Asymptotic diversity order of single carrier cyclic prefix systems with frequency domain decision feedback equalizers

Single carrier cyclic prefix system with frequency domain equalization (SC-CP-FDE) is an attractive technology for broadband wireless communications. In this paper, we investigate the outage probability and diversity order of an uncoded SC-CP system with frequency domain MMSE decision feedback equalizer (FD-DFE) in frequency-selective channels. Based on the linear prediction theory and spectral factorization theory, we give a different derivation and interpretation of the equalizer coefficients and the closed-form MMSE formula at the decision point of the equalizer, from which the asymptotic SINR is obtained when the block length N is sufficiently large compared to the channel length. Adopting outage analysis, we show that with MMSE-FD-DFE, the asymptotic achievable diversity order is L_c +1, where L_c is the number of independent channel paths, i.e., full multipath diversity is asymptotically achieved.