Class-A Impulsive Noise Research Articles

Optimization of capacity in non-Gaussian noise models with and without fading channels for sustainable communication systems

The highest rate at which information may be reliably sent via a communication link is known as its capacity. In the case of non-Gaussian noise, the capacity of the channel depends on the specific characteristics of the noise, which can cause severe errors and reduce the reliability of communication systems over a fading channel. The Gaussian mixture impulsive noise model (GMINM), which is a more general and flexible non-Gaussian model for impulsive noise, has been compared in this paper with the Middleton Class-A impulsive noise model (MCAINM) in terms of derived channel capacity normalized by channel bandwidth (C/BW) with and without Rayleigh fading (Rf) channels. It also investigated the trade-off between complexity and accuracy in modeling the impulsive noise using two simplified Middleton Class-A impulsive noise models based on derived C/BW. The derived C/BW of these models under various conditions, such as different signal-to-noise ratios and impulsive noise parameters and models, have been performed and evaluated using two different scenarios: the exact method and the semi-analytical method. When the impulsive noise parameters and A are both near 0 in GMINM and MCAINM, respectively, the capacity of the impulsive noise channel is found to be equivalent to that of the Gaussian channel sustainable, as shown by the findings based on Monte-Carlo simulations. We have shown that when the impulsive noise decreases, the capacity increases in all models; however, the capacity of Gaussian noise is higher than the capacity of non-Gaussian noise, which in turn is higher than the capacity of non-Gaussian noise over the Rf channel overall values of SNR in dB. Moreover, multi-channel configuration introduces spatial diversity and multiplexing gains that have been proposed to sustainably optimize the ergodic capacity for the challenge case when the channel state information (CSI) is unknown at the transmitter in non-Gaussian noise over Rf channel. In today's rapidly evolving world, sustainable communication systems play a crucial role in ensuring efficient and responsible utilization of resources. As the demand for wireless communication continues to rise, it becomes imperative to optimize the capacity of communication channels, especially in scenarios involving non-Gaussian noise models and fading channels.

A Nonparametric Approach to Signal Detection in Non-Gaussian Noise

This letter proposes a nonparametric detector, termed as Gini Correlation (GC), to solve the classical problem of detecting deterministic signals buried in impulsive noise. With the help of the popular Middleton’s Class-A impulsive noise (MCAN) model, we derive the expectation and variance of GC under alternative hypothesis and null hypothesis, which, along with the central limit theorem, are further employed for determining the detection probability and the detection threshold. The results show that the proposed detector possesses a constant false alarm rate property. Monte Carlo simulations verify not only the correctness of our theoretical findings but also the superiority of GC to other state-of-the-art methods in terms of receiver operating characteristic (ROC) curves and asymptotic relative efficiency (ARE) curves.

Capacity of Middleton Class-A Impulsive Noise Channel with Binary Input

In many applications, the Middleton Class-A model is used to describe the impulsive noise. A very useful and interesting aspect for a channel affected by such, non-Gaussian noise, is to find an expression for the channel capacity. In this paper we present the calculation of capacity for a channel affected by additive Middleton Class-A noise (AWCN), with binary input. We considered the case when the source is uniform, but also when it is not uniform. The channel capacities for impulsive noise, for various values of the parameters that describe its model, are compared with those for the additive white Gaussian noise (AWGN) channel. The numerical results showed that when the parameters A and T are close to 1, the capacity for impulsive noise channel is equal to that of Gaussian channel. When A and T decrease, the AWCN capacity grows. When the probability p0, the probability of bit 0, grows or when the encoding rate decreases, each channel capacity decreases. The Shannon limit values are also given for different encoding rates in the case of the two channels. We have shown that Signal-to-Noise Ratio (SNRb) in dB given only by the Gaussian component of AWCN is closer to SNRb in dB of AWGN, as the AWCN capacity increases.

Rank Correlation Based Detection of Known Signals in Middleton's Class-A Noise

This letter proposes to apply two rank correlations, namely, Kendall's tau (KT) and Spearman's rho (SR), to the fundamental problem of detecting known signals in impulsive noise. Under the popular Middleton's Class-A impulsive noise model, we derived the expectations and variances of KT and SR, which, along with the central limit theorem, are further employed to determing the detection threshold and the detection probability. Monte Carlo simulations not only verified the correctness of our theoretical findings, but also demonstrated the superiority of KT and SR to other five state-of-the-art methods in terms of detection probability.

