Choosing the Optimal Parameters for Mismatched Filter Design

Mismatched Filter is a well known technique for lowering the sidelobes of a given RADAR waveform. Given the filter length and the allowable mismatched loss, the filter design problem is convex, and efficient solvers exist and are able to efficiently provide the filter coefficients. These coefficients, being a solution to a convex optimization problem, will be unique regardless of the solver used. A question remains as for how to best choose the parameters which define the problem - the filter length and mismatched loss. This work presents study of the takeoffs and suggests practical choices of values for those parameters. It also generalizes the problem of obtaining a mismatched filter into minimizing
$L_{P}$
norm of the filtered signal, allowing for sparse solutions to be obtained. It shows that in general the attenuation gained by using the mismatched filter reaches a saturation point, suggesting that for a given problem an optimal set of parameters exist. It also compares different families of waveforms, and shows that the attenuation gain curve are different for different waveforms, which could also assist the radar designer in initial choice of the radar waveform.