A robust sequential detector for BPSK in a slow non-selective Rayleigh fading channel

Wald showed that sequential sampling minimizes the average number of observations required to detect a noisy received signal (1973). But there has been very little work done to robustify the sequential detector. If a detector is both sequential and robust then we get a double advantage. We propose a quantizer which when used with an optimal sequential detector makes it robust to the changes in the characteristics of a frequency nonselective, slow Rayleigh fading channel. The proposed quantizer is easy to design. The decision levels of the quantizer are proven to be symmetric for a symmetric noise density. A closed form expression for the asymptotic relative efficiency for a M level quantizer is derived. A thorough performance analysis is done and it is observed that the quantized detector performs very close to the optimal sequential detector.