Optimization of Generalized Discrete Fourier Transform for CDMA

Generalized Discrete Fourier Transform (GDFT) with non-linear phase is a complex valued, constant modulus orthogonal function set. GDFT can be effectively used in several engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communication systems. The constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used in above mentioned applications over several decades. However, these transforms are suffering from low crosscorrelation features. This problem can be addressed by using GDFT transform. This paper describes the optimization of Generalized Discrete Fourier Transform with Non-Linear Phase for code division multiple access (CDMA). We have also implemented Gold, Walsh and DFT codes. Their performance is analyzed and compared on the basis of various parameters such as Maximum Value of Out-of-Phase Auto-Correlation, Maximum Value of Out-of-Phase Cross-Correlation, Mean-Square Value of Auto-Correlation, Mean-Square Value of CrossCorrelation and merit factor. The result of simulation in the form o f comparison of Bit-error-rate (BER) and Signal-to-noise (SNR) ratio for various spreading codes is presented.