In this paper, we study resource allocation and adaptive modulation inSC-FDMA which is adopted as the multiple access scheme for the uplink in the3GPP-LTE standard. A sum-utility maximization (SUmax), and a joint adaptivemodulation and sum-cost minimization (JAMSCmin) problems are considered. UnlikeOFDMA, in addition to the restriction of allocating a sub-channel to one userat most, the multiple sub-channels allocated to a user in SC-FDMA should beconsecutive as well. This renders the resource allocation problem prohibitivelydifficult and the standard optimization tools (e.g., Lagrange dual approachwidely used for OFDMA, etc.) can not help towards its optimal solution. Wepropose a novel optimization framework for the solution of these problems thatis inspired from the recently developed canonical duality theory. We firstformulate the optimization problems as binary-integer programming problems andthen transform these binary-integer programming problems into continuous spacecanonical dual problems that are concave maximization problems. Based on thesolution of the continuous space dual problems, we derive resource allocation(joint with adaptive modulation for JAMSCmin) algorithms for both the problemswhich have polynomial complexities. We provide conditions under which theproposed algorithms are optimal. We also propose an adaptive modulation schemefor SUmax problem. We compare the proposed algorithms with the existingalgorithms in the literature to assess their performance.
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