  Cell-Free Massive Multiple-input Multiple-output (mMIMO) consists of many
access points (APs) in a coverage area that jointly serve the users. These
systems can significantly reduce the interference among the users compared to
conventional MIMO networks and so enable higher data rates and a larger
coverage area. However, Cell-Free mMIMO systems face multiple practical
challenges such as the high complexity and power consumption of the APs' analog
front-ends. Motivated by prior works, we address these issues by considering a
low complexity hybrid beamforming framework at the APs in which each AP has a
limited number of RF-chains to reduce power consumption, and the analog
combiner is designed only using the large-scale statistics of the channel to
reduce the system's complexity. We provide closed-form expressions for the
signal to interference and noise ratio (SINR) of both uplink and downlink data
transmission with accurate random matrix approximations. Also, based on the
existing literature, we provide a power optimization algorithm that maximizes
the minimum SINR of the users for uplink scenario. Through several simulations,
we investigate the accuracy of the derived random matrix approximations,
trade-off between the 95% outage data rate and the number of RF-chains, and the
impact of power optimization. We observe that the derived approximations
accurately follow the exact simulations and that in uplink scenario while using
MMSE combiner, power optimization does not improve the performance much.
