Optimal receiver ensuring maximum signal-to-noise ratio when affected by non-white non-gaussian noise

Abstract

This paper analyses the problem of optimal reception of a limited duration signal in a communication channel affected by an additive noise such as non-white non-Gaussian noise. Known solutions are based on the use of an additional “whitening” filter either in front of a filter matched with the signal or in front of a correlator where the reference signal matches the shape of the information signal. Such receiving devices are hard to implement in the case of, for example, intentional interference with slowly changing parameters, which requires filter parameters to be altered. It is proposed to simplify the receiver design by eliminating the whitening filter. The feasibility of two optimal technique options is proven mathematically using the theory of the Lagrange function in the isoperimetric problem of finding the type of function that ensures a minimum noise dispersion and a non-zero value of the signal component. For optimal filtration options, an expression is obtained for the complex transmission coefficient of the optimal (in the indicated sense) filter. For the option when a correlator is used, the optimal type of reference signal has been determined. Expressions have been obtained for the signal-to-noise energy ratio for both options. These expressions coincided with each other, and also agreed with a known relationship for receivers with whitening filters, which proves the possibility of implementing the proposed simpler optimal receiver designs.