Calibration of Distributed MIMO Radar Systems

When using a distributed multiple-input multiple-output (MIMO) radar system, one must account for nonideal and unknown effects due to the electronics, cables, antennas, and so on. This article addresses the problem of estimating the MIMO system transfer function coefficients of a linear time-invariant (LTI) MIMO system. The system is considered to be uncalibrated in that its MIMO transfer function, receiver noise powers, and noise spatial correlations are unknown. The problem of estimating the MIMO system transfer function coefficients is shown to be nontrivial due to its inherent Kronecker structure and is shown to be of the form of a class of unsolved problems. Three approaches for estimating the transfer function are derived and shown to achieve good performance in simulation. The first approach relaxes the constraints and finds the corresponding (relaxed) maximum likelihood estimator (MLE). The second approach projects the relaxed MLE solution into the constraint (Kronecker) set. The third approach makes use of the fact that the original transfer function MLE problem is biconvex in the transmit and receive transfer functions, respectively, and employs an alternating minimization algorithm to find them directly.