Noise-Type Radars With Gaussian Statistics: SNR and the Correlation Coefficient

Noise radars have the same mathematical description as a type of quantum radar known as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quantum two-mode squeezing radar</i>. Although their physical implementations are very different, this mathematical similarity allows us to analyze them collectively, for which reason we call them <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">noise-type radars</i>. The target detection performance of noise-type radars depend crucially on a parameter called the “correlation coefficient”. In this paper, we show that the correlation coefficient reduces to the signal-to-noise ratio (SNR) in certain limiting cases when the SNR is appropriately defined. This allows us to translate between the correlation coefficient, which is the more fundamental parameter in the theory of noise-type radars, and the SNR, which is more familiar to engineers. To illustrate the ideas in this paper, we present experimental results from a laboratory-based noise radar.