Fractional QCQP With Applications in ML Steering Direction Estimation for Radar Detection

—This paper deals with the problem of estimating the steering direction of a signal, embedded in Gaussian disturbance, under a general quadratic inequality constraint, representing the uncertainty region of the steering. We resort to the maximum likelihood (ML) criterion and focus on two scenarios. The former assumes that the complex amplitude of the useful signal component fluctuates from snapshot to snapshot. The latter supposes that the useful signal keeps a constant amplitude within all the snapshots. We prove that the ML criterion leads in both cases to a fractional quadratically constrained quadratic problem (QCQP). In order to solve it, we first relax the problem into a constrained fractional semidefinite programming (SDP) problem which is shown equivalent, via the Charnes-Cooper transformation, to an SDP problem. Then, exploiting a suitable rank-one decomposition, we show that the SDP relaxation is tight and give a procedure to construct (in polynomial time) an optimal sol...

• Type: Journal
• Year: 2011
• Where: TSP
• Authors: Antonio De Maio, Yongwei Huang, Daniel Pérez Palomar, Shuzhong Zhang, Alfonso Farina
• Keywords: Constrained Quadratic Problem, Optimal Solution, TSP 2011, Useful Signal