Doppler dispersion effects in matched filter detection and resolution

Conventional matched filters which use pseudorandom or noise-like waveforms attempt to compensate for the Doppler effect by cross-correlating the received waveforms with frequency shifted replicas of the transmitted waveform. However, frequency translation is only an approximation to the actual Doppler effect which is a time-expansion or time-compression of the waveform resulting from the continuous expansion or compression of the transit path. This paper investigates the effects of Doppler dispersion in matched filters which use frequency translation for Doppler compensation. It is found that the effects of Doppler dispersion are independent of the carrier frequency and negligible if the dispersion product, i.e., the absolute magnitude of the product of the signal bandwidth, duration, and delay rate, is less than unity. If the dispersion product is greater than unity the dispersion effects are serious. In the latter case the time and frequency resolution of the system are degraded and the output pulse is reduced in amplitude. The maximum improvement that can be obtained in the signal-to-noise power ratio is equal to the reciprocal of the delay rate magnitude. This maximum signal-to-noise gain is achieved when the time-bandwidth product of the receiver is chosen such that the dispersion product is approximately unity.