Simplified Robust Adaptive Detection and Beamforming for Wireless Communications

8Minimum BER Adaptive Detection and Beamforming

8.1 Introduction

The traditional minimum mean square error (MMSE) detector is the most popular for beamforming. An adaptive implementation of the MMSE can be achieved by minimizing the MSE between the desired output and the actual array output. The LCMV and MVDR beamformers presented in Chapter 7 are different forms of MMSE detectors. For a practical communication system, it is the achievable bit error rate (BER) or block BER (BLER), not the MSE performance, which really matter. Ideally, the system design should be based directly on minimizing the BER, rather than the MSE. For applications to single‐user channel equalization, multi‐user detection, and beamforming, it has been shown that the MMSE solution can, in certain situations, be distinctly inferior to the minimum BER (MBER) solution. However, the BER cost function is not a linear function of the detector or the beamformer, which makes it difficult to minimize. Several adaptive MBER beamformer/detector implementations have been developed [1–29].

It must be stated here that the cost function of the MMSE criterion has a circular shape. This means that we have one global minimum and convergence can be easily achieved. In contrast, the cost function of the BER is highly nonlinear. This means that during minimization we may converge to a local minimum. This can be seen from Figure 8.1 [5]. The MMSE and MBER solutions choose the detector's weight vector very differently. Figure 8.1