Cyclostationary Impulsive Noise Mitigation in the Presence of Cyclic Frequency Offset for Narrowband Powerline Communication Systems  
[PERSON]  
1 Department of Electrical Engineering, National Ilan University, Yilan 26047, Taiwan 1
linear periodically time-varying (LPTV) system. By leveraging the cyclostationarity, FRESH filters are the optimal filters and could reject interference much better than a time-invariant filter. For example, the chaotic signal has a relatively flat spectrum and traditional signal processing methods are barely applicable [24]. However, it has been shown that some chaotic signals exhibit cyclostationary property and such property is possible to be exploited to encode information [25]. In Ref. [26], the authors used the cumulant-based scheme to test the presence of the cyclostationary signals and to estimate the cyclic frequencies. The authors in [20] used one set of FRESH filter with the cyclic frequency associated with the symbol rate for the reconstruction of OFDM signals. In Ref. [21], two sets of FRESH filters were used with two sets of cyclic frequency to retrieve the CSIN and OFDM signals, separately. However, it was assumed in that study that the cyclic frequency associated with the FRESH filter and the channel response of the powerline were perfectly known on the receiver side. In Ref. [22], a time-averaged least mean squared (TA-LMS) algorithm was used to train the weights of each branch of the adaptive FRESH filter for use in resolving the problem of channel estimation in NB-PLC systems. However, they lacked for considering issues pertaining to CSIN estimation or mitigation. The authors in [23] exploited spatial correlation across multiple phases at a receiving modem to enhance the performance of FRESH filters while taking into account the cyclostationarity of CSIN in order to derive an optimal solution by which to minimize the time-averaged mean square error (MSE). In our previous work [14], we proposed using an FRESH-based estimator to serve as the reference impulsive noise sources to an adaptive predictor. In such arrangement, the adaptive predictor could further refine the estimation of IN from the received signal. However, the authors did not consider the issues of cyclic frequency offset, which cause a poor estimation for the reference impulsive noise sources. Without the perfect information about the cyclic frequency associated with the CSIN, the adaptive predictor could have a worse prediction to the CSIN and could paralyze the CSIN estimation algorithm. To the best of our knowledge, few researchers have considered the impact of cyclic frequency offset on FRESH filters. The cyclic period for CSIN is normally half the period of the mains cycle \(T_{AC}\). In Taiwan, the mains frequency is generally 60 Hz, such that the typical cyclic period is 8.33 ms and the corresponding cyclic frequency is 120 Hz. However, the mains frequency is permitted to operate with a \(\pm 4\%\) offset, based on regulations stipulated in Electricity Act of Taiwan [27]. In Ref. [28], the authors demonstrated that even a slight offset in cyclic frequency would be sufficient to spoil the performance of FRESH filters. In the absence of cyclic frequency offset, an adaptive FRESH filter would converge to a linear time-invariant (LTI) filter for each branch of the FRESH filter. However, when there exists a cyclic frequency offset, LTI filters behave as linear periodically time-variant (LPTV) filters. As long as the adaptation algorithm is suited to the conditions, it should be possible for an adaptive FRESH filter to track periodic variations and thereby compensate for cyclic frequency offset [28]. Nonetheless, the convergence rate of adaptive algorithms would have to be carefully selected in order to obtain reasonable results. In this paper, we present an adaptive FRESH-based receiver, mainly comprising one CSIN estimator and one signal restorer. The main contributions of this work are summarized as follows.