MISO Capacity with Per-Antenna Power Constraint

We establish in closed-form the capacity and the optimal signaling scheme for a MISO channel with per-antenna power constraint. Two cases of channel state information are considered: constant channel known at both the transmitter and receiver, and Rayleigh fading channel known only at the receiver. For the first case, the optimal signaling scheme is beamforming with the phases of the beam weights matched to the phases of the channel coefficients, but the amplitudes independent of the channel coefficients and dependent only on the constrained powers. For the second case, the optimal scheme is to send independent signals from the antennas with the constrained powers. In both cases, the capacity with per-antenna power constraint is usually less than that with sum power constraint.Comment: 7 pages double-column, 3 figure

The MISO Free-Space Optical Channel at Low and Moderate SNR

International audienceThe capacity of the multiple-input single-output (MISO) free-space optical channel with a per-antenna peak-power constraint and a sum (over all antennas) average-power constraint is studied. The asymptotic low-signal-to-noise-ratio (low-SNR) capacity is determined exactly and close upper and lower bounds are presented in the low-and moderate-SNR regimes. The asymptotic low-SNR limit is achieved by having each transmit antenna signal either with zero or with the maximally allowed peak power, and the latter only if all stronger antennas also send at maximum peak power. In particular, for almost all channel gains, the input to achieve the asymptotic low-SNR capacity is such that its projection on the channel-gain vector has only two or three positive probability point masses, one of them being at zero. The lower bounds at finite SNR are numerical and are obtained using input distributions whose projection on the channel-gain vector has either two, three, or four positive probability masses. Finally, the paper presents two analytic upper bounds on the capacity of the MISO channel: the first one closely follows the proposed numerical lower bounds in the low-SNR regime, and the second one can improve on previous bounds in the moderate-SNR regime

Exploiting Multi-Antennas for Opportunistic Spectrum Sharing in Cognitive Radio Networks

In cognitive radio (CR) networks, there are scenarios where the secondary (lower priority) users intend to communicate with each other by opportunistically utilizing the transmit spectrum originally allocated to the existing primary (higher priority) users. For such a scenario, a secondary user usually has to trade off between two conflicting goals at the same time: one is to maximize its own transmit throughput; and the other is to minimize the amount of interference it produces at each primary receiver. In this paper, we study this fundamental tradeoff from an information-theoretic perspective by characterizing the secondary user's channel capacity under both its own transmit-power constraint as well as a set of interference-power constraints each imposed at one of the primary receivers. In particular, this paper exploits multi-antennas at the secondary transmitter to effectively balance between spatial multiplexing for the secondary transmission and interference avoidance at the primary receivers. Convex optimization techniques are used to design algorithms for the optimal secondary transmit spatial spectrum that achieves the capacity of the secondary transmission. Suboptimal solutions for ease of implementation are also presented and their performances are compared with the optimal solution. Furthermore, algorithms developed for the single-channel transmission are also extended to the case of multi-channel transmission whereby the secondary user is able to achieve opportunistic spectrum sharing via transmit adaptations not only in space, but in time and frequency domains as well.Comment: Extension of IEEE PIMRC 2007. 35 pages, 6 figures. Submitted to IEEE Journal of Special Topics in Signal Processing, special issue on Signal Processing and Networking for Dynamic Spectrum Acces

Cooperative Multi-Cell Block Diagonalization with Per-Base-Station Power Constraints

Block diagonalization (BD) is a practical linear precoding technique that eliminates the inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. In this paper, we apply BD to the downlink transmission in a cooperative multi-cell MIMO system, where the signals from different base stations (BSs) to all the mobile stations (MSs) are jointly designed with the perfect knowledge of the downlink channels and transmit messages. Specifically, we study the optimal BD precoder design to maximize the weighted sum-rate of all the MSs subject to a set of per-BS power constraints. This design problem is formulated in an auxiliary MIMO broadcast channel (BC) with a set of transmit power constraints corresponding to those for individual BSs in the multi-cell system. By applying convex optimization techniques, this paper develops an efficient algorithm to solve this problem, and derives the closed-form expression for the optimal BD precoding matrix. It is revealed that the optimal BD precoding vectors for each MS in the per-BS power constraint case are in general non-orthogonal, which differs from the conventional orthogonal BD precoder design for the MIMO-BC under one single sum-power constraint. Moreover, for the special case of single-antenna BSs and MSs, the proposed solution reduces to the optimal zero-forcing beamforming (ZF-BF) precoder design for the weighted sum-rate maximization in the multiple-input single-output (MISO) BC with per-antenna power constraints. Suboptimal and low-complexity BD/ZF-BF precoding schemes are also presented, and their achievable rates are compared against those with the optimal schemes.Comment: accepted in JSAC, special issue on cooperative communications on cellular networks, June 201

On the Capacity Region of Multi-Antenna Gaussian Broadcast Channels with Estimation Error

In this paper we consider the effect of channel estimation error on the capacity region of MIMO Gaussian broadcast channels. It is assumed that the receivers and the transmitter have (the same) estimates of the channel coefficients (i.e., the feedback channel is noiseless). We obtain an achievable rate region based on the dirty paper coding scheme. We show that this region is given by the capacity region of a dual multi-access channel with a noise covariance that depends on the transmit power. We explore this duality to give the asymptotic behavior of the sum-rate for a system with a large number of user, i.e., n rarr infin. It is shown that as long as the estimation error is of fixed (w.r.t n) variance, the sum-capacity is of order M log log n, where M is the number of antennas deployed at the transmitter. We further obtain the sum-rate loss due to the estimation error. Finally, we consider a training-based scheme for block fading MISO Gaussian broadcast channels. We find the optimum length of the training interval as well as the optimum power used for training in order to maximize the achievable sum-rate