A Low-Cost Digital Matched Filter for Arbitrary Constant-Envelope Spread-Spectrum Waveforms

In this paper a noncoherent digital matched filter (DMF) with binary quantization is presented which shows good performance for arbitrarily angle modulated constant-envelope waveforms having large time-bandwidth products. The considered DMF represents an extension of the noncoherent DMF with one-bit digitization suggested previously by Turin for binary PSK signals. Analysis of the filter performance in the presence of white Gaussian noise results in a general expression which allows the output SNR of both DMF's to be calculated for any spread-spectrum waveform. Evaluating this expression reveals that the extended DMF can be matched to arbitrary waveforms having constant envelopes in such a way that the SNR loss with reference to the corresponding analog matched filter is less than 2.87 dB. The degradation is as low as 1.96 dB for waveforms with biphase or quadriphase signal samples such as binary PN-PSK, PNQPSK, and offset-PN-QPSK, but also PN-MSK. If both DMF's are applied to waveforms having complex valued envelopes, the extended DMF may outperform Turin's DMF by as much as 3 dB.