# MIMO Capacity with Average Total and Per-Antenna Power Constraints

## TL;DR

This paper analyzes the capacity of MIMO systems under combined total and per-antenna power constraints, providing closed-form solutions for specific cases and optimization algorithms validated through numerical results.

## Contribution

It introduces a comprehensive analysis of MIMO capacity with joint power constraints, including closed-form solutions and low-complexity optimization methods.

## Key findings

- Closed-form solutions for unit-rank channel matrices.
- Derived numerical complexity formulas based on channel rank.
- Validated optimization algorithms with numerical simulations.

## Abstract

MIMO capacity with a joint total and per-antenna average power constraint is considered in this work. The problem arises when, besides having a limited available power at the transmitter, also the individual antennas cannot radiate power beyond the limits of their corresponding RF chains. Closed-form results are illustrated in specific cases and, in particular, in the unit-rank channel matrix case. Lower-complexity optimization problems are derived for the other cases. Numerical complexity is derived in terms of the number of equivalent real variables for the optimization problem and a general formula is provided depending on the channel matrix rank. Numerical results are included to validate and illustrate the application of the proposed optimization algorithms and also to evaluate the time complexity of its implementation.