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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 theassumption that the channel state information at the transmitter (CSIT) islimited to finite precision. In particular, our goal is to identify a parameterregime where a simple layered superposition (SLS) coding scheme achieves theentire GDoF region. With $\alpha_{ij}$ representing the channel strengthparameter 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 fortime-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 convexpolyhedron. The result generalizes to arbitrary $M\geq 3$.

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