Optimal data detection in multiple-input multipleoutput (MIMO) communication systems with a large number of antennas at both ends of the wireless link entails prohibitive computational complexity. In order to reduce the computational complexity, a variety of sub-optimal detection algorithms have been proposed in the literature. In this paper, we analyze the optimality of a novel data-detection method for large MIMO systems that relies on approximate message passing (AMP). We show that our algorithm, referred to as individually-optimal (IO) large-MIMO AMP (short IO-LAMA), is able to perform IO data detection given certain conditions on the MIMO system and the constellation set (e.g., QAM or PSK) are met.

Millimeter-wave (mmWave) communication in combination with massive multiuser multiple-input multiple-output (MU-MIMO) enables high-bandwidth data transmission to multiple users in the same time-frequency resource. The strong path loss of wave propagation at such high frequencies necessitates accurate channel state information to ensure reliable data transmission. We propose a novel channel estimation algorithm called BEAmspace CHannel EStimation (BEACHES), which leverages the fact that wave propagation at mmWave frequencies is predominantly directional. BEACHES adaptively denoises the channel vectors in the beamspace domain using an adaptive shrinkage procedure that relies on Stein's unbiased risk estimator (SURE). Simulation results for line-of-sight (LoS) and non-LoS mmWave channels reveal that BEACHES performs on par with state-ofthe-art channel estimation methods while requiring orders-ofmagnitude lower complexity. To demonstrate the effectiveness of BEACHES in practice, we develop a very large-scale integration (VLSI) architecture and provide field-programmable gate array (FPGA) implementation results. Our results show that adaptive channel denoising can be performed at high throughput and in a hardware-friendly manner for massive MU-MIMO mmWave systems with hundreds of antennas.

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 lineof-sight (LoS) and non-LoS mmWave channel models.

Abstract-This paper deals with linear equalization in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. We first provide simple conditions on the antenna configuration for which the well-known linear minimum meansquare error (L-MMSE) equalizer provides near-optimal spectral efficiency, and we analyze its performance in the presence of parameter mismatches in the signal and/or noise powers. We then propose a novel, optimally-tuned NOnParametric Equalizer (NOPE) for massive MU-MIMO systems, which avoids knowledge of the transmit signal and noise powers altogether. We show that NOPE achieves the same performance as that of the L-MMSE equalizer in the large-antenna limit, and we demonstrate its efficacy in realistic, finite-dimensional systems. From a practical perspective, NOPE is computationally efficient and avoids dedicated training that is typically required for parameter estimation. I. INTRODUCTIONMassive (or large-scale) multi-user multiple-input multipleoutput (MU-MIMO) will be among the key technologies for fifth-generation (5G) wireless systems as it provides (often significantly) higher spectral efficiency than traditional, smallscale MIMO [1], [2]. Data detection at the infrastructure base-stations (BSs) in such massive MU-MIMO systems is among the most critical components from a spectral efficiency and computational complexity perspective. In particular, since optimal data detection is known to be an NP-hard problem [3], a naïve exhaustive search over all possible transmit signals would result in prohibitive computational complexity for such largedimensional systems. Hence, alternative algorithms that achieve high spectral efficiency at low complexity must be deployed in practice. In addition, practical massive MU-MIMO systems suffer-as do traditional MIMO systems-from real-world hardware impairments and model mismatches (for example amplifier nonlinearities, phase noise, quantization artifacts, channel-estimation errors, etc.). Such system nonidealities are known to substantially reduce the performance of optimal data-detection algorithms unless one explicitly models these impairments and estimates the associated parameters [4].