Research On Optimal Receiver In Generalized Gaussian Noise Channel Based On Maximum Likelihood Criterion

Additive noise channel models are usually assumed to be Gaussian,but actually many are non-Gaussian,for example,the generalized Gaussian noise channel.The optimal receiver of digital signaling in additive white generalized Gaussian noise channel is unknown,except for two special cases of generalized Gaussian noise,Gaussian noise channel and Laplace noise channel.Therefore,it is necessary to work on the optimal receiver in non-Gaussian noise channels.It is shown that the matched filter is a special case of a family of optimum,minimum probability of error,detectors that base their detection decision on the integral of a power of the absolute error between the noisy received signal and a noiseless replica of the transmitted signaling waveform.This family of detectors is optimal for detecting a signal in additive white generalized Gaussian noise,having any value of distribution shape parameter ?,which we dubbed the generalized matched filter.The structure of this generalized matched filter is derived and the optimal probability of error for binary signaling in additive white generalized Gaussian noise is derived.The optimal,minimum probability of error detection of digital signals corrupted by generalized Gaussian noise is given by the Q-function and is the function of parameter ? and signal-to-noise ratio(SNR).The quantitative performance of any specific generalized Gaussian distribution detector,with design value ?1 when used as a suboptimal(mismatched)detector in noise having a different value of ?2 is derived.The performance loss of using a matched filter in place of an optimal nonlinear detector is studied.The conclusions of the generalized matched filter are further extended to higher-order modulations and to arbitrary digital signaling with arbitrary signaling sets,equal or unequal signal energies,and equal or unequal signal probabilities using signal space theory.