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In this paper, we introduce a sub-Nyquist sampling-based receiver architecture and method for wideband spectrum sensing. Instead of recovering the original wideband analog signal, the proposed method aims to directly reconstruct the power spectrum of the wideband analog signal from sub-Nyquist samples. Note that power spectrum alone is sufficient for wideband spectrum sensing. Since only the covariance matrix of the wideband signal is needed, the proposed method, unlike compressed sensing-based methods, does not need to impose any sparsity requirement on the frequency domain. The proposed method is based on a multi-coset sampling architecture. By exploiting the inherent sampling structure, a fast compressed power spectrum estimation method whose primary computational task consists of fast Fourier transform (FFT) is proposed. Simulation results are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper details fronthaul optical links using sub-Nyquist sampling rate analog-to-digital converters (ADCs) for Beyond fifth generation (B5G) and 6G sub-THz massive multiple-input multiple-output (Ma-MIMO) beamforming. Unlike Common Public Radio Interface (CPRI) using high speed ADCs in current fronthaul link, the proposed scheme involves ADCs operating at sub-Nyquist sampling rate for each antenna element. Based on pre-allocated relative time delays, pre-processed orthogonal frequency-division multiplexing (OFDM) signals sent from a baseband unit (BBU) can be deaggregated to different Ma-MIMO OFDM signals by sub-Nyquist sampling rate ADCs. In experiments, we assume that each remote radio unit (RRU) is equipped with 32/64 antenna elements and 32/64 ADCs operating at 1/32 and 1/64 of the Nyquist sampling rate. Furthermore, the received Ma-MIMO OFDM signal is then up-converted to 100-GHz for wireless transmission and defined as Ma-MIMO RF OFDM signal. We simulate the 32/64 antenna elements transmission scenario by individually transmit and demodulate each Ma-MIMO RF OFDM signal with 32/64 times of point-to-point antenna transmission. The error vector magnitude (EVM) and signal-to-noise ratio (SNR) of each received Ma-MIMO RF OFDM signal are less than 8% and 26 dB, respectively. And the total received 64 Ma-MIMO RF OFDM signals will require line rate as high as 393.6374 Gb/s according to CPRI option-7. Notably, the proposed scheme reduces the requirement of sampling rate and enables all the Ma-MIMO OFDM signals at baseband without the insertion of guard band. Thus, the proposed scheme can reduce the complexity of signal deaggregation and power consumption in the demodulation process, leading to an improvement in cost efficiency.

Synthetic aperture radar (SAR) imaging with sub-Nyquist sampled echo is a challenging task. Compressed sensing (CS) has been widely applied in this case to reconstruct the unambiguous image. The CS-based methods need to set the iterative parameters manually, but the appropriate parameters are usually difficult to obtain. Besides, such methods require a large number of iterations to obtain satisfactory results, which seriously restricts their practical applications. Moreover, the observation scene of SAR is not sparse in some cases. In this article, we aim at proposing an efficient and effective imaging method for nonsparse observation scenes with reduced data. First, considering the characteristics of nonsparse observation scenes in SAR imaging, we model the SAR imaging problem as a joint low-rank and sparse matrices recovery problem. After that, the iterative alternating direction method of multipliers (ADMMs) to solve the above problem is unrolled into a layer-fixed deep neural network with trainable parameters, in which the learnable parameters are layer-varied. The threshold parameters, as well as the weight parameter between the sparse part and low-rank part of each layer, are learned adaptively instead of manually tuned. Experiments prove that the proposed low-rank and sparse recovery LRSR-ADMM-Net is capable of reconstructing the nonsparse observed scene with high efficiency and precision. Particularly, the proposed LRSR-ADMM-Net yields better reconstruction performance while maintaining high computational efficiency compared with the state-of-the-art iterative recovery methods and the trainable sparse-based network methods. [ABSTRACT FROM AUTHOR]

In cognitive radio (CR) systems, compressed sensing (CS) has emerged as a promising approach for detecting wireless spectrum that is underutilized (i.e., sparse in the frequency domain). The use of CS techniques is believed to reduce the sensing time at minimal hardware overhead compared to the traditional sweeping spectrum scanner, which is a simple energy detector that scans the frequency bins sequentially. Although the sweeping spectrum scanners can be parallelized to reduce the total scanning time, time-multiplexing is still necessary to cover the very large scanning bandwidth. By contrast, the CS spectrum scanner captures the entire spectrum concurrently to detect the occupied frequency bins. Despite the recent popularity of CS spectrum sensing techniques, no published work is available that rigorously compares the performance of these two sensing schemes under similar hardware constraints and same available total sensing time. This paper makes such a comparison and shows that the multi-channel sweeping spectrum scanner outperforms the CS scanner except at the high input signal-to-noise ratios when the two scanners become comparable. The advantage of the sweeping scanner is that although it observes each frequency bin for a shorter time, each sensing is more reliable and not corrupted by the folding of other frequency bins as in the CS scanner.

