STAR-RIS Assisted Cell-Free Massive MIMO System Under Spatially-Correlated Channels

This paper investigates the performance of downlink
simultaneous transmitting and reflecting reconfigurable intelligent
surface (STAR-RIS)-assisted cell-free (CF) massive multiple-input
multiple-output (mMIMO) systems, where user equipments (UEs)
are located on both sides of the RIS. We account for correlated
Rayleigh fading and multiple antennas per access point (AP), while
the maximum ratio (MR) beamforming is applied for the design
of the active beamforming in terms of instantaneous channel state
information (CSI). Firstly, we rely on an aggregated channel
estimation approach that reduces the overhead required for
channel estimation while providing sufficient information for
data processing. We obtain the normalized mean square error
(NMSE) of the channel estimate per AP, and design the passive
beamforming (PB) of the surface based on the long-time statistical
CSI. Next, we derive the received signal in the asymptotic regime
of numbers of APs and surface elements. Then, we obtain a closedform
expression of the downlink achievable rate for arbitrary
numbers of APs and STAR-RIS elements under statistical CSI.
Finally, based on the derived expressions, the numerical results
show the feasibility and the advantages of deploying a STARRIS
into conventional CF mMIMO systems. In particular, we
theoretically analyze the properties of STAR-RIS-assisted CF
mMIMO systems and reveal explicit insights in terms of the
impact of channel correlation, the number of surface elements,
and the pilot contamination on the achievable rate.