Remarkable research activities and major advances have been occurred over the past decade in multiuser multiple-input multiple-output (MU-MIMO) systems. Several transmission technologies and precoding techniques have been developed in order to exploit the spatial dimension so that simultaneous transmission of independent data streams reuse the same radio resources. The achievable performance of such techniques heavily depends on the channel characteristics of the selected users, the amount of channel knowledge, and how efficiently interference is mitigated. In systems where the total number of receivers is larger than the number of total transmit antennas, user selection becomes a key approach to benefit from multiuser diversity and achieve full multiplexing gain. The overall performance of MU-MIMO systems is a complex joint multi-objective optimization problem since many variables and parameters have to be optimized, including the number of users, the number of antennas, spatial signaling, rate and power allocation, and transmission technique. The objective of this literature survey is to provide a comprehensive overview of the various methodologies used to approach the aforementioned joint optimization task in the downlink of MU-MIMO communication systems.

An Overview on Resource Allocation Techniques for Multi-User MIMO Systems

Interference alignment (IA) has been shown to achieve the maximum achievable degrees of freedom in the interference channel. This results in sum rate scaling linearly with the number of users in the high signal-to-noise-ratio (SNR) regime. Linear scaling is achieved by precoding the transmitted signals to align interference subspaces at the receivers given channel knowledge of all transmit-receive pairs, effectively reducing the number of discernible interferers. The theory of IA was derived under assumptions about the richness of scattering in the propagation channel; practical channels do not guarantee such ideal characteristics. This paper presents the first experimental study of IA in measured multiple-input-multiple-output orthogonal frequency-division-multiplexing (MIMO-OFDM) interference channels. Our measurement campaign includes a variety of indoor and outdoor measurement scenarios at The University of Texas at Austin. We show that IA achieves the claimed scaling factors, or degrees of freedom, in several measured channel settings for a three-user two-antenna-per-node setup. In addition to verifying the claimed performance, we characterize the effect of Kronecker spatial correlation on sum rate and present two other correlation measures, which we show to be more tightly related to the achieved sum rate.

The Feasibility of Interference Alignment Over Measured MIMO-OFDM Channels

The interference alignment (IA) is a promising technique to efficiently mitigate interference and to enhance capacity of a wireless communication network. This paper proposes an interference alignment scheme for a network with multiple cells and multiple multiple-input and multiple-output (MIMO) users under a Gaussian interference broadcast channel (IFBC) scenario. We first extend a grouping method already known in the literature to a multiple-cells scenario and jointly design transmit and receiver beamforming vectors using a closed-form expression without iterative computation. Then we propose a new approach using the principle of multiple access channel (MAC) - broadcast channel (BC) duality to perform interference alignment while maximizing capacity of users in each cell. The algorithm in its dual form is solved using interior point methods. We show that the proposed approach outperforms the extension of the grouping method in terms of capacity and basestation complexity. Finally, a rate balancing technique is introduced to maintain fairness among users.

Interference Alignment Techniques for MIMO Multi-Cell Interfering Broadcast Channels

Traditional approaches in the analysis of downlink systems decouple the precoding and the channel estimation problems. However, in cellular systems with mobile users, these two problems are, in fact, tightly coupled. In this paper, this coupling is explicitly studied by accounting for the channel training overhead and estimation error while determining the overall system throughput. This paper studies the problem of utilizing imperfect channel estimates for efficient linear precoding and user selection. It presents precoding methods that take into account the degree of channel estimation error. Information-theoretic lower and upper bounds are derived to evaluate the performance of these precoding methods. In typical scenarios, these bounds are close.

Channel Estimation and Linear Precoding in Multiuser Multiple-Antenna TDD Systems

In multi-user multiple-input multiple-output (MU-MIMO) systems, spatial multiplexing can be employed to increase the throughput without the need for multiple antennas and expensive signal processing at the user equipments. In theory, MU-MIMO is also more immune to most of propagation limitations plaguing single-user MIMO (SU-MIMO) systems, such as channel rank loss or antenna correlation. However, in this paper we show that this is not always true. We compare the capacity and the correlation of measured MU-MIMO channels for both outdoor and indoor scenarios. The measurement data has been acquired using Eurecompsilas MIMO openair sounder (EMOS). The EMOS can perform real-time MIMO channel measurements synchronously over multiple users. The results show that in most scenarios MU-MIMO provides a higher throughput than SU-MIMO also in the measured channels. However, in outdoor scenarios with a line of sight, the capacity drops significantly when the users are close together, due to high correlation at the transmitter side of the channel. In such a case, the performance of SU-MIMO and MU-MIMO is comparable.

