Comparative study of techniques to compute FIR filter weights in adaptive channel equalization

In this article the computation of FIR filter weights in adaptive channel equalization tasks in quasi stationary environments is considered. The problem is formulated as a system of equations. It can be solved via direct matrix inversion (DMI) or iteratively via the LMS or RLS algorithm. Thereby suitable criteria such as least squares (LS) or mean square error (MSE) are minimized. By using these techniques the filter weights are estimated. Another technique is to estimate the channel impulse response (CIR) by exploiting the eigenvalue decomposition (EVD) of cyclic matrices as done in orthogonal frequency domain multiplex (OFDM) systems and computing the FIR filter weights from the CIR via solving the zero forcing matrix equation. Different techniques to solve this equation are presented: One uses a cyclic prefix (CP) based approach, another a QR decomposition. After describing the different techniques they are assessed in terms of ensemble-averaged square error and computational complexity. The EVD based techniques can render the lowest square error and require significant fewer multiplications than iterative methods or the DMI technique.