On the capacity of MIMO broadcast channels with partial side information

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=αlogn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness

Random Beamforming with Heterogeneous Users and Selective Feedback: Individual Sum Rate and Individual Scaling Laws

This paper investigates three open problems in random beamforming based communication systems: the scheduling policy with heterogeneous users, the closed form sum rate, and the randomness of multiuser diversity with selective feedback. By employing the cumulative distribution function based scheduling policy, we guarantee fairness among users as well as obtain multiuser diversity gain in the heterogeneous scenario. Under this scheduling framework, the individual sum rate, namely the average rate for a given user multiplied by the number of users, is of interest and analyzed under different feedback schemes. Firstly, under the full feedback scheme, we derive the closed form individual sum rate by employing a decomposition of the probability density function of the selected user's signal-to-interference-plus-noise ratio. This technique is employed to further obtain a closed form rate approximation with selective feedback in the spatial dimension. The analysis is also extended to random beamforming in a wideband OFDMA system with additional selective feedback in the spectral dimension wherein only the best beams for the best-L resource blocks are fed back. We utilize extreme value theory to examine the randomness of multiuser diversity incurred by selective feedback. Finally, by leveraging the tail equivalence method, the multiplicative effect of selective feedback and random observations is observed to establish the individual rate scaling.Comment: Submitted in March 2012. To appear in IEEE Transactions on Wireless Communications. Part of this paper builds upon the following letter: Y. Huang and B. D. Rao, "Closed form sum rate of random beamforming", IEEE Commun. Lett., vol. 16, no. 5, pp. 630-633, May 201

Spectrum Sharing in mmWave Cellular Networks via Cell Association, Coordination, and Beamforming

This paper investigates the extent to which spectrum sharing in mmWave networks with multiple cellular operators is a viable alternative to traditional dedicated spectrum allocation. Specifically, we develop a general mathematical framework by which to characterize the performance gain that can be obtained when spectrum sharing is used, as a function of the underlying beamforming, operator coordination, bandwidth, and infrastructure sharing scenarios. The framework is based on joint beamforming and cell association optimization, with the objective of maximizing the long-term throughput of the users. Our asymptotic and non-asymptotic performance analyses reveal five key points: (1) spectrum sharing with light on-demand intra- and inter-operator coordination is feasible, especially at higher mmWave frequencies (for example, 73 GHz), (2) directional communications at the user equipment substantially alleviate the potential disadvantages of spectrum sharing (such as higher multiuser interference), (3) large numbers of antenna elements can reduce the need for coordination and simplify the implementation of spectrum sharing, (4) while inter-operator coordination can be neglected in the large-antenna regime, intra-operator coordination can still bring gains by balancing the network load, and (5) critical control signals among base stations, operators, and user equipment should be protected from the adverse effects of spectrum sharing, for example by means of exclusive resource allocation. The results of this paper, and their extensions obtained by relaxing some ideal assumptions, can provide important insights for future standardization and spectrum policy.Comment: 15 pages. To appear in IEEE JSAC Special Issue on Spectrum Sharing and Aggregation for Future Wireless Network

On the Throughput of Large-but-Finite MIMO Networks using Schedulers

This paper studies the sum throughput of the {multi-user} multiple-input-single-output (MISO) networks in the cases with large but finite number of transmit antennas and users. Considering continuous and bursty communication scenarios with different users' data request probabilities, we derive quasi-closed-form expressions for the maximum achievable throughput of the networks using optimal schedulers. The results are obtained in various cases with different levels of interference cancellation. Also, we develop an efficient scheduling scheme using genetic algorithms (GAs), and evaluate the effect of different parameters, such as channel/precoding models, number of antennas/users, scheduling costs and power amplifiers' efficiency, on the system performance. Finally, we use the recent results on the achievable rates of finite block-length codes to analyze the system performance in the cases with short packets. As demonstrated, the proposed GA-based scheduler reaches (almost) the same throughput as in the exhaustive search-based optimal scheduler, with substantially less implementation complexity. Moreover, the power amplifiers' inefficiency and the scheduling delay affect the performance of the scheduling-based systems significantly

MmWave Massive MIMO Based Wireless Backhaul for 5G Ultra-Dense Network

Ultra-dense network (UDN) has been considered as a promising candidate for future 5G network to meet the explosive data demand. To realize UDN, a reliable, Gigahertz bandwidth, and cost-effective backhaul connecting ultra-dense small-cell base stations (BSs) and macro-cell BS is prerequisite. Millimeter-wave (mmWave) can provide the potential Gbps traffic for wireless backhaul. Moreover, mmWave can be easily integrated with massive MIMO for the improved link reliability. In this article, we discuss the feasibility of mmWave massive MIMO based wireless backhaul for 5G UDN, and the benefits and challenges are also addressed. Especially, we propose a digitally-controlled phase-shifter network (DPSN) based hybrid precoding/combining scheme for mmWave massive MIMO, whereby the low-rank property of mmWave massive MIMO channel matrix is leveraged to reduce the required cost and complexity of transceiver with a negligible performance loss. One key feature of the proposed scheme is that the macro-cell BS can simultaneously support multiple small-cell BSs with multiple streams for each smallcell BS, which is essentially different from conventional hybrid precoding/combining schemes typically limited to single-user MIMO with multiple streams or multi-user MIMO with single stream for each user. Based on the proposed scheme, we further explore the fundamental issues of developing mmWave massive MIMO for wireless backhaul, and the associated challenges, insight, and prospect to enable the mmWave massive MIMO based wireless backhaul for 5G UDN are discussed.Comment: This paper has been accepted by IEEE Wireless Communications Magazine. This paper is related to 5G, ultra-dense network (UDN), millimeter waves (mmWave) fronthaul/backhaul, massive MIMO, sparsity/low-rank property of mmWave massive MIMO channels, sparse channel estimation, compressive sensing (CS), hybrid digital/analog precoding/combining, and hybrid beamforming. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=730653

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling