Abstract
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 article 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 article therefore introduces a novel widely linear PTEQ - which is again optimal when the received signals are improper - and additionally proposes to optimally rotate signals in the complex plane prior to transmission. Finally, this article assesses the performance increase obtainable by explicitly accounting for signal impropriety.
Highlights
G .FAST is a digital subscriber line (DSL) standard [1], [2] for discrete multi-tone (DMT)based transmission over short local loops
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 signal-to-interference-plus-noise ratio (SINR) and bit loading expressions from [8]–[18] and the newly developed expressions disappears
It can be concluded that, when the employed channel shortening technique is able to eliminate most of the ISI/ICI, the impact of impropriety is reduced and the gap between the legacy SINR and bit loading expressions from [8]–[18] and the newly developed expressions disappears
Summary
G .FAST is a digital subscriber line (DSL) standard [1], [2] for discrete multi-tone (DMT)based transmission over short local loops. It can be concluded that, even if a channel shortening (P)TEQ filter is able to eliminate all ISI/ICI, improper noise can still be present in the received signal after DMT demodulation. The first objective is to present expressions for the SINR and bit loading that explicitly take all signal impropriety into account, — i.e., the impropriety of the ISI/ICI and of the noise These expressions will be instrumental in assessing the performance of channel shortening methods in LR G.fast systems. The second objective is to use these new SINR and bit loading expressions for PTEQ filter design, and to assess the performance increase that can be obtained in LR G.fast systems by explicitly accounting for signal impropriety. DMT SYSTEM MODEL & PER-TONE EQUALIZATION 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
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