Parameter estimation of impulsive noise for channel coded communication systems

In this paper, an impulsive noise estimation algorithm for generating bit log-likelihood ratios (LLRs) for channel coded systems in impulsive noise environments is proposed. This approach is to design the LLR detector in the maximum-likelihood (ML) sense, which requires the parameters of the impulsive noise. The expectation-maximisation (EM) algorithm is utilised to estimate the parameters of the Bernoulli–Gaussian (B–G) impulsive noise model. The estimated parameters is then used to generate the bit LLRs for the soft-input channel decoder. Simulation results show that over a wide range of impulsive noise power, the proposed algorithm approaches the optimal performance (with ideal estimation) even under Middleton class-A (M-CA) impulsive noise models.

Spatially Coupled Generalized Low-Density Parity-Check Codes Over Class-A Impulsive Noise Channels

In this paper, a class of spatially coupled generalized low-density parity-check (SC-GLDPC) codes with minimum coupling width is introduced to mitigate the Class-A impulsive noise. Codes with minimum coupling width are beneficial to simple code structure, short window decoding delay, and small rate-loss. The SC-GLDPC code is constructed by coupling the multiple identical generalized low-density parity-check (GLDPC) codes. Decoding thresholds over impulsive channels are derived by a recursive extrinsic information transfer function approach and are further estimated by the fast prediction approach. An edge spreading optimization method is proposed to design SC-GLDPC codes with minimum coupling width. The simulation results show that the optimized SC-GLDPC codes with minimum coupling width can show capacity-approaching property over impulsive channels. Benefitting from spatial coupling and generalized check nodes the SC-GLDPC codes show better bit error rate performance over impulsive channels, compared with GLDPC codes and spatially coupled low-density parity-check (SC-LDPC) codes.

Error Analysis of Receive Diversity Noncoherent PLC System in Impulsive Noise Environment

A noncoherent diversity detection power line communication (PLC) system employing multi-level amplitude-shift keying (ASK) modulation in the presence of Middleton Class-A impulsive noise is considered. Hermite numerical integration technique is used iteratively to obtain the statistics of the decision variable of an asymptotically optimal detector, which is utilized to derive series expressions for the symbol error probability (SEP). Numerical optimization of the ASK levels is done to achieve the minimum SEP, which results in the optimal solution being close to the equally spaced ASK constellation. The asymptotic optimality of the proposed detector is validated by the SEP variation with the impulsive index of the noise.

Design of multi-antenna relaying for OFDM in impulsive noise environment

A low-complexity multi-antenna relaying scheme is proposed for Orthogonal Frequency Division Multiplexing (OFDM) in the presence of Class-A Impulsive Noise (IN). One way and two way relaying are considered. The signal is transmitted and received by two terminal nodes, each with a single antenna in two time phases. In the proposed design, the processing at the relay consists of Maximal-Ratio Combining (MRC) or Power-based Selection Combining (PSC) for receive combining, Amplify and Forward (AF) for power scaling, and Space Time Block Coding (STBC) for transmit diversity. Channel State Information (CSI), Discrete Fourier Transform (DFT), and Inverse Discrete Fourier Transform (IDFT) are not needed. The Selective Mapping (SLM) technique is used at the transmitter to reduce the Peak-to-Average Power Ratio (PAPR) of the OFDM signal. Then, at the receiver, the clipping technique is used to reduce the impulses that result from the impulsive noise. The proposed system reduces the complexity of the conventional system, which uses multi-relay with a single antenna. Simulation results show that the Bit Error Rate (BER) of the proposed scheme outperforms that of the conventional scheme due to the diversity inherent in the proposed scheme.

Performance Analysis of Distributed Wireless Sensor Networks for Gaussian Source Estimation in the Presence of Impulsive Noise

Abstract—We address the distributed estimation of a scalar Gaussian source in wireless sensor networks (WSNs). The sensor nodes transmit their noisy observations, using the amplifyand- forward relaying strategy through coherent multiple access channel to the fusion center (FC) that reconstructs the source parameter. In this letter, we assume that the received signal at the FC is corrupted by impulsive noise and channel fading, as encountered for instance within power substations. Over Rayleigh fading channel and in presence of Middleton class-A impulsive noise, we derive the minimum mean square error (MMSE) optimal Bayesian estimator along with its mean square error (MSE) performance bounds. From the obtained results, we conclude that the proposed optimal MMSE estimator outperforms the linear MMSE estimator developed for Gaussian noise scenario. Index Terms—Distributed WSN, MMSE optimal Bayesian estimation, Middleton class-A impulsive noise, Rayleigh fading.

