In this paper, we study resource allocation and adaptive modulation in SC-FDMA which is adopted as the multiple access scheme for the uplink in the 3GPP-LTE standard. A sum-utility maximization (SUmax), and a joint adaptive modulation and sum-cost minimization (JAMSCmin) problems are considered. Unlike OFDMA, in addition to the restriction of allocating a sub-channel to one user at most, the multiple sub-channels allocated to a user in SC-FDMA should be consecutive as well. This renders the resource allocation problem prohibitively difficult and the standard optimization tools (e.g., Lagrange dual approach widely used for OFDMA, etc.) can not help towards its optimal solution. We propose a novel optimization framework for the solution of these problems that is inspired from the recently developed canonical duality theory. We first formulate the optimization problems as binary-integer programming problems and then transform these binary-integer programming problems into continuous space canonical dual problems that are concave maximization problems. Based on the solution of the continuous space dual problems, we derive resource allocation (joint with adaptive modulation for JAMSCmin) algorithms for both the problems which have polynomial complexities. We provide conditions under which the proposed algorithms are optimal. We also propose an adaptive modulation scheme for SUmax problem. We compare the proposed algorithms with the existing algorithms in the literature to assess their performance.
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