Ambiguity function analysis for the chirp diverse waveform (CDW)

We evaluate the radar performance for chirp pulse (linear FM) trains in which the chirp rate is diverse from pulse to pulse. The evaluation consists of deriving the ambiguity function in generalized form for any number of pulses, pulse repetition rate, time bandwidth product, and diversity spread across the pulse train. Since each pulse has a different chirp rate, convolution and factorization cannot provide closed form expressions for the ambiguity functions of interest. However, numerical integration, programmed in MatLab, reveals the effects of the degree of chirp diversity and time bandwidth product on the waveform's ambiguity diagram. The recurrent lobe structure of the three-dimensional ambiguity diagram is of special interest. We present a simple formula for selecting the different chirp rates for particular diversity spreads. We conclude that a dramatic decrease in the range recurrent lobe level occurs as we increase the time bandwidth product and/or degree of chirp diversity.