Gilwon Lee

Two-Stage Beamformer Design for Massive MIMO Downlink By Trace Quotient Formulation

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-plus-noise 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.

Randomly-Directional Beamforming in Millimeter-Wave Multiuser MISO Downlink

In this paper, the performance of opportunistic random beamforming (RBF) and the multiuser (MU) gain in millimeter-wave (mm-wave) MU multiple-input single-output (MISO) downlink systems are analyzed based on the uniform random single-path (UR-SP) channel model suitable for highly directional mm-wave radio propagation channels. It is shown that under the UR-SP channel model, RBF achieves linear sum rate scaling with respect to (w.r.t.) the number of transmit antennas and, furthermore, yields optimal sum rate performance when the number of transmit antennas is large, if the number of users increases linearly w.r.t. the number of transmit antennas. Several beam training and user selection methods are investigated to yield insights into the most effective beamforming and scheduling choice for mm-wave MU-MISO in various operating conditions. Simulation results validate our analysis based on asymptotic techniques for finite cases.

Coordinated Beamforming With Relaxed Zero Forcing: The Sequential Orthogonal Projection Combining Method and Rate Control

In this paper, coordinated beamforming based on relaxed zero forcing (RZF) for transmitter-receiver pair multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) interference channels is considered. In the RZF coordinated beamforming, conventional zero-forcing interference leakage constraints are relaxed so that some predetermined interference leakage to undesired receivers is allowed in order to increase the beam design space for larger rates than those of the zero-forcing (ZF) scheme or to make beam design feasible when ZF is impossible. In the MISO case, it is shown that the rate-maximizing beam vector under the RZF framework for a given set of interference leakage levels can be obtained by sequential orthogonal projection combining (SOPC). Based on this, exact and approximate closed-form solutions are provided in two-user and three-user cases, respectively, and an efficient beam design algorithm for RZF coordinated beamforming is provided in general cases. Furthermore, the rate control problem under the RZF framework is considered. A centralized approach and a distributed heuristic approach are proposed to control the position of the designed rate-tuple in the achievable rate region. Finally, the RZF framework is extended to MIMO interference channels by deriving a new lower bound on the rate of each user.

On the Performance of Random Beamforming in Sparse Millimeter Wave Channels

The performance of random beamforming (RBF) with partial channel state information (CSI) feedback is investigated here for millimeter wave (mmWave) multiuser multiple-input single-output (MU-MISO) downlink systems using the uniform random multipath (UR-MP) channel model. In particular, the required number of users in the cell for RBF to yield linear sum rate scaling with respect to the number of transmit antennas is identified under the UR-MP channel model for different levels of channel sparsity. Then, the problem of user scheduling in MU-MISO downlink is considered when the number of users in the cell is not sufficiently large (sparse user regime) for the system to operate in the identified sufficient user regime. By exploiting the sparsity of mmWave radio channels, several user scheduling algorithms based on beam aggregation with reasonable amount of feedback are proposed for the sparse user regime. Our numerical results show that the proposed algorithms yield very good sum-rate performance in sparse mmWave channels.

A new approach to beamformer design for massive MIMO systems based on k-Regularity

In this paper, a new beamformer design paradigm, named k-regular beamformer, is proposed for massive multiple-input multiple-output (MIMO) transmission systems to achieve most of the gain inherent to a large antenna array without too much complexity. In the proposed k-regular beamforming scheme, each of multiple data streams for MIMO transmission is multiplied by k complex gains and assigned to k out of available NT transmit antennas, and signals assigned to the same transmit antenna are added and transmitted through the assigned antenna. The proposed k-regular beamformer can implement antenna selection (corresponding to k=1) to optimal eigen-beamforming (corresponding to k=NT) by controlling the parameter k, and thus enables arbitrary trade-off between complexity and performance. Two beamformer design algorithms, the maximum correlation method (MCM) and the projected iterative shrinkage-thresholding algorithm (PISTA), are proposed to design k-regular beamforming matrices. Numerical results show that the proposed k-regular beamformer even with small k significantly improves the rate gain over simple antenna selection and achieves most of the optimal eigen-beamforming performance with far less complexity than that required for optimal eigen-beamforming for massive MIMO transmission.

