[论文解读] Nonlinear Interference Alignment in a One-dimensional Space

Mohaned Chraiti, Ali Ghrayeb+1 more|arXiv (Cornell University)|Jun 20, 2016

Advanced Wireless Communication Techniques被引用 5

一句话总结

本文提出了一种新型非线性干扰对齐技术——干扰消解（Interference Dissolution, ID），该技术将一维信道划分为两个子空间，实现两个符号每时隙的传输，每个符号具有1/2的自由度。通过直接对齐信号向量而非信道响应，ID在所有信噪比（SNR）范围内均实现了接近容量的性能，证明在高斯信号调制下，总速率与容量的差距不超过1比特。

ABSTRACT

Real interference alignment is efficient in breaking-up a one-dimensional space over time-invariant channels into fractional dimensions. As such, multiple symbols can be simultaneously transmitted with fractional degrees-of-freedom (DoF). Of particular interest is when the one dimensional space is partitioned into two fractional dimensions. In such scenario, the interfering signals are confined to one sub-space and the intended signal is confined to the other sub-space. Existing real interference alignment schemes achieve near-capacity performance at high SNR for time-invariant channels. However, such techniques yield poor achievable rate at finite SNR, which is of interest from a practical point of view. In this paper, we propose a radically novel nonlinear interference alignment technique, which we refer to as Interference Dissolution (ID). ID allows to break-up a one-dimensional space into two fractional dimensions while achieving near-capacity performance for the entire SNR range. This is achieved by aligning signals by signals, as opposed to aligning signals by the channel. We introduce ID by considering a time-invariant MISO channel. This channel has a one-dimensional space and offers one DoF. We show that, by breaking-up the one dimensional space into two sub-spaces, ID achieves a rate of two symbols per channel use while providing $\frac{1}{2}$ DoF for each symbol. We analyze the performance of the proposed ID scheme in terms of the achievable rate and the symbol error rate. In characterizing the achievable rate of ID for the entire SNR range, we prove that, assuming Gaussian signals, the sum achievable rate is at most one bit away from the capacity. We present numerical examples to validate the theoretical analysis. We also compare the performance of ID in terms of the achievable rate performance to that of existing schemes and demonstrate ID's superiority.

研究动机与目标

• 解决传统实数干扰对齐在时不变一维信道中有限信噪比性能较差的问题。
• 克服传统方案下一维信道无法实现自由度分数共享的局限性。
• 开发一种非线性技术，使在一维空间中同时传输两个符号，每个符号具有1/2自由度。
• 在全信噪比范围内实现接近容量的性能，而不仅限于高信噪比区域。
• 设计最优译码器，并严格分析所提方案的可实现速率与符号误码率。

提出的方法

• 提出干扰消解（ID），一种将一维信道分解为两个子空间的非线性干扰对齐技术。
• 通过信号向量直接对齐信号，而非依赖信道系数，从而实现自由度的分数化。
• 采用具有1个自由度的MISO信道模型，证明可在同一时隙中同时传输两个符号，每个符号具有1/2自由度。
• 应用Khintchine-Groshev定理，推导信号点之间最小距离的下界，确保对干扰的鲁棒性。
• 基于信号空间结构与干扰对齐特性，设计最优译码器，确保最大似然性能。
• 采用高斯信号调制分析可实现速率，并证明在任意信噪比下，总速率与容量的差距不超过1比特。

实验结果

研究问题

• RQ1 在一维时不变MISO信道中，是否可利用非线性技术实现超过一个符号的分数自由度传输？
• RQ2 在有限信噪比下，基于信号级对齐的干扰对齐是否优于传统的基于信道响应的对齐方法？
• RQ3 非线性方案是否可在一维空间中实现全信噪比范围内的接近容量性能？
• RQ4 在高斯信号调制下，此类方案的可实现速率是否存在理论极限？
• RQ5 信号点之间的最小距离如何随系统参数变化？其对误码性能有何保证？

主要发现

• 所提出的干扰消解（ID）方案在一维MISO信道中实现了每时隙两个符号的总传输速率。
• 每个符号实现1/2自由度，使得在一维空间中实现高效的频谱复用。
• 在高斯信号调制下，证明总可实现速率与信道容量的差距不超过1比特，适用于任意信噪比。
• 信号点之间的最小距离按 $ \frac{h^2 A_s^2 \mathcal{K}^2}{Q_s^2} $ 规律缩放，确保对干扰的鲁棒性。
• 数值结果验证了理论分析，表明其可实现速率性能优于现有方案。
• 所提出的最优译码器实现了最大似然性能，证实了该方案的高效性与可靠性。