A design of sub-Nyquist uniform linear array receiver with different sampling rates is proposed, investigated, and reported in this paper. The proposed architecture increases functionality of conventional linear array receiver with modest modifications. Simulation results show that the proposed receiver is capable of determining angle of arrival (AOA) and signal frequencies of multiple continuous-wave/chirp signals over several Nyquist zones.

High-resolution wide-swath synthetic aperture radar (HRWS-SAR) imaging is highly desirable since it allows one to produce high-resolution SAR images of large areas during a short visit time. In this article, staggered coprime pulse repetition frequencies synthetic aperture radar (SCopSAR) is proposed. It divides the time during which a scatterer is illuminated by the antenna beam pattern into two halves where, in each half, pulses are transmitted at the rate of one of two sub-Nyquist pulse repetition frequencies (PRFs). Such PRFs are related to the Nyquist PRF using two coprime subsampling factors. This allows extending the maximum range swath width that can be imaged by a number of times that equals the smaller subsampling factor at the expense of a reduction in the azimuth resolution by half. It further allows for a reduction in the amount of data to be stored and communicated. SCopSAR is an imaging modality suitable for scenes that contain a small number of bright scatterers over a dark background which, for instance, is the case when imaging ships in a calm sea background. Compared with the techniques recently proposed in the literature, SCopSAR simplifies the radar requirements since it uses only one carrier frequency, one waveform, and one channel. Simulations and real ERS-2 satellite raw data are used to validate the theoretical findings presented in this article. [ABSTRACT FROM AUTHOR]

Geosynchronous spaceborne–airborne bistatic synthetic aperture radar (GEO-SA-BiSAR) consists of a GEO transmitter and airborne receiver, which has extensive application prospects in both civilian and military fields for its ability to generate high-resolution images of the ground target with frequent coverage and abundant scattering information. However, the Doppler bandwidth in this configuration exceeds the transmitted pulse repetition frequency (PRF), which leads to sub-Nyquist sampling. To solve this problem, a multireceiving technique has been applied to the receiver to increase the equivalent sampling rate and reconstruct an unambiguous image. In this article, we take a different approach to recover the unambiguous image for GEO-SA-BiSAR with fewer receiving channels. First, the accurate echo model is established based on the “non-stop-and-go” propagation delay model to lay the foundation of accurate imaging. After that, the GEO-SA-BiSAR imaging problem is modeled as a problem of joint sparse and low-rank matrices’ recovery. To reduce the computing time of the traditional recovery method, a modified alternating direction method of multipliers (M-ADMM) is proposed, where the computation and storage of the computational expensive observation matrix are avoided. Furthermore, an M-ADMM method with multiple receiving channels, which combines the recovery theory and multireceiving information, is also proposed to handle the severe sub-Nyquist sampling echo of GEO-SA-BiSAR. Simulation results reveal that the proposed method can recover the original image scene with high computational efficiency. Meanwhile, the number of receiving channels can be reduced compared with the multireceiving technique. [ABSTRACT FROM AUTHOR]

