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.
Highlights
MAJOR CONTRIBUTIONS Generally, this paper focuses on the problem of obtaining a novel closed-form asymptotic approximation of range information (RI) towards a stationary target in radar systems by using information theory
We can derive a closed-form asymptotic approximation of RI based on the normalized a posteriori entropies of low and high signal-to-noise ratio (SNR) and the probability of range distinguishability which is obtained based on the autocorrelation function (ACF) and cross-correlation function (CCF). 3) We reveal the relationship between the RI and uncertainty of the target and derive the closed-form approximations of RI in low, medium and high SNR as special cases
The proposed approximation can achieve better approximation performance when compared to the conventional method [13] in low and medium SNR via theoretical and numerical results
Summary
The major contributions of this work can be summarized as follows: 1) An information extraction model for a stationary target is established by considering a non-fluctuating model with constant echo power With this model, the RI is formulated as the MI between the random variable range and received signal in CAWGN. 2) For the a posteriori PDF, the defined interval of integration can be divided into a signal-noise interval (including peak) and a noise interval According to this approach, we can derive a closed-form asymptotic approximation of RI based on the normalized a posteriori entropies of low and high SNR and the probability of range distinguishability which is obtained based on the ACF and CCF. Our approximation scheme can indicate the three stages of information extraction process in radar detection systems, namely, preliminary detection, rough detection, and accurate detection
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