Unambiguous Delay-Doppler Recovery from Random Phase Coded Pulses

TL;DR

This paper introduces a novel random phase coding method for pulse Doppler radars that jointly processes samples to resolve range-Doppler ambiguity, improving SNR and target detection over traditional MPRF techniques.

Contribution

It proposes a random phase coding approach combined with a joint processing algorithm based on orthogonal matching pursuit to enhance unambiguous range and velocity detection.

Findings

Outperforms MPRF in hit rate in simulations

Increases unambiguous range while preserving Doppler resolution

Works with both Nyquist and sub-Nyquist sampling regimes

Abstract

Pulse Doppler radars suffer from range-Doppler ambiguity that translates into a trade-off between maximal unambiguous range and velocity. Several techniques, like the multiple PRFs (MPRF) method, have been proposed to mitigate this problem. The drawback of the MPRF method is that the received samples are not processed jointly, decreasing signal to noise ratio (SNR). To overcome the drawbacks of MPRF, we employ a random pulse phase coding approach to increase the unambiguous range region while preserving the unambiguous Doppler region. Our method encodes each pulse with a random phase, varying from pulse to pulse, and then processes the received samples jointly to resolve the range ambiguity. This technique increases the SNR through joint processing without the parameter matching procedures required in the MPRF method. The recovery algorithm is designed based on orthogonal matching pursuit so that it can be directly applied to either Nyquist or sub-Nyquist samples. The unambiguous delay-Doppler recovery condition is derived with compressed sensing theory in noiseless settings. In particular, an upper bound to the number of targets is given, with respect to the number of samples in each pulse repetition interval and the number of transmit pulses. Simulations show that in both regimes of Nyquist and sub-Nyquist samples our method outperforms the popular MPRF approach in terms of hit rate.