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The time-domain equalizer (TEQ) design literature is surveyed for complexity reduction techniques, and the complexity requirement of the most popular algorithms are calculated for their original and reduced-complexity implementations. The results suggest that choosing the best equalizer design depends on the bit rate and complexity targets as the per-tone equalizer has the highest achievable bit rate with higher cost and Minimum Delay Spread TEQ has the lowest cost with average performance.

A study is conducted to show that bit rate maximizing time-domain equalizer (BM-TEQ) and bit rate maximizing per-group equalizers (BM-PGEQs), despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. The track variations of transmission channel and noise, which are typical of a digital subscriber line environment, are made possible by these adaptive equalizers.

The minimum mean square error (MMSE) time-domain equalizer design (TEQ), bitrate maximizing TEQ (BM-TEQ), and per-tone equalizer design (PTEQ) for discrete multitone (DMT) transmission and cast them in a common least-squares (LS) based framework are highlighted. The MMSE-TEQ design criterion can be formulated as a constrained linear least-squares (CLLS) criterion that minimizes a time-domain (TD) error energy.

A combined equalizer and windowing design procedure to maximize the achievable bit rate in discrete multitone (DMT)-based modems is highlighted. It is shown that for the same achievable bit rate, equalizer taps can be exchanged for windowing coefficients to reduce complexity during data transmission.

The 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 these signals, the ADSL allows the use of echo cancellation resulting in improved bit rates.

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. Index Terms--Asymmetric digital subscriber line (ADSL), discrete multitone (DMT), equalization, time-domain equalizer (TEQ).

An initialization scheme for the per tone equalization (PTEQ) is described and discussed.

In modern DSL systems, far-end crosstalk is a major source of performance degradation. Crosstalk cancelation schemes have been proposed to mitigate the effect of crosstalk. However, the complexity of crosstalk cancelation grows with the square of the number of lines in the binder. Fortunately, most of the crosstalk originates from a limited number of lines and, for DMT-based xDSL systems, on a limited number of tones. As a result, a fraction of the complexity of full crosstalk cancelation suffices to cancel most of the crosstalk. The challenge is then to determine which crosstalk to cancel on which tones, given a complexity constraint. This paper presents an algorithm based on a dual decomposition to optimally solve this problem. The proposed algorithm naturally incorporates rate constraints and the complexity of the algorithm compares favorably to a known resource allocation algorithm, where a multiuser extension is made to incorporate the rate constraints.

Discrete multitone (DMT) uses an inverse discrete Fourier transform (IDFT) to modulate data on the carriers. The high sidelobes of the IDFT filter bank used can lead to spurious emissions (egress) in unauthorized frequency bands. Applying a window function within the DMT symbol can alleviate this. However, window functions either require additional redundancy or will introduce distortions that are generally not easy to compensate for. In this paper, a special class of window functions is constructed that corresponds to a precoding at the transmitter. These do not require any additional redundancy and need only a modest amount of additional processing at the receiver. The results can be used to increase the spectral containment of DMT-based wired communications such as ADSL and VDSL (i.e., asymmetric, resp., very-high-bitrate digital subscriber loop).

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]

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]