In this paper, we analyse the error performance of selective decode-and-forward based optical wireless communication system utilising subcarrier intensity modulation for arbitrary M-ary signalling over generalised M-distributed atmospheric turbulence. The M-distribution is a generic statistical model for characterising the atmospheric turbulence-induced fading and unifies several existing statistical models for atmospheric turbulence. In particular, we derive a closed-form expression of the approximate average symbol error rate for the considered system with independent and non-identically distributed optical links. Furthermore, we analytically evaluate the diversity order for various distributions (e.g. gamma-gamma distribution, K-distribution and negative exponential distribution), characterised by the generalised M-distribution model. The analytical results have been verified by simulations.