We consider a multiuser multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. In this paper, we establish a duality between what is termed the “dirty paper” achievable region (the Caire–Shamai achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.

Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves near-capacity at sum rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a “sphere encoder ” to perturb the data to reduce the power of the transmitted signal. This paper is comprised of two parts. In this first part, we show that while the sum capacity grows linearly with the minimum of the number of antennas and users, the sum rate of channel inversion does not. This poor performance is due to the large spread in the singular values of the channel matrix. We introduce regularization to improve the condition of the inverse and maximize the signal-to-interference-plus-noise ratio at the receivers. Regularization enables linear growth and works especially well at low signal-to-noise ratios (SNRs), but as we show in the second part, an additional step is needed to achieve near-capacity performance at all SNRs.

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well known zero forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the SNR (in dB) in order to achieve the full multiplexing gain, which is in sharp contrast to point-to-point MIMO systems in which it is not necessary to increase the feedback rate as a function of the SNR. I.

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 — This paper examines communication between a cluster of closely-packed nodes with another cluster of closely-packed nodes. The nodes within each cluster are separated by small distances, relative to the distance between the two clusters. The effect on capacity of cooperation between nodes in the transmitting cluster and cooperation between nodes in the receiving cluster is investigated. I. System Model Consider a system with two transmitters and two receivers, as shown in Fig. 1. TX 1 wishes to communicate to RX 1, and TX 2 wishes to communicate to RX 2. It is assumed that the distance between each of the four transmitter-receiver pairs is the same, and each channel gain is normalized to have amplitude one. Thus, the channels between each transmitterreceiver pair are identical, except for a random uniformly distributed phase. The channel can be written as: jθ1 y1 x1 n1 e e

In this paper, we consider two different models of partial channel state information (CSI) at the basestation for multiple antenna broadcast channels: i.) the shape feedback model where the normalized channel vector of each user is available at the basestation and ii.) the limited feedback model where each user quantizes its channel vector according to a rotated codebook which is optimal in the sense of mean square error and feeds back the codeword index. The paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial basestion CSI models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high SNR regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR.

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.