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

Abstract

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(/spl rho/) 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 /spl Delta/F, 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/sub opt/ of the WA is determined. This optimal value K/sub opt/ is a function of M,F(/spl rho/), /spl Delta/F and E/sub s//N/sub 0/. It is shown that, depending on the E/sub s//N/sub 0/-region under consideration, K/sub opt/ can be approximated by its asymptotic (low or high E/sub 8//N/sub 0/) value. The asymptotic value of K/sub opt/ for low E/sub s//N/sub 0/ depends on M and /spl Delta/F but is independent of F(/spl rho/). The asymptotic value of K/sub opt/ for high E/sub s//N/sub 0/ depends on M, /spl Delta/F and F(/spl rho/).