Performance Analysis of Locally Most Powerful Invariant Test for Sphericity of Gaussian Vectors in Coherent MIMO Radar

Locally most powerful invariant test (LMPIT) for sphericity of Gaussian vectors has been derived by Ramírez et al. Nevertheless, the decision threshold of the LMPIT is not accurate and its detection performance has not yet been addressed. In this paper, the LMPIT is performed for target detection in multiple-input multiple-output (MIMO) radar, and its theoretical decision threshold as well as detection probability are accurately determined. Utilizing asymptotic expansion approach, we calculate the asymptotic null distribution as a function of central chi-square distributions, resulting in precise closed-form formula for thresholding. On the other hand, the nonnull distribution is approximated by weighted sum of noncentral chi-square distributions and Gamma distribution for close and far hypotheses, respectively. This enables us to derive a closed-form formula to precisely evaluate the detection power of the LMPIT. Numerical results demonstrate that our theoretical computations are very accurate in determining the decision threshold and predicting the behaviors of the LMPIT. Moreover, the superiority of the LMPIT for MIMO radar target detection over state-of-the-art methods is demonstrated for spatially colored but temporarily white noise.