| The objective of this work is the development of receiver designs for wireless CDMA communications. Special emphasis is given to the problem of adaptive receiver design whenever high-dimensional adaptive processing with short data records (limited training) is desired. In the context of adaptive nonlinear filter design, we consider a multilayer perceptron (MLP) neural network receiver architecture for the recovery of the information bits of a direct-sequence code-division-multiple-access (DS-CDMA) user. We prove formally that the optimum (nonlinear) DS-CDMA single-user decision boundary exhibits two key properties. Then, we translate these properties into a set of constraints that can be used by any optimization algorithm for the selection (training) of the parameters of a general multi-layer-perceptron neural-network receiver. Using these constraints, the number of parameters to be optimized is reduced by nearly 50% for large-size networks, which effectively doubles the speed of any training procedure. Furthermore, we utilize the properties to develop a new initialization scheme that provides additional improvements on the convergence rate and can be used by any recursive optimization algorithm. Based on the optimization criterion of choice (e.g., mean-square-error or bit error rate), we develop a constrained version of the corresponding training algorithm that incorporates both the proposed constraints and the proposed initialization. Finally, regardless of the chosen optimization criterion (e.g. MSE or BER), the adaptive training algorithm embeds importance-sampling principles directly into the receiver optimization process by altering the received vector statistics. In effect, we achieve a higher parameter-update rate (and, thus, higher convergence rate) by creating virtual high error rate receiver conditions. This is in sharp contrast to the traditional use of IS for system performance evaluation only.;With regard to linear filter theory and under small-sample-support situations, the ill-conditioned sample-average covariance estimate leads to performance degradation of the MVDR filter estimate (commonly referred to as sample-matrix-inversion, or SMI). As a direct result of the required matrix inversion, the estimation error in the sample-average covariance estimate is unduly amplified, thus, causing SMI to perform poorly as a receiver. The proposed quadratically-constrained (QC)-MVDR filter estimate seeks to control (via a bias/variance tradeoff) the inherent error amplification by constraining the operational (input) space to a specific hyper-ellipsoid. The shape of the hyper-ellipsoidal input space is determined by a regularized covariance matrix estimate that is parameterized by a data-dependent scalar. Blind and supervised adaptive control methods are proposed to determine the scalar regularization parameter, or, equivalently, the data-dependent shape of the quadratically-constrained input space. |
