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Power line communication (PLC) systems are being standardized over the globe and some of these standards recommended frequency shift keying (FSK) as their modulation choice. Broadband transmission over a PLC channel is mainly affected by the ever-present background noise and the occasional high-amplitude impulses. It has been recently found that th...
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... baseband equivalent model of the system under study is shown in Fig. 1. An information source feeds symbols to the RS encoder and the encoded outputs are modulated before they can be sent over a noisy PLC channel. RS codes are specific type of Bose, Chaudhuri, and Hoe- quenghem (BCH) codes and belong to the class of linear, non-binary, cyclic block codes. For an (n, k) RS code, the encoder accepts a group ...
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Citations
... In [15], the performance of the FSK modulated data symbols, transmitted over the PLC channels corrupted by impulsive noise leading to channel distortion, is estimated at the receiver end. Moreover, in [16], the error rate performance is evaluated for Reed Solomon coded systems over a PLC channel that encounters background Nakagami-m noise for uncoded BFSK with both coherent and non-coherent detection. Finally, in [17], the authors present an energypattern-based sequence detection algorithm with improvements in complexity, reliability and synchronization using an FSK-based single-phase PLC system. ...
... Similar to the non-multipath PLC channel, we first consider the transmission of BFSK modulated symbols for data modulation. Thus, considering the symbols of the equiprobable BFSK modulation to be given as s 1 = A and s 2 = Ae ȷϕ , the expression for the SEP of the multipath PLC system can be given by using (16) and after algebraic manipulations as ...
A non-multipath and a receive diversity power line communication (PLC) system subject to Rayleigh fading is considered in this paper with the transmitter employing non-orthogonal
$M$
-ary frequency-shift keying (
$M$
FSK) modulation scheme for data transmission. With the PLC systems corrupted by additive complex Nakagami-
$m$
background noise, an optimal receiver for non-multipath PLC system and a Gauss-optimal receiver structure for the multipath PLC system are proposed using which, closed-form expressions for the symbol error probability (SEP) are derived using a characteristic function approach. The optimal correlation coefficients between the symbols of a binary FSK modulation scheme minimizing the SEP of the systems are obtained, which is further generalized by proposing a search-based algorithm to derive the optimal symbol correlation matrix for an
$M$
FSK modulation leading to the minimal SEP values of the PLC systems. Numerical results show that the index value of the optimal correlation matrix depends on the system parameters namely the noise shape parameter and the average signal-to-noise ratio only for the case of the non-multipath PLC system, whereas there is no such dependency in the case of the multipath PLC system.
... The performance of PNC has been analysed in rectangular and hexagonal networks in Yang et al. 15 The combination of PNC with MIMO was investigated in Yang et al. 21 The two-way relay network is designed to get maximum transmission rate in Li et al 22 in order to obtain the modulation-coded (MC) scheme which is implemented in Chattopadhyay et al. 23 The PNC with QPSK using the AWGN channel, Rayleigh multipath flat fading channel, and Rician fading channel are studied to evaluate the BER performance in Sachin et al. 24 To analyse the symbol error rate in PNC, the higher-order modulation techniques has been proposed in Fang et al. 25 Differential-chaos-shift-keying (DCSK) system with network-coding is investigated in Rayleigh fading channels in a two-relay in Cai et al. 26 By implementing a decode-and-forward protocol, when the two relays first decode the orthogonal signals sent by the two users, and then return their XORed version to the users. This proposed method has proved that it could be a successful candidate for wireless sensor networks. ...
This paper assumes two users and a two‐way relay network with the combination of 2×2 multi‐input multi‐output (MIMO) and nonorthogonal multiple access (NOMA). To achieve network reliability without sacrificing network throughput, network‐coded MIMO‐NOMA schemes with convolutional, Reed‐Solomon (RS), and turbo codes are applied. Messages from two users at the relay node are network‐coded and combined in NOMA scheme. Interleaved differential encoding with redundancy (R‐RIDE) scheme is proposed together with MIMO‐NOMA system. Quadrature phase‐shift keying (QPSK) modulation technique is used. Bit error rate (BER) versus signal‐to‐noise ratio (SNR) (dB) and average mutual information (AMI) (bps/Hz) versus SNR (dB) in NOMA and MIMO‐NOMA schemes are evaluated and presented. From the simulated results, the combination of MIMO‐NOMA system with the proposed R‐RIDE‐Turbo network‐coded scheme in two‐way relay networks has better BER and higher AMI performance than conventional coded NOMA system. Furthermore, R‐RIDE‐Turbo scheme in MIMO‐NOMA system outperforms the other coded schemes in both MIMO‐NOMA and NOMA systems.
