Stochastic analysis of random frequency modulated waveforms for noise radar systems

Noise radars are electromagnetic systems that use random signals for detecting and locating reflecting objects. Besides high performance against external interferences (intentional or not), the stochastic nature of the transmitted waveforms may lead to the suppression of range ambiguity in the detection of targets and low range sidelobes, if systems parameters are properly chosen. This paper addresses a probabilistic analysis to derive mathematical expressions for the signal-to-noise ratios, the peak-to-sidelobe ratios and the signal-to-interference ratios (due to ambiguous targets) throughout a typical receiver processing chain of a pulsed FM noise radar. A receiver that employs matched filtering and pulse integration prior to detection was considered. Pulse compression and integration gains (in signal-to-noise and signal-to-interference, due to ambiguous targets, ratios) are also derived. The analysis provides closed-form expressions relating the precise dependence of sidelobe levels as well as interference levels due to ambiguous targets to the integration time, the transmit signal bandwidth, and the number of integrated pulses.