Prefiltering for improved correlation detection of bandlimited transient signals

Abstract

Prefiltering, or limiting the passband of a received signal, can be used to improve ordinary correlation threshold detector performance for an unknown source model. For the known source model, the cross-correlation detector is equivalent to matched filtering, and intrinsically contains prefiltering. Prefiltering also improves higher-order correlation threshold detector performance, but often with more advantage than seen in the ordinary correlation detector. This is true for both the unknown and known source models. Geometric interpretations are given to provide insight into the origin of potential higher-order advantage. Eight energy signals, each with three different Fourier magnitude-based filters, are used to test the cross-correlation, bicorrelation, and tricorrelation detectors by Monte Carlo simulation and hypothesis testing. Significant signal-to-noise ratio (SNR) gains are evident for both the known and unknown source models with the tricorrelation exhibiting the largest gains. The tricorrelation detector has superior performance versus the cross-correlation detector for all the eight test signals in the unknown source case, and was superior for seven of the eight test signals in the known source case. For the narrow pulse test signal, a probability of detection of 0.5 at probability of false alarm 0.001 was achieved at a power SNR −23.57 dB in the known source model, and at SNR −20.28 dB in the unknown source model. Some other test signals have lower SNRs in the unknown source model. Higher-order detectors can be limited to have equivalent information to that of the ordinary correlation detector. An example illustrating this case is given.