... Particularly, although communication signals are transmitted in high frequencies, (i.e., in the MHz band), power cables are designed to transfer low-frequency power signals. To this end, a great amount of effort has been put on analyzing the performance of PLC systems [4][5][6][7][8][9][10][11][12][13][14][15][16] , as well as on presenting new transmission and reception schemes 17,18 . ...
... The impact of Nakagami-background noise on the performance of a PLC system in terms of the error rate and outage probability has been studied in the literature [5][6][7][8][9][10][11][12][13][14] . Particularly, Kim et al. 6 presented a closed-form expression for the probability distribution function (PDF) of the Nakagami-noise, while expressions for the bit error rate (BER) of PLC systems employing binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) modulation, respectively, were proposed in more recent works 7,8 . ...
This paper studies the error performance of power line communication (PLC) sys- tems, in the presence of background noise with Nakagami-𝑚 distributed envelope and uniformly distributed phase. In this sense, we present closed-form expressions for the symbol error rate (SER) of PLC systems employing binary pulse amplitude modulation, and generalize the analysis to accommodate the 𝑀-ary pulse amplitude modulation (PAM). Besides, novel closed-form expressions for the SER upper-bound of rectangular quadrature amplitude modulation (RQAM) PLC systems are derived. Interestingly, these expressions can be considered as tight SER approximations in the high signal-to-noise-ratio region, and, thus, can efficiently evaluate the operational bound of a PLC system.
... Closed-form BER expressions for both coherent and noncoherent binary FSK (BFSK) in a PLC channel corrupted with background noise only have been obtained in [12]. Similar expressions have been derived for Reed-Solomon (RS) coded BFSK signalling with both coherent and non-coherent detection of a PLC system affected by impulsive and background noise in [13]. In [14], the authors have provided simulation results for BER performance of a non-coherent maximum-likelihood (ML) block decoder for uncoded and RS with run limited length coded BFSK modulated symbols. ...
... It is to be noted that the simplification of the noise model in (13) becomes more accurate with a smaller value of A which corresponds to the presence of heavy impulsive noise [13,25]. Upon further simplification of (13), s^a o is given by (see (14)) where σ 0 2 , σ 1 2 , σ 2 2 are given by (3b) for u = 0, 1, 2, respectively, and the constants α and β are defined by ...
... It is to be noted that the simplification of the noise model in (13) becomes more accurate with a smaller value of A which corresponds to the presence of heavy impulsive noise [13,25]. Upon further simplification of (13), s^a o is given by (see (14)) where σ 0 2 , σ 1 2 , σ 2 2 are given by (3b) for u = 0, 1, 2, respectively, and the constants α and β are defined by ...
The authors consider a single-channel power line communication (PLC) system in the presence of Middleton Class-A impulsive noise employing multi-level amplitude-shift keying (ASK) modulation at the transmitter and non-coherent detection at the receiver. An asymptotically optimal detector for the PLC system is obtained using a tight approximation of the noise statistics. The magnitude of the received symbol is obtained as the decision variable, whose statistics is utilised to derive a series expression for the symbol error rate (SER). An asymptotic expression for the SER at high signal-to-noise ratio (SNR) is also obtained which is further utilised to find the optimal ASK constellation minimising the SER. It is shown by numerical examples that the optimal solution is extremely close to the equally spaced ASK constellation set at high SNR. It is also observed that the SER variation of the system with the impulsive index of the noise validates the optimality of the proposed detector at high SNR.
... which are calculated by an LPC algorithm. For the background noise, the spectral density can be expressed by the Nakagami-m attenuation formula (2) [29,30]: Nakagami-m will obey the Rayleigh distribution. When m is greater than the channel attenuation, which is inversely proportional to the m value, we can imply that when ∞ = m , there will be no attenuation. ...
