Amplitude Constrained MIMO Channels: Properties of Optimal Input Distributions and Bounds on the Capacity

Area of Science:

• Information Theory
• Wireless Communications
• Signal Processing

Background:

• Multiple-input multiple-output (MIMO) channels are crucial for modern wireless systems.
• Understanding capacity limitations under input constraints is vital for system design.
• Existing research often focuses on average power constraints, leaving other input constraints less explored.

Purpose of the Study:

• To investigate the capacity of MIMO channels with input support constraints.
• To characterize the structure of capacity-achieving input distributions.
• To develop novel bounds for channel capacity under various input constraints, particularly amplitude constraints.

Main Methods:

• Analysis of the general structure of capacity-achieving input distributions.
• Derivation of new topological and measure-theoretic properties of input supports.
• Development and analysis of novel upper and lower bounds on channel capacity.
• Application to MIMO channels with amplitude constraints.

Main Results:

• Capacity-achieving input distributions are shown to have small supports, both topologically and in measure.
• Explicit conditions are derived for input distributions to be concentrated on the boundary of the input space.
• Novel upper and lower bounds for capacity are presented for channels with arbitrary input support constraints.
• For amplitude-constrained MIMO channels, bounds are within a constant gap to capacity (if the channel matrix is invertible) and tight in the high amplitude regime.
• Capacity scales linearly with the minimum number of transmit/receive antennas in the high amplitude regime.

Conclusions:

• The structure of capacity-achieving inputs for MIMO channels with support constraints is precisely characterized.
• New capacity bounds provide tighter performance analysis, especially for amplitude-constrained systems.
• The findings reveal that capacity scales favorably with antenna numbers under high amplitude conditions, mirroring power-constrained scenarios.