This paper deals with the simultaneous adaptive target detection and parameter estimation utilizing a Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar. At the design stage, a linearized model of the received signal is derived, leveraging the centro-Hermitian (persymmetric) structure of the array manifold and considering potential steering vector mismatches related to the actual target parameters. Exploiting this model, the detection problem is formulated and tackled leveraging adaptive detection approaches, resorting to the Persymmetric Generalized Likelihood Ratio (PGLR) and Persymmetric Adaptive Matched Filter (PAMF), respectively. However, they demand the Maximum Likelihood (ML) estimates of target incremental range (i.e., the deviation of the target actual position from the center of the range bin) and angle. Two iterative methods are devised to solve the ML estimation problem. The former is based on Dinkelbach's algorithm, which is capable of achieving the global optimum, whereas the latter is a fast-converging alternative approach relying on the Coordinate Descent (CD) framework. Numerical results highlight the effectiveness of the proposed simultaneous detection and estimation strategies, also in comparison with suitable benchmarks and counterparts.

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.