Joint Estimation of Carrier and Sampling Frequency Offsets Using OFDM WLAN Preamble

Abstract

In this paper, the problem of joint estimation of carrier and sampling frequency offsets is considered, for IEEE 802.11ac-based OFDM wireless LAN systems, based on the guard interval and two long symbols (GI2L) in the preamble of a packet. The measurement model of the GI2L is developed, in the presence of both carrier and sampling frequency offsets. One method based on the GI2L is proposed and compared with some existing relevant methods based on long symbol/data symbols. An improved performance, measured by estimation error and bit error rate, is achieved by this method, at a similar computational load.

Appendix: Robust Channel Estimation Using GI2L

Define

$$\begin{aligned} {\mathbf{v}}_{k}&= {} \left[ z_{0}^{ -\,16 k (1+\zeta )}, \ldots , z_{0}^{ - k(1+\zeta )}, \right. \\&\left. 1,z_{0}^{ k (1+\zeta )},\ldots , z_{0}^{ (2N-1) k (1+\zeta )} \right] ^{T} \\ {\mathbf{V}}_{\zeta }&= {} \left[ {\mathbf{v}}_{-26}, \ldots , {\mathbf{v}}_{-1}, {\mathbf{v}}_{1}, \ldots , {\mathbf{v}}_{26} \right] \\ {\mathbf{E}}_{\psi ,\zeta }&= {} { diag}\left[ z_{0}^{ -\,16(1+\zeta )\psi }, \ldots , z_{0}^{ -(1+\zeta )\psi },\right. \\&\left. 1,z_{0}^{ (1+\zeta )\psi },\ldots , z_{0}^{ (2N-1)(1+\zeta )\psi } \right] \\ {\mathbf{S}}&= {} { diag}\left[ s(-26),\ldots ,s(-1),s(1),\ldots ,s(26)\right] \\&{\mathbf{A}}_{\psi ,\zeta } = {\mathbf{E}}_{\psi ,\zeta } {\mathbf{V}}_{\zeta } {\mathbf{S}} \\ {{\mathcal {H}}}&= {} \left[ H_{-26},\ldots ,H_{-1},H_{1},\ldots ,H_{26}\right] ^{T} \\ \hat{{\mathbf{y}}}&= {} \left[ {\hat{y}}(-\,16),\ldots ,{\hat{y}}(-1),{\hat{y}}(0), {\hat{y}}(1), \ldots ,{\hat{y}}(2N-1)\right] ^{T} \\ {\varvec{\xi }}&= {} \left[ \xi (-\,16),\ldots ,\xi (-1),\xi (0), \xi (1), \ldots ,\xi (2N-1)\right] ^{T}. \end{aligned}$$

Then the noisy GI2L samples in (10) can be written in a matrix-vector form as $\hat{\mathbf{y}} = {\mathbf{A}}_{\psi ,\zeta } {{\mathcal {H}}} + {\varvec{\xi }}.$ For the noisy GI2L and given a pair of estimates ${\hat{\psi }}={\hat{\psi }}_{gl}+{\hat{\epsilon }},{\hat{\zeta }}$, where ${\hat{\epsilon }},{\hat{\zeta }}$ are given by a fine-tuning method, the channel response vector ${{\mathcal {H}}}$ can be estimated as

$$\begin{aligned} {\hat{\mathcal {H}}} = \left( {\mathbf{A}}_{{\hat{\psi }},{\hat{\zeta }}}^{H} {\mathbf{A}}_{{\hat{\psi }},{\hat{\zeta }}}\right) ^{-1} {\mathbf{A}}_{{\hat{\psi }},{\hat{\zeta }}}^{H} \hat{{\mathbf{y}}}. \end{aligned}$$

(156)

Expressions (11) and (12) of [3] can also be used to calculate an estimate of $H_{k_{1}}$. The resulting estimates are found to be much less accurate than that in (156) and thus are not used in this paper.