L1 LMS theoretical tap-weight vector update — derivation and simulation results

In this paper, the L
₁
LMS algorithm is considered as an alternative to conventional cross-correlation processing for generating an estimate of a radar range profile. The update equation for the L
₁
LMS filter tap weight vector is derived to enhance the reader's understanding. Results achieved in simulation using MATLAB
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are shown, which illustrate robust performance achieved by an LMS-type algorithm employing a regularization term in the cost function to be minimized when processing simulated radar data for which the transmit noise waveform's spectrum contains multiple notches.