Costas Array Waveforms for Closely Spaced Target Detection

In this paper, we consider requirement-driven selection of Costas arrays for the detection of closely spaced targets. We review existing order selection strategies in terms of the time-bandwidth product and treat selection of specific Costas arrays separably. Our computational analyses prioritize a clear central region in single-pulse discrete ambiguity functions (DAFs) and also address maximum frequency hops. Using finite field arithmetic, we significantly generalize results about 1s in the central square DAF regions for Welch and Lempel-Golomb arrays, and prove two general results about the nonexistence of such clear regions. We find that order 14 is very beneficial for target detection in which Costas arrays having an almost entirely clear 5 \times 5 square central region in the single-pulse DAF exist and feature the corresponding time-bandwidth product of 196 within an example. We feature a first-principles system simulation with such an order-14 Costas array to obtain a 3-dB target detection improvement. Since radars commonly use burst waveforms, we also consider three different kinds of bursts and discuss their merits using ambiguity function analyses. We provide supporting computational database surveys on central rectangular 3 \times m regions.