Beyond Diagonal RIS-Aided Networks: Performance Analysis and Sectorization Tradeoff

Reconfigurable intelligent surfaces (RISs) have
emerged as a spectrum- and energy-efficient technology to
enhance the coverage of wireless communications within the
upcoming 6G networks. Recently, novel extensions of this technology,
referred to as multi-sector beyond diagonal RIS (BDRIS),
have been proposed, where the configurable elements are
divided into L sectors (L ≥ 2) and arranged as a polygon
prism, with each sector covering 1/L space. This paper presents
a performance analysis of a multi-user communication system
assisted by a multi-sector BD-RIS operating in time-switching
(TS) mode. Specifically, we derive closed-form expressions for the
moment-generating function (MGF), probability density function
(PDF), and cumulative density function (CDF) of the signalto-
noise ratio (SNR) per user. Furthermore, exact closed-form
expressions for the outage probability, achievable spectral and
energy efficiency, symbol error probability, and diversity order
for the proposed system model are derived. To evaluate the
performance of multi-sector BD-RISs, we compare them with the
simultaneously transmitting and reflecting (STAR)-RISs, which
can be viewed as a special case of multi-sector BD-RIS with
only two sectors. Interestingly, our analysis reveals that, for a
fixed number of configurable elements, increasing the number of
sectors improves outage performance while reducing the diversity
order compared to the STAR-RIS configuration. This trade-off
is influenced by the Rician factors of the cascaded channel and
the number of configurable elements per sector. However, this
superiority in slope is observed at outage probability values
below 10−5, which remains below practical operating ranges
of communication systems. Additionally, simulation results are
provided to validate the accuracy of our theoretical analyses.
These results indicate that increasing the number of sectors
in multi-sector BD-RIS-assisted systems significantly enhances
performance, particularly in spectral and energy efficiency. For
instance, our numerical results show a notable 182% increase in
spectral efficiency and a 238% increase in energy efficiency when
transitioning from a 2-sector to a 6-sector configuration.