With the development of new energy technology, more and more plug-in electric vehicles (PEVs) have appeared in our lives. In vehicle to grid (V2G) information exchange, the method that PEVs use to access the grid for information and vehicular data collection is the key factor that affects the reliability and real-time nature of V2G communication. Vehicular Power Line Communication (VPLC) reuses vehicular power cables as a communication medium, which avoids the need for an additional vehicular communication line and optimizes the in-vehicle space. VPLC is being considered as a more competitive solution to reduce the complexity of design, weight and cost associated with the rapid growth of electronic devices installed in vehicles, especially for PEVs. Nevertheless, there are factors that impact VPLC in such a way that disrupts reliability and introduces problems. One of these challenges is VPLC channel noise, which can reduce communication reliability. Hence, in this work, we introduce a V2G information interaction system structure, based on power line communication, to establish a VPLC channel model for vehicular data collection system. The model is developed in Simulink and leverages various vehicular noise models and binary frequency shift keying (BFSK) modulation; it also analyses the channel characteristics by examining different types of noise based on BFSK. Our simulation results demonstrate the feasibility of PLC under BFSK modulation and demodulation, often used in PEVs, which could provide guidance to the implementation of VPLC in support of practical engineering.
... Moreover, due to the popularity of Rayleigh fading channels, numerous work has been carried out to investigate the BER performances of PNC schemes over the Rayleigh fading channel. An approximate BER expression is derived for BPSK-based PNC in a bi-directional relay network over the Rayleigh fading channel in [30]. The authors of [31] derive an asymptotical closed-form tight bound of PNC over the Rayleigh fading channel. ...
The essential idea behind physical-layer network coding (PNC) is to superimpose signals so as to improve throughput. Current studies focus mainly on PNC over the AWGN or Rayleigh channels without consideration of burst pulses. This paper aims to evaluate the bit error rate (BER) performance of classical PNC, over a mixed channel that considers the combined effects of Gaussian noise and burst pulses. Besides, this paper explores the use of Reed-Solomon (RS) codes to improve the BER performance of PNC over the mixed channel. Simulation results show that burst pulses deteriorate the BER significantly, and RS codes are able to compensate for substantial BER performance degradation.
... This type of modulation was also studied in [7][8][9] under Nakagami background noise and in [10] under a mixture of Nakagami background noise and Middleton impulsive noise. Finally, the bit error rate (BER) performance of frequency shift keying under Nakagami noise was analysed in [11][12][13]. ...
... In the latter case, the BERs of equal gain combining (EGC) and maximum ratio combining (MRC) are derived and compared. Benchmarking with the existing literature, the performance under Nakagami-m noise was investigated in [5][6][7][8][9][10][11][12][13]. The noise PDF was derived in [5] for the case m < 1; in this paper, by adopting a different calculation method we prove that this PDF holds for the case m ≥ 1 as well. ...
... The noise PDF was derived in [5] for the case m < 1; in this paper, by adopting a different calculation method we prove that this PDF holds for the case m ≥ 1 as well. While the authors of [6,7,[10][11][12][13] ignore fading, our derivations incorporate lognormal fading. Under Nakagami-m noise, the BER performance of single-channel PLC systems with lognormal fading was studied in [8] where the derived expressions were reported in integral forms. ...
In this study, the authors evaluate the bit error rate (BER) performance of multichannel power line communication (PLC) systems under lognormal fading and Nakagami-m background noise. The information signal propagates over two parallel, but correlated channels while maximum ratio combining and equal gain combining are implemented at the receiver side. By appropriately approximating the tail of the probability density function of a single Nakagami-m noise term and of the weighted sum of two Nakagami-m noise terms, they derive accurate expressions of the BER. They prove that single-channel and multichannel PLC systems both benefit from an infinite diversity order and that this quantity increases logarithmically with the signal-to-noise ratio. In this case, the advantage of the diversity combining techniques resides in their impact on the average energy of the fading gain; a quantity that they derive analytically by applying the lognormal-sum approximation.
... The two-term mixture Gaussian noise model considered in [8] is a very special case of the more generalised Middleton class A distribution. In [14], the analytical BER of the PLC system assuming binary frequency shift keying modulation under the background noise and impulsive noise is derived. However, the envelope of the impulsive noise is assumed to be complex Gaussian such that the real and imaginary components of the impulsive noise are Gaussian distributed. ...
... Although the detector given by (6) is not an optimum detector for the cases considered, but it is sufficient to analyze the performance of the considered PLC system in presence of both background and impulsive noises more accurately compared to [8] and [14]. ...
