[论文解读] Channel Estimation via Gradient Pursuit for MmWave Massive MIMO Systems with One-Bit ADCs

In-Soo Kim, Junil Choi|arXiv (Cornell University)|Dec 18, 2019

Millimeter-Wave Propagation and Modeling参考文献 50被引用 15

一句话总结

该论文针对使用一比特ADC的毫米波大规模MIMO系统，提出了BMSGraSP与BMSGraHTP算法，采用带最大选择（BMS）硬阈值技术，提升对病态感测矩阵的鲁棒性。所提方法在精度与效率方面优于现有方法，通过基于FFT的加速实现低复杂度下的近最优性能。

ABSTRACT

In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, one-bit analog-to-digital converters (ADCs) are employed to reduce the impractically high power consumption, which is incurred by the wide bandwidth and large arrays. In practice, the mmWave band consists of a small number of paths, thereby rendering sparse virtual channels. Then, the resulting maximum a posteriori (MAP) channel estimation problem is a sparsity-constrained optimization problem, which is NP-hard to solve. In this paper, iterative approximate MAP channel estimators for mmWave massive MIMO systems with one-bit ADCs are proposed, which are based on the gradient support pursuit (GraSP) and gradient hard thresholding pursuit (GraHTP) algorithms. The GraSP and GraHTP algorithms iteratively pursue the gradient of the objective function to approximately optimize convex objective functions with sparsity constraints, which are the generalizations of the compressive sampling matching pursuit (CoSaMP) and hard thresholding pursuit (HTP) algorithms, respectively, in compressive sensing (CS). However, the performance of the GraSP and GraHTP algorithms is not guaranteed when the objective function is ill-conditioned, which may be incurred by the highly coherent sensing matrix. In this paper, the band maximum selecting (BMS) hard thresholding technique is proposed to modify the GraSP and GraHTP algorithms, namely the BMSGraSP and BMSGraHTP algorithms, respectively. The BMSGraSP and BMSGraHTP algorithms pursue the gradient of the objective function based on the band maximum criterion instead of the naive hard thresholding. In addition, a fast Fourier transform-based (FFT-based) fast implementation is developed to reduce the complexity. The BMSGraSP and BMSGraHTP algorithms are shown to be both accurate and efficient, whose performance is verified through extensive simulations.

研究动机与目标

• 解决由于量化粗糙和动态范围高导致的一比特ADC在毫米波大规模MIMO系统中通道估计不准确的问题。
• 克服因毫米波信道高相干性导致感测矩阵病态时GraSP与GraHTP算法性能崩溃的问题。
• 设计一种鲁棒的迭代近似MAP估计器，利用信道稀疏性，在一比特量化下提升收敛性与估计精度。
• 通过基于FFT的快速实现降低计算复杂度，同时保持高估计精度。
• 证明所提算法在估计精度与计算效率方面均优于现有最先进方法。

提出的方法

• 提出带最大选择（BMS）硬阈值技术，替代GraSP与GraHTP中的朴素硬阈值，提升对病态感测矩阵的鲁棒性。
• 将BMS集成至GraSP与GraHTP框架中，构建BMSGraSP与BMSGraHTP算法，通过基于带最大准则选择索引，迭代优化信道估计。
• 将MAP信道估计问题建模为稀疏性约束优化问题，利用毫米波虚拟信道的稀疏特性。
• 开发目标函数与梯度计算的基于FFT的快速实现，将复杂度从O(M⁴)降低至O(M² log M)。
• 利用Bussgang分解建模一比特ADC，并推导MAP估计框架下的似然函数。
• 应用带支持恢复与阈值的迭代梯度追踪，近似满足稀疏性约束下的最大后验估计。

实验结果

研究问题

• RQ1 能否使GraSP与GraHTP算法在使用一比特ADC的毫米波大规模MIMO系统中对病态感测矩阵具有鲁棒性？
• RQ2 与标准硬阈值相比，所提出的BMS硬阈值技术是否能提升梯度追踪算法的估计精度？
• RQ3 BMS-based算法是否能在一比特ADC系统中实现高精度的同时保持低计算复杂度？
• RQ4 BMSGraSP与BMSGraHTP算法在NMSE与可实现速率方面与现有估计器（如BG-GAMP与FISTA）相比表现如何？
• RQ5 基于FFT的快速实现能在多大程度上降低计算复杂度而不牺牲估计精度？

主要发现

• BMSGraSP与BMSGraHTP算法的NMSE显著低于BG-GAMP与FISTA，尤其在中高信噪比（SNR）区域。
• BMS-based算法优于FISTA，因其基于真实MAP估计，而FISTA假设拉普拉斯先验，与实际信道分布不匹配。
• BG-GAMP算法性能较差，源于Bussgang分解模型不匹配，尤其在BRX与BTX较大时，且在高相干性条件下发散。
• BMSGraSP与BMSGraHTP的平均迭代次数分别为2.1710与2.0043，表明收敛速度快。
• 当BRX ≥ 192且BTX ≥ 192时，BMSGraSP与BMSGraHTP的归一化复杂度低于15（以BG-GAMP为基准），证实其计算效率。
• 基于FFT的实现将计算复杂度从O(M⁴)降低至O(M² log M)，使算法在大规模毫米波系统中具备可扩展性。