particular, a linear MMSE estimate of x$_{m}$ based on y$_{m}$ in (6) is given by [7] where ( · ) † denotes conjugate transpose, and Γ is a diagonal matrix with γ$_{k,k}$ = 1 / ( 1 − [( I + H$_{m}$H † $_{m}$/σ $^{2}$) − $^{1}$]$_{k,k}$ ) . Note that the tone-by-tone linear MMSE equalization in (7) involves inverting 2 × 2 matrices and hence the computational complexity is not significant. Denote ˆ x ( k ) ≜ [ˆ x ( k ) 1 , . . . , ˆ x ( k ) M ] $^{T}$. We finally apply the IDFT on ˆ x ( k ) to obtain the estimated data symbols In this section we provide simulation results to compare the optical DFT- spread OFDM system with the optical OFDM system in terms of both the PAPR performance and the bit error rate (BER) performance. The number of subcarriers is M = 256. A long-haul fiber optic system is considered with n$_{E}$ = 12 cascaded spans (each of length L = 80 km ). The laser wavelength is λ = 1 . 55 µm . The CD parameter is D = 17 ps/nm/km . We assume that periodic dispersion map is employed and the CD is compensated for by DCF after each span. The DGD parameter is D$_{p}$ = 0 . 15 $_{ps/}$√$_{km}$$_{. The}$ ˆ x$_{m}$ = ΓH † $_{m}$( σ $^{2}$I + H$_{m}$H † $_{m}$) − $^{1}$y$_{m}$ = Γ ( σ $^{2}$I + H † $_{m}$H$_{m}$ ) − $^{1}$H † $_{m}$y$_{m}$ , m = 1 , . . . , M, (7) ˆ s ( k ) = F $^{†}$ˆ x ( k $^{)}$, k = 1 , 2 . (8) 4 Simulation Results 8