Multi-coset Sampling Research Articles

Blind power spectrum reconstruction for multi-sinusoid signals with generative multicoset sampling

As the target frequency increases, the Nyquist rate is hard to reach due to hardware limitations. Alternatives to high-rate sampling have attracted considerable research interest. Compressed covariance sensing based on multicoset sampling (MCS) is a prevalent sub-Nyquist sampling strategy for blind power spectrum reconstruction. However, it requires the sampling pattern of MCS to be a minimal sparse ruler. In this paper, a generative multicoset sampling (GMCS) is proposed to minimize the number of cosets. In the sampling stage, a minimal MCS, delay coprime scheme is proposed to ensure the recoverability of the power spectrum. In the recovery stage, a new function, i.e., multifold correlation is constructed for blind power spectrum reconstruction. We prove that the power spectrum of a multi-sinusoid signal (MSS) can be estimated by its multifold correlation and the sample density of multifold correlation can be increased by correlation operations. Owing to multifold correlation, GMCS can generate virtual cosets satisfying the sparse ruler criterion through only two physical cosets and then efficiently recover the power spectrum by least-squares estimation. Moreover, we demonstrate the feasibility of GMCS for linear frequency modulation (LFM) signals. Finally, the effectiveness of GMCS are verified by numerical simulations and blade tip timing experiments (a non-contact vibration measurement). By reducing the average sampling rate and hardware complexity, GMCS opens new avenues for blind sampling and power spectrum reconstruction.

Wideband spectrum compressive sensing utilizing photonic multi-coset sampling with dual low-rate optical pulses

A wideband spectrum compressive sensing approach for sparse multiband signals utilizing photonic multi-coset sampling (MCS) is presented. The method employs dual low-rate optical pulses, initially modulated by separate pseudo-random binary sequences (PRBSs), which are then multiplexed to achieve the desired multi-coset pattern. It results in a substantial reduction of the rate requirements for both the sampling optical pulses and PRBSs, leading to a significant enhancement of system bandwidth. In simulations, an instantaneous system bandwidth of 21 GHz is achieved at a low mean sampling rate of 4.8 GS/s, employing two optical pulses with rates of 8.4 GHz and 6 GHz, respectively. The spectra of a mixed signal with six passbands are accurately identified, illustrating the capability of the scheme to recognize the spectra of various types of multiband signals. Furthermore, a comparative analysis of the performance between our proposed scheme and traditional MCS techniques is conducted.

Multicoset-based deterministic measurement matrices for compressed sensing of sparse multiband signals

Signal acquisition is a basic function in signal processing systems. In the context of digital communications, the analog-to-digital (ADC) converters have to be carefully designed as part of the radio frequency front end, to reduce power consumption while avoiding aliasing. When operating with sparse multiband signals, compressive sampling becomes an attractive alternative to enable low sampling rates at the front end. Starting from previous results on multicoset sampling and compressed sensing, we analyze sampling strategies for sparse multiband signals based on the operation of a set of ADC converters working in parallel. Different architectures are considered, with equal and different sampling rates in the ADCs, and their associated deterministic measurement matrices and sampling patterns are studied. The matrices involved in the corresponding reconstruction equations for the different architectures are also analyzed in terms of their mutual coherence. As a result, we are able to design different universal multicoset sampling patterns. We obtain the parameters for the different sampling architectures that guarantee reconstruction of the multiband sparse signal, even at high compression rates. Simulation results show the effectiveness of the theoretical designs for sparse reconstruction of this type of signals.

