Effects of signal randomization on performance of binary communications systems

In this paper, effects of signal randomization are studied for binary communications systems. First, it is stated that the average probability of error for a power-constrained binary communications system is minimized when each symbol is randomized between at most two signal values. Then, a fixed detector is considered, and sufficient conditions under which its performance can or cannot be improved via signal randomization are presented. After that, the joint design of detectors and signal structures is studied, and an optimization problem is formulated to determine the optimal system parameters. Finally, numerical results are presented to exemplify the improvements via signal randomization.