Optimal averaging filter length of the Viterbi and Viterbi carrier synchronizer for a given frequency offset

The influence of a frequency offset on the operation of the nondecision-aided feedforward carrier synchroniser for MPSK is analyzed. The synchroniser uses a nonlinearity F(ρ) to eliminate the influence of the data symbols and a window accumulator (WA) of length K to reduce the influence of the additive noise. For a given frequency offset ΔF, the window length K cannot be chosen arbitrarily large because increasing K reduces the useful component at the output of the averaging filter. The optimal (minimal linearized phase error variance) length K _opt of the WA is determined. This optimal value K_opt is a function of M,F(ρ), ΔF and E_s/N₀ . It is shown that, depending on the E_s/N₀-region under consideration, K_opt can be approximated by its asymptotic (low or high E₈/N₀ ) value. The asymptotic value of K_opt for low E_s /N₀ depends on M and ΔF but is independent of F(ρ). The asymptotic value of K_opt for high E_s/N₀ depends on M, ΔF and F(ρ)