Training Beam Sequence Design for Millimeter-Wave MIMO Systems: A POMDP Framework

In this paper, adaptive training beam sequence design for efficient channel estimation in large millimeter-wave (mmWave) multiple-input multiple-output (MIMO) channels is considered. By exploiting the sparsity in large mmWave MIMO channels and imposing a Markovian random walk assumption on the movement of the receiver and reflection clusters, the adaptive training beam sequence design and channel estimation problem is formulated as a partially observable Markov decision process (POMDP) problem that finds non-zero bins in a two-dimensional grid. Under the proposed POMDP framework, optimal and suboptimal adaptive training beam sequence design policies are derived. Furthermore, a very fast suboptimal greedy algorithm is developed based on a newly proposed reduced sufficient statistic to make the computational complexity of the proposed algorithm low to a level for practical implementation. Numerical results are provided to evaluate the performance of the proposed training beam design method. Numerical results show that the proposed training beam sequence design algorithms yield good performance.

Dual-Domain Adaptive Beamformer Under Linearly and Quadratically Constrained Minimum Variance

In this paper, a novel adaptive beamforming algorithm is proposed under a linearly and quadratically constrained minimum variance (LQCMV) beamforming framework, based on a dual-domain projection approach that can efficiently implement a quadratic-inequality constraint with a possibly rank-deficient positive semi-definite matrix, and the properties of the proposed algorithm are analyzed. As an application, relaxed zero-forcing (RZF) beamforming is presented which adopts a specific quadratic constraint that bounds the power of residual interference in the beamformer output with the aid of interference-channel side-information available typically in wireless multiple-access systems. The dual-domain projection in this case plays a role in guiding the adaptive algorithm towards a better direction to minimize the interference and noise, leading to considerably faster convergence. The robustness issue against channel mismatch and ill-posedness is also addressed. Numerical examples show that the efficient use of interference side-information brings considerable gains.

Asymptotically optimal simple user scheduling for massive MIMO downlink with two-stage beamforming

In this paper, a simple user-scheduling-and-beamforming method is proposed for massive multi-user multiple-input multiple-output (MU-MIMO) downlink adopting two-stage beamforming. The key ideas of the proposed scheduling-and-beamforming method are to divide users into several candidate subsets according to the level of alignment of user channels to the dominant directions of the channel covariance matrix and select the user in each candidate subset based on a certain channel quality indicator (CQI) and to apply post-selection zero-forcing beamforming (ZFBF) to the selected users based on their channel state information (CSI). It is proved that the proposed scheduling-and-beamforming method is asymptotically optimal as the number of users increases. Furthermore, the proposed method significantly reduces the feedback overhead and shows superior sum rate performance compared to existing scheduling methods for MU-MIMO downlink.

Coordinated beamforming with relaxed zero forcing

In this paper, a new beam design paradigm for coordinated beamforming (CB) for current and future cellular networks is proposed based on a relaxed zero-forcing (RZF) constraint. In the conventional zero-forcing (ZF) CB, each cooperating transmitter designs its transmit beamforming matrix to null out interference to undesired receivers completely. In the proposed RZF paradigm, however, the ZF constraint is relaxed so that a tolerable amount of interference leakage to undesired receivers is allowed for the beam design at each transmitter. By relaxing the ZF constraint in such a way, transmitters have more degrees of freedom for their beam design to increase the overall data rate of the network. An efficient algorithm for the RZFCB is proposed based on a projected subgradient method. Numerical results show that the proposed RZFCB shows a noticeable gain over the conventional ZFCB.

On the performance of randomly directional beamforming between line-of-sight and rich scattering channels

In this paper, the performance of random beamforming (RBF) which requires only partial channel state information (CSI) feedback is investigated for millimeter-wave (mmwave) multiple-input multiple-output (MIMO) downlink systems under a new channel model that captures both the independent and identically-distributed (i.i.d.) Rayleigh fading MIMO channel model and the uniform random line-of-sight (UR-LoS) channel model and bridges the two channel models. Under the proposed channel model, we answer the basic question “how many users in the cell are required for RBF to achieve linear sum rate scaling with respect to (w.r.t.) the number of transmit antennas?”