Doppler-tolerant signal waveforms

When Doppler distortions of radar signals can be neglected, correlation or matched-filter processing is relatively simple. In those applications where high resolution requirements and high target speeds combine, the distortions in the waveform lead to severe processing problems. One way around these difficulties is the so-called Doppler-invariant waveform, which stays matched to the filter in the presence of an arbitrarily large Doppler effect; however, in many situations this waveform cannot be used. This paper extends the idea of Doppler invariance to only parts of the waveform, the complex modulation function and the real envelope. We then obtain waveforms which simplify the Doppler search rather than eliminate it entirely, and hence are referred to as Doppler-tolerant. The addition of a constant-carrier term to the Doppler-invariant signal leads to the signal of which only the modulation function is Doppler-invariant. It permits independent measurement of range and range rate at the expense of having to search for the Doppler shift of the carrier. For applications of the principle to the envelope of a signal, the type of signal which is of particular interest is the pulse train. It is shown that a Doppler-tolerant pulse train can be designed such that it can be processed by a delay line with fixed taps even if the pulse spacing is significantly changed by the Doppler effect. This approach is useful for both coherent and incoherent pulse trains.