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Cyclic prefixed communications, such as multicarrier communications, first became widely used in the context of digital subscriber lines (DSL). In DSL, bit loading is allowed at the transmitter, and the performance metric is the bit rate that can be provided without exceeding a given bit error rate (BER). Wireless cyclic prefixed systems are now becoming increasingly popular, and in such systems the appropriate performance metric is the BER for a given bit loading at the transmitter. Cyclic prefixed systems perform well in the presence of multipath, provided that the channel delay spread is shorter than the guard interval between transmitted blocks. If this condition is not met, a channel shortening equalizer can be used to shorten the channel to the desired length. Previous work on channel shortening has largely been in the context of DSL, thus it has focused on maximizing the bit rate. In this paper, we propose a channel shortener that attempts to directly minimize the BER for a multiple-input multiple-output channel model. We simulate the performance of the resulting channel shortener and compare it to existing designs and the matched filter bound [ABSTRACT FROM PUBLISHER]

Abstract: In a previous paper, we proposed a bitrate maximizing design criterion for time-domain equalizers (TEQ) in DMT transceivers to shorten the channel impulse response, as needed in, e.g., ADSL receivers. The proposed criterion truly maximizes the bitrate, as it is based on an exact formulation of the subchannel SNR as a function of the TEQ taps. In this paper, we show how the BM-TEQ design can be used in a bitrate maximizing per group equalizer (BM-PGEQ): the active tones are divided into groups and each group is provided with a bitrate maximizing equalizer. This BM-PGEQ design allows for a trade-off between memory requirement and performance, keeping computational complexity during data transmission roughly at the same level. It encompasses the BM-TEQ design and the so-called per tone equalization scheme (PTEQ) as extreme cases. We also present an adaptation algorithm to design the BM-TEQ and BM-PGEQ. Through simulation, we show that the BM-PGEQ scheme outperforms an earlier presented tone grouping scheme where the whole tone group was assigned the PTEQ of the group center tone. The BM-PGEQ scheme appears as a useful intermediate between BM-TEQ and PTEQ and closely approaches the PTEQ performance for as few as four tone groups in an ADSL scenario, even in harsh environments with narrowband interference and crosstalk. [Copyright &y& Elsevier]

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQIBM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment. [ABSTRACT FROM AUTHOR]

We reconsider the minimum mean square error (MMSE) time-domain equalizer (TEQ), bitrate maximizing TEQ (BMTEQ), and per-tone equalizer design (PTEQ) for discrete multitone (DMT) transmission and cast them in a common least-squares (LS) based framework. The MMSE-TEQ design criterion can be formulated as a constrained linear least-squares (CLLS) criterion that minimizes a time-domain (TD) error energy. From this CLLS-based TD-MMSE-TEQ criterion, we derive two new least-squares (LS) based frequency-domain (FL)) MMSE-TEQ design criteria: a CLLS-based FD-MMSE-TEQ criterion and a so-called separable nonlinear LS (SNLLS) based FD-MMSE-TEQ design. Finally, the original BM-TEQ design is shown to be equivalent to a so-called iteratively-reweighted (IR) version of the SNLLS-based FD-MMSE-TEQ design. This LS-based framework then results in the following contributions. The new, IR-SNLLS-based BM-TEQ design criterion gives rise to an elegant, iterative, fast converging, Gauss-Newton-based design algorithm that exploits the separability property. The intermediate FD-MMSE-TEQ designs establish a link between the TD-MMSE-TEQ on one hand and the BM-TEQ and the PTEQ on the other hand. Moreover, the considered LS-based equalizer designs-although at first sight very different in nature—exhibit remarkable correspondence when turned into equivalent generalized eigenvalue problems. [ABSTRACT FROM AUTHOR]

In discrete multitone (DMT) receivers, as for instance in asymmetric digital subscriber lines (ADSLs), the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex 1-tap frequency domain equalizers (FEQs). Additionally, receiver windowing can be applied to mitigate the bad spectral containment of the demodulating DFT sidelobes. In this paper, we focus on a combined equalizer and windowing design procedure to maximize the achievable bit rate in DMT-based modems. Whereas the combination of a tEQ with a single window treats all the data carrying tones in a common way, the presented design method can also be used in a "per group" fashion, where smaller groups of tones receive each a different equalizer-window pair. When such groups contain only one single tone, the design procedure can be linked to the performance of an unbiased minimum mean square error (MMSE) per tone equalizer (PTEQ), which then also implicitly implements a per tone window. The general framework introduced in this paper allows us to treat equalizer-only and window-only designs as well, which appear as special cases in a natural way. This set of bit rate maximizing techniques can serve either as practical design methods or as upper bounds for existing (suboptimal) methods. We will also show that for the same achievable bit rate, equalizer taps can be exchanged for windowing coefficients to reduce complexity during data transmission. [ABSTRACT FROM AUTHOR]

