Challenges in Designing of an Optimal Time-Frequency Filter for the Non-Linear FM Signal Estimation and the Possible Solution

Nonstationary linear frequency modulated (FM) noisy signals are efficiently estimated by using recently developed optimal (Wiener) time-frequency filtering solution. It is developed based on the estimation of instantaneous frequency (IF) of the filtered noisy signal and on its correspondence to the filter's region of support. Multiple-clock-cycle hardware design of this solution is firstly proposed, whereas the signal adaptive and the fully pipelined versions of the same solution, with the optimized time and hardware requirements and in their one-dimensional and two-dimensional forms, have also been recently developed. However, the non-liner FM signals cannot be ideally concentrated at their IFs and, hence, these signals cannot be efficiently estimated by using the IF estimation-based filtering solutions. Therefore, in this paper, challenges in estimation of the non-linear FM signals are analyzed in detail. Simultaneously, the consideration of the modified IF estimation-based algorithm suitable to provide high quality estimation of these signals is presented.