Hardware-Efficient and Short Sensing-Time Multicoset-Sampling Based Wideband Spectrum Sensor for Cognitive Radio Network

This work proposes implementation friendly algorithm for multicoset sampling based wideband spectrum sensing that alleviates computational space and enables parallel execution, incurring lower latency. Based on this proposed algorithm, we provide a new hardware-efficient VLSI architecture of wideband spectrum sensor (WSSR), which offers short sensing time while sensing the wideband spectrum. Additionally, this paper presents a comprehensive discussion of all the submodule micro-architectures of the proposed WSSR. Subsequently, extensive performance analyses performed in the AWGN channel environment have demonstrated that our WSSR delivers adequate detection probability of 0.9 at -5 dB of SNR. Furthermore, the proposed WSSR design also uses a Zynq UltraScale+ FPGA board with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$14.16~\mu \text{s}$ </tex-math></inline-formula> sensing time and a 2.63 GHz maximum sensing bandwidth. Comparison of our hardware implementation results has shown that the proposed WSSR achieves 38.5% higher sensing bandwidth and 90% shorter sensing time, in comparison to the state-of-the-art work. Eventually, this paper concludes by showing the ASIC synthesis and post-layout simulation results of the proposed WSSR in 90 nm-CMOS technology, which senses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.4\times $ </tex-math></inline-formula> wider bandwidth than the state-of-the-art implementation.

I-Q multi-coset sampling and timing skew calibration for wideband spectrum sensing at sub-Nyquist rates

Sampling GHz wideband signals at Nyquist rate is challenging. Some well-known sub-Nyquist sampling methods such as multi-coset sampling (MCS), have been proposed to overcome the sampling bottleneck. In the schemes based on MCS, inaccuracy of delay elements, clock offset and channel discrepancies cause undesired timing skews which consequently lead to measurement errors and degrade the spectrum reconstruction performance. In this paper, we propose an I-Q MCS architecture and a corresponding timing skew calibration approach. The new architecture performs two sets of MCS after implementing quadrature amplitude modulation on the received continuous-time signal. Unknown timing skews are estimated with the sub-Nyquist samples and used for calibrating the sensing model, which is built based on the relation between the sub-Nyquist spectrum and the Nyquist spectrum. Experiments show that the proposed method is able to reconstruct the spectrum with desirable performance even under significant timing skews. Robust spectrum sensing is accomplished at sub-Nyquist rates.

A Low Complexity Sensing Algorithm for Non-Sparse Wideband Spectrum.

The vast majority of existing sub-Nyquist sampling wideband spectrum sensing (WSS) methods default to a sparse spectrum. However, research data suggests that in the near future, the wideband spectrum will no longer be sparse. This article proposes a sub-Nyquist sampling WSS algorithm that can adapt well to non-sparse spectrum scenarios. The algorithm continues to implement the idea of our previously proposed “no reconstruction (NoR) of spectrum” algorithm, thus having low computational complexity. The new one is actually an advanced version of the NoR algorithm, so it is called AdNoR. The key to its advancement lies in the establishment of a folded time-frequency (TF) spectrum model with the same special structure as in the fold spectrum model of the NoR algorithm. For this purpose, we have designed a comprehensive sampling technique which consists of multicoset sampling, digital fractional delay, and TF transform. It is verified by simulation that the AdNoR algorithm maintains a good sensing performance with low computational complexity in the non-sparse scenario.

Characteristics analysis of blade tip timing signals in synchronous resonance and frequency recovery based on subspace pursuit algorithm

Long-term high cycle fatigue vibration will lead to the reduction of life of the blade. Blade Tip Timing (BTT) technology is a research hotspot in the non-contact measurement of blades. Due to the limitation of the number of sensors, BTT signals present serious undersampled conditions. Identifying the frequency of blade vibration through the analysis of undersampled signals is the key problem of the current BTT technology. A sub-Nyquist technique, called multi-coset sampling (MCS), which is suitable for the BTT sampling model can be applied. In this paper, the characteristics of BTT signals under blade synchronous resonance are described and the deficiency of this feature in the recovery process using the orthogonal matching pursuit (OMP) algorithm is found. Based on the problem, the subspace pursuit (SP) algorithm adapted to this feature is proposed. The validity of the algorithm is verified by the blade rotation experiment. The advantage of this algorithm is that the synchronous resonance frequency of the blades can be recovered with a higher probability, which provides a new idea for the development of BTT technology.

