Detection with compressive measurements corrupted by sparse errors

Compressed sensing (CS) integrates sampling and compression into a single step to reduce the processed data amount. However, the CS reconstruction generally suffers from high complexity. To solve this problem, compressive signal processing (CSP) is recently proposed to implement some signal processing tasks directly in the compressive domain without reconstruction. Among various CSP techniques, compressive detection achieves the signal detection based on the CS measurements. This paper investigates the compressive detection problem of random signals when the measurements are corrupted. Different from the current studies that only consider the dense noise, our study considers both the dense noise and sparse error. The theoretical performance is derived, and simulations are provided to verify the derived theoretical results.

Due to the broad bandwidth nature of the direct sequence spread spectrum (DSSS) signal, the application of narrowband interference (NBI) cancelation algorithms based on the Nyquist‐Shannon sampling theory are limited by the high sampling rate. To solve the sampling and processing difficulty in the traditional DSSS communication interference cancelation method, we used the compressive sensing (CS) to reduce the sampling rate of the DSSS communication system, and further proposed a compressed domain NBI elimination method in this study. We proved that NBI with a certain bandwidth and DSSS signal are both sparse in specific dictionaries and proposed the corresponding sparse dictionary construction method. Detailed analysis of the compressed domain features of NBI and the DSSS signal demonstrated that it is possible to extract the strong NBI components from the compressed measurements. Two compressed domain NBI cancelation algorithms were proposed based on this idea. The extracted NBI components were filtered out from the compressed measurements directly in the first algorithm, and then we achieved the DSSS signal demodulation in compressed domain using the separated DSSS signal components with the orthogonal matching pursuit (OMP) algorithm. A proposed extraction filter block sparse Bayesian learning (EFBSBL) framework algorithm was utilized to estimate the NBI from the compressed measurements in the second algorithm. The estimated NBI was eliminated from the received signal, and then we recompressed the DSSS signal after NBI cancelation and realized the DSSS signal demodulation in compressed domain with the OMP algorithm. Simulation results support our theoretical analysis results and reveal that the two proposed algorithms are both effective for NBI cancelation and significant interference cancelation performance are achieved.

One of the challenges of modulation techniques used in Fifth-Generation (5G) is their robustness in noisy environment. Conventional Orthogonal Frequency Division Multiplexing (OFDM) cannot be considered as a 5G waveform in its original form because of its certain limitations, such as performance degradation by impulsive noise (IN) and high peak to average power ratio (PAPR). Numerous modulation schemes proposed for 5G communications are able to overcome these drawbacks. Generalised Frequency Division Multiplexing (GFDM) is one of them. This paper analyses the performance of GFDM in presence of Additive White Gaussian Noise (AWGN), IN and Narrow Band Interference (NBI). It is found that GFDM is able to perform better than OFDM and Vector Orthogonal Frequency Division Multiplexing (VOFDM) in presence of noises, which can potentially be present in 5G applications. Simulation results show that GFDM achieve lower PAPR and Symbol Error Rate (SER) and an average of 10.73 dB and 4.73 dB gain in Signal to Noise Ratio (SNR) in presence of IN and combined IN and NBI respectively, as compared to OFDM and VOFDM.

In process industries, multivariate statistical process monitoring (MSPM) has become an important technique for enhancing product quality and operation safety. Among the family of MSPM methods, principal component analysis (PCA) may be the most commonly used one, due to its capabilities of dimensionality reduction and highlighting variation in a data set. However, the performance of a PCA model often degrades significantly when there are gross sparse errors, i.e. outliers, contained in the training data, since PCA assumes that the training data matrix only contains an underlying low-rank structure corrupted by dense noise. In this paper, a robust matrix recovery method named stable principal component pursuit (SPCP) is adopted to solve this problem, based on which a process modeling and online monitoring procedure is developed. Such a method inherits the benefits of PCA while being robust to outliers. The effectiveness of the SPCP-based monitoring method is illustrated using the benchmark Tennessee Eastma...

We investigate the use of Low Rank Parity Check Codes (LRPC), originally designed for cryptography applications in the context of Power Line Communication (PLC). Particularly we propose a new code design and an efficient probabilistic decoding algorithm. The main idea of decoding LRPC codes is based on calculations of vector spaces over a finite field F q . This family of codes can be seen as the equivalent of classical LDPC codes for the rank metric. We compare the performance of this code against the Reed-Solomon Code (RS) through a PLC channel. We show by simulation that the proposed system outperforms the traditional scheme where the PLC channel is subjected to both impulsive noise and narrowband interference.

