1. A method for carrier frequency offset (CFO) estimation for coherent optical orthogonal-frequency-division-multiplexing (CO-OFDM) broadband systems, comprising: obtaining an initial estimate of a normalized CFO with an estimation range equal to +L/2 subcarrier subspacing using a single training symbol with L identical portions; storing the initial estimate in a memory device; and obtaining a maximum likelihood (ML) estimate of the CFO by performing a local grid search based on the initial estimate, wherein the ML estimate is calculated by maximizing over a set of grid search results that fall within a range around the initial estimate defined by an empirically designed parameter, and wherein the ML estimate is calculated as: ε ML = arg ⁢ ⁢ max  ε - ε ^ ini  ≤ ε b ⁢ { ⁢ ( ∑ l = 1 L - 1 ⁢ p ⁡ ( l ) ⁢ ⅇ - j ⁢ ⁢ 2 ⁢ ⁢ π ⁢ ⁢ ε ⁢ ⁢ l / L ) } , where ε is a normalized CFO, {circumflex over (ε)} ini is an initial CFO estimate ε b is an empirically designed parameter, and p(l) provides correlations.