Deep Learning Based Frequency-Selective Channel Estimation for Hybrid mmWave MIMO Systems

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 {4-10} dB with respect to the Cramer Rao Lower Bound (CRLB), the proposed algorithms reduce the CRLB gap to only {1-1.5} dB, while reducing complexity by two orders of magnitude.