Single Carrier FDMA (SC-FDMA) plays an important role in modern wireless communications as an alternative to OFDM mainly since it exhibits low peak-to-average power ratio. Accordingly, SC-FDMA is employed as the uplink scheme for the 3GPP long term evolution (LTE). In the presence of multipath, the SC-FDMA signal may arrive at the receiver perturbed by inter-symbol-interference, which renders the single-tap frequency-domain equalization suboptimal. Optimum maximum likelihood detection for SC-FDMA is often prohibitively complex, and hence useful mostly as a performance bound for suboptimal detection schemes. In this work, the optimum-detector performance is analyzed in detail; the analysis can be easily applied to any SC frequency-domain equalization scheme. Closed form bounds on the achievable bit error rate are provided for low and high SNR regimes in correlated and uncorrelated Rayleigh fading channels. The bounds reveal that the diversity order at high SNR is significantly smaller than in the low SNR regime. Moreover, error rate flaring behavior is demonstrated under optimum detection of SC-FDMA. The analytical results are verified by simulations.