Linear Regression for Implicit Standard Interference Function in Wireless Networks under General Fading Environments

Understanding and analyzing the effects of channel fading is crucial for mitigating signal degradation, enhancing transmission reliability, and improving overall communication service quality. In this paper, we study the outage probability under general fading environments. Due to the complexity of obtaining a precise closed-form expression theoretically and mathematically, we employ regression analysis to effectively tackle the outage probability. We consider a special class of utility maximization problem subject to general outage probability constraints, which might not be expressed explicitly or in deterministic form. We then show that these constraints can be reformulated into constraints involving implicit standard interference functions that exhibit affine linearity. Hence, despite their implicit characteristics, we can simply employ linear regression to convert these standard interference functions into explicit forms. Subsequently, we can utilize the convergence properties of the standard interference functions to efficiently resolve the utility maximization problem. Finally, we present numerical results to demonstrate that our approach is theoretically sound and practically implementable. © 2024 IEEE.