Optimization of pilot symbol assisted BPSK with diversity

The cross-correlation of the output of a correlator receiver and the output of a pilot symbol channel estimator is derived. Pilot symbol assisted binary phase shift keying operating in flat, slow Rayleigh fading is optimized to yield minimum bit error rate. A closed-form expression gives the optimum number of pilot symbols in terms of the signal-to-noise ratio and the data frame length. A simple, yet very general engineering "rule of thumb" is given for determining the number of pilot symbols.