A weighted mean square error (WMSE) approach to optimising digital filters is delineated. It is applied in the current work to optimising the classical Al‐Alaoui IIR differentiators to obtain new improved wideband differentiators of varying orders. These can be directly used for analog to digital conversion and in many digital signal processing applications. The weighted MSE approach is motivated by the Al‐Alaoui WMSE approach to pattern recognition. In addition, the differentiators are converted to integrators of similar orders that are further optimised. Various examples and comparisons are presented to demonstrate the viability of the proposed approach.

A novel reservation Aloha scheme is presented for OFDMA systems. The proposed scheme is based on two dimensional reservation in time and frequency. The proposed approach is compared to other OFDMA extensions of reservation Aloha. The proposed scheme is shown to be superior in terms of increasing sum-rate, reducing the number of users in outage, and reducing the collision probability in the reservation phase.

The Al-Alaoui algorithm is a weighted mean-square error (MSE) approach to pattern recognition. It employs cloning of the erroneously classified samples to increase the population of their corresponding classes. The algorithm was originally developed for linear classifiers. In this paper, the algorithm is extended to multilayer neural networks which may be used as nonlinear classifiers. It is also shown that the application of the Al-Alaoui algorithm to multilayer neural networks speeds up the convergence of the back-propagation algorithm.

A new weighted mean-square-error (MSE) procedure for pattern classification is introduced. The method iteratively repeats the misclassified samples. Three theorems on redundancy and the least square generalized inverse solution for an inconsistent set of equations are presented and proved. The resulting algorithm is presented together with a convergence proof for the linearly separable case. Several examples are included that demonstrate the advantage of the method over the MSE solution for both the separable and nonseparable cases.