Unification and evaluation of equalization structures and design algorithms for discrete multitone modulation systems

Abstract

Abstract-To ease equalization in a multicarrier system, a cyclic prefix (CP) is typically inserted between successive symbols. When the channel order exceeds the CP length, equalization can be accomplished via a time-domain equalizer (TEQ), which is a finite impulse response (FIR) filter. The TEQ is placed in cascade with the channel to produce an effective shortened impulse response. Alternatively, a bank of equalizers can remove the interference tone-by-tone. This paper presents a unified treatment of equalizer designs for multicarrier receivers, with an emphasis on discrete multitone systems. It is shown that almost all equalizer designs share a common mathematical framework based on the maximization of a product of generalized Rayleigh quotients. This framework is used to give an overview of existing designs (including an extensive literature survey), to apply a unified notation, and to present various common strategies to obtain a solution. Moreover, the unification emphasizes the differences between the methods, enabling a comparison of their advantages and disadvantages. In addition, 16 different equalizer structures and design procedures are compared in terms of computational complexity and achievable bit rate using synthetic and measured data.

Low complexity channel shortening for discrete multitone modulation systems

“…In order to allow for a shorter CP while keeping the benefits of DMT, a channel shortening technique, also called time-domain equalization (TEQ), is typically adopted (we refer the reader to [2] for a survey on the topic). This technique makes use of a filter on the time-domain received signal that compensates for the effects of a shorter CP.…”

“…Various solutions for the design of the channel shortening filter have been proposed in the literature [2]. Among those, the iterative minimum delay spread (MDS) method of [1] always converges, while computing one matrix inversion per iteration, thus yielding significant computational complexity and memory requirement.…”

Adaptive inverse filtering of room acoustics

“…These techniques have been extended to the multiple-input/multiple-output (MIMO) case in [12] [13]. A common frame work and an overview of the design techniques for channel shortening can be found in [14]. The motivation behind employing such techniques for our acoustic system equalization application is based on the fact that the early reflections in room acoustics can, in certain cases, enhance the speech intelligibility [15].…”

Tap Loading of Subcarrier Equalizers for Wireless Multicarrier Transceivers

“…There exists four major equalizer architectures for multicarrier systems: 1) a TEQ combined with a bank of single-tap FEQs [6]- [8]; 2) a bank of multitap FEQs [3], [6], [9]; 3) a TEQ filter bank [6]; and 4) a single linear system combining the TEQ, the analysis filter bank, and the bank of FEQs [6]. With TEQ implementations operating in the time domain of the multicarrier transceiver, there nevertheless exists several TEQ design methods that take into account the subchannel signalto-noise ratio (SNR) values when designing the finite-impulse response filter coefficients, i.e., these methods jointly optimize the time-frequency behavior of the equalized channel in designing the TEQ coefficients.…”

“…For a detailed quantitative comparison of the communication performance versus implementation complexity tradeoffs of several equalizer architectures, see the paper by Martin et al [11]. One implementation of a frequencydomain equalizer architecture is the per-tone equalizer (PTEQ) approach [6], [12], which is designed to move the TEQ into the bank of single-tap FEQs to obtain a bank of multitap FEQs. This transformation is made possible by the fact that the TEQ, analysis filter bank, and FEQ are all linear systems in cascade.…”