Character Error Probabilities for M-ary Signaling in Impulsive Noise Environments

This paper is concerned with the calculation of the probability of character error and comparison of coherent, -ary, digital communication systems operating in impulsive noise environments. The receiver is assumed to be a maximum likelihood detector for white, Gaussian interference and therefore has the form of a parallel bank of matched filters followed by decision circuitry. By employing a Poisson or generalized shot noise model for the impulsive noise, a closed form expression for the joint characteristic function of the noise components of the matched filter outputs may be obtained. The characteristic function depends on the parameter where is the average number of noise impulses occurring per second and is the signal duration. Approximate results for the error probability are obtained by taking this parameter to be either very small or very large. Experimental measurements of the error probability are presented and compared with theory. Comparisons of various modulation schemes are made under the constraints of equal rate and equal bandwidth. These comparisons show that the detrimental effects of impulsive noise can be combatted by representing the transmitted data as sums of orthonormal functions, thereby allowing the signal duration to be made very long in comparison with the noise impulse durations without an appreciable increase in bandwidth or decrease in transmitter rate.