Probability of error for binary permutation modulation on a fading Gaussian channel

The probability of error for binary permutation modulation with diversity on fading Gaussian channels is considered. Upper bounds on the probability of error are found in a simple manner. These bounds indicate that the probability of error decreases exponentially with increasing transmitter memory as long as the transmitter´s rate is less than the ratio of average received signal power to noise power per unit bandwidth. This asymptotic behavior is true for any form of binary permutation modulation with the proper order of diversity. Furthermore, orthogonal signals are found to be the most efficient form of binary permutation modulation.