ZF和MMSE串扰消除器的大矩阵渐近分析 有线信道

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摘要翻译：
本文给出了具有线性译码器的多用户有线系统中用户吞吐量的渐近表达式。这种分析可以看作是对无线通信所得结果的推广。有线信道矩阵的对角元素的特性使得无线渐近分析不适用于有线系统。此外，直接应用随机矩阵理论(RMT)的结果得到了一个平凡的下界。本文提出了一种新的渐近分析方法，其中构造一个包含感兴趣系统的交替系统序列，以逼近线性迫零(ZF)和最小均方误差(MMSE)串扰消除器的频谱效率。利用大维随机矩阵领域的工作，我们证明了该序列中的用户速率收敛到一个非零速率。对于ZF和MMSE消除器，用户速率的近似值非常容易评估，并且不需要考虑特定的信道实现。分析揭示了吞吐量随发射功率和信道串扰的变化规律。对于其他系统中的线性解码器，还没有观察到这种独特的行为。对于下一代G.Fast有线系统，本文提出的近似比早期数字用户线(DSL)系统更有用，因为以前计算的性能界仅在低频处严格大于零。我们还对实测和模拟的DSL信道进行了数值性能分析，结果表明，即使对于相对低维的系统，这种近似也是准确的，并且对于实际DSL系统中的许多场景都是有用的。
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英文标题：
《Large Matrix Asymptotic Analysis of ZF and MMSE Crosstalk Cancelers for
  Wireline Channels》
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作者：
Itsik Bergel, S. M. Zafaruddin, Amir Leshem
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  We present asymptotic expressions for user throughput in a multi-user wireline system with a linear decoder, in increasingly large system sizes. This analysis can be seen as a generalization of results obtained for wireless communication. The features of the diagonal elements of the wireline channel matrices make wireless asymptotic analyses inapplicable for wireline systems. Further, direct application of results from random matrix theory (RMT) yields a trivial lower bound. This paper presents a novel approach to asymptotic analysis, where an alternative sequence of systems is constructed that includes the system of interest in order to approximate the spectral efficiency of the linear zero-forcing (ZF) and minimum mean squared error (MMSE) crosstalk cancelers. Using works in the field of large dimensional random matrices, we show that the user rate in this sequence converges to a non-zero rate. The approximation of the user rate for both the ZF and MMSE cancelers are very simple to evaluate and does not need to take specific channel realizations into account. The analysis reveals the intricate behavior of the throughput as a function of the transmission power and the channel crosstalk. This unique behavior has not been observed for linear decoders in other systems. The approximation presented here is much more useful for the next generation G.fast wireline system than earlier digital subscriber line (DSL) systems as previously computed performance bounds, which are strictly larger than zero only at low frequencies. We also provide a numerical performance analysis over measured and simulated DSL channels which show that the approximation is accurate even for relatively low dimensional systems and is useful for many scenarios in practical DSL systems.
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PDF链接：
https://arxiv.org/pdf/1803.06019

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关键词：MMS mse Applications Optimization Transmission 速率 矩阵 linear zero 序列