Per-Wavelet Equalization for Discrete Wavelet Transform Based Multi-Carrier Modulation Systems

The Discrete Wavelet Transform (DWT) has gained attention in the area of Multi-Carrier Modulation (MCM) because it can overcome some well known limitations of Discrete Fourier Transform (DFT) based MCM systems. Its improved spectral containment removes the need for a cyclic prefix, be it that appropriate equalization then has to be added as the cyclic convolution property no longer holds. Most DWT based MCM systems in the literature use Time-domain EQualizers (TEQs) to mitigate the channel distortion. In this paper, a Per-Wavelet EQualizer (PWEQ) is proposed which directly maximizes the Signal-to-Interference-plus-Noise Ratio (SINR) per symbol and is applicable to any wavelet family. The proposed PWEQ provides a performance upper bound for the TEQs for DWT based MCM systems. The computational complexity of the PWEQ is reduced by modifying the Filter Bank (FB) structure of the DWT. Simulations are performed to compare the PWEQ performance against the TEQs for DWT based MCM systems and the similar Per-Tone EQualizer (PTEQ) for DFT based MCM systems. The simulations are performed using measured Asymmetric Digital Subscriber Line (ADSL) and G.fast channels with Fejér-Korovkin (FK) wavelets. The proposed PWEQ increases the SINR on the received symbols compared to the TEQs at the cost of an increased computational complexity.

Introduction

Discrete Multi-Tone (DMT) modulation has dominated broadband wireline [1], [2], [3], [4] and wireless [5], [6] communications over the last decades. It is a Discrete Fourier Transform (DFT) based Multi-Carrier Modulation (MCM) system with a fairly simple receiver structure where, because of the use of an appropriately long cyclic prefix, channel equalization can be done with a single-tap filter per tone, i.e. one complex multiplication per tone. However, the cyclic prefix length  ν  has to be equal to or longer than the channel impulse response length, and hence reduces the symbol rate by  ν/(N+ν) , where  N  is the block size.