First and Second-Order Semi-Hidden Fritchman Markov models for a multi-carrier based indoor narrowband power line communication system

Abstract

The realization of a Semi-Hidden Fritchman Markov models (SHFMMs) for power line communication (PLC) channel is only practicable if combined with efficient algorithms for learning and inference. This article thus reports First and Second-Order SHFMMs for the bit error pattern at the output of an Orthogonal Frequency Division Multiplexing based system for in-home narrowband PLC applications. Accurate SHFMMs have been derived for a residential and laboratory environment using the efficient iterative Baum–Welch algorithm. The log-likelihood ratio plots, the error-free run distribution plots, the mean square error and Chi-Square $\left({\chi }^2\right)$ test validates the accuracy of the derived models. The reliability and accuracy of resulting models are confirmed by a close match between the measured bit error sequences and the model generated bit error sequences. The estimated Second-Order SHFMMs have been validated to be superior to the First-Order models, although at the expense of more computational complexity. Resulting models assist designers to speed up and facilitate the process of designing and evaluating novelties for PLC systems.

Introduction

The ubiquitous power line network (PLN) utilized for data transmission in in-home PLC technology possesses extremely hostile channel properties. Reliable communication through the channel is inhibited by impedance mismatch (due to aging cables), the use of unshielded cables, dynamics of loads connected, and multipath signal propagation associated with increasing attenuation with distance and frequency increase. Noise impairment such as impulsive noise thus lead to burst errors, corrupting transmitted data and thus inhibiting reliable and efficient data transmission. Accurate and suitable channel models assist designers to speed up and facilitate the process of designing and evaluating novelties for PLC systems.

Several modeling approaches have been employed in literature. The PLC was modeled based on its multipath behavior in [[1], [2]]. In [2], apart from a multipath scenario considered, Zimmermann and Dostert also took into consideration the impact of attenuation to the signal as a result of the cable’s length. Attempts have also been made to model PLC channel as a two-conductor transmission line [3] and three-conductor transmission line [4]. In [3], the adopted model approach shows how using a two-port transmission matrices can allow for computing analytically and a priori, the transfer function of any power line network in a deterministic way. Likewise, in [4], the transfer function of power lines in an indoor environment was modeled using the multi-conductor transmission line theory, with the approach allowing for the determination of equivalent circuits that accurately characterizes the underlying physics of signal propagation over power line.

In [5], the estimates of probability distributions for the amplitude, width and inter-arrival time of noise impulses measured at both residential and industrial indoor environment was reported. The noise impulse features were summarized, while the estimates practicably complements the noise spectral density estimates reported in other literatures. In [6], a novel approach for modeling PLC impulsive noise at their source was reported. Noise at the receiver was regarded as the noise model at the source filtered by the PLC channel. The authors identified and classified into six classes effective in-device sources of impulsive noises, from which six representative impulse noise classes was proposed. In [7], Shongwe et al. reported a study on impulse noise and its models. The authors discussed memoryless impulse noise models (Bernoulli–Gaussian, Middleton Class A and Symmetric alpha-stable), and memory impulse noise models (Markov–Gaussian and Markov–Middleton). A bit error rates (BER) performance of some impulse noise model variants, as well as BER performance of single-carrier and multi-carrier digital communication systems affected by impulse noise was carried out. In [8], the authors based on existing models reports a systemic approach for extracting and parameterizing individual subtype of low voltage power line (PL) noise, covering the PL noise behavior traversing both narrowband and broadband. An FPGA-based emulator was proposed to flexibly emulate PL noise scenarios based on the characterization. Sample measurements and their emulation were also obtained from a low voltage PL noise measuring setup.

