Per-tone Equalization Research Articles

Turbo-per-Tone Equalization for ADSL Systems

We study the equalization procedure in discrete multitone (DMT)-based systems, in particular, in DMT-based ADSL systems. Traditionally, equalization is performed in the time domain by means of a channel shortening filter. Shifting the equalization operations to the frequency domain, as is done in per-tone equalization, increases the achieved bitrate by 5–10%. We show that the application of the turbo principle to per-tone equalization can provide significant additional gains. In the proposed receiver structure, referred to as a "turbo-per-tone equalization" structure, equalization and decoding are performed in an iterative fashion. Equalization is done by means of a linear minimum mean squared error (MMSE) equalizer, using a priori information. We give a description of an efficient implementation of such an equalizer in the per-tone structure. Simulations show that we obtain a bitrate increase of 12–16% compared to the original per-tone equalization-based receiver structure.

Combined per tone equalization and receiver windowing in DSL receivers: WiPTEQ

In this report, a novel technique is described for the combination of per-tone equalization (PTEQ) with receiver windowing. The PTEQ is an equalization technique for discrete multitone modulation (DMT) based modems, such as asymmetric digital subscriber line (ADSL) modems and very high bitrate digital subscriber line (VDSL) modems, optimizing the SNR (and thus capacity) of each carrier separately. Windowing functions are very useful in multitone communications systems, to prevent a narrow band noise source from causing wide band interference. Combining both techniques in a windowed PTEQ (referred to as WiPTEQ) leads to a robust communication system. The described technique is especially useful in case of a trapezoidal or raised cosine window, and when the window taper length is large compared to the number of equalizer filter taps.

Joint window and time domain equalizer design for bit rate maximization in DMT-receivers

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. 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 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.

Split SR-RLS for the Joint Initialization of the Per-Tone Equalizers and Per-Tone Echo Cancelers in DMT-Based Receivers

In asymmetric digital subscriber lines (ADSL), the available bandwidth is divided in subcarriers or tones which are assigned to the upstream and/or downstream transmission direction. To allow efficient bidirectional communication over one twisted pair, echo cancellation is required to separate upstream and downstream channels. In addition, intersymbol interference and intercarrier interference have to be reduced by means of equalization. In this paper, a computationally efficient algorithm for adaptively initializing the per-tone equalizers (PTEQ) and per-tone echo cancelers (PTEC) is presented. For a given number of equalizer and echo canceler taps per-tone, it was shown that the joint PTEQ/PTEC receiver structure is able to maximize the signal-to-noise ratio (SNR) on each subcarrier and hence also the achievable bit rate. The proposed initialization scheme is based on a modification of the square root recursive least squares (SR-RLS) algorithm to reduce computational complexity and memory requirement compared to full SR-RLS, while keeping the convergence rate acceptably fast. Our performance analysis will show that the proposed method converges in the mean and an upper bound for the step size is given. Moreover, we will indicate how the presented initialization method can be reused in several other ADSL applications.

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.

Time-domain and frequency-domain per-tone equalization for OFDM over doubly selective channels

In this paper, we propose new time- and frequency-domain per-tone equalization techniques for orthogonal frequency division multiplexing (OFDM) transmission over time- and frequency-selective channels. We present one mixed time- and frequency-domain equalizer (MTFEQ) and one frequency-domain per-tone equalizer. The MTFEQ consists of a one-tap time-varying (TV) time-domain equalizer (TEQ), which converts the doubly selective channel into a purely frequency-selective channel, followed by a one-tap frequency-domain equalizer (FEQ), which then equalizes the resulting frequency-selective channel in the frequency-domain. The frequency-domain per-tone equalizer (PTEQ) is then obtained by transferring the TEQ operation to the frequency-domain. While the one-tap TEQ of the MTFEQ optimizes the performance on all subcarriers in a joint fashion, the PTEQ optimizes the performance on each subcarrier separately. This results into a significant performance improvement of the PTEQ over the MTFEQ, at the cost of a slight increase in complexity. Through computer simulations we show that the MTFEQ suffers from an early and high error floor, while the PTEQ outperforms the MMSE equalizer for OFDM over purely frequency-selective channels, it can approach the performance of the block MMSE equalizer. An important feature of the proposed techniques is that no bandwidth expansion or redundancy insertion is required except for the cyclic prefix.

