Optimality of Simple Layered Superposition Coding in the 3 User MISO BC with Finite Precision CSIT

TL;DR

This paper proves that a simple layered superposition coding scheme is GDoF optimal for a 3-user MISO broadcast channel with finite precision CSIT under specific channel strength conditions, extending to more antennas.

Contribution

It identifies conditions under which simple layered superposition coding achieves the entire GDoF region without time-sharing, generalizing previous results to arbitrary number of antennas.

Findings

Layered superposition coding is GDoF optimal under certain channel conditions.

The GDoF region forms a convex polyhedron under these conditions.

Results extend to M ≥ 3 antennas at the transmitter.

Abstract

We study the $K=3$ user multiple input single output (MISO) broadcast channel (BC) with $M=3$ antennas at the transmitter and $1$ antenna at each receiver, from the generalized degrees of freedom (GDoF) perspective, under the assumption that the channel state information at the transmitter (CSIT) is limited to finite precision. In particular, our goal is to identify a parameter regime where a simple layered superposition (SLS) coding scheme achieves the entire GDoF region. With $\alpha_{ij}$ representing the channel strength parameter for the link from the $j^{th}$ antenna of the transmitter to the $i^{th}$ receiver, we prove that SLS is GDoF optimal without the need for time-sharing if $\max(\alpha_{ki},\alpha_{im})\leq\alpha_{ii}$ and $\alpha_{ki}+\alpha_{im}\le\alpha_{ii}+\alpha_{km}$ for all $i,k\in[3],m\in[M]$. The GDoF region under this condition is a convex polyhedron. The result generalizes to arbitrary $M\geq 3$.