On the MIMO Capacity with Multiple Linear Transmit Covariance Constraints

Abstract

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 to the computation of the MIMO capacity. Specifically, a modified 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

“…On the other hand, Algorithm 1 becomes more efficient when the size of the system increases. In the next numerical experiment we compare the convergence rate of Algorithm 2 with a subgradient method for solving (15). In particular, we plot the convergence of both algorithms for the first subproblem (i.e.…”

“…instead of the objective in (15). That is we include the constants omitted when deriving (15). If C s (X) < 0, it is replaced by 0.…”

“…However, the incurred complexity (including the memory requirement) is very high when N t is large, which is the case for massive MIMO. Our goal in this section is to derive a more efficient method for solving (15). To this end we note that the spectrahedron X spc is simple in the sense that the projection onto it can be computed efficiently as shall be seen shortly.…”

“…To this end we note that the spectrahedron X spc is simple in the sense that the projection onto it can be computed efficiently as shall be seen shortly. To exploit this fact, we resort to the CoMirror algorithm presented in [23] to solve (15).…”

“…In a MIMO communications system, each transmit antenna can be equipped with a separate RF chain, and thus a perantenna power constraint (PAPC) is more practically relevant than constraining the sum power [15], [16]. In this regard, the secrecy capacity with joint SPC and PAPC has been studied in [17], [18] for the Gaussian MIMO WTC, and more recently in [19] for the MISO Gaussian WTC.…”