptive Design of Binary Spreading Codes

Over the real/complex field, the spreading code that maximizes the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR linear filter is the minimum-eigenvalue eigenvector of the interference autocovariance matrix. In the context of binary spreading codes, the maximization problem is NP-hard with complexity exponential in the code length. A new method for the optimization of binary spreading codes under a rank-2 approximation of the inverse interference autocovariance matrix is presented where the rank-2-optimal binary code is obtained in lower than quadratic complexity. Significant SINR performance improvement is demonstrated over the common binary hard-limited eigenvector design which is shown to be equivalent to the rank-1-optimal solution.     

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     

Capacity, throughput, and delay of slotted ALOHA DS-CDMA links with adaptive space-time auxiliary-vector receivers

We investigate the user capacity, throughput, and delay characteristics of a mobile slotted ALOHA direct-sequence code-division-multiple-access (DS-CDMA) link with dedicated signatures under multipath fading and packet-rate adaptive antenna array signal reception. For a given system transmission bit rate, the packet size is designed to be sufficiently small to conform with the coherence time of the channel. Then, on an individual packet-by-packet basis, a phase-ambiguous spatial-temporal channel estimate is produced by a blind (unsupervised) eigensubspace procedure. The space-time channel estimate is phase corrected via a few pilot packet mid-amble bits and used for joint spatial-temporal multiple-access-interference suppression according to the principles of auxiliary-vector filtering. Subsequently, packet success probabilities are derived in the presence or absence of forward error correction and are used to evaluate the throughput and delay characteristics of the link.     

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 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.