Revisiting the MIMO Capacity With Per-Antenna Power Constraint: Fixed-Point Iteration and Alternating Optimization

Abstract

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.

Alternating Optimization for Capacity Region of Gaussian MIMO Broadcast Channels with Per-Antenna Power Constraint

“…However, as mentioned in [14] and also observed in [16], the convergence of such a naive AO method is not guaranteed. The novelty of our proposed AO algorithm is that, instead of optimizing the original objective in (12) which can lead to fluctuations, we opt to minimize an upper bound of the objective in (12).…”

WITHDRAWN: Optical Satellite Sensor and Positioning Accuracy Assessment for The Hongqi-H9 Wide-Range Satellite in Different Terrains

“…Despite the rapid advancement in satellite remote sensing technology, two key requirements to obtain high spatial resolution satellite images remain to be attained [1][2][3]. The first requirement corresponds to the fixed-point fast revisit capability, which is primarily influenced by the timeliness of the satellites [4][5]; for instance, satellites can generally provide real-time images of disaster areas within a few minutes in natural disaster events [6]. The second requirement corresponds to the prompt updating capacity for a large-scale area, which mainly depends on the swath width of the satellite.…”

A Low-Complexity Algorithm for Achieving Secrecy Capacity in MIMO Wiretap Channels

“…We remark that the same idea was also used in [8] in a different context. Then K n+1 is an optimal solution to the following convex problem…”

“…Motivated by the above discussions, our aim in this paper is to derive a low-complexity and scalable method for finding the optimal transmit covariance matrix of the secrecy rate maximization problem under a total transmit power constraint. Suggested by the structure of the equivalent minimax problem, we apply the concept of alternating optimization (AO), but in a novel way, to find a saddle point [7], [8]. We remark that the proposed method is entirely different from the one introduced in [9].…”