  In cell-free massive multiple-input multiple-output (MIMO) the fluctuations
of the channel gain from the access points to a user are large due to the
distributed topology of the system. Because of these fluctuations, data
decoding schemes that treat the channel as deterministic perform inefficiently.
A way to reduce the channel fluctuations is to design a precoding scheme that
equalizes the effective channel gain seen by the users. Conjugate beamforming
(CB) poorly contributes to harden the effective channel at the users. In this
work, we propose a variant of CB dubbed enhanced normalized CB (ECB), in that
the precoding vector consists of the conjugate of the channel estimate
normalized by its squared norm. For this scheme, we derive an exact closed-form
expression for an achievable downlink spectral efficiency (SE), accounting for
channel estimation errors, pilot reuse and user's lack of channel state
information (CSI), assuming independent Rayleigh fading channels. We also
devise an optimal max-min fairness power allocation based only on large-scale
fading quantities. ECB greatly boosts the channel hardening enabling the users
to reliably decode data relying only on statistical CSI. As the provided
effective channel is nearly deterministic, acquiring CSI at the users does not
yield a significant gain.
