Optimization of linear receivers for data communication signals

The optimization of receivers constrained to consist of a (linear) filter and level slicer is considered for general data communication signals in additive white Gaussian noise. Special consideration is given to the two limiting cases of arbitrarily low and high signal-to-noise ratios (SNRs). The low-SNR case results in an average matched filter receiver; the high-SNR filter is shown to be the solution to a specific nonlinear mathematical problem with a simple geometric interpretation. An efficient algorithm is developed to solve the problem. The results are illustrated for a duobinary minimum-shift-keyed signal observed over an interval of three-symbol-period duration