Transmission along two paths with Rayleigh fading - Optimized receivers

Optimal reception for a digital signal following two trajectories during transmission employing the ionosphere is explored. The transmission path is modelled as the signal transmitted, the dispersion and fading of the signal, and additive noise, with the signal centered around the carrier frequency. Reception is analyzed in terms of the detection of the presence of the signal, and for digital transmission, the selection of one of two signals of equal energy. Optimality is then defined as the minimization of error at the receiver. The error probability is calculated, along with indices of quality. The temporal distance between transmitter and receiver is assumed to be known with an accuracy equal to the inverse of the bandwidth of the transmitted signal, and an optimized receiver is obtained by a quadratic treatment of the emission by an adaptive filter for the transmitted signal