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Baseband processing algorithms often require knowledge of the noise power, signal power, or signal-to-noise ratio (SNR). In practice, these parameters are typically unknown and must be estimated. Furthermore, the mean-square error (MSE) is a desirable metric to be minimized in a variety of estimation and signal recovery algorithms. However, the MSE cannot directly be used as it depends on the true signal that is generally unknown to the estimator. In this paper, we propose novel blind estimators for the average noise power, average receive signal power, SNR, and MSE. The proposed estimators can be computed at low complexity and solely rely on the large-dimensional and sparse nature of the processed data. Our estimators can be used (i) to quickly track some of the key system parameters while avoiding additional pilot overhead, (ii) to design low-complexity nonparametric algorithms that require such quantities, and (iii) to accelerate more sophisticated estimation or recovery algorithms. We conduct a theoretical analysis of the proposed estimators for a Bernoulli complex Gaussian (BCG) prior, and we demonstrate their efficacy via synthetic experiments. We also provide three application examples that deviate from the BCG prior in millimeter-wave multi-antenna and cell-free wireless systems for which we develop nonparametric denoising algorithms that improve channel-estimation accuracy with a performance comparable to denoisers that assume perfect knowledge of the system parameters. 

We propose blind estimators for the average noise power, receive signal power, signal-to-noise ratio (SNR), and mean-square error (MSE), suitable for multi-antenna millimeter wave (mmWave) wireless systems. The proposed estimators can be computed at low complexity and solely rely on beamspace sparsity, i.e., the fact that only a small number of dominant propagation paths exist in typical mmWave channels. Our estimators can be used (i) to quickly track some of the key quantities in multi-antenna mmWave systems while avoiding additional pilot overhead and (ii) to design efficient nonparametric algorithms that require such quantities. We provide a theoretical analysis of the proposed estimators, and we demonstrate their efficacy via synthetic experiments and using a nonparametric channel-vector denoising task with realistic multi-antenna mmWave channels. 

Massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems operating at millimeter-wave (mmWave) frequencies enable simultaneous wideband data transmission to a large number of users. In order to reduce the complexity of MU precoding in all-digital basestation architectures that equip each antenna element with a pair of data converters, we propose a two-stage precoding architecture which first generates a sparse precoding matrix in the beamspace domain, followed by an inverse fast Fourier transform that converts the result to the antenna domain. The sparse precoding matrix requires a small amount of multipliers and enables regular hardware architectures, which allows the design of hardware-efficient all-digital precoders. Simulation results demonstrate that our methods approach the error-rate performance of conventional Wiener filter precoding with more than 2x lower complexity. 

We propose sparsity-adaptive beamspace channel estimation algorithms that improve accuracy for 1-bit data converters in all-digital millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) basestations. Our algorithms include a tuning stage based on Stein's unbiased risk estimate (SURE) that automatically selects optimal denoising parameters depending on the instantaneous channel conditions. Simulation results with line-of-sight (LoS) and non-LoS mmWave massive MIMO channel models show that our algorithms improve channel estimation accuracy with 1-bit measurements in a computationally-efficient manner. 

Massive multi-antenna millimeter wave (mmWave) and terahertz wireless systems promise high-bandwidth communication to multiple user equipments in the same time-frequency resource. The high path loss of wave propagation at such frequencies and the fine-grained nature of beamforming with massive antenna arrays necessitates accurate channel estimation to fully exploit the advantages of such systems. In this paper, we propose BEAmspace CHannel EStimation (BEACHES), a low-complexity channel estimation algorithm for multi-antenna mmWave systems and beyond. BEACHES leverages the fact that wave propagation at high frequencies is directional, which enables us to denoise the (approximately) sparse channel state information in the beamspace domain. To avoid tedious parameter selection, BEACHES includes a computationally-efficient tuning stage that provably minimizes the mean-square error of the channel estimate in the large-antenna limit. To demonstrate the efficacy of BEACHES, we provide simulation results for line-of-sight (LoS) and non-LoS mmWave channel models.