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.

Per-tone equalization for mimo ofdm systems

This paper focuses on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with channel order larger than the cyclic prefix (CP) length. Writing the demodulating fast Fourier transform (FFT) as a sliding FFT followed by a downsampling operation, we show in this paper that by swapping the filtering operations of the MIMO channel and the sliding FFT, the data model for the temporally smoothened received signal of each individual tone of the MIMO OFDM system is very similar to the data model for the temporally smoothened received signal of a MIMO single-carrier (SC) system. As a result, to recover the data symbol vectors, the conventional equalization approach for MIMO SC systems can be applied to each individual tone of the MIMO OFDM system. This so-called per-tone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative to the recently developed time-domain equalization (TEQ) approach for MIMO OFDM systems. In the second part of this paper, we focus on direct per-tone equalizer design and adapt an existing semi-blind equalizer design method for space-time block coding (STBC) SC systems to the corresponding semi-blind per-tone equalizer design method for STBC OFDM systems.

Per-tone echo cancellation for DMT-based systems

A new echo cancellation structure for discrete multitone systems is presented, where each used tone has its own per-tone echo canceller in addition to a per-tone equalizer, which provides an alternative to currently employed time domain and time/frequency domain approaches. The per-tone approach enables us to optimize the signal-to-noise ratio for each tone separately by solving a minimum mean-square error problem for each tone, with implicit so-called joint shortening. Complexity during data transmission is compared for time domain, time/frequency domain, and per-tone echo cancellation. Structures with reduced complexity are derived for an interpolated and a decimated rate setup. Finally, simulation results for an asymmetric digital subscriber line setting demonstrate improved performance over time domain (or time/frequency domain) echo cancellation.

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

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 is 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.

RLS-based initialization for per-tone equalizers in DMT receivers

Per-tone equalization has recently been proposed as an alternative receiver structure for discrete multitone-based systems improving upon the well-known structure based on time-domain equalization. Fast initialization of all the equalizer coefficients has been identified as an open problem. In this letter, a recursive initialization scheme based on recursive least squares with inverse updating is presented for the per-tone equalizers. Simulation results show convergence with an acceptably small number of training symbols. Complexity calculations are made for per-tone equalization and for the case where tones are grouped. It is demonstrated with an example that in the latter case, initialization complexity becomes sufficiently low and comparable to complexity during data transmission.

Sonics and ultrasonics : Ranging and data transmission using digital encoded fm-‘chirp’ surface acoustic wave filters Burnsweig, J., Wooldridge, J. SU-20 (April 1973) 190–197

In this report, a novel technique is described for the combination of per-tone equalization (PTEQ) with receiver windowing. The PTEQ is an equalization technique for discrete multitone modulation (DMT) based modems, such as asymmetric digital subscriber line (ADSL) modems and very high bitrate digital subscriber line (VDSL) modems, optimizing the SNR (and thus capacity) of each carrier separately. Windowing functions are very useful in multitone communications systems, to prevent a narrow band noise source from causing wide band interference. Combining both techniques in a windowed PTEQ (referred to as WiPTEQ) leads to a robust communication system. The described technique is especially useful in case of a trapezoidal or raised cosine window, and when the window taper length is large compared to the number of equalizer filter taps.

Adaptive Forgetting-factor RLS-based Initialisation Per-tone Equalisation in Discrete Multitone Systems

An adaptive forgetting-factor inverse square-root recursive least squares (AF-iQRRLS) with inverse of correlation matrix updating is presented for per-tone equalisation in discrete multitone-based systems. The proposed inverse covariance update of the square-root covariance Kalman filter is introduced to prepare for the signal flow graph (SFG). This reduced derivation of adaptive inverse square-root recursive least squares algorithm can modify via SFG. In order to reduce the computational complexity, the forgetting-factor parameter for each group called per-group forgettingfactor (PGFF) approach based on AF-iQRRLS algorithm is introduced. The forgetting-factor from the middle of each group is selected as a representative in order to find an optimal forgetting-factor parameter by using AF-iQRRLS algorithm. After convergence, it is fixed for remaining tones of whole group. Simulation results reveal that the trajectories of modified PGFF of the proposed algorithm for each individual tone can converge to their own equilibria. Moreover, the performance of the proposed algorithms are improved as compared with the existing algorithm.