In [9], over non-Gaussian broadband PLC channels furnished with two non-linear preprocessors at the receiver, the performance of vector orthogonal frequency division multiplexing (VOFDM) was investigated, with the intrinsic low PAPR attribute of the VOFDM harnessed to further boost the efficiency of the non-linear preprocessors. For same system conditions, results show a 2 dB saving in transmit power compared to conventional OFDM. Furthermore, an increase in the vector block size of the VOFDM leads to more significant achievable gains. In [10], for PLC systems in impulsive noise environments, Himeur and Boukabou developed a novel estimation and noise mitigation technique. Based on a recursive estimation of the impulse noise, utilizing the signal to impulsive noise power ratio (SINR), and PAPR in the time domain following channel equalization and OFDM demodulation, the author proposed an adaptive recursive noise compensator (ARNC) algorithm. Estimation and detection of the impulsive bursts was carried out by an introduced new clipping/blanking function. In an attenuated 15-paths condition, high performance is achieved by the proposed technique when BER and MSE are evaluated. For the estimation and suppression of impulsive noise on the OFDM PLC channel, in [11], Himeur and Boukabou developed an adaptive noise cancellation method established on the adaptive neuro-fuzzy inference system (ANFIS) and a chaotic interleaver. The ANFIS is dependent on a hybrid learning algorithm for the purpose of identifying parameters of Sugeno-type fuzzy inference system. Under differing impulsive noise scenarios, simulation results for an OFDM transmission well-suited for HomePlug AV standard shows the scheme’s ability in detecting and removing impulsive noise, at the same time keeping a high level of security by utilizing the chaotic interleaver. In [12], for high speed OFDM based PLC systems, the authors developed a turbo coded-chaotic interleaving and frequency-domain equalization scheme. At stage 1 of the proposed scheme, random interleaver commonly utilized in traditional turbo codes were replaced with the chaotic interleaver. At stage 2, a new clipping/blanking function is utilized by the frequency-domain equalizer to carry out estimation of the impulsive noise samples following OFDM demodulation. The developed scheme combines the gains of having extremely good error correcting capability with low complexity, high security level, and effective impulse noise cancellation with no previous knowledge about the features of impulsive noise. Results obtained from computer simulation shows that the developed scheme achieves superior BER performance when compared to the traditional block interleaving. Moreover, the proposed scheme with frequency-domain equalization offers a decent trade-off between the performance of the system and bandwidth efficiency.

Furthermore, Fritchman model was adopted in [13] to model the distribution of random impulsive events in an office and residential site. In [14], Gilbert and Fritchman model were adopted in modeling in-vehicle power line communication channel based on empirical bit error data. We reported a First-Order semi-hidden Fritchman Markov modeling of an indoor CENELEC A narrowband power line noise based on signal level measurement and experimentally obtained noise data in [15]. Several other modeling efforts have been reported in literature [[16], [17]].

Graphical models such as Semi-Hidden Fritchman Markov models (SHFMMs), offers a powerful and universal framework for formulating statistical models of physical communication channel problems (such as noise, perturbation and interference). However, the formulation of SHFMMs are only practicable if combined with efficient algorithms for learning and inference. In addition, varying noise parameters are obtained from country to country, as noise impairments are dependent on: main voltages, topology of power line, dynamics of load connected, place and time of measurement. Thus, there is the need for constant measurement campaigns before statistical mathematical models are derived. This article thus reports a First and Second-Order SHFMM of the bit error pattern at the output of an OFDM-based PLC system for in-home narrowband applications. Accurate First and Second-Order SHFMMs have been derived based on measured bit error sequence and analytically validated to ascertain the precision of the realized model through validation metrics such as: log-likelihood ratio, error-free run distribution, mean square error (MSE) and Chi-Square $\left({\chi }^2\right)$ test. The estimated Second-Order SHFMMs have been analytically validated and ascertained to be a more superior model than the First-Order SHFMMs, although this comes at the expense of more computational complexity. A performance comparison of the different OFDM schemes used is also carried out.

The remaining part of this article is structured as follows. Section 2 gives a concise description of the PLC discrete channel model elements and discusses the adopted SHFMM with associated model parameters. The iterative Baum–Welch Algorithm for SHFMM parameter estimation is concisely discussed in Section 2.3. Section 3 gives a description of the transmitter (TX) and receiver (RX) coupling circuit design, the NB-PLC transceiver system model and the modeling methodology adopted. In Section 4, the resulting models are presented and validated. The article is summarized with concluding remarks in Section 5.