Abstract

Consider a multiple-input single-output system, where the
nonnegative, peak-limited inputs $X_1,..., X_{n_T} \in [0, A]$ are
subject to first- and second-moment sum-constraints on all
antennas. The paper characterizes all probability distributions
that can be induced for the “channel image,” which is given by the
inner product of the input vector with a given channel vector. Key
to this result is the description of input vectors that achieve a
given deterministic channel image with the smallest energy, where
“energy” of an input vector refers to a weighted sum of its one-
and two-norms. Minimum-energy input vectors have an interesting
structure: depending on the desired channel image, some of the
weakest antennas are silenced, and the remaining antennas are
chosen according to a shifted and amplitude-constrained
beamforming rule.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Mon Jan 31 09:31:35 CET 2022