Orthogonal and projected orthogonal matched filter detection

Abstract

This paper considers the generic problem of detecting in the presence of additive noise, which one from a set of known signals has been received. In place of the classical matched filter (MF) receiver we propose a modified receiver. When the transmitted signals are linearly independent this receiver is referred to as an orthogonal matched filter (OMF) receiver, and when the transmitted signals are linearly dependent it is referred to as a projected orthogonal matched filter (POMF) receiver. Two equivalent representations of the receiver are developed with different implications in terms of implementation. In the first, the demodulator consists of a MF demodulator followed by an optimal whitening transformation on a space formed by the transmitted signals, that optimally decorrelates the MF outputs prior to detection. In the second, the demodulator consists of a bank of correlators with correlating signals that are projections of a set of orthogonal signals, and are closest in a least-squares sense to the transmitted signals. We provide simulation results that suggest that in certain cases the OMF and POMF receivers can significantly increase the probability of correct detection over the MF receiver in non-Gaussian noise with only a minor impact on performance in Gaussian noise.