Junyoung Nam

Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szegos asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users.

Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.

Joint spatial division and multiplexing: Realizing massive MIMO gains with limited channel state information

We propose Joint Spatial Division and Multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the channel vectors correlation in order to allow for a large number of base station antennas while requiring a considerably reduced channel state information (CSI) feedback from the users. Thanks to the reduced CSI requirement, JSDM allows the use of a large number of base station antennas also in FDD systems. This work presents the correlated channel model, the main idea of JSDM precoding, and the design of JSDM precoding, formed by the concatenation of a pre-beamforming matrix based only on the structure of the channel covariance, with suitable multiuser precoding based on the CSI of the reduced dimensional transformed channels. We show that in some cases JSDM incurs no loss of optimality with respect to the MIMO broadcast channel with full CSI.

A new outer bound on the capacity region of Gaussian interference channels

The best known outer bound on the capacity region of the two-user Gaussian interference channel is given as the intersection of regions of genie-aided outer bounds, in which a genie provides extra side information to the receivers. In this paper, we present a new outer bound that does not resort to a genie-aided channel but make use of auxiliary random variables. In order to obtain such bound, we introduce a conditional version of the worst additive noise lemma. The new bound is shown to be tighter than genie-aided bounds for certain range of parameters.

Fundamental limits in correlated fading MIMO broadcast channels: Benefits of transmit correlation diversity

We investigate fundamental limits of the capacity of correlated fading MIMO broadcast channels (BCs) in several regimes of system parameters, with a particular interest in the large-scale array (or massive MIMO) regime. It is advocated in this paper that transmit correlation can be of use to increase both multiplexing gain and power gain in multiuser MIMO systems. In particular, it is shown to improve the system multiplexing gain up to by a factor of the number of degrees of transmit correlation diversity that captures how favorable structure users have in their transmit correlations.

User Grouping of Two-Stage MU-MIMO Precoding for Clustered User Geometry

This letter investigates how user grouping, more specifically group partitioning, affects the sum-rate performance of a two-stage multiuser MIMO precoding scheme referred to as joint spatial division and multiplexing (JSDM). Taking a clustered user geometry model into account, we propose a new criterion for user grouping to noticeably improve the sum-rate performance of JSDM. Numerical results confirm that the user grouping based on the proposed criterion yields substantial performance enhancement.

Joint spatial division and multiplexing — Benefits of antenna correlation in multi-user MIMO

We show that the sum capacity of “spatially well-correlated” Gaussian MIMO broadcast channel (BC) is rather larger than that of the uncorrelated (i.i.d. Rayleigh fading) Gaussian MIMO BC, assuming a special structure of transmit correlation of users. Moreover, a potential sum-rate gap of an ideal correlated Rayleigh fading channel is shown to be M log M over the uncorrelated case, where M is the number of transmit antennas. Finally, we propose a joint spatial division and multiplexing (JSDM) scheme based on opportunistic beamforming that can achieve the optimal multiuser diversity gain with very limited channel state information (CSI) feedback in realistic scenarios, not requiring the special structure of transmit correlation.

Cholesky Based Efficient Algorithms for the MMSE-SIC Receiver

The minimum mean square error with successive interference cancellation (MMSE-SIC) receiver is known to achieve the capacity of multiple-input multiple-output (MIMO) fast fading channels in the presence of knowledge of the channel at the receiver. This paper presents efficient and numerically stable Cholesky decomposition based detection algorithms for MMSE-SIC, exploiting a property of ordering of MMSE-SIC. The proposed algorithms are shown to significantly reduce the computational complexity of existing efficient algorithms for SIC in MIMO flat fading channels.

A modified turbo principle for iterative detection and decoding

This paper presents a modified turbo principle (MTP) for iterative detection and decoding in multiple-antenna systems whose detector uses the max-log-MAP algorithm. The modified turbo principle intensionally introduces dependency between the messages of the max-log-MAP detector and the decoder. Our simulation results show that the proposed MTP significantly reduces the performance loss due to the suboptimal detection algorithm, max-log-MAP. We also substantiate our claims by analyzing the proposed MTP from an information theoretic perspective.

Block triangularization: A new linear precoding strategy for Gaussian MIMO BC

Finding an optimal linear precoding transmission strategy still remains an open problem, since it cannot be transformed to a convex problem. In this paper, we introduce some condition under which a duality of the rate regions of MMO broadcast channel (BC) and MIMO multiple-access channel (MAC) with linear precoding is established. In particular, we convert the non-convex and untractable sum rate optimization problem at hand to a well-structured dual problem like the dirty-paper coding (DPC) strategy. We provide sum-rate analysis of the proposed linear precoding strategy, referred to as block triangularization (BT), and address its optimality at high SNR. Specifically, we show that not only BT, but also the more familiar block diagonalization (BD) strategy is asymptotically optimal at high SNR. However, BT is shown to be always at least as good as BD over the entire SNR range. A sum-rate optimal solution at any SNR for the proposed BT strategy is also found.