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