... In Fig. 2, the plot of the average BER of the PLC system under the influence of both the Nakagami-m distributed background noise and the Middleton class A distributed impulsive noise is shown. The computational curves are obtained using (14), after plugging in the expressions of P e,b from (15) and P e,bi from (22). The BER plots have been obtained for Table I in [8], namely, the heavy impulse (IAT = 0.0196s, t i = 0.0641ms), the moderate impulse (IAT = 0.96s, t i = 0.0607ms), and the weak impulse (IAT = 8.1967s, t i = 0.1107ms) situations. ...
Power line communication (PLC) is the use of power lines for the purpose of electronic data transmission. The presence of additive noise, namely, background noise and impulsive noise, significantly affects the performance of a PLC system. While the background noise is modeled by Nakagami-m distribution, the impulsive noise is modeled using Middleton class A distribution. In this paper, we study the performance of a PLC system under the combined effect of Nakagami-m background noise and Middleton class A impulsive noise assuming binary phase shift keying signalling. The probability density function of decision variable under the influence of additive noise (sum of background noise and impulsive noise) is derived. We also derive an analytical expression for the average bit error rate of the considered PLC system. The analytical expressions are validated by close matching to the simulation results. The analysis presented in this paper closely predicts the behavior of the PLC system under the combined effect of background and impulsive noises.
... The current text not only extends the formulation to a more realistic channel model which includes effect of impulses but also provides more realizable error rate equations consisting of finite range single integrals (in contrast to the infinite range double integrals in [22]) and discusses the effect of RS coding at length. Part of these results were published in a conference paper [23]. ...
Power line communication (PLC) systems are being standardized over the globe and some of these standards recommended frequency shift keying (FSK) as their modulation choice. Broadband transmission over a PLC channel is mainly affected by the ever-present background noise and the occasional high-amplitude impulses. It has been recently found that the background noise in PLC can be suitably modelled with Nakagami-m distribution while a standard model for characterizing impulses is to assume Gaussian distributed amplitude and Poisson distributed arrivals. Considering such a model, at first, simple analytical bit error rate (BER) expressions of uncoded binary FSK (BFSK) signals are derived in the paper. The derived expressions are simple, involve only elementary functions, and the analytical BER values match perfectly with computer simulations. Next, a unified analytical framework is presented for evaluating BER when a Reed Solomon (RS) code is used to mitigate the noise effects. The results reveal that when the signal to background noise ratio (SBNR) is low, there is a clear impact of the noise parameter m and the choice of demodulation method (coherent/ non-coherent) on the error performance of the coded system. On the contrary, at higher SBNR, impulsive noise dominates over background noise, and these effects vanish as the BER curves become flat. Numerical evaluations dictated that by allowing a lower code rate (0.7) this error floor may be reduced significantly (up to 10^{−15}). Further, the code gain of the system was found to be an inverse function of the code rate and codeword length.
This study endeavors to investigate the effectiveness of machine learning-based methodologies in enhancing the performance and reliability of Power Line Communication (PLC) systems. PLC systems constitute a critical component within the domains of energy management, monitoring, and automation. The fundamental objective herein is to contribute significantly to the scholarly discourse by conducting a comprehensive review encompassing research investigations and practical applications documented in the extant literature. The primary motivation underpinning this research is predicated upon the necessity for a meticulous evaluation of machine learning techniques that hold the potential to enhance the efficacy and stability of PLC systems. The deployment of these techniques bears the promise of engendering heightened levels of efficiency across the spectrum of energy management, communication, and automation systems. Within this scholarly quest, the study posits a hypothesis: Machine learning-based methodologies possess the capacity to effect marked improvements in the performance and reliability of PLC systems. Methodological scrutiny is executed through a comprehensive evaluation of diverse machine learning techniques, including, but not limited to, deep learning, support vector machines, and random forests, facilitated by a series of empirical experiments and simulations. Empirical findings resoundingly corroborate the proposition, substantiating a significant enhancement in the operational performance of PLC systems when these machine learning methods are judiciously employed. In summation, this study assumes the role of a catalyst in exploring latent, untapped potential inherent within machine learning-based methodologies, customarily calibrated to resonate within the intricate matrix of PLC systems. The zenith of this rigorous investigation stands poised to illuminate the path toward transformative advancements in the domains of energy management, communication, monitoring, and automation systems. The findings contribute significantly to the academic discourse, offering a compass for future research inquiries and practical applications within this burgeoning and dynamic field.
