Optimal design of phase function in Generalized DFT

Recently, a theoretical framework for Generalized DFT (GDFT) with nonlinear phase functions exploiting the phase space to design various constant modulus orthogonal transforms was introduced. This paper extends prior work to design longer bases widely used in real world communications systems. GDFT provides flexibilities in phase space yielding performance improvements over other code families including DFT in correlation metrics. GDFT phase functions are optimally designed in order to reduce inter carrier interference (ICI) and inter-symbol interference (ISI) that dictate the performance of a multiuser channel. It is presented in the paper that superior correlation of GDFT over DFT manifests itself in improved BER performance in direct sequence CDMA based multi-user communications systems