Group theory in radar and signal processing

This paper describes some key mathematical ideas in the theory of radar from a group theoretic perspective. The intention is to elucidate how radar theory motivates interesting ideas in representation theory and, conversely, how representation theory affords a better understanding of the inherent limitations of radar. Although most of the results presented here can be found in (Wilcox, 1991) and (Miller, 1991), there are significant differences in the selection and presentation of material. Moreover, compared with (Wilcox, 1991), (Miller, 1991) and (Moran, 2001), greater emphasis is placed here on the group theoretic approach, and in particular, its ability to arrive quickly and succinctly at basic results about radar. Central to radar theory is the ambiguity function. Specifically, corresponding to any waveform w(t) is a two dimensional function Aw(t, f), called the ambiguity function, which measures the ability of that particular waveform to allow the radar system to estimate accurately the location and velocity of the target. Some waveforms perform better than others, and it is the challenge of radar engineers to design waveforms with desirable ambiguity functions while simultaneously meeting