A recursive approach to compute bit error rate in underwater channels with multiple paths

In underwater acoustic channels, signal is transmitted over several distinct paths, eigenpaths, from transmitter to receiver due to reflections at sea boundaries, where each eigenpath contains a dominant specular component and a number of scattered components. As a result, an underwater acoustic channel response is the superposition of several dominant specular components and numerous scattered components. Bit error rate (BER) in multipath fading channels has been extensively studied in the past. However, limited research has been conducted on fading channels with several dominant specular components. In this paper, BER in multipath channels with several specular components is studied. A new formula to compute the BER recursively and efficiently is derived. Then using Jensen's inequality, one specular component, Rice fading, is shown to provide the lowest possible BER. Upon using the new BER formula and Lagrange multipliers to solve a constrained optimization problem, it is further shown that for two dominant specular components, BER achieves its maximum when the two components are equally weighted. More results on BER for three and four specular paths are also presented. The results shed light on the impact of the number of specular paths on BER, as well as the maximum and minimum values of BER, which are of interest in underwater communication systems.