TIGHT BOUNDS ON RICIAN-TYPE ERROR PROBABILITIES AND SOME APPLICATIONS

Consider the classic problem of evaluating the probability that one Ri cian random variable exceeds another, possibly correlated, Rician rand om variable. This probability is given by Stein [I] in terms of the Ma rcum's Q-function, which requires numerical integration on the compute r for its evaluation. To facilitate application in many digital commun ication problems, we derive here tight upper and lower bounds on this probability. The bounds are motivated by a classic result in communica tion theory, namely, the error probability performance of binary ortho gonal signaling over the Gaussian channel with unknown carrier phase. Various applications of the bounds are reported, including the evaluat ion of the bit error probabilities of MDPSK and MPSK with differential detection and generalized differential detection, respectively. The b ounds prove to be tight in all cases, Further applications will be rep orted in the future.