Mismatched filter optimization for radar applications using quadratically constrained quadratic programs

A Sequence-Filter Joint Optimization

“…It also explains how an optimal mismatched filter can be obtained through an optimisation problem, for a given sequence. More details are given in [4].…”

“…This loss-in-processing gain can be inserted as a convex constraint in optimisation problems, depending on s and q, as noticed in [4]:…”

“…This optimisation problem is equivalent to the following QCQP (Quadratically Constrained Quadratic Program) [4]:…”

“…On the other hand, a mismatched filter is not subject to the constant modulus constraint, so that the corresponding optimisation problem is much simpler. It has indeed been shown in [4] and in [5] that an optimal mismatched filter that minimises the ISL or the PSLR can be calculated through a convex problem. For instance, in [4], the mismatched optimisation problem is reformulated as an equivalent convex quadratically constrained quadratic program (QCQP).…”

“…It has indeed been shown in [4] and in [5] that an optimal mismatched filter that minimises the ISL or the PSLR can be calculated through a convex problem. For instance, in [4], the mismatched optimisation problem is reformulated as an equivalent convex quadratically constrained quadratic program (QCQP). It may thus be possible to find a global minimum, so-to-speak an optimal mismatched filter for a given sequence.…”