A geometric interpretation of adaptive locally optimum processing

Adaptive locally optimum processing has been applied to the detection of communication signals in the presence of interference. Maximum likelihood arguments are used to obtain a transformation of the received signal inphase/quadrature sample pairs into inphase/quadrature communication signal estimates. This technique leads to simple formulas for locally optimum transforms by expressing the probability density functions of received signal magnitudes as sums of Gaussian kernels. The inphase/quadrature sample pairs are viewed as two-dimensional vectors, and it is shown that locally optimum magnitude transforms estimate projections of the communication signal and Gaussian noise onto the received signal vector