Performance analysis of non‐coherent PLC with multi‐level ASK in impulsive noise environment

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.

Mitigating Class-A Impulsive Noise of Long Term Evolution Uplink and Downlink

Mitigating Class-A Impulsive Noise of Long Term Evolution Uplink and Downlink

Capacity-Achieving Input Distributions of Additive Quadrature Gaussian Mixture Noise Channels

This paper studies the characterization of the optimal input and the computation of the capacity of additive quadrature Gaussian mixture (GM) noise channels under an average power constraint. The considered model can be used to represent a wide variety of channels with impulsive interference, such as the well-known Bernoulli-Gaussian and Middleton class-A impulsive noise channels, as well as multiple-access interference channels and cognitive radio channels under imperfect sensing. At first, we demonstrate that there exists a unique input distribution that achieves the channel capacity, and the capacity-achieving input distribution has a uniformly distributed phase. By examining the Kuhn-Tucker alignment conditions (KTCs), we further show that, if the optimal input amplitude distribution contains an infinite number of mass points on a bounded interval, the channel output must be Gaussian-distributed. However, by using Bernstein's theorem to examine the completely monotonic condition, it is shown that the assumption of a Gaussian-distributed output is not valid. As a result, there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. In addition, by applying a novel bounding technique on the KTC and using the envelop theorem, we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points. This gives us the unique solution of the optimal input having discrete amplitude with a finite number of mass points. Given this discrete nature of the optimal input, we then develop a simple method to compute the discrete optimal input and the corresponding capacity. Our numerical examples show that, in many cases, the capacity-achieving distribution consists of only one or two mass points.

Estimation of PN Code of DS-CDMA Signals over Frequency selective Fading Channel in presence of Impulsive noise

Spread spectrum signals are widely used for secure communications, as well as for multiple access interference (MAI). They have many interesting properties, including low probability of interception. Indeed, direct sequence spread spectrum systems (DSSSS) use a periodical pseudo-random sequence to modulate the baseband signal before transmission. Interception of DSSS signals is a difficult task due to the hiding of the PN sequence, especially if the accompanied noise is non-Gaussian and the channel is frequency selective. In this paper, a receiver is proposed to intercept asynchronous direct sequence code division multiple access (DS-CDMA) signals received from different users and estimate the PN sequences of each one of them. The signals are assumed to be transmitted over frequency selective fading channel and contaminated with Class-A impulsive noise. The proposed interception receiver is based on Independent Component Analysis (ICA), the pseudo random sequences is estimated from the eigenvector subspace in case of single path. In multipath situations, the estimation is the overlapped form of the pseudo random sequences, a triple correlation function (TCF) is introduced to eliminate the influence of multipath. The performance of proposed receiver is evaluated in terms of the number of correct estimated codes for m-sequence over typical urban channel in presence of impulsive noise. The results show that the interception receiver performs is 100% code estimation at -8dB signal to noise ratio.

Performance Analysis of Turbo-Coded Decode-and-Forward Relay Channels with Middleton Class-A Impulsive Noise

Performance Analysis of Turbo-Coded Decode-and-Forward Relay Channels with Middleton Class-A Impulsive Noise

Bayesian Estimation of a Gaussian Source in Middleton's Class-A Impulsive Noise

The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the soft-limiter and the blanker, which are two popular suboptimal estimators characterized by very low complexity. The MMSE-optimum thresholds for such suboptimal estimators are obtained by practical iterative algorithms with fast convergence. The paper derives also the optimal thresholds according to a maximum-SNR (MSNR) criterion, and establishes connections with the MMSE criterion. Furthermore, closed form analytic expressions are derived for the MSE and the SNR of all the suboptimal estimators, which perfectly match simulation results. Noteworthy, these results can be applied to characterize the receiving performance of any multicarrier system impaired by a Gaussian-mixture noise, such as asymmetric digital subscriber lines (ADSL) and power-line communications (PLC).