Asymmetric digital subscriber lines (ADSLs) employ discrete multitone modulation (DMT) as transmission format, where subcarriers are assigned to the up- and/or downstream transmission direction. To separate up- and downstream signals, the ADSL standard allows the use of echo cancellation resulting in improved bit rates, reach, and/or noise margins. In DMT-based modems, typically, the mixed time/frequency (MTF) domain echo canceling scheme, as proposed by Ho et at, is implemented. This technique estimates the echo filter in the frequency domain using the least mean square (LMS) algorithm with the transmitted echo symbols as update directions. Since not every tone of the transmitted echo signal will carry data, i.e., will be excited, the MTF adaptation process does not lead to a good estimate for the echo channel, unless extra power on unused echo tones is transmitted. However, transmitting extra power on such tones is often undesired. In this paper, we present an alternative echo canceling scheme referred to as the circulant decomposition canceler (CDC), which works without extra power requirements and with comparable complexity as the method of Ho et al. Similar to MTF echo canceling, the CDC scheme can easily be incorporated into a multirate environment with different transmit and receive rates and can also cheaply be combined with per-tone equalization and double talk cancellation to allow fast tracking and/or convergence in the presence of a far-end signal. [ABSTRACT FROM AUTHOR]

A time-domain equalizer (TEQ) is inserted in discrete multitone (DMT) receivers to impose channel shortening. Many algorithms have been developed to initialize this TEQ, but none of them really optimizes the bitrate. We present a truly bitrate-maximizing TEQ (BM-TEQ) cost function that is based on an exact formulation of the subchannel signal-to-noise ratio as a function of the TEQ taps. The performance of this BM-TEQ comes close to the performance of the per-tone equalizer. [ABSTRACT FROM AUTHOR]

In discrete multitone receivers, the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex one-tap frequency domain equalizers. An alternative receiver is based on a per tone equalization (PTEQ), which optimizes the signal-to-noise ratio (SNR) on each tone separately and, hence, the total bitrate. In this paper, a new initialization scheme for the PTEQ is introduced, based on a combination of least mean squares (LMS) and recursive least squares (RLS) adaptive filtering. It will be shown that the proposed method has only slightly slower convergence than full square-root RLS (SR-RLS) while complexity as well as memory cost are reduced considerably. Hence, in terms of complexity and convergence speed, the proposed algorithm is in between LMS and RLS. [ABSTRACT FROM AUTHOR]

In discrete multitone receivers, a time domain equalizer (TEQ) is used to shorten the channel impulse response, so that the equalized channel impulse response is shorter than the inserted prefix. The aim of this paper is to show that the minimum mean square error (MMSE) channel shortening problem with two different energy constraints, remarkably, lead to the same TEQ coefficients, up to a scaling factor. Moreover, implying the two energy constraints together in the MMSE optimization again yields the same result and comes down to a canonical correlation analysis between the subspace spanned by the transmitted samples and the received samples, respectively. Hence, the TEQ obtained by these three distinct MMSE cases yields the same performance in terms of bit rate. Since the resulting problem can easily be reformulated as a maximization problem, an iterative procedure based on power iterations can be devised to reduce the computational complexity. [Copyright &y& Elsevier]

Several high-speed communication standards modulate encoded data on multiple-carrier frequencies using the fast Fourier transform (FFT). The real part of the quantized inverse FFT samples form a symbol. The symbol is periodically extended by prepending a copy of its last few samples, also known as a cyclic prefix. When the cyclic prefix is longer than the channel order, amplitude and phase distortion can be equalized entirely in the frequency domain. In the receiver, prior to the FFT, a time-domain equalizer, in the form of a finite-impulse response filter, shortens the effective channel impulse response. Alternately, a bank of equalizers tuned to each carrier frequency can be used. In earlier literature, we unified optimal multicarrier equalizer design algorithms as a product of generalized Rayleigh quotients. In this paper, we convert the unified theoretical framework into a framework for fast design algorithms. The relevant literature is reviewed and classified according to this framework. We analyze the achieved bit rate versus implementation complexity (in terms of multiply-and-accumulate operations) tradeoffs in the original and fast design algorithms. The comparison includes multiple implementations of each of 16 different equalizer structures and design algorithms using synthetic and measured discrete multitone modulated data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]