Due to the unequispaced pulse repetition interval (PRI), the low-oversampling ratio and the range-variant blockage, the echo of the low-oversampled staggered SAR (LS-SAR) is nonuniformly sampled with sub-Nyquist and range-variant rate. However, the existing LS-SAR processing methods lack robustness with regards to the scenario type and the PRI variation mode. In this article, a compressive-sensing-based image reconstruction method for the LS-SAR is proposed. First, a hybrid-domain model (HDM) of the LS-SAR echo is presented. In the HDM, the coupled range cell migration (RCM), the unequispaced PRI, and the conflict blockage are formulated as the matrix multiplications with a 3-D tensor, a 2-D matrix, and a Hadamard product, respectively. Based on the HDM, the image reconstruction is realized through the 2-D fast iterative shrinkage thresholding algorithm (ISTA), in which the gradient is derived by exploiting the properties of the tensor and matrix trace. The fast Fourier transform (FFT) and the nonuniform FFT are implemented to accelerate the computation. Due to good accommodation of the RCM and the LS-SAR sampling characteristics, the proposed method can work well for various PRI variation modes and scenario types. Simulations using the point scatter and the distributed target with wide-swath extension demonstrate the effectiveness as well as the robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract Compressed sensing (CS) is a new theory for sampling and recovering signal-based sparse transformation. This theory could help us to acquire complete signal at low cost. Therefore, it also satisfies the requirement of low-cost sampling since bandwidth and capability of sampling is not sufficient. However, wireless sensor network is an open scene, and signal is easily affected by noise in the open environment. Specially, CS theory indicates a method of sub-Nyquist sampling which is effective to reduce cost in the process of data acquirement. However, the sampling is “imperfect”, and the corresponding data is more sensitive to noise. Consequently, it is urgently requisited for robust and antinoise reconstruction algorithms which can ensure the accuracy of signal reconstruction. In the article, we present a proximal gradient algorithm (PRG) to reconstruct sub-Nyquist sampling signal in the noise environment. This algorithm iteratively uses a straightforward shrinkage step to find the optimum solution of constrained formula, and then restores the original signal. Finally, in the experiment, PRG shows excellent performance comparing to OMP, BP, and SP while signal is corrupted by noise.

We demonstrate a cost- and spectrum-effective orthogonal frequency-division multiple access passive optical network downstream scheme based on multi-band and modified sub-Nyquist sampling over transmission reach of 20km. The sampling rate and bandwidth of ADC are reduced effectively, and double spectrum efficiency is obtained. The aggregate bit rate achieves 50.4 Gb/s. The influence of bit resolution of ADC/DAC is investigated and 8-bit resolution is regarded as a reasonable choice. The performance of receiver sensitivity and nonlinearity tolerance is studied. A 20km PON downstream transmission with splitter ratio of 1:64 is considered and the FEC limit of $3.8\times 10 ^{-3}$ is met. The research results show that the proposed scheme is suitable for the short reach communication systems and could be regarded as a promising candidate for the system beyond NG-PON2.

In this paper, we consider the problem of analog-to-information conversion for nonstationary signals, which exhibit time-varying properties with respect to spectral contents. Nowadays, sampling for nonstationary signals is mainly based on Nyquist sampling theorem or signal-dependent techniques. Unfortunately, in the context of the efficient `blind' sampling, these methods are infeasible. To deal with this problem, we propose a novel analog-to-information conversion architecture to achieve the sub-Nyquist sampling for nonstationary signals. With the proposed scheme, we present a multi-channel sampling system to sample the signals in time-frequency domain. We analyze the sampling process and establish the reconstruction model for recovering the original signals. To guarantee the wide application, we establish the completeness under the frame theory. Besides, we provide the feasible approach to simplify the system construction. The reconstruction error for the proposed system is analyzed. We show that, with the consideration of noises and mismatch, the total error is bounded. The effectiveness of the proposed system is verified in the numerical experiments. It is shown that our proposed scheme outperforms the other sampling methods state-of-the-art.