This article presents a novel scheme for video denoising based on improved matrix recovery strategy. The proposed scheme attempts to go beyond the conventional approaches that focus on the rank properties of the matrix by making use of a priori knowledge derived from the characteristics of video and noise. In this paper, we will first demonstrate that the conventional approach such as robust PCA (principal component analysis) is not effective when the video is corrupted by the mixture of impulse and Gaussian noises. The impulse noise can be considered sparse in the image domain and can be effectively filtered by matrix recovery. However, the dense Gaussian noise cannot be easily filtered because it is not sparse in either spatial or frequency domain. We shall show that this Gaussian noise corrupted video can be considered sparse in the 3D total variation domain. Based on this, we formulate the problem as a 3D total variation optimization and design an algorithm to solve this convex problem efficiently. Experimental results show that the proposed scheme achieves noticeable improvement over the state-of-the-art algorithm VBM3D [5].

This letter presents a joint impulsive noise mitigation and sparse channel estimation algorithm for single-carrier systems in mobile underwater acoustic communication (UAC) to address the challenges posed by impulsive noise interference. The basis expansion model (BEM) is introduced to describe the underwater acoustic time-varying channels and reduce the channel parameters to be estimated. Based on the model, the variational Bayesian inference algorithm is employed to derive an iterative estimation expression for jointly estimating the sparse BEM channel coefficients and the impulsive noise. The proposed algorithm mitigates the impact of impulsive noise, leading to enhanced communication reliability. Simulations and sea trials validate the effectiveness of the proposed algorithm, highlighting its potential for practical applications in mobile underwater acoustic communication systems.

Over the last few years there has been an emerging interest in non-coherent ultrawideband (UWB) communication, particularly as a technology for low-data rate applications because of its low-complexity and low-power consumption. However, the presence of narrowband interference (NBI) severely degrades the communication performance since the energy of the NBI signals is also collected. In this paper, we compare the performance of two non-coherent UWB receiver structures ¿ the autocorrelation receiver (AcR) and the energy detection (ED) receiver ¿ in terms of the bit error probability (BEP). The AcR is based on the transmitted reference signaling with binary pulse amplitude modulation, while the ED receiver is based on the binary pulse position modulation. We analyze the BEPs for the two non- coherent systems in a multipath fading channel, both in the absence and presence of NBI. We consider two NBI cases: a) single NBI, where the interfering node is located at a fixed distance from the receiver, and b) multiple NBI, where the interfering nodes with the same carrier frequency are scattered according to a spatial Poisson process. Our framework is simple enough to allow a tractable analysis and provide insights that can be of value in the design of practical UWB systems subject to interference. In particular, we show that the ED receiver is more robust to NBI than the AcR, we quantify how the optimal integration time of the receivers depends on the different system parameters, and we establish a clear relationship between the effect of the aggregate NBI and the interferer parameters such as density and power.

On the PLC channel, noise is generated by electrical loads and by radiated disturbances from the environment. In the frequency range of 9-140 KHz, it is dominated by narrowband interferences and impulsive noise. Impulsive noise is caused by on/off switching events and is different from frequently occurring periodic events. For instance, we have vacuum cleaners; hand-held drilling machines; Switch Mode Power Supply (SMPS) and heaters which are used daily in the network and introduce a lot of impulsive noise into the channel. This leads to an enormous loss in the capacity, as well as a decrease in the error rate performance. Impulsive noise can cause bit and bust errors in PLC. The bit error rate represents an important first order statistic of the data channel, but does not contain information about how the errors are distributed. In this paper, the distribution of errors at the output of a narrowband modem is investigated using gap recording. A gap recorder has been implemented for setting up a stochastic model. The Fritchman Markov model has been investigated to model the distribution of random impulsive events. Values of the model parameters were obtained by analysing the distributions of the lengths of error gaps (error free intervals). Two sets of measurements have been taken, one in an office building and the other in a residential house.