Broadband Vibration Signal Measurement Based on Multi-Coset Sampling in Phase-Sensitive OTDR System

The frequency response of phase-sensitive optical time-domain reflectometry ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR) is strictly limited by the repetition rate of the injected sampling pulses in conventional sensing scheme. To fully reconstruct an arbitrary vibration signal, the pulse repetition rate is required to be lower bounded by twice the maximum frequency of the vibration signal according to the Nyquist sampling theorem and at the same time upper bounded by the sensing fiber length to avoid generations of mixed Rayleigh backscattered signals from more than one optical pulse within the sensing fiber, making high-frequency vibration sensing over long distance impossible. In this work, we propose a novel method based on the serial multi-coset sampling (MCS) strategy which can recover sparse broadband vibration signals with sub-Nyquist sampling rates, which is thus able to break through the tradeoff between the measurable vibration frequency bandwidth and the sensing range. Pulses with non-uniform intervals are adopted to realize MCS for the Rayleigh backscattered lights along the entire sensing fiber rather than the traditional uniform pulse train. A continuous to finite (CTF) block is used to determine the active spectrum ranges of the sparse signal. By using a serial MCS sequence with an average sampling rate of 4.8 kHz, both a 4 kHz single-frequency sinusoidal signal and a 0.2 kHz bandwidth chirped signal with a center frequency of 4.6 kHz were sampled and recovered successfully in the simulation. In experiments, a single frequency vibration signal of 15 kHz and a chirped vibration signal with frequency ranging from 15 to 16 kHz were successfully identified and reconstructed over a sensing distance of 4 km using an average sampling rate of 21.6kHz, respectively, which however is not possible in conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR system. Furthermore, accurate identification of a broadband vibration signal with a maximum frequency of 6 kHz over a 10km-long sensing fiber shows that this method is also practically valid in long-distance sensing.

Approaching Sub-Nyquist Boundary: Optimized Compressed Spectrum Sensing Based on Multicoset Sampler for Multiband Signal

Compressed spectrum sensing naturally pursues the use of fewer sampling resources to achieve spectrum support reconstruction and signal recovery. The theoretical lower boundary of averaging sampling rate to recover the multiband signal has been proved to be twice the Landau rate. However, it is still unreachable in practice. Based on the multicoset sampling architecture, this paper analyzes the influencing factors on perfect spectrum reconstruction from three aspects: data model, sampling pattern and greedy reconstruction algorithms, for which practical and feasible optimization schemes are proposed. To reduce redundant reconstruction for the multiple measurement vectors (MMV) signal model, a block MMV model is proposed to improve the accuracy in the spectrum support set reconstruction process. A sampling pattern selection algorithm is proposed to ensure a higher success rate of the spectrum support reconstruction to optimize the sensing matrix. We also deduced the representation of the signal and noise energy in the reconstructed spectrum based on the mathematical model of compressed sensing. We thus proposed a non-orthogonal double-threshold matching pursuit algorithm to avoid a high false-alarm rate due to the manually set converging conditions for matching pursuit algorithms. Numerical experiments on real-world wideband signals are carried out to demonstrate the feasibility and advantages of the proposed approaches. With integrated optimization, the required sampling density to ensure perfect reconstruction is approaching the sub-Nyquist sampling boundary.

Time-Frequency Sparse Reconstruction of Non-Uniform Sampling for Non-Stationary Signal

We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique.