In synthetic aperture radar (SAR) imaging, moving target is generally mixed with stationary targets. Meanwhile, the image of a moving target is distorted and displaced due to the lack of its prior velocity information. Furthermore, imaging of a moving target for geosynchronous (GEO) spaceborne-airborne bistatic SAR (GEO SA-BiSAR) is a more challenging problem because the echo is sub-Nyquist sampled in azimuth. In this article, a simultaneous moving and stationary target imaging method for GEO SA-BiSAR is proposed. First, range models and the corresponding echo models of moving and stationary targets are established. The observation models for both moving and stationary targets with two receiving channels are derived based on the inverse of an efficient imaging algorithm. After that, the imaging problem of moving and stationary targets is modeled as a joint velocity estimation and sparse decomposition problem, which aims at optimizing the entropy of the moving target image and residual error of the formed images at the same time. Finally, a joint optimization method based on the particle swarm optimization (PSO) method and alternating direction method of multipliers (ADMM) is applied to achieve the imaging of moving and stationary targets and estimation of the moving target velocity. With two receiving channels, the accurate separation and focusing of stationary and moving targets as well as the precise estimation of moving target velocity can be achieved with sub-Nyquist sampling echo. Simulation results are presented to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Low-earth-orbit (LEO) synthetic aperture radar (SAR) can achieve advanced remote sensing applications benefiting from the large beam coverage and long duration time of interested area provided by a geosynchronous (GEO) SAR illuminator. In addition, the receiving LEO SAR system is also cost-effective because the transmitting module can be omitted. In this article, an imaging method for GEO-LEO bistatic SAR (BiSAR) is proposed. First, the propagation delay characteristics of GEO-LEO BiSAR are studied. It is found that the traditional “stop-and-go” propagation delay assumption is not appropriate due to the long transmitting path and high speed of the LEO SAR receiver. Then, an improved propagation delay model and the corresponding range model for GEO-LEO BiSAR are established to lay the foundation of accurate imaging. After analyzing the sampling characteristics of GEO-LEO BiSAR, it is found that only 12.5% sampling data can be acquired in the azimuth direction. To handle the serious sub-Nyquist sampling problem and achieve good focusing results, an imaging method combined with multireceiving technique and compressed sensing is proposed. The multireceiving observation model is first obtained based on the inverse process of a nonlinear chirp-scaling imaging method, which can handle 2-D space-variant echo. Following that, the imaging problem of GEO-LEO BiSAR is converted to an $L_{1}$ regularization problem. Finally, an effective recovery method named complex approximate message passing (CAMP) is applied to obtain the final nonambiguous image. Simulation results show that the proposed method can suppress eight times Doppler ambiguity and obtain the well-focused image with three receiving channels. With the proposed method, the number of required receiving channels can be greatly reduced. [ABSTRACT FROM AUTHOR]

Recently developed variable pulse width finite rate of innovation (VPW-FRI) theory offers an efficient way for sampling pulse streams with various shapes at the sub-Nyquist rate. Unfortunately, for real signals, noise, and model mismatch will induce inaccuracies to such scheme in the reconstruction process. In this paper, an optimization model-based sub-Nyquist sampling system for pulses with various shapes is proposed, which improves the performance of VPW-FRI scheme under noise and model mismatch situation. Since the real pulse streams with various shapes may be modeled as the sum of an unknown number of Lorentzian pulses and a model mismatch error signal, we build an optimization object function with the purpose of minimizing the energy of this model mismatch error signal. Then, for solving such function, we propose a two-channel sub-Nyquist sampling system to obtain a Fourier coefficients subset and several discrete samples from the input signal. We demonstrate that the best number of Lorentzian pulses and the corresponding pulse parameters can be found by using an improved particle swarm optimization algorithm. Finally, simulations with the electrocardiogram signals in MIT-BIH database have shown that the proposed method has better performance and stability than traditional VPW-FRI scheme.

Compressed sensing (CS) is a new theory for sampling and recovering signal-based sparse transformation. This theory could help us to acquire complete signal at low cost. Therefore, it also satisfies the requirement of low-cost sampling since bandwidth and capability of sampling is not sufficient. However, wireless sensor network is an open scene, and signal is easily affected by noise in the open environment. Specially, CS theory indicates a method of sub-Nyquist sampling which is effective to reduce cost in the process of data acquirement. However, the sampling is "imperfect", and the corresponding data is more sensitive to noise. Consequently, it is urgently requisited for robust and antinoise reconstruction algorithms which can ensure the accuracy of signal reconstruction. In the article, we present a proximal gradient algorithm (PRG) to reconstruct sub-Nyquist sampling signal in the noise environment. This algorithm iteratively uses a straightforward shrinkage step to find the optimum solution of constrained formula, and then restores the original signal. Finally, in the experiment, PRG shows excellent performance comparing to OMP, BP, and SP while signal is corrupted by noise. [ABSTRACT FROM AUTHOR]

We present a cognitive prototype that demonstrates a colocated, frequency-division-multiplexed, multiple-input multiple-output (MIMO) radar, which implements both temporal and spatial sub-Nyquist sampling. The signal is sampled and recovered via the Xampling framework. Cognition is due to the fact that the transmitter adapts its signal spectrum by emitting only those subbands that the receiver samples and processes. Real-time experiments demonstrate sub-Nyquist MIMO recovery of target scenes with 87.5% spatio-temporal bandwidth reduction and signal-to-noise-ratio of $-$ 10 dB. [ABSTRACT FROM AUTHOR]

