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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 …