Adaptive Compressed Spectrum Sensing for Multiband Signals

Adaptive compressed spectrum sensing (ACSS) can effectively save sampling resources in wideband spectrum sensing. Almost all of the existing ACSS algorithms are based on the discrete multitone signal model. However, real-world spectra are always multiband signals. In this paper, we derive mathematical models and algorithms enabling the ACSS suitable for multiband signals, which can save sampling resources and has lower computational complexity. Firstly, we introduce the multicoset sampling system into ACSS to sample multiband signals. Besides, we propose a leave-one-out cross-validation (LOOCV) based ACSS scheme with low sampling costs. To save sampling resources, we choose only one sampling channel as a testing subset to validate reconstructed signal and repeat this several times with different sampling channels. Then, we use the mean of the multiple validation results to determine the accuracy of the reconstructed signal. To reduce computational complexity, we propose a LOOCV-ACSS algorithm, in which we only perform the least square method several times in the LOOCV procedure, rather than the complicated compressed sensing reconstruction algorithms. Numerical simulations and real-world signal test results demonstrate that our derivation and algorithms are effective to reduce the sampling cost while keeping the same performance as conventional algorithms.

Multi-coset angular sampling-based compressed sensing of blade tip-timing vibration signals under variable speeds

Blade Tip-Timing (BTT) has been regarded as a promising way of on-line blade vibration monitoring. But blind multi-band BTT vibration reconstruction is a big challenge under variable speeds and under-sampling. In order to deal with it, a novel Compressed Sensing (CS) method is proposed based on Multi-Coset Angular Sampling (MCAS) in this paper. First, multi-coset sampling scheme of BTT vibration signals is presented. Then the CS model of BTT vibration signals is derived in order domain. A sufficient condition of the number of BTT sensors is derived for perfect reconstruction and optimal placement of BTT sensors is determined by minimizing the condition number. In the end, numerical simulations are done to validate the proposed method and the performances of four reconstruction algorithms are compared, i.e., Orthogonal Matching Pursuit (OMP), Multiple Signal Classification (MUSIC), Basis Pursuit Denoising (BPDN) and Modified Focal Underdetermined System Solver (MFOCUSS). Influences of the sensor placement, the number of BTT sensors and measurement noises on the reconstruction performances are also testified. The results demonstrate that the proposed method is feasible and the overall performance of the BPDN algorithm is the best among the four algorithms. Also the reconstruction performance decreases with the accelerations of rotating speed.

A rapid coarse-grained blind wideband spectrum sensing method for cognitive radio networks

Spectrum sensing aims to sense the potential spectrum resources available in the cognitive radio environment. It is also the premise of spectrum management and spectrum sharing in cognitive radio systems. To perceive the primary user’s activity and make full use of spectrum holes, rapid detection of a broad frequency span is an essential part of cognitive radio technology. Reducing the observation time for the data collection, the data storage requirements, and hardware/software computational complexity are urgent and challenging issues in wideband spectrum sensing. High accuracy power spectral density estimation is not the primary requirement; of course, the accuracy must be controlled within the appropriate range and can support the primary user activity’s determination. This paper proposes a sub-Nyquist wideband spectrum sensing method based on compressive covariance sensing for the rapid wideband spectrum sensing. Compared with the traditional Nyquist-rate method, this method can use low-speed ADC to detect wideband signals and effectively control the observation time and computational complexity. This paper’s main contributions include: (1) developing a sub-Nyquist sampling structure based on the multi-coset sampling banks, (2) proposing a coarse-grained power spectral density estimation method for wideband spectrum sensing with short observation time and low complexity. Simulations show that the proposed method exhibits this method is suitable for fast spectral detection. At the same time, the error of spectrum analysis is basically within the acceptable range.

A Joint Optimization Algorithm Using Adaptive Minimum Coset Number Based Discrete Multi-Coset Sampling

We address the problem of sparse multi-band signal reconstruction in the case of unknown band position through the discrete multi-coset sampling (DMCS). In this article, the signal has complex frequency components, and the minimum coset number is determined on the assumption that there is only one frequency component with same characteristics. According to the frequency characteristics, we analyze the influence of the parameterized compressed matrix on the two reconstruction algorithms, and get that a single algorithm does not have universal adaptability to different frequency components. In order to solve this problem, under the discrete multi-coset sampling model, a joint optimization algorithm with discriminant factor (DF-JOA) is proposed to identify the different characteristics and automatically select an appropriate algorithm for signal reconstruction, numerical simulation experiments show the effectiveness of the algorithm. We also simulate the reconstruction success ratio of amplitude and the total coset number under different compressed matrices, determine the influence law, and confirm the improvement of signal reconstruction probability by joint optimization algorithm. Our method ensures the spectrum reconstruction of the multi-band signal. This article can guide how to better select the coset parameters under the condition that the channels of the discrete multi-coset sampling system are limited but the minimum coset number can be guaranteed. It will have a great significance to the sub-Nyquist sampling technique.

