In this study, the performance of Quasisynchronous DS-CDMA (QS-CDMA) communication system with a maximal ratio combiner (MRC) over a frequency selective time non-selective multipath Generalized Gamma (GG) fading channel is derived for not only any deterministic spreading sequence but also any chip-limited chip waveform. Numerical and simulation results show that the performance of QS-CDMA is as good as or slightly better than synchronous CDMA (S-CDMA) when the maximum quasisynchronous delays do not need to be less than some specific values depending on the path power scattering. With this flexibility of quasisynchronous delays for the better performance, both the transmitter and receiver complexity is reduced as quasisynchronous communication is a challenging task for researchers. Lastly, a measure, Partial Power Ratio (PPR), is defined based on the partial autocorrelation functions, to select or design a chip waveform for quasisynchronous communication. Results show that QS-CDMA using the chip waveform whose PPR is greater, has better performance.