Convex optimization for detection in structured communication problems

Abstract

The receiver in a wireless communication system has the task of computing good estimates for the data symbols that have been transmitted. The best (optimum) detector is the Maximum Likelihood (ML) detector. However, it requires a high computational complexity. This work aims to efficiently detect the transmitted symbols with a reduced complexity. In order to produce a near optimum receiver, two methods are presented. These methods are obtained by convex optimization relaxations which yield global optimum solutions. The relaxations are combined with the idea of using the structure of the channel matrix to reduce the computational complexity. The channel matrix exhibits a banded Toeplitz structure. In each case, the dual problem of the convex optimization relaxation is solved to estimate the noise power. Gradient descent algorithm is used to solve the dual problem in the first relaxation while the bisection method is applied for the second relaxation. In both cases, the result is a Generalized Minimum Mean Squared Error (GMMSE) detector which has a form similar to the Minimum Mean Square Error (MMSE) detector and a performance almost the same as the MMSE detector, but it is not require the knowledge of the noise power. The GMMSE detectors can be used in scenarios where adapted or blind adaptive detection is not suitable, for instance when the channel is rapidly changing. Using a circular approximation of banded Toeplitz matrix the Fast Fourier Transform (FFT) can be applied to reduce the computational complexity of the detectors. Finally, the local search method is applied to enhance the performance of the proposed GMMSE detector. The proposed detector is a near optimum detector with low computational complexity.