On Coding for Orthogonal Frequency Division Multiplexing Systems
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The main contribution of this thesis is the statistical analysis of orthogonal frequency di- vision multiplexing (OFDM) systems operating over wireless channels that are both fre- quency selective and Rayleigh fading. We first describe the instantaneous capacity of such systems using a central limit theorem, as well as the asymptotic capacity of a power lim- ited OFDM system as the number of subcarriers approaches infinity. We then analyse the performance of uncoded OFDM systems by first developing bounds on the block error rate. Next we show that the distribution of the number of symbol errors within each block may be tightly approximated, and derive the distribution of an upper bound on the total variation distance. Finally, the central result of this thesis proposes the use of lattices for encodingOFDMsystems. For this, we detail a particular method of using lattices to encode OFDMsystems, and derive the optimalmaximumlikelihood decodingmetric. Generalised Minimum Distance (GMD) decoding is then introduced as a lower complexity method of decoding lattice encoded OFDM. We derive the optimal reliability metric for GMD decod- ing of OFDM systems operating over frequency selective channels, and develop analytical upper bounds on the error rate of lattice encoded OFDM systems employing GMD decod- ing.