The complex-valued collaborative coding multiple access (CV-CCMA) scheme has been previously proposed by the authors to provide a practical means of implementing CCMA over radio channels. The technique employs complex-valued collaborative codes and spatial diversity to estimate the complex channel gain coefficients representing the amplitude and phase associated with each user path and to detect the data of each user in a combined manner. The authors present the complex-valued coding scheme extended to operate in fading channels with equal and unequal users' channel gain coefficients. The conditions for choosing a valid T-user collaborative code set are described and various T-user M-PSK code sets are constructed. The maximum achievable rate region for two-user 2-PSK CV-CCMA is also obtained. The T-user M-PSK CV-CCMA schemes employing these code sets are evaluated in Rayleigh and Rician fading channels and-presented in terms of the probability of error against Eb/N0 per user. The error-performance of these schemes is also investigated with the use of dual and higher-order space diversity and it is shown to give a significant performance gain