Probability of Errors for Quadratic Detectors

A general class of data receivers have decision logic based on observing at the output the sign of a quadratic form 2165 21G6 THE BELL SYSTEM TECHNICAL J O U R N A L , NOVEMBER 19G5 q = 2 QijWiWj = w+Qw. i,j= l (1 ) Examples of such quadratic detectors and the reduction of their output to the form (1) are given in Sections IV and V, and a schematic representation in Fig. 1. Let it suffice for the present to say that the real symmetric matrix Q is determined by the system filters, while the real TV-dimensional vector w and its transpose w + are related to the received signal plus noise. During a considerable portion of this paper we shall be concerned with the asymptotic evaluation of the probability of error for such receivers when the noise is additive gaussian. To develop the tools Fig. 1 -- Model of the quadratic detector.