August W. Rihaczek

Radar resolution properties of pulse trains

The concept of pulse compression has stimulated interest in the range and Doppler resolution properties of radar signals, but most of the theoretical investigations to date have been concerned with single pulse signals. The properties of coherent pulse trains, a practically important class of radar signals, have not received adequate treatment in the literature. Little information appears to be available on pulse trains using pulse-to-pulse waveform coding, frequency shifting, or repetition period staggering. The present paper attempts to fill a gap in the radar literature by analyzing the resolution potential of pulse trains. The treatment is limited to the practical class of pulse trains where all component pulses have identical envelopes and bandwidths, but the waveforms under these envelopes, frequency bands and repetition interval are left arbitrary. The results of the study convey an understanding of the effects of pulse train coding and thus give a clear indication of both the potential and the limitations of pulse trains in radar applications.

Delay-Doppler Ambiguity Function for Wideband Signals

The conventional ambiguity function is extended to include the Doppler distortions of the modulation function. The distinctive features of the extension are the use of the complex notation for wideband signals, and inclusion of the Doppler effect on the signal amplitude. The result is an ambiguity function from which Woodwards form can be found by inspection. It is shown that the well-known volume constraint also applies, in unchanged form, to the generalized ambiguity function. For the volume to be constant, it is not required that the distortions of the modulation function be neglected. Rather, the volume constancy is related to the sinusoidal fluctuations of a modulated carrier-type signal and thus is strictly a matter of the percentage bandwidth of the signal.

Matched-Filter Responses of the Linear FM Waveform

Although the properties of the linear FM signal have been studied previously in considerable detail, such studies have involved rather narrow aspects of the theory. This paper extends the work in several respects. By presenting three-dimensional projections of the conventional ambiguity function of the linear FM signal in more detail than was available before, we can study the sidelobe behavior off as well as on the axes, without weighting, with unilateral weighting in the receiver, and with bilateral weighting. These plots reveal interesting properties related to the signal symmetry in time and frequency. The matched-filter response is then extended to include Doppler distortions of the modulation function. The results show that Woodwards ambiguity function is valid only for signals with relatively modest sophistication, even though in most practical situations one is interested only in those undistorted parts of the matched-filter response in the vicinity of the delay axis. Plots of the response are presented for various degrees of distortion, for signals with and without weighting. Lastly, we consider the effects of a mismatch in range acceleration, again for the various cases of interest. The results convey a thorough insight into the properties of chirp radar under a broad range of operational conditions.

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.