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This paper investigates the performance of downlink simultaneous transmittingand reflecting reconfigurable intelligent surface (STAR-RIS)-assisted cell-free(CF) massive multiple-input multiple-output (mMIMO) systems, where userequipments (UEs) are located on both sides of the RIS.  We account for correlated Rayleigh fading and multiple antennas per accesspoint (AP), while the maximum ratio (MR) beamforming is applied for the designof the active beamforming in terms of instantaneous channel state information(CSI). Firstly, we rely on an aggregated channel estimation approach thatreduces the overhead required for channel estimation while providing sufficientinformation 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 thereceived signal in the asymptotic regime of numbers of APs and surfaceelements. Then, we obtain a closed-form expression of the downlink achievablerate for arbitrary numbers of APs and STAR-RIS elements under statistical CSI.Finally, based on the derived expressions, the numerical results show thefeasibility and the advantages of deploying a STAR-RIS into conventional CFmMIMO systems. In particular, we theoretically analyze the properties ofSTAR-RIS-assisted CF mMIMO systems and reveal explicit insights in terms of theimpact of channel correlation, the number of surface elements, and the pilotcontamination on the achievable rate.

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