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Multicarrier code division multiple access (MC-CDMA) is a promising technique for high data rate and high capacity (large number of users) transmission. However, rapidly time varying channels degrade the performance due to loosing the orthogonality among the subcarriers as well as code patterns. Channel estimation is very important to design adaptive system for improvement in all round performance. This paper proposes an efficient channel estimation for Rayleigh fading channel in high capacity carrier interferometry /multi-carrier code division multiple access (CI/MC-CDMA) system with variable data rate using Genetic algorithms (GAs). The system implementation is done by allocating all sub-carriers to the users who transmit high data rate and alternate odd and even subcarriers are assigned to the other sets of users transmitting at low data rate. GAs is used to estimate a near optimal solution of the set of parameter values on frequency selective Rayleigh fading channel. Objective function is formed from the weighted average of channel capacity and bit error rate. Simulation results show that both channel capacity and bit error probability are improved with the increase of number of iterations/generations.