Efficient Series Expansion for Matrix Inversion with Application to MMSE Equalization

Abstract

In this paper, we describe an efficient approach to overcome the need for matrix inversion required in most wired applications encoutered in practice. In particular, MMSE equalization based on series expansion to approximate the matrix inversion is addressed. By adjusting a scaling factor, the series expansion is directly optimized according to a fixed order with respect to a system performance criterion. In comparison with previous approaches, the resulting equalizer enables improved BER performance according to a fixed order, in addition to low complexity without the need for a complicated eigenvalue calculation procedure.

Reduced Complexity Polynomial Expansion Approximation to MMSE-DFE

“…When there is no feedback filter (in which case, the MMSE-DFE simplifies to the simpler MMSE-LE), our results simplify to the results obtained in [4] for the MMSE-LE. As in [4], the received Signal to Interference plus Noise Ratio is used to optimize the polynomial expansion parameters. In particular, the parameters have been optimized with respect to a fixed polynomial order.…”

“…We demonstrate through simulations that our proposed equalizer outperforms earlier approaches in terms of bit error rate (BER). From the simulation results, it is also found that the polynomial approximation technique is more attractive for the MMSE-DFE case as it achieves high performance even with a lowerorder polynomial approximation compared to the higher-order polynomial approximations needed for the MMSE-LE case studied in [4].…”

“…when the number of feedback taps is set equal to the channel memory [3]. In the literature, some methods ( [4], [5], [6]) have been proposed to reduce the cubic computational complexity involved in the matrix inversion for the MMSE-DFE in the general case. These methods involve approximating the matrix inversion with a polynomial expansion.…”

“…References [5] and [6] used two different approaches for setting the polynomial expansion scaling parameters. In [4], a different method was used to find the scaling parameter, namely, by maximizing a system performance criterion. However, the parameters for the polynomial expansion were derived for the simpler case of the Minimum Mean Squared Error -Linear Equalizer (MMSE-LE).…”

“…In this paper, the polynomial expansion parameters are found by using a similar criterion as in [4]. However, these parameters are derived for the more sophisticated MMSE-DFE equalizer.…”