Deterministic uncertain nonlinear formulatións for wireless ofdma networks with applicatións on semidefinite programming

Abstract

In this thesis, modern optimization techniques such as semidefinite programming (SDP), robust optimization, stochastic programming, lagrangian relaxations and polyhedral baseduncertainty approaches are used to deal with the problem of resource allocation in wireless OFDTVIA networks. The thesis starts in chapter 1 by giving an introcluction to the resource allocation problem. Then, in chapter 2 a brief theoretical background clescribingsome concepts ancl methods which are necessary for the development of the thesis are proviclecl. In Chapter 3, the main mathematical formulations from the literature related to uplink channels are presentecl while an uplink OFDTVIA "M " -Allocation scheme is proposecl uncler the feasibility assumption of a new cletection scheme of at most "M" incoming signals on each sub-carrier (sub-channel). A polynomial complexity algorithm is derivecl from the lagrangian relaxation of its mathematical formulation. Numerical results show that the algorithm outperforms DICOPT solver when fincling the maximum local optimum capacity. TVIoreover, the cpu times are significantly decreased. In chapter4, two binary quadratically constrainecl quadratic programs (BQCQP) for minimizingpower subject to bit rate ancl sub-carrier allocation constraints for downlink OFDMA are proposecl ancl two SDP relaxations are derived. Numerical results show tight near optimallm,ver bouncls when comparecl to the optimal solution of the problem. In chapter 5, we stucly three robust optimization approaches. The study is made on the basis of a BQCQP from chapter 4. Two SDP relaxations and a second order conic program are formulated under these robust optimization approaches. Numerical results show near optimal lower bouncls again when compared to the optimal solution of the problem. In chapter 6, further uncertainty approaches are formulatecl. In particular, we propase three BQCQP models for clownlink OFDMA using stochastic programming and a polyheclral uncertainty basecl approach. The numerical results show that the lower bounds obtained with the SDP relaxations are better than those obtainecl with linear programming relaxations, howeverthey are not near optimal. Finally in chapter 7, we give the main contributions and general conclusions of the thesis. Besicles, we provicle some future research clirections for the OFDMA resource allocation problem.