## 2 Related Works  
The countermeasure to the problem of CFO in the wireless access from multiple sensors to the FC is considered to be that in the uplink cellular system.  
In [10], the estimation of the CFO in uplink LTE is proposed by evaluating the phase rotating speed of the spectrum detected by a fast Fourier transform (FFT). For suppressing MAI, the estimated CFO is averaged using multiple subcarriers. Since the dynamic range of the received signal power among the users is significantly high, the suppression of MAI by averaging the estimated CFO is not effective. The estimation scheme of CFO with the suppression of MAI via interference cancellation is proposed [11]. A signal subspace analysis based on MIMO suppresses the MAI and then it estimates CFO [12; 13] assuming that the estimation of CSI is ideal. The degradation of estimating CSI causes significant degradation of accuracy of subspace analysis. Since the impact of CFO is modeled by the cyclical convolutional operation, after compensating the impact of CFO, the residual MAI is suppressed by interference cancellation [14]. The extension version of it is constructed using the estimation of CSI [15]. These techniques require multiple antenna reception and the iterative processing and thus the processing delay and the complexity of the process are considerably large. The estimation technique of both CFO and CSI based on maximal likelihood sequence detection (MLSE) is considered [16] but its computational complexity is large. A self-cancellation technique for suppressing the MAI caused by CFO is proposed [17; 18] but the usage efficiency of the frequency spectrum is reduced by half.  
Various compensation techniques of CFO for WSN have been considered under the assumption of narrow band wireless communication systems. Recently, a low power wide area (LPWA) is gaining considerable attention as the long-range wireless sensor network. In [19; 20], the random-access channel (RACH) for narrow band IoT uses the frequency hopping scheme as the wireless access protocol and thus the suppression of MAI and the estimation of CFO through RACH are considered. In [21], the frequency synchronization scheme based on global positioning system for LPWA is considered. The unique word for estimating CFO is considered [22]. In [23], the lower bound of the accuracy of CFO estimation in the single carrier communication is derived. In the compensation of COR for LPWA, the pilot signal for estimating CFO is required. Since the data rate of LPWA is small, the overhead of inserting pilot signal to the payload is large.  
From these conventional considerations, the suppression of MAI is an important task under the multiple access environment, which is in the access from multiple sensors to a FC. The interference cancellation is one of the most powerful techniques for suppressing MAI. Since MAI is widely spread owing to CFO, the estimation of CSI in the wide band channels is necessary. However, WSN, such as LPWA and PhyC-SN, is narrow band communication and thus the overhead of the pilot signal for wide band channels is much large. In addition, the construction of MAI and the ICI replica is necessary, but any other paper does not consider it in the narrow band communications.  
This paper proposes the estimation of CSI and CFO using data signal in PhyC-SN. The overhead for estimating CSI and CFO is limited. This paper also considers the construction of the wide spread ICI from the signal of the narrow band communication. This construction has not been considered yet in the WSN including LPWA. In addition, the insertion of ID to the data channel is proposed using fractional CFO in PhyC-SN. The overhead of inserting ID is limited. The multiple dimensional tracking for the highly accurate data separation is proposed. As a result, the recognition of individual data can be achieved via the PhyC-SN with the ID insertion of small overhead.