We provide an overview of the extensive recent results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends

Although the capacity of multiple-input/multiple-output (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in round-robin ZFBF and proportional-fair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.

In this paper we consider the problem of maximizing sum rate of a multiple-antenna Gaussian broadcast channel. It was recently found that dirty paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e. the optimal transmit covariance structure) given the channel conditions and power constraint must be found. However, obtaining the optimal trans-mission policy when employing dirty paper coding is a computationally complex non-convex problem. We use duality to transform this problem into a well-structured convex multiple-access channel problem. We exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the multiple-access channel, which can easily be mapped to the optimal broadcast channel policies.

We show that the Gaussian multipleaccess channel (MAC) and broadcast channel (BC) are duals. The dual channels we consider have the same channel gains and the same noise power at all receivers. We nd an expression for the capacity region of the BC in terms of the capacity region of the dual MAC, and vice versa. Duality applies to many dierent channel models and capacity de nitions.

Abstract — In MIMO downlink channels, the capacity is achieved by dirty paper coding (DPC). However, DPC is difficult to implement in practical systems. This work investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum-rate capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we propose an algorithm for determining which users should be active in ZFBF transmission. These users are semiorthogonal to one another, and when fairness among users is required, can be grouped for simultaneous transmissions to enhance the throughput of fair schedulers. We provide numerical results to confirm the optimality of ZFBF and to compare its performance with that of various MIMO downlink strategies. I.

Abstract—This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple “beams ” directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum’s scheme and, thus, offers an attractive alternative to DP-based schemes. Index Terms—Beamforming, downlink, multiuser diversity. I.

Abstract—We compare the capacity of dirty-paper coding (DPC)to that of time-division multiple access (TDMA)for a multiple-antenna (multipleinput multiple-output (MIMO)) Gaussian broadcast channel (BC). We find that the sum-rate capacity (achievable using DPC)of the multiple-antenna BC is at most ��� @ A times the largest single-user capacity (i.e., the TDMA sum-rate)in the system, where is the number of transmit antennas and is the number of receivers. This result is independent of the number of receive antennas and the channel gain matrix, and is valid at all signal-to-noise ratios (SNRs). We investigate the tightness of this bound in a time-varying channel (assuming perfect channel knowledge at receivers and transmitters)where the channel experiences uncorrelated Rayleigh fading and in some situations we find that the dirty paper gain is upper-bounded by the ratio of transmit-to-receive antennas. We also show that ��� @ A upper-bounds the sum-rate gain of successive decoding over TDMA for the uplink channel, where is the number of receive antennas at the base station and is the number of transmitters. Index Terms—Broadcast channel (BC), channel capacity, dirty-paper coding (DPC), multiple-input multiple-output (MIMO) systems, timedivision multiple access (TDMA). I.

In this paper, a downlink communication system, in which a Base Station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system. For the asymptotic case when N tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the base station, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.

Multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit pre-coding to multiplex multiple users and pre-cancel inter-user interference. In such a system the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain. This paper proposes two precoding methods that use extra transmit antennas, beyond the minimum required, to provide additional degrees of diversity. The approach taken is to solve for a unitary transmit precoder, under a zero inter-user interference constraint, that minimizes an upper bound on the symbol error rate (SER) for each user. Solutions where all transmit antennas are employed as well as subsets of antennas (to reduce analog components) are described. Numerical results confirm a dramatic improvement in terms of SER and mutual information over single user MIMO methods and static allocation methods. For example, the proposed techniques achieve an SNR improvement of 6-10 dB at an uncoded SER of 10 −3, with only one extra transmit antenna.

It has been shown recently that the dirty-paper coding is the optimal strategy for maximizing the sum rate of multiple-input multiple-output Gaussian broadcast channels (MIMO BC). Moreover, by the channel duality, the nonconvex MIMO BC sum rate problem can be transformed to the convex dual MIMO multiple-access channel (MIMO MAC) problem with a sum power constraint. In this paper, we design an efficient algorithm based on conjugate gradient projection (CGP) to solve the MIMO BC maximum sum rate problem. Our proposed CGP algorithm solves the dual sum power MAC problem by utilizing the powerful concept of Hessian conjugacy. We also develop a rigorous algorithm to solve the projection problem. We show that CGP enjoys provable convergence, nice scalability, and great efficiency for large MIMO BC systems. 1