  We investigate the coexistence of underlay spectrum sharing in cell-free
massive multiple-input multiple-output (MIMO) systems. A primary system with
geographically distributed primary access points (P-APs) serves a multitude of
primary users (PUs), while a secondary system serves a large number of
secondary users (SUs) in the same primary/licensed spectrum by exploiting the
underlay spectrum sharing. To mitigate the secondary co-channel interference
inflected at PUs, stringent secondary transmit power constraints are defined
for the secondary access points (S-APs). A generalized pilots sharing scheme is
used to locally estimate the uplink channels at P-APs/S-APs, and thereby,
conjugate precoders are adopted to serve PUs/SUs in the same time-frequency
resource element. Moreover, the effect of a user-centric AP clustering scheme
is investigated by assigning a suitable set of APs to a particular user. The
impact of estimated downlink (DL) channels at PUs/SUs via DL pilots beamformed
by P-APs/S-APs is investigated. The achievable primary/secondary rates at
PUs/SUs are derived for the statistical DL and estimated DL CSI cases.
User-fairness for PUs/SUs is achieved by designing efficient transmit power
control policies based on a multi-objective optimization problem formulation of
joint underlay spectrum sharing and max-min criteria. The proposed orthogonal
multiple-access based analytical framework is also extended to facilitate
non-orthogonal multiple-access. Our analysis and numerical results manifest
that the primary/secondary performance of underlay spectrum sharing can be
boosted by virtue of the average reduction of transmit powers/path-losses,
uniform coverage/service, and macro-diversity gains, which are inherent to
distributed transmissions/receptions of cell-free massive MIMO.
