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The rising traffic demand is exerting pressure on the licensed spectrum of Long Term Evolution (LTE). To address this, mobile operators are leveraging the unlicensed spectrum alongside the existing licensed spectrum. Yet, employing LTE in the unlicensed spectrum presents challenges, notably the coexistence of LTE with other unlicensed communication technologies, such as Wi-Fi. This paper introduces a novel coexistence mechanism that ensures a balanced coexistence between LTE and Wi-Fi networks operating in unlicensed bands. Our approach strategically allocates resource blocks in eNodeB to LTE users, promoting efficient and fair use of the unlicensed spectrum for both LTE users and Wi-Fi networks. We cast the challenge of wireless resource allocation and fair coexistence between LTE and Wi-Fi as a non-linear integer programming problem. Subsequently, we design a Polynomial-Time …