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In this paper, we revisit the fundamental problem of computing MIMO capacity under per-antenna power constraint (PAPC). Unlike the sum power constraint counterpart which likely admits water-filling-like solutions, MIMO capacity with PAPC has been largely studied under the framework of generic convex optimization. The two main shortcomings of these approaches are (i) their complexity scales quickly with the problem size, which is not appealing for large-scale antenna systems, and/or (ii) their convergence properties are sensitive to the problem data. As a starting point, we first consider a single user MIMO scenario and propose two provably-convergent iterative algorithms to find its capacity, the first method based on fixedpoint iteration and the other based on alternating optimization and minimax duality. In particular, the two proposed methods can leverage the water-filling algorithm in each iteration and converge faster, compared to current methods. We then extend the proposed solutions to multiuser MIMO systems with dirty paper coding (DPC) based transmission strategies. In this regard, capacity regions of Gaussian broadcast channels with PAPC are also computed using closed-form expressions. Numerical results are provided to demonstrate the outperformance of the proposed solutions over existing approaches.

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.

In this paper, an efficient approach for weighted sum rate maximization (WSRMax) for zero-forcing(ZF)methods with general linear transmit covariance constraints (LTCCs) is proposed. This problem has been extensively studied separately for some special cases such as for sum power or per-antenna power constraints (PAPC). Due to some practical and regulatory requirements, these power constraints alone are not in general sufficient, which motivates the consideration of general LTCCs. On the other hand, the zero-forcing (ZF) is a simple linear precoding technique to mitigate inter-user interference. The problem of WSRMax for ZF methods with LTCCs was studied previously using a gradient descent algorithm with barrier functions, but this method was also shown to converge slowly. To derive an efficient solution to this problem, we first reformulate it as an equivalent minimax problem using Lagrangian duality. The obtained result in fact resembles BC-MAC duality but is specialized for ZF methods. We then combine alternating optimization and concave-convex procedure to efficiently compute a saddle point of the minimax problem. The proposed method is numerically shown to converge very fast and its complexity scales linearly with the number of users.

This paper proposes an efficient (semi-closed-form) zero-forcing (ZF) precoder design for the weighted sum-rate maximization problem under per-antenna power constraint (PAPC). Existing approaches for this problem are based on either interior-point methods that do not favor-ably scale with the problem size or subgradient methods that are widely known to converge slowly. To address these shortcomings, our proposed method is derived from three elements: minimax duality, alternating optimization (AO), and successive convex approximation (SCA). Specifically,the minimax duality is invoked to transform the considered problem into anequivalent minimax problem, for which we then recruit AO and SCA to finda saddle point, which enables us to take advantages of closed-form expressions and hence achieve fast convergence rate. Moreover, the complexity of the proposed method scales linearly with the number of users, compared to cubically for the standard interior-point methods. We provide an analytical proof for the convergence of the proposed method and numerical results to demonstrate its superior performance over existing approaches.Our proposed method offers a powerful tool to characterize the achievable rate region of ZF schemes under PAPC for massive multiple-input multiple-output