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.

中文翻译：

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离散多音系统中的信号不当和宽线性每音均衡

在最近提出了G.fast的长距离（LR）扩展的数字用户线（DSL）系统的背景下，人们对不增加循环前缀（CP）而处理长信道脉冲响应（CIR）的技术产生了兴趣离散多音调（DMT）调制的长度最近已经浮出水面。本文中考虑的技术称为通道缩短 ，并对接收到的信号应用FIR滤波器以缩短视在CIR。将考虑时域均衡（TEQ）以及最佳单音均衡（PTEQ）FIR滤波器。在分析信道缩短技术时，通常会忽略通常在DMT解调后接收到的信号不当当CP太短时。因此，用于评估系统性能的最新信号干扰加噪声比（SINR）和位负载表达式隐式地假设接收的信号是正确的，但它却错误地代表了可实现的真实性能。因此，提出了SINR和比特加载的新表达式，这些表达式明确考虑了信号的不当性。根据这些表达式，可以观察到-如果接收的信号不正确-PTEQ FIR滤波器将不再是最佳的，并且可实现的位负载取决于发射信号所经历的特定相移。因此，本文介绍了一种新颖的宽线性PTEQ（在接收信号不正确时再次达到最佳状态），并建议在传输之前在复平面中优化旋转信号。最后，本文评估了通过明确考虑信号不当所获得的性能提升。