Fast Compressed Power Spectrum Estimation: Toward a Practical Solution for Wideband Spectrum Sensing

There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the problem of compressed power spectrum estimation whose objective is to reconstruct the power spectrum of a wide-sense stationary signal based on sub-Nyquist samples. By exploring the sampling structure inherent in the multicoset sampling scheme, we develop a computationally efficient method for power spectrum reconstruction. An important advantage of our proposed method over existing compressed power spectrum estimation methods is that our proposed method, whose primary computational task consists of fast Fourier transform (FFT), has a very low computational complexity. Such a merit makes it possible to efficiently implement the proposed algorithm in a practical field-programmable gate array (FPGA)-based system for real-time wideband spectrum sensing. Our proposed method also provides a new perspective on the power spectrum recovery condition, which leads to a result similar to what was reported in prior works. Simulation results are presented to show the computational efficiency and the effectiveness of the proposed method.

Output-Only Vibration-Based Monitoring of Civil Infrastructure via Sub-Nyquist/Compressive Measurements Supporting Reduced Wireless Data Transmission

The consideration of wireless acceleration sensors is highly promising for cost-effective output-only system identification in the context of operational modal analysis (OMA) of large-scale civil structures as they alleviate the need for wiring. However, practical monitoring implementations for OMA using wireless units suffer a number of drawbacks related to wireless transmission of densely sampled acceleration time-series including the energy self-sustainability of the sensing nodes. In this work, two recently proposed approaches for output-only modal identification addressing the above issues through balancing monitoring accuracy with data transmission costs are comparatively studied and numerically assessed using field recorded acceleration datasets from two different structures: (i) an operating on-shore wind turbine, (ii) an open to traffic highway bridge. One approach utilizes non-uniform-in-time deterministic multi-coset sampling at sub-Nyquist rates to capture structural response acceleration time-series under ambient excitation assuming stationary signal conditions. In this approach, a power spectrum blind sampling technique is used to estimate the response acceleration power spectral density matrix from the low-rate sampled measurements and is coupled with the Frequency Domain Decomposition method of OMA. The other is a spectro-temporal compressive sensing approach which recovers response acceleration signals through time-series reconstruction in the time domain from sub-Nyquist non-uniform-in-time randomly sampled measurements. Prior knowledge of signal structure in the spectral domain is exploited through smart on-sensor operations and sensor/server communication. The benefits and limitations of the considered approaches are discussed and demonstrated by processing the field recorded datasets for different levels of signal compression and by estimating battery lifetime gains at a single sensor achieved by reduced data transmission. It is concluded that the two approaches are readily applicable in OMA of large-scale structures and can be used complementarily depending on the requirements of any particular acceleration monitoring campaign: time-series extraction for further interrogation vs. solely modal properties estimation.

Using FFT to reduce the computational complexity of sub-Nyquist sampling based wideband spectrum sensing

Sub-Nyquist sampling based wideband spectrum sensing can usually be summarized as two steps. The first step estimates the signal power spectrum. The second step uses the energy detection method to make a decision. The traditional method usually adopts the least square algorithm to estimate the power spectrum. In order to reduce the computational complexity of the power spectrum estimation, a novel algorithm is proposed to replace the least square algorithm. We find the system matrix of Multi-Coset Sampling (MCS) based power spectrum estimation has a special structure. Its row vectors are all selected from the row vectors of the Discrete Fourier Transform (DFT) matrix. We exploit this special structure and use Fast Fourier Transform (FFT) to reduce the computational complexity of power spectrum estimation. Simulation shows the proposed algorithm can achieve the spectrum sensing performance similar to the traditional method at much lower computational complexity.

