## 5 Conclusions and Discussion  
This paper presents a novel FRESH-filter receiver, which exploits variations in spectral correlation among additive CSIN and received OFDM symbols aimed at mitigating the CSIN parts, while enhancing the OFDM signal parts. We also devised a method by which to estimate the cyclic frequency offset issue associated with the FRESH filter. The efficacy of the proposed scheme was verified using computer simulations with parameters conforming to IEEE 1901.2 standard. Our simulation results are summarized as follows:  
1. Cyclic frequency offset could degrade the performance of the FRESH-filter receiver to below that of the case without CSIN mitigation. Without the compensation for cyclic frequency offset, it could results in a loss of required \(E_{b}/N_{0}\) about 0.9 dB and 3.3 dB for the case of no CSIN mitigation and the case of no cyclic frequency offset, respectively.
2. Our approach to estimating cyclic frequency offset by observing the phase variation of the tap weights of the FRESH filter made it possible to suppress the cyclic frequency relative error by at least 15.45 dB (from 3.85% to 0.65%).
3. Following compensation for cyclic frequency offset, attaining a BER of \(10^{-4}\) imposed an \(E_{b}/N_{0}\) loss of only 0.7 dB compared with the ideal case (\(\Delta=0\) Hz).
4. When the value of \(E_{b}/N_{0}\) was fixed at 24 dB, the resulting BERs were as follows: proposed method (\(3.2\times 10^{-5}\)) and the case without cyclic frequency offset compensation (\(7.3\times 10^{-3}\)).  
Cyclostationary signal processing and the FRESH filtering have been applied in various fields, such as non-orthogonal multiplexed cognitive radio system, spectrum sensing, and chaotic communications. However, if the FRESH filters have no perfect information of cyclic frequency associated with cyclostationary signals, the cyclic frequency offset issue should be considered. In addition, we considered the cyclic frequency offset is deterministic but unknown in this paper. In our future work, we will integrate our algorithm into a feedback loop such that the offset can be continuously tracked. Moreover, we will plan and conduct real experiments to measure the CSIN noise sources and time-varying cyclic frequency offset to further validate our proposed method on real NB-PLC communications.  
Figure 9: Resulting bit error rate (BER) performance under various cases.  
**Author Contributions:** Conceptualization, Y.-R.C.; Data curation, J.-L.L.; Formal analysis, Y.-R.C. and J.-L.L.; Funding acquisition, Y.-R.C.; Investigation, Y.-R.C. and J.-L.L.; Methodology, Y.-R.C. and J.-L.L.; Project administration, Y.-R.C.; Resources, Y.-R.C. and H.-W.T.; Software, J.-L.L.; Supervision, Y.-R.C. and H.-W.T.; Validation, Y.-R.C. and H.-W.T.; Visualization, Y.-R.C. and [PERSON]-L.L.; Writing--original draft, Y.-R.C. and [PERSON]-L.L.; Writing--review & editing, Y.-R.C., [PERSON]-L.L. and H.-W.T. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Ministry of Science and Technology (MOST), Taiwan, under the Grant MOST 108-2221-E-197-010.  
**Conflicts of Interest:** The authors declare no conflict of interest.