Closed-Form Asymptotic Approximation of Target’s Range Information in Radar Detection Systems

Abstract

The echoes of the radar systems can provide useful information about the target, including range, velocity, shape, and angular direction. Extensive studies have utilized the information of the target to improve system performance, whereas the problem of a favorable closed-form asymptotic approximation of the target's range information (RI) is seldom investigated. In this paper, we address the problem of obtaining a closed-form asymptotic approximation of the target's RI in all SNR regions for radar detection systems. The RI is formulated as the mutual information (MI) between the random range and the received signals with complex additive white Gaussian noise (CAWGN). The basis of our scheme is to employ the a posteriori probability density function (PDF) of the range to extract RI from the echoes. We show the a posteriori PDF is a function of the autocorrelation function (ACF) of signal and the cross-correlation function (CCF) of signal-noise. By dividing the integration interval of the a posteriori PDF into the signal-noise interval and noise interval, a closed-form asymptotic approximation of RI is derived based on the probability of range distinguishability and the normalized a posteriori entropies of low and high signal-to-noise ratio (SNR). The results also reveal an interesting relationship between the RI and the uncertainty of the target. As special cases, the closed-form approximations of RI in low and high SNR are obtained. Moreover, for the problem of slightly looser in medium SNR approximation, a better approximation is derived based on a linear model approach. Numerical results are presented to validate the proposed theory and verify the effectiveness of the proposed approximation.

Approximate expressions of target’s scattering information

“…Next, we discuss the information acquisition process of radar based on information theory. The purpose of radar detection is to estimate the location and the scattering property from the receiving signal .The location information has been discussed in detail before [7][8][9] . This paper deals only with the scattering information .…”

“…Considering the received waveform resulted from the true phase value at a snapshot, we can rewrite (2) as . Substituting it into (9) and utilizing related properties, the result is (9) where is still a Gaussian white noise. For two special cases, high SNR and low SNR, the posterior probability expression can be discussed differently to obtain a more concise approximate expression.…”

“…From these works, it is apparent that they only consider the location information and ignore the scattering information of the target. In [7][8][9], the location information and the scattering information were studied simultaneously for the first time, and the approximate upper bound of the distance information and the closed expression of the location information were obtained.…”