We derive new closed-form expressions for the marginal cumulative distribution function (c.d.f.) and marginal probability density function (p.d.f.) of the ordered eigenvalues of complex noncentral Wishart matrices. These results are used to analyze the performance of singular value decomposition (SVD) based MIMO systems in Ricean fading channels. New expressions are derived for the exact symbol error rate (SER), as well as the diversity order and array gain. Our results show that the global SER performance is dominated by the subchannel SER corresponding to the minimum channel singular value. Numerical results are presented to validate the theoretical analysis.