This paper investigates the diversity gain of a distributed cyclic delay diversity (CDD) scheme for cyclic-prefixed single carrier systems in non-identical frequency selective fading channels. Two conditions are used to obtain an equivalent channel matrix that is free of intersymbol interference. These conditions allows the system to achieve the maximum diversity order at a full rate in frequency selective fading channels. A given number of CDD transmitters is obtained from the set of cooperative transmitters in the system and is shown to be determined by the symbol block size and the maximum time dispersion of the channel. A new expression for the received signal-to-noise ratio (SNR) is derived by using order statistics. To estimate the achievable maximum diversity gain provided by the distributed CDD scheme, we employ asymptotic analysis in the high SNR regime. From the analytical framework, it is shown that the maximum diversity is achieved even for non-identical frequency selective fading channels. Link-level simulations are conducted to verify the maximum achievable diversity gain.