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.

We investigate the use of cell-free massive multiple input multiple output (MIMO) systems in serving unmanned aerial vehicles (UAVs) and ground user equipments (GUEs) in underlay spectrum access mode by considering UAVs as secondary users and GUEs as primary users. We derive a novel lower bound on complement of interference violation probability (IVP). This result helps determine the power margin required at secondary access points (APs) to meet the IVP constraint. We deduce new analytical expressions for spectral efficiency (SE) and bit error rate (BER) of UAVs and GUEs. This analysis entails finding expectation of secondary AP transmit power based on order statistics of the strongest interference channel between secondary APs and GUEs. We prove that for lower pilot power, a larger power margin is required to keep IVP fixed. We show that for a given IVP, the larger the interference threshold is, the greater (lower) the likelihood for the UAVs (GUEs) to obtain higher SE is. For a given interference threshold, probability that UAVs attain higher SE increases as IVP increases for a fixed number of secondary APs ($N$) or as$N$increases for a given IVP. Impact of interference threshold and height of UAVs on BER is elucidated.