We consider a two-way half-duplex decode-and-forward (DF) relaying system
with multiple pairs of single-antenna users assisted by a cell-free (CF)
massive multiple-input multiple-output (mMIMO) architecture with
multiple-antenna access points (APs). Under the practical constraint of
imperfect channel state information (CSI), we derive the achievable sum
spectral efficiency (SE) for a finite number of APs with maximum ratio (MR)
linear processing for both reception and transmission in closed-form. Notably,
the proposed CF mMIMO relaying architecture, exploiting the spatial diversity,
and providing better coverage, outperforms the conventional collocated mMIMO
deployment. Moreover, we shed light on the power-scaling laws maintaining a
specific SE as the number of APs grows. A thorough examination of the interplay
between the transmit powers per pilot symbol and user/APs takes place, and
useful conclusions are extracted. Finally, differently to the common approach
for power control in CF mMIMO systems, we design a power allocation scheme
maximizing the sum SE.Comment: 15 pages, 8 figures, This work was accepted in IEEE Trans. Green
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