  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.
