Scaling laws of multiple antenna group-broadcast channels

Broadcast (or point to multipoint) communication has attracted a lot of research recently. In this paper, we consider the group broadcast channel where the users' pool is divided into groups, each of which is interested in common information. Such a situation occurs for example in digital audio and video broadcast where the users are divided into various groups according to the shows they are interested in. The paper obtains upper and lower bounds for the sum rate capacity in the large number of users regime and quantifies the effect of spatial correlation on the system capacity. The paper also studies the scaling of the system capacity when the number of users and antennas grow simultaneously. It is shown that in order to achieve a constant rate per user, the number of transmit antennas should scale at least logarithmically in the number of users

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

Performance of Orthogonal Beamforming for SDMA with Limited Feedback

On the multi-antenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to CSI inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser-interference-limited regime, the throughput of PU2RC is shown to scale logarithmically with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and also linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.Comment: 27 pages; to appear in IEEE Transactions on Vehicular Technolog

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

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection -- Secure DoF and Jammer Scaling Law

In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of $S$ jammers among which Bob selects $K$ jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than $KN_j$ receive antennas, where $N_j$ is the number of jammer's transmit antenna each, and hence $KN_j$ can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.Comment: Accepted with minor revisions, IEEE Trans. on Signal Processin

Bit Allocation Law for Multi-Antenna Channel Feedback Quantization: Single-User Case

This paper studies the design and optimization of a limited feedback single-user system with multiple-antenna transmitter and single-antenna receiver. The design problem is cast in form of the minimizing the average transmission power at the base station subject to the user's outage probability constraint. The optimization is over the user's channel quantization codebook and the transmission power control function at the base station. Our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem. We start by showing that uniformly quantizing the channel magnitude in dB scale is asymptotically optimal, regardless of the magnitude distribution function. We derive the optimal uniform (in dB) channel magnitude codebook and combine it with a spatially uniform channel direction codebook to arrive at a product channel quantization codebook. We then optimize such a product structure in the asymptotic regime of $B\rightarrow \infty$, where $B$ is the total number of quantization feedback bits. The paper shows that for channels in the real space, the asymptotically optimal number of direction quantization bits should be ${(M{-}1)}/{2}$ times the number of magnitude quantization bits, where $M$ is the number of base station antennas. We also show that the performance of the designed system approaches the performance of the perfect channel state information system as $2^{-\frac{2B}{M+1}}$. For complex channels, the number of magnitude and direction quantization bits are related by a factor of $(M{-}1)$ and the system performance scales as $2^{-\frac{B}{M}}$ as $B\rightarrow\infty$.Comment: Submitted to IEEE Transactions on Signal Processing, March 201