Design and Analysis of Invariant Receivers for Gaussian Targets

The purpose of this paper is to elaborate on the invariant framework proposed in “An invariant approach to adaptive radar detection under covariance persymmetry” (A. De Maio and D. Orlando, IEEE Trans. Signal Processing, vol. 63, no. 5, pp. 1297-1309, May 2015) so as to account for target fluctuations at the design stage. To this end, we assume that the radar cross section of the target is ruled by an exponential distribution (Swerling 1 target model) and derive the complete statistical characterization of a maximal invariant statistic. Hence, we exploit the obtained probability density functions to synthesize both the optimum and the locally optimum (in the low Signal-to-Interference-plus-Noise Ratio regime) invariant receivers. Finally, we discuss some invariant sub-optimum decision rules based on theoretically solid design criteria and analyze their performances in comparison with the benchmark invariant test.