A space-time nonlinear receiver for a DS-CDMA synchronous channel is proposed for jointly mitigating impulsive noise and multiple access interference. The proposed scheme combines linear decorrelators and antenna arrays with nonlinear front ends based on the affinity matched myriad nonlinear filter. This myriad (log Cauchy) filter is incorporated to combat the impulsive noise and prevent it from entering the system. The proposed detector also incorporates a structure for estimating the impulsive noise parameter in order to update a filter parameter called the nonlinearity parameter. Monte Carlo simulation results of the proposed space-time receiver are presented to justify the relative merits of nonlinear signal processing in the space-time domain.

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.

Power lines are characterized by high, unpredictable and time variant noise. The latter are summation of background noise, impulsive noise and narrowband interferences. The background noise is usually taken to be constant in simulation of power line channels due to its slow change. In this paper, the time dependency of power line background noise in an indoor power line setting and its effect on channel capacity and efficiency of transceivers are studied. It is seen that the average channel capacity at night time is 22.4% and 2% more than that of day time for narrowband and broadband transmission respectively. The comparatively high noise in day time increases the Bit Error Rate of Orthogonal Frequency Division Multiplexing transceivers up-to 29% of the night value. This time dependency of background noise therefore cannot be neglected and has to be considered in implementation of successful power line communication systems. A background channel simulator following the statistics is proposed.

Broadband over power lines, or what the Europeans prefer to call power line communications, has long been one of those just-around-the-corner technologies that holds a great deal of promise in principle but has never quite taken off. Enabling technologies on both the transmission and consumer ends have made the service easier to deliver at an attractive price. Consumers naturally would like to have broadband connections that give them more options for where they work or play. There is definitely interest in the ability to plug your notebook into an electrical socket anywhere in your home or while traveling. However, the main problem is noise. Intellon Corp., a small, fabless designer of advanced ICs based in Ocala, FL, addressed this problem while making it cheaper to implement, more secure, and easier to use. Intellon's chip sets combine orthogonal frequency division modulation, dozens of carrier channels, and automatic channel switching. This design ensures that data packets using power lines as an on-ramp to the information highway can switch lanes when they encounter problems, such as varying impedances, narrow-band interference, and impulse noise, that are inherent to that medium. To convey high-speed Internet into homes and businesses, power line communications providers must transmit their data in the form of radio signals. These signals typically have a frequency between 2 and 80 MHz, meaning they occupy the same frequency range used by hams, CB radio users, and aircraft operators. Ideally, the signals would remain confined to power lines, but because these wires are not shielded in the way coaxial cable is, they often behave like long antennas.

Land mobile radio channels are modeled as fading dispersive channels, because of the multipath propagation and the randomly changing medium characteristics. Many types of impairments are observed on these channels such as multipath spread (or delay spread), fading, Doppler spread, nonlinear distortion, frequency offset, phase jitter, impulse noise, thermal noise, and co-channel and adjacent channel interference arising from spectrum sharing. This chapter concentrates on the effects of delay spread, fading, Doppler spread, thermal noise, and co-channel interference. Delay spread causes interference between adjacent symbols, known as intersymbol interference (ISI), a large Doppler spread indicates rapid channel variations and necessitates a fast convergent algorithm when an adaptive receiver is employed, and fading results in a very low received signal-to-noise ratio or signal-to-interference ratio when the channel exhibits a deep fade.

In this letter, a novel robust two-dimensional nearfield millimeter-wave (MMW) image reconstruction algorithm is developed based on compressed sensing (CS) in the presence of impulsive measurement noise. To enable the sparse MMW image recovery, the CS algorithm usually employs the popular l 2 -norm as the data fidelity term and a combination of multiple sparsityinduced functions as the penalty term. The l 2 -norm is non-robust against impulsive noise since the Gaussian noise distribution assumption is not valid, and the presence of impulsive noise will severely degrade the robustness of the compressive MMW image recovery. To gain more robustness performance, a complex correntropy based data-fitting term, namely complex correntropic loss (CC-loss), is used to replace the l2-norm for the near-field MMW measurement contaminated by impulsive noise. In order to solve the corresponding minimization problem, an additive half quadratic method is used to transform the CC-loss term to its convex form, and then a parallel primal-dual process is used to guarantee the convergence of the proposed algorithm. In total, 150-GHz MMW experimental results show that the proposed algorithm can achieve accurate image reconstruction from compressive measurements under different impulsive noise levels.