Low-Complexity Complex KLMS based Non-linear Estimators for OFDM Radar System

Recently, kernel-based adaptive filtering (KAF) algorithms have found widespread application in numerous nonlinear signal processing problems; one of them being radar signal processing. In particular, considering the inherent non-linearity in a radar system, KAF has been recently applied for estimation of delay and found to achieve lower variance as compared to classical Fourier-Transform based approach. However, as the radar-return is complex-valued in general, using a traditional complex Gaussian kernel in KAF based estimator yields inaccurate estimates. In this work, we explore Wirtinger's calculus-based complexification of a reproducing kernel Hilbert space (RKHS) for estimation of delay and Doppler-shift, which guarantees lower estimator-variance, and kernel-stability. Furthermore, since the choice of suitable kernel-width is crucial for RKHS-based estimation of delay and Doppler parameters, we derive an adaption for joint-estimation of kernel-width for the proposed normalized complex kernel least mean square (NCKLMS) based estimator from the radar return. Simulations performed over orthogonal frequency division multiplexed (OFDM)-radar system indicate that the proposed NCKLMS based estimator converges to a significantly lower dictionary-size, thereby leading to simpler implementation, receiver-simplicity, and latency whilst maintaining equivalent squared error performance, which makes the proposed estimators suitable for practical OFDM-radar systems.