Diversity gain for MIMO-OTH radar target detection under product of complex Gaussian reflections

Consider a multiple-input multiple-output skywave over-the-horizon (MIMO-OTH) radar system withM transmit and N receive antennas employing the conventional optimal detector for a single complex Gaussian target. The signal from the mth transmit antenna reaches the target after being reflected by the ionosphere via Q_m ray paths. Each of these multipath signals bounce off the target and reach the nth receiver after being reflected by the ionosphere again via H_mn ray paths. Thus the transmitted signals are reflected once off the target and twice by the ionosphere before arriving at the receive end, and any of these three reflections can be either categorized as being complex Gaussian or deterministic. If either one or two of the reflections are modeled as complex Gaussian while the others are modeled as deterministic, it is shown that the largest possible diversity gain is upper bounded by equation.