Maximum diversity in single-carrier frequency-domain equalization

In broadband wireless communications, multipath propagation often results in an overall channel with a long impulse response that could span tens or even hundreds of symbol intervals. To equalize such long channels, conventional single-carrier time-domain equalization becomes infeasible due to high computational complexity. Relying on the use of fast Fourier transform, single-carrier frequency-domain equalization (SC-FDE) offers low-complexity equalization as well as other desirable features. In this correspondence, we prove that SC-FDE is also capable of collecting full multipath diversity even without channel coding. As far as we are aware, this is the first analytical proof of the diversity gain of SC-FDE. This conclusion justifies those existing simulation results regarding the performance comparison between SC-FDE and orthogonal frequency-division multiplexing (OFDM), and offers important guidelines for further improving SC-FDE and OFDM.