Per-Tone Precoding and Per-Tone Equalization for OFDM and DMT Transmission Systems: Duality, Filter Optimization, and Resource Allocation

Verdyck, Jeroen; Lefevre, Yannick; Tsiaflakis, Paschalis; Moonen, Marc

doi:10.1109/ojsp.2020.3035060

Cited by 3 publications

(12 citation statements)

References 37 publications

(78 reference statements)

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“…Finally, in Section VI, LR G.fast DSL simulation results will demonstrate that explicitly taking signal impropriety into account leads to an increased achievable bit loading when residual ISI/ICI is present in the system. When the employed channel shortening method is able to eliminate most of the ISI/ICI, the impact of impropriety is reduced and the gap between the state-of-the-art SINR and bit loading expressions from [8]- [18] and the newly developed expressions disappears.…”

Section: Contributions and Outlinementioning

confidence: 99%

“…This section introduces a general model for DMT systems with per-tone equalization (PTEQ), and presents expressions for the achieved SINR and achievable bit loading as they are commonly found in literature [14]- [18]. 3 Fig.…”

Section: Dmt System Model and Per-tone Equalizationmentioning

confidence: 99%

“…Equivalent SINR expressions have been used for the design and/or performance evaluation of DMT systems in, among others, [14]- [18]. Despite this widespread adoption of the SINR expression as in (15), however, it seems ill-advised to model the ICI coming from subcarrier n * as uncorrelated noise on subcarrier n. While the considered interfering signalwhich is given as X * n [k] due to (6) -is indeed uncorrelated with X n [k], it is not independent of X n [k] and will cause a loss of orthogonality and difference in scaling between the real and imaginary parts of X n [k] inX n [k] rather than contributing to the total interference-plus-noise.…”

Section: Signal-to-interference-plus-noise Ratiomentioning

confidence: 99%

“…When channel shortening performance is analyzed in the context of DMT systems [8]- [18], there is a particular aspect that is often overlooked: if the CP is too short, then the received signal after DMT demodulation (prior to a soft/hard decision operation) is generally improper [19], [20]. A zero-mean complex random variable Z is proper if its pseudovariance vanishes [21] -i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Even though signal impropriety seems to be inherent to DMT systems with a too-short CP using either TEQ or PTEQ, its effects are not taken into account in [8]- [18]. As a result, the state-of-the-art signal-to-interference-plus-noise ratio (SINR) and bit loading expressions employed to assess system performance in these works -which implicitly assume that the received signal after DMT demodulation is propermis-represent the true achievable performance.…”

Section: Introductionmentioning

confidence: 99%

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Signal Impropriety in Discrete Multi-Tone Systems and Widely Linear Per-Tone Equalization

Verdyck

Lefevre

Tsiaflakis

et al. 2021

IEEE Open J. Commun. Soc.

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In the context of digital subscriber line (DSL) systems, where the long-reach (LR) extension of G.fast has recently been proposed, interest in techniques dealing with long channel impulse responses (CIRs) without increasing the cyclic prefix (CP) length of the discrete multi-tone (DMT) modulation has recently resurfaced. The technique under consideration in this paper is referred to as channel shortening, and applies FIR filters to the received signal to shorten the apparent CIR. Time-domain equalization (TEQ) as well optimal per-tone equalization (PTEQ) FIR filters will be considered. When channel shortening techniques are analyzed, it is often overlooked that the received signals after DMT demodulation are generally improper when the CP is too short. Hence, the state-of-the-art signal-to-interference-plus-noise ratio (SINR) and bit loading expressions employed to assess system performance, which implicitly assume the received signals to be proper, misrepresent the true achievable performance. New expressions for the SINR and bit loading are therefore presented that explicitly take signal impropriety into account. Based on these expressions, it is then observed that-if the received signals are improper-the PTEQ FIR filters are no longer optimal, and that the achievable bit loading depends on a particular phase shift experienced by the transmitted signals. This paper therefore introduces a novel widely linear PTEQ-which is again optimal when the received signals are improperand additionally proposes to optimally rotate signals in the complex plane prior to transmission. Finally, this paper assesses the performance increase obtainable by explicitly accounting for signal impropriety.

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Section: Contributions and Outlinementioning

confidence: 99%

Section: Dmt System Model and Per-tone Equalizationmentioning

confidence: 99%

Section: Signal-to-interference-plus-noise Ratiomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Signal Impropriety in Discrete Multi-Tone Systems and Widely Linear Per-Tone Equalization

Verdyck

Lefevre

Tsiaflakis

et al. 2021

IEEE Open J. Commun. Soc.

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MIMO Per-Tone Equalizer Design for Long Reach xDSL

Sharma

Verdyck

Lefevre

et al. 2022

IEEE Open J. Commun. Soc.

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Recently, long reach x-digital subscriber line (LR-xDSL) has been proposed to extend the reach of conventional DSL systems. The extended loop lengths are characterized by a longer channel impulse response (CIR), which requires a similarly longer cyclic prefix (CP) to successfully eliminate the inter-symbol interference (ISI) between successive time-domain discrete multi-tone (DMT) symbols and inter-carrier interference (ICI) between the carriers or tones of the same DMT symbol. This adds a large overhead to the transmitted symbols and results in throughput loss. A per-tone equalizer (PTEQ) is an attractive alternative to deal with extended loop lengths. However, it imposes a large initialization computational complexity and memory requirement, hindering the use of a PTEQ in practical multiple-input multiple-output (MIMO) scenarios. To tackle this problem, a specific structure in the MIMO DSL channel, namely that the combined ISI and ICI signal power from the crosstalk channels is significantly lower than the desired and combined ISI and ICI signal power from the direct channels, may be exploited in deriving a novel low complexity/memory solution, here referred as sparse MIMO PTEQ, with negligible impact (≈ 0.5% drop) on performance compared to a full MIMO PTEQ. For a conventional DSL binder size of 16 lines and a PTEQ order of 3, the proposed sparse MIMO PTEQ performs at 42% of the initialization computational complexity and 29.7% of the memory requirement, with negligible performance degradation, compared to a full MIMO PTEQ. The initialization computational complexity and memory requirement is further reduced by the proposed diagonal MIMO PTEQ which operates at 0.4% of the initialization computational complexity of a full MIMO PTEQ and requires 6.25% memory compared to a full MIMO PTEQ, with some degradation in the performance compared to the full MIMO PTEQ. The diagonal MIMO PTEQ has the additional benefit that it can be applied in both upstream and downstream scenarios, in contrast to the full and sparse MIMO PTEQ which can be used only in upstream scenarios.

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