Precoding coefficients can be compressed based on user equipment signal interference to noise ratio or path loss in front haul cloud radio access network systems. For example, a baseband unit can compute a precoder matrix from an estimated channel associated with an uplink signal. Once the baseband unit computes the channel, it can determine the coefficients for the linear combination of the basis vectors, which are known at the baseband unit and the radio unit as well. The baseband unit can estimate the path loss and the signal interference to noise ratio and determine the basis vectors. The baseband unit can then compress the coefficients and transmit the coefficients to the radio unit. When the radio unit receives the compressed coefficients, the radio unit can reconstruct the precoder matrix and apply to reference signals and data traffic channels.