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Correlation and capacity of measured multi-user MIMO channels

Assuming perfect channel state information at the transmitter of a Gaussian broadcast channel, strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel. For the general sum capacity maximizing solution, which has recently been found, a method is proposed that transforms each of the resulting vector channels into a set of scalar channels. This makes possible to achieve capacity by simply using scalar coding and detection techniques. The high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero-forcing allocation strategy that directly results in a set of virtually decoupled scalar channels. Simulation results show that this technique tightly approaches the performance of the optimum solution, i.e., complexity reduction comes at almost no cost in terms of sum capacity. As the optimum solution, the zero-forcing allocation strategy applies to any number of transmit antennas, receive antennas and users

Subchannel Allocation in Multiuser Multiple-Input&#8211;Multiple-Output Systems

Recently, the capacity region of the Gaussian broadcast channel has been characterized. For a given transmit power constraint, those points on the boundary of the capacity region can be regarded as the set of optimal operational points. The present work addresses the problem of selecting the point within this set that satisfies given constraints on the ratios between rates achieved by the different users in the network. This problem is usually known as rate balancing. To this end, the optimum iterative approach for general MIMO channels is revisited and adapted to an OFDM transmission scheme. Specifically, an algorithm is proposed that exploits the structure of the OFDM channel and whose convergence speed is essentially insensitive to the number of subcarriers. This is in contrast to a straightforward extension of the general MIMO algorithm to an OFDM scheme. Still, relatively high complexity and the need of a time-sharing policy to reach certain rates are at least two obstacles for a practical implementation of the optimum solution. Based on a novel decomposition technique for broadcast channels a suboptimum non-iterative algorithm is introduced that does not require time-sharing and very closely approaches the optimum solution.

Rate Balancing in Multiuser MIMO OFDM Systems

We consider a multiuser MIMO-OFDMA scheme which exploits multiuser diversity in all dimensions: time, frequency and space. The main contribution of this paper is the evaluation and explanation of multiuser MIMO in a real world scenario, i.e. a large office room, based on measured channels. We report interesting results of a measurement campaign which suggest that significant MIMO gains are possible in an indoor environment even under strong line-of-sight condition as long as the distance of the users from the base station is larger than a reverberation distance which only depends on room surface and material. We show results on the achievable multiuser MIMO data rates for the given scenario compare to theoretical limits and discuss the results in the light of the insights gained from the measurement campaign. We also introduce restrictions on the rate distribution between users, i.e. QoS constraints. It is shown that the theoretical limits can be approximately achieved provided that the users which compete for the spatial resources are carefully chosen.

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Multiuser MIMO Channel Measurements and Performance in a Large Office Environment

To avoid the complexity of nearly optimum implementations for dirty paper coding (DPC) linear zero-forcing approaches are often preferred. Finding the optimum user allocation, transmit and receive filters for maximizing sum rate in the multiple-input multiple-output (MIMO) broadcast channel constitutes a non-convex combinatorial optimization problem. Here we present an efficient linear zero-forcing algorithm for this problem, which is derived from maximizing a lower bound for the sum rate. It successively allocates data streams to users and in contrast to state of the art approaches thereby also determines the corresponding receive filters. Compared to existing approaches drastic complexity reductions can be achieved even with slight performance gains.

Efficient linear successive allocation for the MIMO broadcast channel

Multiple antennas at both transmitter and receiver enable the application of spatial multiplexing as a way of increasing transmission rate. However, this technique suffers from severe performance degradation as soon as fading processes in the MIMO channel exhibit significant correlation. If the transmit correlation matrix of the channel is known at the transmitter, performance can be improved by multiplexing signals across beams pointing along the directions of the eigenvectors of the transmit correlation matrix. However, the effectiveness of this technique decisively depends on bit and power loading across eigenbeams. Here, a method for bit and power loading is presented that based on the notion of pairwise error probability (PEP) leads to an optimum distribution of bits and power for a given transmit power and spectral efficiency in an OFDM context. Optimality refers to the minimization of a figure of merit that is obtained from adding expected PEPs over single eigenbeams. The effectiveness of this method is verified by means of simulated curves for three channels with different correlation properties.

Pedro Tejera

Papers

Subchannel Allocation in Multiuser Multiple-Input–Multiple-Output Systems

Rate Balancing in Multiuser MIMO OFDM Systems

Multiuser MIMO Channel Measurements and Performance in a Large Office Environment

Efficient linear successive allocation for the MIMO broadcast channel

Joint bit and power loading for MIMO OFDM based on partial channel knowledge

Pedro Tejera

Papers

Subchannel Allocation in Multiuser Multiple-Input&#8211;Multiple-Output Systems

Rate Balancing in Multiuser MIMO OFDM Systems

Multiuser MIMO Channel Measurements and Performance in a Large Office Environment

Efficient linear successive allocation for the MIMO broadcast channel

Joint bit and power loading for MIMO OFDM based on partial channel knowledge

Subchannel Allocation in Multiuser Multiple-Input–Multiple-Output Systems