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arXiv 2501.06178eess.SP
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基于字符多项式码的有限反馈MIMO系统预编码设计

Precoding Design for Limited-Feedback MIMO Systems via Character-Polynomial Codes

Northeastern University(东北大学);University of California San Diego(加州大学圣地亚哥分校)

Siva Aditya Gooty, Samin Riasat, Hessam Mahdavifar, Robert W. Heath

AI总结:

本文提出基于字符多项式码的预编码设计,通过调整码率实现反馈位数与波束成形增益的平衡,并在不同衰落模型下验证了其有效性。

摘要:

我们考虑了在有限反馈条件下多输入多输出(MIMO)通信的问题,其中发射端依赖于与信道状态信息(CSI)相关的有限位数,这些信息在接收端(CSIR)可用,但在发射端(无CSIT)不可用,并通过反馈链路发送。我们展示了如何利用字符多项式(CP)码,一种模拟子空间码(也称为格拉斯曼码),用于格拉斯曼空间中的相应量化问题。所提出的基于CP码簿的预编码设计通过简单调整底层CP码的速率,实现了反馈位数与波束成形增益之间的平滑权衡。我们为多输入单输出(MISO)通信系统提出了CP码簿的均方量化误差的理论上界,并利用它来对具有完美CSIT的相应失真进行上界估计。我们证明失真在渐近情况下趋于零。我们计算了MIMO系统中两个接收天线的EGT基线增益,并观察到CP增益接近MIMO系统的EGT增益。结果还通过不同类型的衰落模型在MISO和MIMO系统中进行模拟验证。

英文摘要:

This paper presents a precoding codebook design for limited-feedback multiple-input multiple-output (MIMO) systems under the equal-gain transmission (EGT) constraint. In particular, we demonstrate that character--polynomial (CP) codes provide a structured solution that achieves constant-envelope transmission, low storage complexity, and Grassmannian packing without dependence on array geometry or channel statistics. In contrast to geometry-dependent discrete Fourier transform (DFT) codebooks used in current 5G systems and unstructured Grassmannian codebooks with high storage complexity, CP codebooks combine practical implementation advantages with near-optimal packing performance. For multiple-input single-output (MISO) systems, we derive an upper bound on the mean squared quantization error and show that the distortion relative to the EGT baseline vanishes asymptotically as the number of transmit antennas increases and the code rate approaches one. For MIMO systems with two receive antennas, we develop an iterative method to establish the EGT baseline. Simulation results under Rayleigh, correlated, and clustered delay line (CDL) channel models show that CP codebooks approach the EGT baseline across all channel conditions while outperforming phase shift keying (PSK) and 5G DFT codebooks in several operating regimes, and, in the Rayleigh fading case, incur negligible packing loss relative to numerically optimized Grassmannian codebooks obtained via the alternating projection (AP) method.

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