[论文解读] Jamming in Fixed-Rate Wireless Systems with Power Constraints - Part II: Parallel Slow Fading Channels

George T. Amariucai, Shuangqing Wei+1 more|ArXiv.org|Aug 26, 2008

Advanced MIMO Systems Optimization参考文献 13被引用 11

一句话总结

本文研究了在短时和长时功率约束下，固定速率、多载波无线系统在并行慢衰落信道（如OFDM）中的最优干扰与抗干扰策略。将问题建模为零和博弈，利用混合策略推导出纳什均衡，并表明信道状态信息（CSI）反馈可显著降低中断概率，尤其在中等信噪比（SNR）区域，此时高SNR近似失效。

ABSTRACT

This is the second part of a two-part paper that studies the problem of jamming in a fixed-rate transmission system with fading. In the first part, we studied the scenario with a fast fading channel, and found Nash equilibria of mixed strategies for short term power constraints, and for average power constraints with and without channel state information (CSI) feedback. We also solved the equally important maximin and minimax problems with pure strategies. Whenever we dealt with average power constraints, we decomposed the problem into two levels of power control, which we solved individually. In this second part of the paper, we study the scenario with a parallel, slow fading channel, which usually models multi-carrier transmissions, such as OFDM. Although the framework is similar as the one in Part I \cite{myself3}, dealing with the slow fading requires more intricate techniques. Unlike in the fast fading scenario, where the frames supporting the transmission of the codewords were equivalent and completely characterized by the channel statistics, in our present scenario the frames are unique, and characterized by a specific set of channel realizations. This leads to more involved inter-frame power allocation strategies, and in some cases even to the need for a third level of power control. We also show that for parallel slow fading channels, the CSI feedback helps in the battle against jamming, as evidenced by the significant degradation to system performance when CSI is not sent back. We expect this degradation to decrease as the number of parallel channels $M$ increases, until it becomes marginal for $M o \infty$ (which can be considered as the case in Part I).

研究动机与目标

• 对固定速率、多载波无线系统中的最优干扰与抗干扰问题进行建模与求解，信道为慢衰落。
• 解决慢衰落中帧间功率分配的挑战，其中每帧由其特有的信道实现表征，与快衰落不同。
• 分析信道状态信息（CSI）反馈对系统性能的影响，特别是其在干扰环境下降低中断概率的作用。
• 将第一部分（快衰落）的框架扩展至并行慢衰落信道，某些情况下引入第三级功率控制。
• 在有无CSI反馈的情况下，推导出在短时和长时功率约束下混合策略的纳什均衡。

提出的方法

• 将系统建模为在M个并行子信道上，发射机与干扰者之间的零和博弈，每个子信道经历独立的慢衰落。
• 使用每个子信道的瞬时互信息：$ I(h_m, P_m, J_m) = \log\left(1 + \frac{h_m P_m}{J_m + \sigma_N^2}\right) $，其中$ h_m $为信道增益。
• 定义帧级平均功率约束：$ P_M = \frac{1}{M}\sum P_m $，$ J_M = \frac{1}{M}\sum J_m $，以及帧级互信息$ I_M = \frac{1}{M}\sum I(h_m, P_m, J_m) $。
• 应用KKT条件求解长时约束下的最优功率分配策略，将问题视为极小化极大博弈。
• 由于慢衰落中帧特定信道实现的唯一性，某些情况下引入三级功率控制结构。
• 使用博弈论分析证明，KKT条件的解构成纳什均衡，且在单边偏离下具有稳定性。

实验结果

研究问题

• RQ1 与快衰落信道相比，最优干扰与抗干扰策略在并行慢衰落信道中如何不同？
• RQ2 在受干扰的固定速率、多载波系统中，CSI反馈对中断概率有何影响？
• RQ3 由于帧特定信道实现的存在，慢衰落中帧间功率分配的结构有何不同？
• RQ4 能否在本慢衰落模型中，为短时和长时功率约束下的混合策略推导出纳什均衡？
• RQ5 当干扰者无法获取CSI时，中断概率如何变化？这种性能退化如何随子信道数M变化？

主要发现

• CSI反馈在慢衰落、多载波系统中显著降低了中断概率，且因缺乏反馈导致的性能退化随子信道数M增加而减小。
• 当M较大时，有与无CSI反馈系统的性能差距趋于微小，趋近于第一部分中快衰落情况下的行为。
• 极小化极大问题的KKT条件解构成纳什均衡，证明了所推导功率分配策略的最优性。
• 当干扰者的功率低于发射机功率约束允许的最大值时，即使发射机不完全知晓干扰者功率上限，其策略仍为最优。
• 类似地，若发射机功率低于干扰者约束允许的最大值，干扰者的策略仍为最优，证实了贝叶斯均衡的鲁棒性。
• 在所推导策略下，中断概率被最小化，最优功率分配依赖于特定的信道实现向量$ \mathbf{h} $，且在凸性与拟凹性假设下解唯一。