A general analysis technique for performance of diversity receivers corrupted by partial-band noise interference

Error probability analyses for complicated communications systems often yield mathematics which defy analytical solution. In these situations, it is desirable - for added insight and reduced computational burden - to carry the solution analytically as far as practical before resorting to numerical analysis. Analyses of communications systems with diversity and partial-band noise interference often yield such complicated mathematics, as does the analysis of communications systems with convolutional coding and soft decision decoding. In these systems, some components of the decision statistics are affected by partial-band interference, while others are not. Therefore, each decision statistic is a function of many random variables involving at least two distinct probability density functions. The authors describe a general way to calculate the probability density function for a random variable that is the sum of random variables, employing a new technique to evaluate the inverse Laplace transform as an integral of a real integrand over a finite range. This integral is often better suited for numerical evaluation than the usual inverse Laplace transform integral, thereby offering a generally applicable simplification to decision statistical analysis for complicated communications systems. The new technique is applied to BPSK with AWGN and to a fast frequency-hopped M-ary FSK signal corrupted by partial-band interference.