On the MIMO Capacity with Multiple Linear Transmit Covariance Constraints

This paper presents an efficient approach to computing the capacity of multiple-input multiple-output (MIMO) channels under multiple linear transmit covariance constraints (LTCCs). LTCCs are general enough to include several special types of power constraints as special cases such as the sum power constraint (SPC), per-antenna power constraint (PAPC), or a combination thereof. Despite its importance and generality, most of the existing literature considers either SPC or PAPC independently. Efficient solutions to the computation of the MIMO capacity with a combination of SPC and PAPC have been recently reported, but were only dedicated to multipleinput single-output (MISO) systems. For the general case of LTCCs, we propose a low-complexity semi-closed-form approach tothecomputationoftheMIMOcapacity.Specifically,amodified minimax duality is first invoked to transform the considered problem in the broadcast channel into an equivalent minimax problem in the dual multiple access channel. Then alternating optimization and concave-convex procedure are utilized to derive water-filling-based algorithms to find a saddle point of the minimax problem. This is different from the state-of-the-art solutions to the considered problem, which are based on interiorpoint or subgradient methods. Analytical and numerical results are provided to demonstrate the effectiveness of the proposed low-complexity solution under various MIMO scenarios

On the Secrecy Capacity of MIMO Wiretap Channels: Convex Reformulation and Efficient Numerical Methods

This paper presents novel numerical approaches to finding the secrecy capacity of the multiple-input multiple-output (MIMO) wiretap channel subject to multiple linear transmit covariance constraints, including sum power constraint, per antenna power constraints and interference power constraint. An analytical solution to this problem is not known and existing numerical solutions suffer from slow convergence rate and/or high per-iteration complexity. Deriving computationally efficient solutions to the secrecy capacity problem is challenging since the secrecy rate is expressed as a difference of convex functions (DC) of the transmit covariance matrix, for which its convexity is only known for some special cases. In this paper we propose two low-complexity methods to compute the secrecy capacity along with a convex reformulation for degraded channels. In the first method we capitalize on the accelerated DC algorithm which requires solving a sequence of convex subproblems, for which we propose an efficient iterative algorithm where each iteration admits a closed-form solution. In the second method, we rely on the concave-convex equivalent reformulation of the secrecy capacity problem which allows us to derive the so-called partial best response algorithm to obtain an optimal solution. Notably, each iteration of the second method can also be done in closed form. The simulation results demonstrate a faster convergence rate of our methods compared to other known solutions. We carry out extensive numerical experiments to evaluate the impact of various parameters on the achieved secrecy capacity

Dynamic Resource Allocation in Cognitive Radio Networks: A Convex Optimization Perspective

This article provides an overview of the state-of-art results on communication resource allocation over space, time, and frequency for emerging cognitive radio (CR) wireless networks. Focusing on the interference-power/interference-temperature (IT) constraint approach for CRs to protect primary radio transmissions, many new and challenging problems regarding the design of CR systems are formulated, and some of the corresponding solutions are shown to be obtainable by restructuring some classic results known for traditional (non-CR) wireless networks. It is demonstrated that convex optimization plays an essential role in solving these problems, in a both rigorous and efficient way. Promising research directions on interference management for CR and other related multiuser communication systems are discussed.Comment: to appear in IEEE Signal Processing Magazine, special issue on convex optimization for signal processin

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