Elsevier

Signal Processing

Volume 84, Issue 2, February 2004, Pages 327-339
Signal Processing

A frequency-domain training approach for equalization and noise suppression in discrete multitone systems

https://doi.org/10.1016/j.sigpro.2003.10.017Get rights and content

Abstract

In discrete multitone (DMT) transceivers, a time-domain equalizer (TEQ) is used to shorten the effective channel impulse response such that a shorter cyclic prefix can be used. In this paper, we pose the TEQ design problem completely in the frequency domain by defining a frequency-domain weighted least-squares cost function. The definition of the frequency-domain TEQ design criterion, we show, allows for the introduction of a weighting function to control the spectral shape of the TEQ, and facilitates important extensions particularly useful for the DMT system. The TEQ can be used to suppress the noise and interference in the DMT system, a feature especially useful in the frequency division multiplexing-based DMT system. Also, in the echo-cancellation-based DMT system, the TEQ can be used to jointly shorten the echo response thus reducing the complexity of the echo canceler. We present corresponding algorithms for these two objectives and simulation results, which show that the weighted frequency-domain least-squares algorithm and the two extensions we derive can achieve the shortening (channel or channel and echo) as well as noise suppression objectives effectively.

Introduction

Multi-carrier modulation (MCM) has been proposed for parallel communication in the late 1950s [8] based on the concept of creating multiple orthogonal subchannels over which several data streams can be sent without intersymbol interference (ISI). This modulation scheme provides flexibility for adapting to different channel environments by adjusting the energy and constellation size of each carrier. One implementation of MCM is the discrete multitone (DMT) system which uses the discrete Fourier transform (DFT) for modulation [17], [23]. DMT is chosen as the industry modulation standard for asymmetrical digital subscriber line (ADSL) modems and is also a candidate modulation scheme for very-high-speed digital subscriber line (VDSL) systems.

In the DMT system, a cyclic prefix (CP) of length γ provides a guard time between transmitted symbols. If the channel response is of length γ+1 or shorter, DMT symbols can be transmitted free of ISI. Using large γ values to compensate for the length of the channel response, however, decreases the efficiency (introduces an overhead of γ/(N+γ) where N is the DMT symbol length). A time-domain equalizer (TEQ) to shorten the effective channel impulse response has been the most popular equalization approach for the DMT systems [2], [6], [12], [15], [16], [20], [21], [22]. In addition, the TEQ is considered to be part of the overall channel response, hence its spectral shape plays an important role for maximizing the bit-rate over the channel [9], [11].

In this paper, we pose the TEQ design problem completely in the frequency domain, introduce the weighted frequency-domain least-squares (WFD-LS) approach and derive the corresponding algorithm by minimizing a squared frequency-domain cost function. We show that by introducing a weighting function, we can control the TEQ spectral shape and improve the overall performance of the DMT system. We compare the performance of WFD-LS algorithm to the time-domain optimal (TD-OP) and time-domain least-squares (TD-LS) algorithms given in [15] and show that different weighting functions can lead to different TEQ spectral shapes for the WFD-LS algorithm, which cannot be realized easily by the current TEQ methods that primarily work in the time domain.

We also show two important extensions of our TEQ design approach to further improve the DMT system performance. First, we demonstrate that we can modify the WFD-LS cost function and apply it to jointly shorten the channel impulse response and suppress the noise and interference in the DMT systems. We apply the stopband WFD-LS algorithm to the frequency division duplex (FDD) DMT-ADSL systems to jointly shorten the channel response and suppress a “virtual” noise as in [11], where the stopband is defined as the unallocated or highly noisy subchannels. It is shown by simulations that the stopband WFD-LS algorithm can effectively serve the two purposes of shortening the channel impulse response and suppressing the noise and interference.

The second extension we present is based on the observation that in echo-cancellation (EC)-based DMT system, the TEQ is placed prior to the echo canceler, hence it can affect the effective echo impulse response as well [10], [24]. We incorporate the joint shortening idea of [15] into our TEQ design method and show that we can define a composite squared cost function in the frequency domain to account for these two shortening purposes. Simulation results show that both channel and echo responses are effectively shortened by applying the joint WFD-LS algorithm.

The rest of the paper is organized as follows. In Section 2, we first present an overview of the TEQ training approach for DMT systems. We then formulate the TEQ design problem in the frequency domain and derive the WFD-LS algorithm to obtain the TEQ coefficients. We present simulations to show that this TEQ design approach is effective in shortening the channel response and a weighting function can be used to control the resultant TEQ spectral shape. Then in Section 3, the WFD-LS algorithm is extended such that the noise and interference can also be suppressed. Finally, we apply the WFD-LS algorithm to jointly shorten channel and echo responses in Section 4. Simulation results are presented for each case, and Section 5 includes the discussions.

Section snippets

Background

TEQ design approaches typically approximate the channel transfer function in DMT systems by an autoregressive moving average (ARMA) modelH(z−1)=B(z−1)A(z−1)=z−di=0L−1biz−ii=0M−1aiz−i.

A TEQ whose transfer function is equal to A(z−1) can be introduced at the receiver side, such that the cascade of the channel H(z−1) and the TEQ approximate a sufficiently short target response B(z−1). In Eq. (1), L is the length of the target response, M is the length of the TEQ filter, and d is the delay of the

Joint impulse response shortening and noise suppression for DMT systems

A major advantage of the DMT system is that its modulation and demodulation can be implementated by an efficient algorithm, the inverse FFT(IFFT)/FFT. However, due to the finite length of the FFT operation in the DMT receiver, the neighboring subchannels interfere with each other, creating leakage effect. Hence the narrowband noise and interference can be spread outside the band deteriorating the neighboring subchannel SNRs [7], [11]. In [11], Kerckhove and Spruyt propose a constrained mean

Joint channel and echo response shortening for DMT systems

In the ADSL standard, two types of DMT systems are defined for full-duplex operation. One is the FDD DMT, where frequency bandwidth is split into upstream and downstream bands. The other version of the DMT system is called EC-based DMT, where the frequency bands for upstream and downstream data transmission are overlapped. The lowest subchannels are not used to avoid the interference with the plain old telephone service (POTS). The frequency range from 30 to 138kHz is used for upstream data

Conclusions

We introduce a frequency-domain approach for designing the time-domain equalizer for the DMT system. The least-squares cost defined in the frequency domain allows for control of the TEQ magnitude response by a weighting function. The performance of the algorithm derived, WFD-LS, is comparable to that of time-domain least squares TEQ design when no weighting is used. As the simulation results suggest, by appropriate choice of the weighting function, the resulting TEQ shape can be controlled with

Acknowledgements

The authors would like to thank Aleksandar Purkovic for his comments and input.

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    Research supported in part by Maryland Industrial Partnerships and Nortel Networks under Grants MIPS-2218.12 and MIPS-2218.24.

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