MISO Capacity with Per-Antenna Power Constraint

TL;DR

This paper derives the exact capacity and optimal signaling strategies for MISO channels under per-antenna power constraints, considering both known and unknown channel states, revealing capacity limitations compared to sum power constraints.

Contribution

It provides closed-form capacity expressions and optimal signaling schemes for MISO channels with per-antenna power constraints under different channel knowledge scenarios.

Findings

Optimal beamforming for known channels with phase matching.

Independent signaling for unknown Rayleigh fading channels.

Capacity under per-antenna constraints is generally less than sum power constraints.

Abstract

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.