Sparse emission source microscopy (ESM) is an efficient method to identity radiating sources. With the purpose to minimize the number of required measurement points, the presented work investigates how numerical properties of sparse ESM affects the quality of source reconstruction. A simulation model of a simple printed circuit board was used instead of measurements to isolate the observed effect of the two-dimensional (2-D) discrete Fourier transformation (DFT) and the plane wave spectrum's numerical properties. The paper shows that sub-Nyquist is achievable and suggests uniform sampling is superior to nonuniform, in contrast to other reported uses of microwave imaging. Finally, the study shows that if the source reconstruction is based on uniform 2-D DFT care should be taken with the previously suggested intelligent selection of sparse samples based on real-time observation of the measured field. [ABSTRACT FROM AUTHOR]

• Different sampling rates result in different frequency locator polynomial evaluations. • Multiband Signal can be blindly detected even in SNR = −20dB. • Probability of false alarm is efficiently lowered. A novel multirate sampling scheme is proposed for wideband spectrum sensing. The signal is subsampled by shifted parallel channels working at same rate. However, the rate switches among several rates between neighboring snapshots where the spectrum aliases at different frequencies. Basing on this, we propose a blind multiband signal detection algorithm. In this method, we construct frequency locator polynomials (FLPs) to locate the nonzero components of the original spectrum from the subsampled signal for each snapshot. We compute the FLP evaluations, which differs in the snapshots sampled with distinct rates. The evaluations are statistically described by the complex Gaussian distributions for each detected frequency. The detection is then completed by fusing these probabilities contributed by the latest several snapshots. Simulation results show that the proposed algorithm can efficiently lower the false alarms. [ABSTRACT FROM AUTHOR]

Due to the growth of wireless networks, efficient use of the spectrum is necessary, a solution is Cognitive Radio. In one of the stages of this technology, spectrum sensing is carried out, that is, determining on a frequency whether there are primary users and, if they do not exist, occupying the available spectrum; this is achieved by applying sensing techniques, each technique requires hardware resources and can identify different characteristics of a signal. Nowadays, high propagation frequencies are used, it is necessary for the processing stage to perform a Sub Nyquist sampling, that is, less than twice the maximum frequency. An alternative solution is to use an algorithm based on Matrix Completion, called by the authors like IZMA-SD. The results show that in different signals sampled at% 75 of Nyquist and under different SNR, when the algorithm is applied, the reconstruction of the signal is performed, to which the sensing techniques can be applied. [ABSTRACT FROM AUTHOR]

The direct space-to-information converter (DSIC) unifies conventional delay-and-sum analog conventional beamforming (CBF) with compressive sampling (CS) rapid direction-of-arrival (DOA) finding into a single, reconfigurable phased-array receiver architecture. Where current CBF-based DOA scanners need to exhaustively search through multiple DOA angles, the DSIC is able to receive energy from all possible angles by modulating its antenna weights psuedo-randomly. The DSIC RF-ASIC can operate from 1 to 3 GHz, was fabricated in 65-nm CMOS, and includes eight direct-conversion paths each delivering 32-dB conversion gain, 3.3-dBm in-band IIP3, and 6.4-dB NF while consuming 19.8 mW from 1.2 V. The DSIC RF-ASIC has two modes of operation, CS-DOA and CBF-Reception and can switch between them in less than $1~\mu \text{s}$. In CS-DOA mode, the DSIC RF-ASIC finds the DOA of a single signal in $1~\mu \text{s}$ consuming 158 nJ which is 4 $\times $ faster and 1.5 $\times $ less energy than a comparable CBF-based DOA scanner. [ABSTRACT FROM AUTHOR]