Performance Analysis of Distributed Space–Time Block Coding Schemes in Middleton Class-A Noise

A performance analysis of distributed space-time block coding (STBC) schemes involving multiple decode-and-forward relays is carried out in the case of Middleton class-A impulsive noise, which is one of the major sources of performance degradation in many wireless systems. The considered cooperative communication framework, according to which the signal transmitted by each relay is the product of an STBC matrix and a proper vector of length L, encompasses both centralized and decentralized protocols. Since an insightful theoretical analysis of the maximum-likelihood (ML) detector is very challenging in non-Gaussian environments, an ideal version of the ML detector, which is referred to as ideal ML (IML), is considered, along with the suboptimal minimum-distance (MD) detector. It is analytically proven that, with respect to Gaussian noise, the presence of impulsive noise does not affect the performance of both the IML and MD detectors in terms of asymptotic (i.e., when the transmit power is infinitely large) diversity order R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> , which is equal to the minimum between L and the maximum number of cooperating nodes (relays plus source); in the case of the IML detector, the coding gain is also unaffected. Closed-form formulas involving the main parameters of noise and STBC highlight that the major effect of impulse noise on the performance of the IML and MD detectors concerns the finite signal-to-noise ratio (SNR) diversity order, which does not monotonously increase as the SNR rises; in the case of the MD detector, the coding gain is also affected by the impulsiveness of noise. In particular, it is shown that, in the case of complex orthogonal STBC, the adverse effect of impulse noise on the performance of the IML detector tends to completely disappear for sufficiently large values of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> , whereas increasing values of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> emphasize the weakness of the MD detector against non-Gaussian noise. Finally, simulation results are provided for the ML, IML, and MD detectors to corroborate and supplement the results theoretically derived.

Adaptive Selection Combining Receiver over Time Varying Frequency Selective Fading Channel in Class-A Noise

An adaptive selection combining (SC) scheme is proposed for time varying mobile communication channel in Class-A impulsive noise. The receiver adaptively selects a diversity branch out of the available branches and discards the others. This is performed by computing the maximum likelihood (ML) metric of each diversity branch and selects the branch with the maximum metric. The proposed adaptive SC scheme dynamically adjusts the threshold value according to the time variations of the channel. Equalization and data detection are performed after combining using maximum likelihood sequence estimation implemented by Viterbi algorithm (MLSE-VA). The minimum survivor technique is employed to reduce the complexity of the receiver.

OPTIMUM RECEPTION OVER IMPULSIVE NOISE CHANNELS

The paper presents an optimum receiver for digitally modulated signals in additive class-A impulsive noise. The receiver is based on maximum likelihood (ML) approach. The performance of the receiver is derived theoretically. The performance is measured by the bit error probability. Computer simulations are illustrated to validate the theoretical developments. It is shown that the performance of the developed receiver is sensitive to the impulsive index of the noise. Decreasing the value of the impulsive index degrades the performance of the receiver and reduces the receiver resistivity against frequency offset.

OPTIMUM RECEIVER UNDER CLASS-A IMPULSIVE NOISE FOR FLAT FADING CHANNELS

The paper presents an optimum receiver for digitally modulated signals in additive class-A impulsive noise for flat fading channels. The receiver is based on maximum likelihood (ML) approach. Two algorithms are presented to estimate the unknown fading channel. The convergence properties of the estimation algorithms are investigated and compared. The performance of the receiver is evaluated by simulation. The performance is measured by the bit error probability. Computer simulations are illustrated to validate the theoretical developments. It is shown that the performance of the developed receiver is sensitive to the impulsive index of the noise. Decreasing the value of the impulsive index degrades the performance of the receiver and reduces the receiver resistivity against frequency and time offset.

Bit-Interleaved Coded Modulation With Iterative Decoding in Impulsive Noise

Power-line communications (PLC) suffers performance degradation due mainly to impulsive noise interference generated by electrical appliances. This paper considers the application of bit-interleaved coded modulation with iterative decoding (BICM-ID) in Class-A impulsive noise environment to improve the spectral efficiency and error performance of PLC. In particular, the optimal soft-output demodulator and its suboptimal version are presented for an additive Class-A noise channel so that iterative demodulation and decoding can be performed at the receiver. The effect of signal mapping on the error performance of BICM-ID systems in impulsive noise is investigated, with both computer simulation and a tight error bound on the asymptotic performance. Extrinsic information transfer chart analysis is carried out to illustrate the convergence properties of different mappings. The superior performance of BICM-ID compared to the orthogonal frequency-division multiplex technique is also clearly demonstrated