Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems typically employ hybrid mixed signal processing to avoid expensive hardware and high training overheads. {However, the lack of fully digital beamforming at mmWave bands imposes additional challenges in channel estimation. Prior art on hybrid architectures has mainly focused on greedy optimization algorithms to estimate frequency-flat narrowband mmWave channels, despite the fact that in practice, the large bandwidth associated with mmWave channels results in frequency-selective channels. In this paper, we consider a frequency-selective wideband mmWave system and propose two deep learning (DL) compressive sensing (CS) based algorithms for channel estimation.} The proposed algorithms learn critical apriori information from training data to provide highly accurate channel estimates with low training overhead. In the first approach, a DL-CS based algorithm simultaneously estimates the channel supports in the frequency domain, which are then used for channel reconstruction. The second approach exploits the estimated supports to apply a low-complexity multi-resolution fine-tuning method to further enhance the estimation performance. Simulation results demonstrate that the proposed DL-based schemes significantly outperform conventional orthogonal matching pursuit (OMP) techniques in terms of the normalized mean-squared error (NMSE), computational complexity, and spectral efficiency, particularly in the low signal-to-noise ratio regime. When compared to OMP approaches that achieve an NMSE gap of \$\unit[\{4-10\}]{dB}\$ with respect to the Cramer Rao Lower Bound (CRLB), the proposed algorithms reduce the CRLB gap to only \$\unit[\{1-1.5\}]{dB}\$, while significantly reducing complexity by two orders of magnitude.

中文翻译：

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混合毫米波MIMO系统中基于深度学习的选频信道估计

毫米波（mmWave）大规模多输入多输出（MIMO）系统通常采用混合混合信号处理，以避免昂贵的硬件和高培训开销。{然而，在毫米波频段缺乏全数字波束成形给信道估计带来了额外的挑战。尽管实际上在实践中，与mmWave通道相关的大带宽导致了频率选择通道，但是关于混合架构的现有技术主要集中在贪婪优化算法上以估计平坦的窄带mmWave通道。在本文中，我们考虑了频率选择宽带mmWave系统，并提出了两种基于深度学习（DL）压缩感知（CS）的算法来进行信道估计。}拟议算法从训练数据中学习关键先验信息，从而以较低的训练开销提供高精度的信道估计。在第一种方法中，基于DL-CS的算法会同时估算频域中的信道支持，然后将其用于信道重构。第二种方法利用估计的支持来应用低复杂度的多分辨率微调方法，以进一步提高估计性能。仿真结果表明，所提出的基于DL的方案在归一化均方误差（NMSE），计算复杂度和频谱效率方面，特别是在低信噪比方面，明显优于传统的正交匹配追踪（OMP）技术。政权。