The performances of three receivers, namely, the hard-limited, the linear, and the maximum-likelihood combiners for the detection of frequency-hopped multilevel frequency-shift keyed signals transmitted from mobiles to base have been reported earlier . Only the hard-limited combiner has been analyzed with respect to base-to-mobile link . Here, we give new results on the performance of the likelihood and the linear combining receivers operating at the mobiles. Whereas it is possible to find exactly the union bound on the probability of hit error for a linear combiner, for a likelihood receiver, bounding and approximation techniques such as simple Chernoff bound and saddle point integration were employed. We also observe the asymptotic (SNR → ∞) equivalence of the hard-limited and the likelihood receivers. This, together with the approximate error estimates at finite SNR, leads us to believe that the likelihood receiver is only marginally superior to a hard-limited combiner. As expected, the linear combiner performs poorly.
Viswanathan, R. and Gupta, S. C. "Performance Comparison of Likelihood, Hard-Limited, and Linear Combining Receivers for FH-MFSK Mobile Radio--Base-to-Mobile Transmission." (May 1983).