Hybrid mmWave MIMO-OFDM Channel Estimation Based on the Multi-Band Sparse Structure of Channel

This paper presents a hybrid channel estimator for multiple-input multiple-output orthogonal frequency-division multiplexing mmWave systems based on the sparse nature of the angular channel and leveraging the compressed sensing (CS) tools. The angular support is recovered without any discretization by treating the angular channel in a continuous framework which resolves the limited angular resolution of the discrete sparse channel models used in the previous CS-based channel estimators. The power leakage problem is also addressed by modeling the continuous angular channel as a multi-band signal with the bandwidth of each sub-band being proportional to the amount of power leakage caused by the limited antenna array length. The RF combiner is implemented using a network of low-power switches for antenna subset selection based on a multi-coset sampling pattern. Simulation results validate the low reconstruction error and good performance of the proposed channel estimator.

Distributed Compressive Sensing Augmented Wideband Spectrum Sharing for Cognitive IoT

The increasing number of Internet of Things (IoT) objects has been a growing challenge of the current spectrum supply. To handle this issue, the IoT devices should have cognitive capabilities to access the unoccupied portion of the wideband spectrum. However, most IoT devices are difficult to perform wideband spectrum sensing using either conventional Nyquist sampling system or sub-Nyquist sampling system since both power-hungry sampling components and intricate sub-Nyquist sampling hardware are unrealistic in the power-constrained IoT paradigm. In this paper, we propose a blind joint sub-Nyquist sensing scheme by utilizing the surround IoT devices to jointly sample the spectrum based on the multicoset sampling theory. Thus, only the off-the-shelf low-rate analog-to-digital converters on the IoT devices are required to form coset samplers and only the minimum number of coset samplers are adopted without the prior knowledge of the number of occupied channels and signal-to-noise ratios. Moreover, to further reduce the number of coset samplers and transfer part of the computational burden from the IoT devices to the core network, we adopt the data from geo-location database when applicable. The experimental results on both simulated and real-world signals verify the theoretical results and effectiveness of the proposed scheme. At the meanwhile, it is shown that the adaptive number of coset samplers could be adopted without causing the degradation of the detection performance and the number of coset samplers could be further reduced with the assists from geolocation database even when the obtained information is partially correct.

A multi-sensor sub-Nyquist power spectrum blind sampling approach for low-power wireless sensors in operational modal analysis applications

A novel multi-sensor power spectrum blind sampling (PSBS) approach is proposed supporting low-power wireless sensor networks (WSN) for Operational Modal Analysis (OMA) applications. The developed approach relies on arrays of wireless sensors, employing deterministic non-uniform in time multi-coset sampling to acquire structural response acceleration signals at sub-Nyquist sampling rates, treated as realizations of stationary random processes without making any assumption about the average signal frequency content and spectral support. The acquired compressed measurements are transmitted to a central server and collectively processed via a PSBS technique, herein extended to the multi-sensor case, to estimate the power spectral density matrix of an underlying spatially correlated stationary response acceleration random process directly from the compressed measurements. Structural modal properties are then extracted through standard frequency domain decomposition (FDD). The efficacy of the proposed approach to resolve closely-spaced modes is numerically tested for various data compression levels using noisy response acceleration signals of a white-noise excited finite element model of a space truss as well as field-recorded acceleration time-histories of an instrumented bridge under operational loading. It is shown that accurate mode shapes based on the modal assurance criterion can be obtained from as low as 89% less measurements compared to conventional non-compressive FDD at Nyquist sampling rate. Further, significant gains in energy consumption and battery lifetime prolongation of the order of years are estimated, assuming wireless sensors operating on multi-coset sampling at different data compression levels. It is, therefore, concluded that the proposed PSBS approach could provide long-term structural health monitoring systems with low-maintenance cost once wireless sensors with multi-coset sampling capabilities become commercially available.