The performance of digital matched filters for multilevel signals

Consideration is given to the analysis and optimization of digital matched filters (DMFs) with multilevel quantizers that are matched to multilevel amplitude- and phase-modulated signals. For the case in which the interference has a symmetric, differentiable probability density distribution, quite general expressions for the DMF's output signal-to-noise ratio are obtained. It is shown that for interference of this type the signal-to-noise ratio is separable into two factors; these represent, respectively, the effects of the quantization and correlation operations of the DMF. It is noted that the two factors can be optimized independently of each other. The optimal quantizer strategy for Gaussian interference is proven to be (within the limits of practical approximation and also asymptotically) one with equal spacings of the quantizer levels and thresholds. It is also shown that no improvement in the performance of the one-bit DMF can be achieved by increasing the complexity of the signaling from two-level amplitude-modulated or biorthogonal phase-modulated to multilevel amplitude-modulated/phase-modulated.