Cell-Free Massive MIMO Based Underlay Spectrum Access Under Interference Outage Probability Constraint Over Limited Capacity Fronthaul

We analyze the uplink (UL) of a cell-free massive multiple input multiple output (mMIMO) based underlay network over limited capacity fronthaul in which the secondary users (SUs) transmit under an interference outage probability (IOP) constraint and the impact of quantization is modeled based on Bussgang decomposition. We first develop novel statistical models for the squared l 2 -norm (SLN) of the true and the quantized channel estimates (QCE) based on Gamma distribution and find the corresponding shape and scale parameters. We then derive new expressions for mean SU transmit power and correlation between SLN of true and QCE. We also develop new expressions for IOP and UL spectral efficiency (SE) of SUs and primary users (PUs) as a function of the Bussgang gain and quantization noise variance which in turn depends on the number of quantization levels. We show that to keep IOP fixed, larger back-off in SU transmit power is required when fewer bits are employed for quantization. Furthermore, the likelihood of PUs or SUs achieving a higher SE increases as number of quantization bits increases and 4 bits are sufficient to obtain same performance as an infinite capacity fronthaul. Impact of spatial correlation on SE is also elucidated.