Synchronization Between Sender and Receiver & CFO Correction

解决同步问题和频率偏移问题是下面论文的关键，接下来结合论文进行详细解读

解读论文：Verification and Redesign of OFDM Backscatter

论文pdf：https://www.usenix.org/system/files/nsdi21spring-liu-xin.pdf

论文ppt：talkV6 (usenix.org)

In this section, we build a mathematical model for the synchronization and carrier frequency offset (CFO) correction (i.e., part (i) in Fig. 11).用于同步和载波频率偏移（CFO）校正的数学模型

同步问题分析

The preamble includes two long training (LT) sample sequences. Each sequence is composed of 64 samples. By identifying where the two peak values of the correlation between the received samples and training pattern occur, the WiFi receiver can find where the symbol starts [15]. Therefore, to avoid changing the training sample’s value, when TScatter detects the WiFi transmission by using the RF energy detector, it first uses continuous square waves to only reflect the preamble and does not embed any data into the preamble. After the square waves, TScatter starts to modulate the WiFi samples.

  1.使用两个长训练序列，每个序列有64个采样点(WiFi preamble部分的LTF)

 2.找到接收样本和训练模式(已知序列)之间存在的相关峰，来定位符号的开始

 3.和传统做法一样，使用了RF energy detector实现packet-level的识别

 4.对于前导部分，不作相位上的调制，只使用方波实现移频

该做法是很经典的做法，tag调制不破坏前导部分以便于接收机识别

例如下图来自于论文：Spatial Stream Backscatter Using Commodity WiFi

 Phase Offset Analysis 相位偏差分析

此处的θn是tag调制的数据：If we change θn according to the tag data, the tag data is embedded into the sample. For example, if the tag wants to use the 4-phase scheme (0, π/2, π and 3π/2) to transmit the tag data, we can define the tag data ‘00’ as θn = 0, ‘01’ as θn = π/2, ‘10’ as θn = π and ‘11’ as θn = 3π/2.

由于接收样本序列受到了上述三方面的相位误差，该误差将会对相关峰检测带来影响吗？

根据下面的算法原理，可见由于是模值平方检测，相位的影响会被省略

就是正常的寻找相关峰的算法

 获得两个相关峰的位置，实现精准同步

频率偏移分析

根据论文：Frequency Offset Estimation and Correction in the IEEE 802.11a WLANFrequency offset estimation and correction in the IEEE 802.11a WLAN - Vehicular Technology Conference, 2004. VTC2004-Fall. 2004 IEEE 60th (openofdm.readthedocs.io)

提到的频率偏移模型，引起CFO和SFO的本质原因是一样的

CFO引入的额外相位偏差

定义：The received frame at frequency fc is down-converted with a local carrier frequency (1+ε)fc

l是在时间轴上的定义

α = 2πε fc / fs 是每次采样的相位偏差

基于接收到的两个LT序列，可以实现CFO的精细估测

tag的存在不会影响接收机的同步，所以接收机可以基于前述的相关峰检测得到采样的序号

 

该算法和我之前的博文解读的论文“Robust Frequency and Timing Synchronization for OFDM”中提到的短训练序列类似

由此，可以抵消CFO的影响

SFO引入的额外相位偏差

在进行DFT时采样点发生了偏移

、

 所以要估计SFO，先估计CFO

由此，可以抵消SFO的影响