Local Accuracy Analysis of FSK-Based Joint Communications and Radar

Abstract

This paper analyses frequency shift keying (FSK)-based waveforms for joint communications and radar (JCR) in terms of radar estimation local accuracy. More specifically, the Cramer-Rao lower bounds for delay and Doppler shift estimation are characterised using the root mean square (RMS) time duration and RMS bandwidth of the waveform. We show that the Doppler shift estimation performance of the proposed waveform is invariant to the frequency sequence, under the analysis-friendly assumption that the width of the pulse shaping function does not exceed the pulse repetition interval. Under a similar assumption in the frequency domain, we derive an accurate approximation of the RMS bandwidth and its distribution, which allows the delay estimation accuracy to be quantified. The frequency permutation-based waveform is highlighted as a special case. Importantly, we show that FSK achieves an acceptable delay local accuracy by deriving the probability that its RMS bandwidth is greater than a given fraction of the permutation-based value. Finally, the observations are generalised by relaxing the previous assumptions. Numerical results illustrate the accuracy of the derived approximations and the performance of the proposed scheme. Comparisons between FSK and benchmarks indicate that it is a suitable candidate for resource-limited JCR scenarios.