  Cell-free massive multiple-input multiple-output (MIMO) provides more uniform
spectral efficiency (SE) for users (UEs) than cellular technology. The main
challenge to achieve the benefits of cell-free massive MIMO is to realize
signal processing in a scalable way. In this paper, we consider scalable
fullpilot zero-forcing (FZF), partial FZF (PFZF), protective weak PFZF
(PWPFZF), and local regularized ZF (LRZF) combining by exploiting channel
statistics. We derive closed-form expressions of the uplink SE for FZF, PFZF,
and PWPFZF combining with large-scale fading decoding over independent Rayleigh
fading channels, taking channel estimation errors and pilot contamination into
account. Moreover, we investigate the impact of the number of pilot sequences,
antennas per AP, and APs on the performance. Numerical results show that LRZF
provides the highest SE. However, PWPFZF is preferable when the number of pilot
sequences is large and the number of antennas per AP is small. The reason is
that PWPFZF has lower computational complexity and the SE expression can be
computed in closed-form. Furthermore, we investigate the performance of PWPFZF
combining with fractional power control and the numerical results show that it
improves the performance of weak UEs and realizes uniformly good service for
all UEs in a scalable fashion.
