A Laguerre polynomial-based bound on the symbol error probability for adaptive antennas with optimum combining

We derive a simple closed-form upper bound on the symbol error probability for coherent detection of M-ary phase-shift keying using antenna arrays with optimum combining, in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. The new bound, based on Laguerre polynomials, is valid for an arbitrary number of antenna elements as well as arbitrary number of interferers, and it is proven to be asymptotically tight. Comparisons with Monte Carlo simulation are also provided, showing that our bound is useful in many cases of interest.