In this paper, a novel direct learning algorithm is proposed to identify the digital predistortion (DPD) coefficients that linearize a power amplifier (PA) using sub-Nyquist sampled intermediate frequency (IF) output of a heterodyne transmitter observation receiver (TOR). The learning algorithm is complemented with a joint time and phase alignment procedure to compensate for the unknown phase of the IF carrier as well as the delay between the PA input and output signals. By sub-Nyquist sampling at IF, the proposed method avoids the need for challenging receiver calibration that compensates for significant IQ imbalance exhibited by direct conversion receivers. Furthermore, it provides a very attractive flexibility in choosing the IF and consequently allows for a high subsampling factor. It is also extended to account for the nonflat frequency response of the TOR, thus avoiding the need for an explicit calibration step. Finally, measurement results were performed to linearize a PA demonstrator driven by a 320-MHz wide carrier aggregated LTE signal centered at 31 GHz using a complexity reduced Volterra-based DPD. Excellent linearization capacity (ACPR of 50 dBc and normalized mean square error of 2%) using significantly low sampling rates (as low as 40 Msps) is reported. [ABSTRACT FROM AUTHOR]

Rotating blades play a functional role during the working process of turbomachinery, but they are prone to failure due to harsh working conditions. Blade tip timing (BTT) is a potential technique for operational blade health monitoring due to its noncontact feature and efficiency. The critical issue in the application of BTT is extracting vibration parameters or reconstructing the spectrum for subsequent fault diagnosis. However, the nonuniform and undersampling characteristics of the BTT signal challenge signal processing. In this work, we developed an effective and efficient time delay-based spectrum reconstruction method. On this basis, we proposed the conditions (minimal probe number and delay sampling criterion) for the spectrum reconstruction. The proposed reconstruction conditions apply to most BTT methods for parameter identification or spectrum reconstruction and provide guidance for BTT measurement. Finally, the effectiveness of the proposed method and the correctness of the reconstruction conditions were demonstrated by a series of simulations and experiments. [ABSTRACT FROM AUTHOR]

En este trabajo se muestra las distribuciones de probabilidad que presentan los valores singulares, obtenidos de la matriz de autocorrelación de las muestras de señales continuas, adquiridas con muestreo Sub-Nyquist random demodulator. Los resultados provienen de un proceso experimental a nivel de simulación desarrollado en Matlab®. El proceso de simulación parte de la experimentación con tonos senoidales puros, continuando con señales con modulación am, y finalizando con modulación en frecuencia. Estas señales se encuentran inmersas en ruido blanco aditivo gaussiano, con el fin de acercarse a la realidad. Artí­culo Resultado de Investigación

Software defined radio (SDR) and cognitive radio have become the development trend for military or civilian radio stations. This paper analyzes the digital to analog (DAC) system based on software defined radio applications. The measurement procedure and calibration technique for hybrid signal system are described in detail. In order to maximize the utilization of the image spectrum and achieve better performance for communication, the sub-Nyquist rate DAC system with different construction modes is introduced. The two-phase holding reconstruction mode utilizes higher order image spectrum by adjusting duty cycle of the two phases. This technique based on SRD has the merit of lower power consumption and higher efficiency for communication system. [ABSTRACT FROM AUTHOR]

Sub-Nyquist sampling technology can ease the conflict between high resolution and wide swath in a synthetic aperture radar (SAR) system. However, the existing sub-Nyquist SAR imposes a constraint on the type of the observed scene and can only reconstruct the scene with small sparsity (i.e., number of significant coefficients). The information channel model of microwave imaging radar based on information theory, in which scene, echo, and the mapping relation between the two correspond to information source, sink, and channel, is built, and noisy-channel coding theorem explains the reason for the aforementioned under this model. To allow the wider application of sub-Nyquist SAR, this paper proposes sub-Nyquist SAR based on pseudo-random space-time modulation. This modulation is the spatial and temporal phase modulation to the traditional SAR raw data and can increase the mutual information of information source and sink so that the scenes with large sparsity can be reconstructed. Simulations of scenes with different sparsity, e.g., an ocean with several ships and urban scenes, were run to verify the validity of our proposed method, and the results show that the scenes with large sparsity can be successfully reconstructed.

