In this paper, randomly-directional beamforming (RDB) is considered for millimeter-wave (mmwave) multi-user (MU) multiple-input single-output (MISO) downlink systems. By using asymptotic techniques, the performance of RDB and the MU gain in mm-wave MISO are analyzed based on the uniform random line-of-sight (UR-LoS) channel model suitable for highly directional mm-wave radio propagation channels. It is shown that there exists a transition point on the number of users relative to the number of antenna elements for non-trivial performance of the RDB scheme, and furthermore sum rate scaling arbitrarily close to linear scaling with respect to the number of antenna elements can be achieved under the UR-LoS channel model by opportunistic random beamforming with proper user scheduling if the number of users increases linearly with respect to the number of antenna elements.The provided results yield insights into the most effective beamforming and scheduling choices for mm-wave MU-MISO in various operating conditions. Simulation results validate our analysis based on asymptotic techniques for finite cases. Index TermsMillimeter-Wave, Multi-User MIMO, Massive MIMO, Opportunistic Random Beamforming, RandomlyDirectional Beamforming † Corresponding authorThe authors are with

In this paper, the problem of outer beamformer design based only on channel statistic information is considered for two-stage beamforming for multi-user massive MIMO downlink, and the problem is approached based on signal-to-leakage-plusnoise ratio (SLNR). To eliminate the dependence on the instantaneous channel state information, a lower bound on the average SLNR is derived by assuming zero-forcing (ZF) inner beamforming, and an outer beamformer design method that maximizes the lower bound on the average SLNR is proposed. It is shown that the proposed SLNR-based outer beamformer design problem reduces to a trace quotient problem (TQP), which is often encountered in the field of machine learning. An iterative algorithm is presented to obtain an optimal solution to the proposed TQP. The proposed method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics. Numerical results show that the proposed outer beamformer design method yields significant performance gain over existing methods.Index Terms-Massive MIMO systems, two-stage beamforming, signal-to-leakage-plus-noise ratio (SLNR), trace quotient problem (TQP), adaptive weighting factor.

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In this paper, a new user-scheduling-and-beamforming method is proposed for multi-user massive multiple-input multiple-output (massive MIMO) broadcast channels in the context of two-stage beamforming. The key ideas of the proposed scheduling method are 1) to use a set of orthogonal reference beams and construct a double cone around each reference beam to select 'nearly-optimal' semi-orthogonal users based only on channel quality indicator (CQI) feedback and 2) to apply postuser-selection beam refinement with zero-forcing beamforming (ZFBF) based on channel state information (CSI) feedback only from the selected users. It is proved that the proposed scheduling-andbeamforming method is asymptotically optimal as the number of users increases. Furthermore, the proposed scheduling-and-beamforming method almost achieves the performance of the existing semiorthogonal user selection with ZFBF (SUS-ZFBF) that requires full CSI feedback from all users, with significantly reduced feedback overhead which is even less than that required by random beamforming. Index TermsUser scheduling, multi-user MIMO, massive MIMO, two-stage beamforming, multi-user diversity, zero-forcing beamforming † Corresponding author Gilwon Lee and Youngchul Sung are with The multi-user multiple-input and multiple-output (MU-MIMO) technology has served as one of the core technologies of the fourth generation (4G) wireless systems. With the current interest in large-scale antenna arrays at base stations (BSs), the importance of the MU-MIMO technology further increases for future wireless systems. The MU-MIMO technology supports users in the same frequency band and time simultaneously based on spatial-division multiplexing, exploiting the degrees-of-freedom (DoF) in the spatial domain. There has been extensive research on MU-MIMO ranging from transmit signal or beamformer design to user scheduling in the past decade [2]-[5]. It is known that the capacity of a Gaussian MIMO broadcast channel is achieved by dirty paper coding (DPC) [2], [3], [6]. However, due to the difficulty of practical implementation of DPC, linear beamforming schemes for transmit signal design for MU-MIMO have become dominant in current cellular standards [7]. In general, linear beamforming schemes such as zeroforcing beamforming (ZFBF) and minimum mean-square-error (MMSE) beamforming perform worse than DPC. However, an astonishing remedy was brought to these linear beamforming schemes for MU-MIMO downlink, based on multi-user diversity [4], [5], [8], [9]. That is, with proper user selection or scheduling, the performance degradation of the linear beamforming schemes compared to DPC is negligible as the number of users in the served cell becomes large [4], [5], and the seminal results in [4], [5] have provided guidance on how to select simultaneous users in practical MU-MIMO downlink systems. In this paper, we revisit the user scheduling and beamforming problem for MU-MIMO downlink in the context of up-to-date massive MU-MIMO downlink with two-stage beamforming [10], although the pro...

In this paper, we investigate hybrid analog/digital beamforming for multiple-input multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs) for millimeter wave (mmWave) communications. In the receiver, we propose to split the analog combining subsystem into a channel gain aggregation stage followed by a spreading stage. Both stages use phase shifters. Our goal is to design the two-stage analog combiner to optimize mutual information (MI) between the transmitted and quantized signals by effectively managing quantization error. To this end, we formulate an unconstrained MI maximization problem without a constant modulus constraint on analog combiners, and derive a two-stage analog combining solution. The solution achieves the optimal scaling law with respect to the number of radio frequency chains and maximizes the MI for homogeneous singular values of a MIMO channel. We further develop a two-stage analog combining algorithm to implement the derived solution for mmWave channels. By decoupling channel gain aggregation and spreading functions from the derived solution, the proposed algorithm implements the two functions by using array response vectors and a discrete Fourier transform matrix under the constant modulus constraint on each matrix element. Therefore, the proposed algorithm provides a near optimal solution for the unconstrained problem, whereas conventional hybrid approaches offer a near optimal solution only for a constrained problem. The closed-form approximation of the ergodic rate is derived for the algorithm, showing that a practical digital combiner with two-stage analog combining also achieves the optimal scaling law. Simulation results validate the algorithm performance and the derived ergodic rate.Index Terms-Two-stage analog combining structure, lowresolution ADCs, mutual information, ergodic rate.