Diversity Performance of the Wide-Band FSK System in a Three-Component Two-Path Channel

In several space relay communication channels signal energy can be described as following two transmission paths. The first is the direct path from the transmitter to the receiver in which the signal is corrupted only by additive Gaussian noise. The second is the reflected path involving a reflection boundary, which may distort and delay the signal in that path. At the receiver the combined signal from the two paths exhibits multipath effects (primarily signal fading). In addition, substantial Doppler is frequently encountered so that the carrier frequency can be treated as a random variable. This paper describes a detailed mathematical model of this channel. This allows one to study the effects of such important parameters as Doppler, rate of fade, diversity, and the degree of correlation between the direct and reflected path transmission. The envelope of the reflect signal is assumed to be statistically described as a Rician random process and the modulation is assumed to be frequency shift keying (FSK). The model is used to derive performance equations for this system. It was found that a priori knowledge of the nature of the fade is necessary to determine whether diyersity is advantageous. Thus, for example, reflections from extremely smooth boundaries (specular reflections) show small degradations in performance with the use of diversity, while for most diffuse reflection cases, a significant improvement can be achieved through the use of diversity.