Comparison of Nonlinear and Linear Multireceiver Detection Systems

Detection of a binary transmission by both optimum and suboptimum nonlinear and linear multireceivers is considered by comparing their asymptotic performance characteristics. The multichannel model is presumed to be of the Rician type. Particularly, we consider Turin's nonlinear specular-coherent multi-receiver and the nonlinear noncoherent Pierce-Stein multireceiver. These two termination error rate characteristics are graphically compared for low and high output signal-to-noise ratios. The performance characteristics of two other coherent linear multireceivers, one optimum and one easier implemented suboptimum, are derived and compared with the above-mentioned nonlinear multireceivers. The numerical results indicate system design trends and provide information on the degradation or improvement afforded by employing nonlinear detection systems as compared with linear detection systems. In particular, the optimum nonlinear coherent multireceiver is difficult to implement. It is shown that, for multichannels which are largely specular in nature, a more easily implemented linear coherent unit behaves optimally for all practical purposes. For channels which are largely scatter in nature it is shown that the linearized suboptimum system performance is highly inferior to the corresponding optimum coherent unit. In these situations, the noncoherent "square-law combining" system would be more reliable than the suboptimum coherent unit. In fact, for large scatter components we find that the noncoherent unit performs almost identically to the nonlinear coherent unit. This is due to the signal suppression effects known to occur in all nonlinear detectors throughout the field of statistical detection theory.