Long Term Evolution (LTE)-License Assisted Access (LAA), which leverages unlicensed resource sharing with the Wi-Fi network, is a promising technique to address the spectrum scarcity issue in present and future wireless networks. However, unlicensed spectrum sharing between Wi-Fi and LAA requires fair resource allocation with specific performance guarantees for both sets of Wi-Fi and LAA stations. In this paper, an optimal communication policy is devised for LAA stations coexisting on a single unlicensed channel with Wi-Fi stations. The inter-network collisions are avoided through nonoverlapping transmission phases for Wi-Fi and LAA networks. The throughput performance of LAA network is maximized while guaranteeing a proportionally fair performance among LAA stations and a fair share for Wi-Fi stations. The proposed scheme, unlike the state-of-the-art coexisting mechanism, jointly optimizes the transmission probability and the transmission rate for each LAA station. The formulated optimization problem to maximize network throughput is solved analytically. The numerical results demonstrate a significant improvement in the LAA throughput, more than 75 %, as compared to the case when transmission probabilities are not optimized. Moreover, a notable gain of 8 − 9 % in the fairness index reflects the intranetwork fairness of the proposed LAA network over the conventional LAA network.INDEX TERMS Licensed assisted access (LAA), Wi-Fi, proportional fairness, random channel access, transmit power control.