Tone Equalization Research Articles

Tone-Independent Orthogonalizing Lattice Equalization for Insufficient Cyclic-Prefix OFDM Transmissions

Tone-independent orthogonalizing lattice per tone equalizer (TOL-PTEQ) is introduced and its convergence is analyzed. Cyclic-prefix redundancy, one of the major drawbacks of orthogonal frequency division multiplexing (OFDM), can be reduced by TOL-PTEQ. Fast convergence and low computational complexity of TOL-PTEQ are also suitable properties for packet-based wireless communications and detections in which OFDM is widely deployed for their modulation technique.

Performance Analysis of SVM-Type Per Tone Equalizer Using Blind and Radius Directed Algorithms for OFDM Systems

In this paper, we present Support Vector Machine (SVM)-based blind per tone equalization for OFDM systems. Blind per tone equalization using Constant Modulus Algorithm (CMA) and Multi-Modulus Algorithm (MMA) are used as the comparison benchmark. The SVM-based cost function utilizes a CMA-like error function and the solution is obtained by means of an Iterative Re-Weighted Least Squares Algorithm (IRWLS). Moreover, like CMA, the error function allows to extend the method to multilevel modulations. In this case, a dual mode algorithm is proposed. Dual mode equalization techniques are commonly used in communication systems working with multilevel signals. Practical blind algorithms for multilevel modulation are able to open the eye of the constellation, but they usually exhibit a high residual error. In a dual mode scheme, once the eye is opened by the blind algorithm, the system switches to another algorithm, which is able to obtain a lower residual error under a suitable initial ISI level. Simulation experiments show that the performance of blind per tone equalization using support vector machine has better than blind per tone equalization using CMA and MMA, from viewpoint of average Bit-Error Rate (BER).

Blind per tone equalization of multilevel signals using support vector machines for OFDM in wireless communication

We present an efficient support vector machine (SVM)-based blind per tone equalization for OFDM systems. Blind per tone equalization using constant modulus algorithm (CMA) and multi-modulus algorithm (MMA) are used as the comparison benchmark. The SVM-based cost function utilizes a CMA-like error function and the solution is obtained by means of an iterative re-weighted least squares algorithm (IRWLS). Moreover, like CMA, the error function allows to extend the method to multilevel modulations. In terms of bit error rate (BER), simulation experiments show that the blind per tone equalization using SVM performs better than blind per tone equalization using CMA and MMA.

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.

Linear and decision-feedback per tone equalization for DMT-based transmission over IIR channels

The per-tone equalizer (PTEQ) has been presented as an attractive alternative for the classical time-domain equalizer (TEQ) in discrete multitone (DMT) based systems, such as ADSL systems. The PTEQ is based on a linear minimum mean-square-error (L-MMSE) equalizer design for each separate tone. In this paper, we reconsider DMT modulation and equalization in the ADSL context under the realistic assumption of an infinite impulse response (IIR) model for the wireline channel. First, optimum linear zero-forcing (L-ZF) block equalizers for arbitrary IIR model orders and cyclic prefix (CP) lengths are developed. It is shown that these L-ZF block equalizers can be decoupled per tone, hence they lead to an L-ZF PTEQ. Then, based on the L-ZF PTEQ, low-complexity L-MMSE PTEQ extensions are developed: the linear PTEQ extension exploits frequency-domain transmit redundancy from pilot and unused tones; alternatively, a closely related decision-feedback PTEQ extension can be applied. The PTEQ extensions then add flexibility to a DMT-based system design: the CP overhead can be reduced by exploiting frequency-domain transmit redundancy instead, so that a similar bitrate as with the original PTEQ is achieved at a lower memory and computational cost or, alternatively, a higher bitrate is achieved without a considerable cost increase. Both PTEQ extensions are also shown to improve the receiver's robustness to narrow-band interference.

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.

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.

Combination of per tone equalization and windowing in DMT-receivers

High speed digital subscriber line (DSL) systems transmit signals that overlap in spectrum with the bands used for radio communications. AM broadcast stations and radio amateur transmitters result into electromagnetic interference impairing the DSL-receiver. For discrete multitone systems, windowing, in combination with radio frequency interference (RFI) cancellation has been proposed to make DSL-transceivers robust to radio ingress. This paper shows how windowing has an equivalent implementation by means of the so-called per tone equalization (Van Acker et al., IEEE Trans. Commun. 49(1) (2001) 109; Proceedings of IEEE Global Telecommunications Conference, Globecom, December 1999, p. 2311). Attractive to the per tone equalizer structure is that the equalizer can be optimized on a per carrier basis to reduce susceptibility to RFI for each tone separately.

Per tone equalization for DMT-based systems

An alternative receiver structure is presented for discrete multitone-based systems. The usual structure consisting of a (real) time-domain equalizer in combination with a (complex) 1-tap frequency-domain equalizer (FEQ) per tone, is modified into a structure with a (complex) multitap FEQ per tone. By solving a minimum mean-square-error problem, the signal-to-noise ratio is maximized for each individual tone. The result is a larger bit rate while complexity during data transmission is kept at the same level. Moreover, the per tone equalization is shown to have a reduced sensitivity to the synchronization delay.