Gert Cuypers

Bitrate maximizing time-domain equalizer design for DMT-based systems

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.

Combined RLS-LMS initialization for per tone equalizers in DMT-receivers

In classical discrete multi tone receivers, the equalizer structure consists of a (real) time domain equalizer (TEQ) combined with (complex) 1-taps frequency domain equalizers. Recently, an alternative receiver was introduced based on a separate per tone equalization, where the SNR on each tone and hence the bitrate is maximized. In this paper, a new adaptive initialization scheme for this per tone equalizer (PTEQ) is introduced, based on a combination of Least Mean Squares (LMS) and Recursive Least Squares (RLS) with inverse updating. It will be shown that the proposed method exhibits only slightly slower convergence compared to full RLS with inverse updating, while complexity as well as memory cost are reduced considerably.

Combining per tone equalization and windowing in DMT receivers

A novel equalization technique for Discrete multitone (DMT) based modems is proposed which incorporates receiver windowing operations. The method is especially useful in an environment dominated by crosstalk and narrowband interference, such as digital subscriber line (DSL). The high sidelobe level of the DFT filters present in classical DMT receivers leads to considerable performance degradation due to intercarrier interference and broadband susceptibility to narrowband disturbers. Window functions can be used to alleviate this, but they are difficult to combine with equalization techniques, e.g. per tone equalization [1]. The presented method offers a way to do so without unduly increasing the complexity.

Combining raised cosine windowing and per tone equalization for RFI mitigation in DMT receivers

Discrete multitone (DMT) offers an elegant way to achieve high capacity, dividing the spectrum into small bands and processing these individually. The per tone equalizer (PTEQ) optimizes the capacity for each band individually, thus optimizing the whole. However, it provides little protection against narrow band radio frequency interference (RFI), being spread over all tones because of the high side lobes of the DFT filter band used in the receiver. The use of windowing functions limits this noise spreading, but is difficult to combine with the PTEQ. This paper describes a method to combine the PTEQ with a raised cosine window, while keeping the complexity reasonable. Extensions to other windowing functions are also given.

On time-domain and frequency-domain MMSE-based TEQ design for DMT transmission

We reconsider the minimum mean square error (MMSE) time-domain equalizer (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. 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 (FD) 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.

Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems

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-TEQ/BM-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.

Intra-symbol windowing for egress reduction in DMT transmitters

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).

Bitrate maximizing per group equalization for DMT-based systems

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.

Chebyshev interpolation for DMT modems

Sampling clock synchronization in discrete multitone systems, such as digital subscriber line modems can be done with a phase locked loop. This requires expensive analog hardware, such as a voltage controlled oscillator. However, it is possible to use a cheaper free-running oscillator and tackle the problem in the digital domain. Using resampling or interpolation, the timing correction becomes transparent for subsequent equalizers. This article describes a novel resampling technique using Chebyshev polynomials.

Echo cancellation for discrete multitone frame-asynchronous ADSL transceivers

In the past, several papers have reported on echo canceller (EC) structures developed for discrete multitone transmission (DMT) based asymmetric digital subscriber lines (ADSL) transmission. The most commonly known scheme, developed by Ho, Cioffi and Bingham, is based on canceling the received echo noise efficiently in times as well as in the frequency domain. The time domain processing part, which is commonly called cyclic echo synthesis (CES), can be minimized by choosing the optimal temporal alignment between the echo transmitter and the EC in the modem. This paper improves previously published work by minimizing the CES complexity without choosing a specific temporal alignment. Moreover, the obtained structure is highly suitable for making the update process of the echo canceller coefficients independent of the far end signal, leading to improved convergence behavior.