Superimposed Pilots for Cell-Free Massive MIMO Over Spatial-Correlated Rician Fading Channels

In Cell-Free Massive multi-input multi-output (CF mMIMO), it is challenging to assign regular pilots due to the pre-log pilot overhead on spectral efficiency (SE). This paper explores a superimposed-pilot-(SP)-assisted CF mMIMO system which avoids the separate pilot training duration by superimposing pilot symbols onto data symbols. We consider spatial-correlated Rician fading channels with and without random phase shifts, where linear minimum-mean-square-error (LMMSE) estimators are performed at each access point locally. Then, we derive the closed-form SE expressions with maximal-ratio (MR) combining. To fill the gap, we introduce novel expressions of MMSE combining vectors and compare their SE performance with approximate MMSE combining vectors. Next, a generic model is provided for the optimal large-scale fading decoding (LSFD), and we derive the closed-form suboptimal LSFD solutions with MR combining. A line-of-sight-based combining scheme is proposed based on the approximate analysis, where closed-form SE expressions are derived using MR and MMSE combining and corresponding optimal LSFD coefficients. Numerical results show that the combination of MMSE and optimal LSFD yields almost 200% enhancement over the combination of MR and simple centralized decoding in 95% likely per-user SE without phase shifts, and 111% enhancement when phase shifts exist.