In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than N, the maximal multiplexing gain can be achieved with many different transmission reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and or to enable interference-aware receive combining. In this paper, we try to answer the question if the N data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user-the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.
The sum-rate maximization problem is nonconvex and combinatorial @cite_20 , thus only suboptimal strategies are feasible in practice. Such low-complexity algorithms have been proposed in @cite_6 @cite_7 @cite_17 @cite_27 , among others, by successively allocating data streams to users in a greedy manner. Simulations have indicated that fewer than @math streams should be used when @math and @math are small, and that spatial correlation makes it beneficial to divide the streams among many users. Simulations in @cite_7 indicates that the probability of allocating more than one stream per user is small when @math grows large, but @cite_7 only considers users with homogeneous channel conditions and all the aforementioned papers assume perfect CSI.
@cite_7 @cite_6 @cite_27 @cite_20 @cite_17
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We consider the MIMO broadcast channel (MIMO-BC) where an array equipped with M antennas transmits distinct information to K users, each equipped with N antennas. We propose a linear precoding technique, called multiuser eigenmode transmission (MET), based on the block diagonalization precoding technique. MET addresses the shortcomings of previous ZF-based beamformers by transmitting to each user on one or more eigenmodes chosen using a greedy algorithm. We consider both the typical sum-power constraint (SPC), and a per-antenna power constraint (PAPC) motivated by array architectures where antennas are powered by separate amplifiers and are either co-located or spatially separated. Numerical results show that the proposed MET technique outperforms previous linear techniques with both SPC and PAPC. Asymptotically as the number of user K increases without bound, we show that block diagonalization with receive antenna selection under PAPC and SPC are asymptotically optimal. Block diagonalization (BD) combined with coordinated transmitter-receiver processing and scheduling between users is a simple and straightforward linear method to utilize the available spatial degrees of freedom in downlink multi-user multiple-input multiple-output (MIMO) channel for increasing the system throughput. In this paper, an efficient scheduling algorithm is proposed to maximize the downlink spectral efficiency of the BD method for any number of users and antennas at both the transmitter and the receivers. The performance is compared to the spectral efficiency available with several other scheduling algorithms and to the sum-rate capacity. It is shown that the performance of the BD method with the proposed scheduling approaches the sum rate capacity at high signal-to-noise ratio (SNR) as the number of users increases. It is also noticed that due to the inherent noise amplification problem with linear BD method, the maximum spectral efficiency is often achieved by transmitting to less users beams than the spatial dimensions available, especially, at low SNR region with a high number of transmit antennas and with a low number of users Achieving the boundary of the capacity region in the multiple-input multiple-output (MIMO) broadcast channel requires the use of dirty paper coding (DPC). As practical nearly optimum implementations of DPC are computationally complex, purely linear approaches are often used instead. However, in this case, the problem of maximizing a weighted sum rate constitutes a nonconvex and, in most cases, also a combinatorial optimization problem. In this paper, we present two heuristic nearly optimum algorithms with reduced computational complexity. For this purpose, a lower bound for the weighted sum rate under linear zero-forcing constraints is used. Based on this bound, both greedy algorithms successively allocate data streams to users. In each step, the user is determined that is given an additional data stream such that the increase in weighted sum rate becomes maximum. Thereby, the data stream allocations and filters obtained in the previous steps are kept fixed and only the filter corresponding to the additional data stream is optimized. The first algorithm determines the receive and transmit filters directly in the downlink. The other algorithm operates in the dual uplink, from which the downlink transmit and receive filters can be obtained via the general rate duality leading to nonzero-forcing in the downlink. Simulation results reveal marginal performance losses compared to more complex algorithms. Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectral densities dynamically in response to physical channel conditions. Due to co-channel interference, the achievable data rate of each user depends on not only the power spectral density of its own, but also those of others in the system. Given any channel condition and assuming Gaussian signaling, we consider the problem to jointly determine all users' power spectral densities so as to maximize a system-wide utility function (e.g., weighted sum-rate of all users), subject to individual power constraints. For the discretized version of this nonconvex problem, we characterize its computational complexity by establishing the NP-hardness under various practical settings, and identify subclasses of the problem that are solvable in polynomial time. Moreover, we consider the Lagrangian dual relaxation of this nonconvex problem. Using the Lyapunov theorem in functional analysis, we rigorously prove a result first discovered by Yu and Lui (2006) that there is a zero duality gap for the continuous (Lebesgue integral) formulation. Moreover, we show that the duality gap for the discrete formulation vanishes asymptotically as the size of discretization decreases to zero. A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98 of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.