Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to avoid energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully-connected architecture requiring a large number of phase shifters, which is also energyintensive. In this paper, we focus on the more energy-efficient hybrid precoding with sub-connected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multi-user signal detection, we first propose to decompose the total achievable rate optimization problem with non-convex constraints into a series of simple sub-rate optimization problems, each of which only considers one sub-antenna array. Then, we prove that maximizing the achievable sub-rate of each sub-antenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SICbased hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10% as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify the near-optimal performance of SIC-based hybrid precoding.Index Terms-MIMO, mmWave communications, hybrid precoding, energy-efficient, 5G.

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For uplink large-scale MIMO systems, minimum mean square error (MMSE) algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss-Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose a approximated method to compute log-likelihood ratios (LLRs) for soft channel decoding with a negligible performance loss. The analysis shows that the proposed GS-based algorithm can reduce the computational complexity from O(K 3 ) to O(K 2 ), where K is the number of users. Simulation results verify that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm, and achieves the near-optimal performance of the classical MMSE algorithm with a small number of iterations.Index Terms-Large-scale MIMO, signal detection, minimum mean square error (MMSE), Gauss-Seidel (GS) method, low complexity.

Abstract-Millimeter-wave massive MIMO with lens antenna array can considerably reduce the number of required radiofrequency (RF) chains by beam selection. However, beam selection requires the base station to acquire the accurate information of beamspace channel. This is a challenging task, as the size of beamspace channel is large while the number of RF chains is limited. In this paper, we investigate the beamspace channel estimation problem in mmWave massive MIMO systems with lens antenna array. Specifically, we first design an adaptive selecting network for mmWave massive MIMO systems with lens antenna array, and based on this network, we further formulate the beamspace channel estimation problem as a sparse signal recovery problem. Then, by fully utilizing the structural characteristics of mmWave beamspace channel, we propose a support detection (SD)-based channel estimation scheme with reliable performance and low pilot overhead. Finally, the performance and complexity analyses are provided to prove that the proposed SD-based channel estimation scheme can estimate the support of sparse beamspace channel with comparable or higher accuracy than conventional schemes. Simulation results verify that the proposed SD-based channel estimation scheme outperforms conventional schemes and enjoys satisfying accuracy, even in the low SNR region as the structural characteristics of beamspace channel can be exploited.

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Millimeter-wave (mmWave) MIMO with large antenna array has attracted considerable interests from academic and industry communities, as it can provide larger bandwidth and higher spectrum efficiency. However, with hundreds of antennas, the number of radio frequency (RF) chains required by mmWave MIMO is also huge, leading to unaffordable hardware cost and power consumption in practice. In this paper, we investigate low RF-complexity technologies to solve this bottleneck. We first review the evolution of low RF-complexity technologies from microwave frequencies to mmWave frequencies. Then, we discuss two promising low RF-complexity technologies for mmWave MIMO systems in detail, i.e., phased array based hybrid precoding (PAHP) and lens array based hybrid precoding (LAHP), including their principles, advantages, challenges, and recent results. We compare the performance of these two technologies to draw some insights about how they can be deployed in practice. Finally, we conclude this paper and point out some future research directions in this area. PLACE PHOTO HEREAkbar M. Sayeed (F'12) received the Ph.D. degree from the University of Illinois at Urbana-Champaign, USA, in 1996. He is a Professor of Electrical and Computer Engineering at the University of Wisconsin-Madison. His research interests include wireless communications, statistical signal processing, communication and information theory, wireless channel modeling, time-frequency analysis, and development of basic theory, system architectures, and prototypes for new wireless technologies.

Hybrid precoding is a promising technique for mmWave massive MIMO systems, as it can considerably reduce the number of required radio-frequency (RF) chains without obvious performance loss. However, most of the existing hybrid precoding schemes require a complicated phase shifter network, which still involves high energy consumption. In this paper, we propose an energy-efficient hybrid precoding architecture, where the analog part is realized by a small number of switches and inverters instead of a large number of high-resolution phase shifters. Our analysis proves that the performance gap between the proposed hybrid precoding architecture and the traditional one is small and keeps constant when the number of antennas goes to infinity. Then, inspired by the cross-entropy (CE) optimization developed in machine learning, we propose an adaptive CE (ACE)-based hybrid precoding scheme for this new architecture. It aims to adaptively update the probability distributions of the elements in hybrid precoder by minimizing the CE, which can generate a solution close to the optimal one with a sufficiently high probability. Simulation results verify that our scheme can achieve the near-optimal sum-rate performance and much higher energy efficiency than traditional schemes.

Minimum mean square error (MMSE) signal detection algorithm is nearoptimal for uplink multi-user large-scale multiple input multiple output (MIMO) systems, but involves matrix inversion with high complexity. In this letter, we firstly prove that the MMSE filtering matrix for largescale MIMO is symmetric positive definite, based on which we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion. The complexity can be reduced from O(K 3 ) to O(K 2 ), where K is the number of users. We also provide the convergence proof of the proposed algorithm. Simulation results show that the proposed signal detection algorithm converges fast, and achieves the near-optimal performance of the classical MMSE algorithm.Introduction: Large-scale multiple input multiple output (MIMO) employing hundreds of antennas at the base station (BS) to simultaneously serve multiple users is a promising key technology for 5G wireless communications [1]. It can achieve orders of magnitude increase in spectrum and energy efficiency, and one challenging issue to realize such goal is the low-complexity signal detection algorithm in the uplink, due to the increased dimension of large-scale MIMO systems [2]. The optimal signal detection algorithm is the maximum likelihood (ML) algorithm, but its complexity increases exponentially with the number of transmit antennas, making it impossible for large-scale MIMO. The fixedcomplexity sphere decoding (FSD) [3] and tabu search (TS) [4] algorithms have been proposed with reduced complexity, but their complexity is unfordable when the dimension of the large-scale MIMO system is large or the modulation order is high [5]. Low-complexity linear detection algorithms such as zero-forcing (ZF) and minimum mean square error (MMSE) with near-optimal performance have been investigated [2], but these algorithms have to use unfavorable matrix inversion, whose high complexity is still not acceptable for large-scale MIMO systems. Very recently, the Neumann series approximation algorithm has been proposed to approximate the matrix inversion [6], which converts the matrix inversion into a series of matrix-vector multiplications. However, only marginal complexity reduction can be achieved.In this letter, we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method [7] to avoid the complicated matrix inversion. We firstly prove a special property of large-scale MIMO systems that the MMSE filtering matrix is symmetric positive definite, based on which we propose to exploit the Richardson method to avoid the complicated matrix inversion. Then we prove the convergence of the proposed algorithm for any initial solution when the relaxation parameter is appropriate. Finally, we verify through simulations that the proposed signal detection algorithm can efficiently solve the matrix inversion problem in an iterative way until the desired accuracy is attained, and achieve the near-optimal performance of the MMSE algori...