A Novel Data-Aided Joint Timing and Carrier Frequency Offset Estimation Based on Central Symmetry ZC Sequence in OFDM/OQAM Systems

Abstract

In this paper, a new data-aided joint timing and carrier frequency offset estimation algorithm in OFDM/OQAM system is proposed by utilizing identical central-symmetry ZC sequences before polyphase structure efficient implementation. Based on excellent auto-correlation performance of ZC sequence we derive a timing offset estimator with high accuracy and arbitrary capture range compared with two existed approaches. After the precision timing, a new frequency offset estimator is proposed by two parts, which considered both the identical and central-symmetry properties separately. Computer simulation indicates conspicuous performance improvement in timing offset and frequency offset estimation, especially in a AWGN channel which the proposed method possesses significant advantages while in multipath channel the new estimator can still reveal better performance when selecting the correct weighting factor.

Appendix: Proof of Central-Symmetry in Eq. 17

First, the prototype function $g(kT_s)$ is discrete and real-symmetry with length $\beta N$ and omit the $T_s$ for simplification.

$$\begin{aligned} g(k)=g(\beta N-1-k),\quad k\in \{0,1,\ldots ,\frac{\beta }{2}N-1\} \end{aligned}$$

(35)

The nth polyphase decomposition of prototype function g(k) is given by Eq. 17

$$\begin{aligned} g_n(l)=g(l+nN) \end{aligned}$$

(36)

where $l\in \{0,1,\ldots ,N-1\}$ and $n\in \{0,1,\ldots ,\beta -1\}$. In order to prove the center-symmetry

$$\begin{aligned} \sum _{n=0}^{\beta -1}g_n(l)= \sum _{n=0}^{\beta -1}g_n(N-1-l),\quad l\in \{0,1,\ldots ,N/2-1\} \end{aligned}$$

(37)

Consider the difference value

$$\begin{aligned} \begin{aligned}&\sum _{n=0}^{\beta -1}g_n(l)-\sum _{n=0}^{\beta -1}g_n(N-1-l) \\ &\quad =\sum _{n=0}^{\beta -1}g(l+nN)-\sum _{n=0}^{\beta -1}g(N-1-l+nN) \\ &\quad=\sum _{n=0}^{\beta -1}\left[ g(l+nN)-g(N-1-l+nN)\right] \\ &\quad=\sum _{n=0}^{\beta -1}\left[ g(l+nN)-g(\beta N-1-(N-1-l'+nN))\right] \\ &\quad=\sum _{n=0}^{\beta -1}\left[ g(l+nN)-g(l+(\beta -1-n)N)\right] \end{aligned} \end{aligned}$$

(38)

and for every $n\in \{0,1,\ldots ,\beta -1\}$, the corresponding $\beta -1-n\in \{0,1,\ldots ,\beta -1\}$ satisfy a one-to-one correlation matching with n. Obviously, the answer to Eq. 38 is

$$\begin{aligned} \sum _{n=0}^{\beta -1}g_n(l)-\sum _{n=0}^{\beta -1}g_n(N-1-l) = 0 \end{aligned}$$

(39)

That is the conclusion that the sum of all $\beta$ parts of those polyphase decomposition meet the condition of central-symmetry.