Long term evolution (LTE) and LTE-Advanced (LTE-A) based transmissions extended from licensed to unlicensed bands, known as LTE-unlicensed and licensed assisted access, can effectively alleviate the congestion of cellular bands. Efficient integration of the dual-spectrum in small-cells can further improve the achievable spectrum efficiency. In this paper, we optimize the power and resource allocation for LTE small-cells by jointly utilizing licensed and unlicensed bands, where practical issues like imperfect channel state information (CSI) and the characteristics of LTE unlicensed traffic are considered. More specifically, we formulate a stochastic mixed-integer non-linear programming (MINLP) problem to maximize the expected sum-rate (ESR) of the system. To solve this NP-hard problem, the so-called reduced-complexity joint licensed and unlicensed resource allocation (RC-JLURA) algorithm is proposed, where the original problem is transformed to a deterministic MINLP problem by employing an analytic approximation. Thanks to the Lagrange dual optimization based on a framework of alternate iteration, the proposed method can provide a near-optimum closed-form solution to the problem concerned, while maintaining a low computational complexity. The achievable performance of the LTE dual-spectrum mechanism is evaluated through simulations, which demonstrate the superiority of the proposed algorithm.
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