Geert Ysebaert

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

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.

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.

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 and hence overcome the need for a too long cyclic prefix. Many algorithms have been developed to initialize this TEQ, but none of them really optimizes the bitrate. In this paper, we present a new bitrate maximizing TEQ (BM-TEQ), cost function that results in a TEQ design/initialization that outperforms any other TEQ design. In the derivation, we exploit the fact that the frequency-domain equalizers (FEQ) do not alter the SNR on the individual tones. The performance of this BM-TEQ comes close to the performance of the per-tone equalizer (PTEQ), an alternative DMT equalization structure that ensures consistently better performance than a TEQ. Finally, the presented BM-TEQ design is also used in a per group equalization scheme (PGEQ), which is intermediate (in terms of memory requirement and performance) between TEQ and PTEQ. The PGEQ design then encompasses BM-TEQ and PTEQ design procedures as extreme cases.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.

Implementation Complexity and Communication Performance Tradeoffs in Discrete Multitone Modulation Equalizers

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

Bit Error Rate Minimizing Channel Shortening Equalizers for Cyclic Prefixed Systems

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

Constraints in channel shortening equalizer design for DMT-based systems

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.

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.

Echo cancellation in DMT-receivers: circulant decomposition canceler

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 al., 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.

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.