The application of two-dimensional (2-D) infinite impulse response (IIR) spatially-bandpass (SBP) filters as a digital beamformer for a wide spectrum of practical applications spanning wireless cognitive radio communications, doppler radar, and radio astronomy instrumentation is discussed. The paper starts with an introduction of the recently proposed 2-D SBP filter. The first application is a spectrum sensing scheme for dynamic spectrum access based cognitive radios. A 2-D IIR SBP filter is used in conjunction with a sub-Nyquist wideband signal reconstruction technique to achieve aperture-array directional spectrum sensing using sub-Nyquist sparse sampling based on the recently reported Eldar algorithm. The second application is related to wideband pulse and continuous-wave frequency modulated Doppler radar sensing. The SBP filter is integrated with a wideband radar back-end connected to an electronically-steerable aperture antenna. A a low-complexity directional localization algorithm is presented, which estimates the range and angle of a target scatterer with a signal to interference ratio improvement of 10 dB. We also present applications of 2-D IIR SBP in the fields of classification and remote sensing of unmanned aerial vehicles. Finally, a digital aperture-array wideband beamforming model using the 2-D IIR SBP filters is presented for radio telescope systems based on dense aperture arrays and time-domain beamforming. A well-known example is the study of pulsar astrophysics using a highly-directional aperture antenna system. The 2-D IIR SBP beamformer is simulated as the digital backend of the time-domain beamforming system with array signals synthesized using measured time-domain signatures from the Crab pulsar obtained from the GAVRT. The SBP filter shows a gain of 12.3 dB with an order of magnitude lower circuit complexity compared to traditional phased-array digital beamformers. To obtain comparable levels of SINR improvement, the wideband phased-array beamformers require 48-point FFTs per antenna. Assuming the optimum three real-multiplications per complex multiplication for the Gauss algorithm, it is discovered that the proposed 2-D IIR SBP beamformers are more than 97 % lower in digital multiplier complexity compared to traditional FIR phased-array FFT-beamformers. [ABSTRACT FROM AUTHOR]

Many conventional Doppler analysis techniques for radar sensors suffer from velocity ambiguity when confronted with targets that are moving at speeds higher than the Nyquist velocity. This paper proposes a signal processing method for estimating accurately the Doppler velocity of targets from such sub-Nyquist radar data. The hypothesis tested in the paper is the possibility of circumventing the velocity ambiguity by exploiting the high range resolution of ultra-wideband radar sensors, more specifically incorporating the texture method applied to the signal envelope intensity profile. We employ a millimeter-wave radar sensor operating at 60 GHz to measure a rotating cylinder and a walking human to investigate the applicability of the proposed approach. The experimental results indicate that the proposed method can estimate the Doppler velocity accurately without aliasing from sub-Nyquist data, demonstrating that the use of the texture method is promising for resolving the ambiguity caused by sub-Nyquist sampling. The advantage of the proposed method is that the ambiguity can be resolved simply with the signal processing technique, and the approach does not require any custom hardware, such as nonuniform samplers. An important future study based on this paper is the application of the proposed approach to develop a low-cost radar system with a low sampling rate that can measure fast-moving targets. [ABSTRACT FROM PUBLISHER]

In Cognitive Radio (CR) systems seeks to make an efficient use of radio resources, therefore the Spectrum Sensing (SS) is a critical function, since of the SS function depends that the CR system has an adequate knowledge of the spectral bands sub used. Traditional methods of SS, presents major implementation challenges because they require high sampling rates above the Nyquist rate, doing that the number of samples to be processed is high. To address this problem, in this paper a method for estimating the center frequency of continuous signals is presented, The signal is acquired at lower frequencies established by Nyquist sampling theorem. With the obtained data autocorrelation matrix is calculated, then the singular values of this matrix are obtained and compared with preset values, from these values, the center frequency of the signal is estimated. [ABSTRACT FROM AUTHOR]

Third-generation full-waveform (FW) light detection and ranging (LIDAR) systems collect time-resolved 1-D signals generated by laser pulses reflected off of intercepted objects. From these signals, scene depth profiles along each pulse path can be readily constructed. By emitting a series of pulses toward a scene using a predefined scanning pattern and with the appropriate sampling and processing, an image-like depth map can be generated. Unfortunately, massive amounts of data are typically acquired to achieve acceptable depth and spatial resolutions. The sampling systems acquiring this data, however, seldom take into account the underlying low-dimensional structure generally present in FW signals and, consequently, they sample very inefficiently. Our main goal and focus here is to develop efficient sampling models and processes to collect individual time-resolved FW LIDAR signals. Specifically, we study sub-Nyquist sampling of the continuous-time LIDAR FW reflected pulses, considering two different sampling mechanisms: 1) modeling FW signals as short-duration pulses with multiple band-limited echoes; and 2) modeling them as signals with finite rates of innovation. [ABSTRACT FROM PUBLISHER]

Efficient spike acquisition techniques are needed to bridge the divide from creating large multielectrode arrays (MEA) to achieving whole-cortex electrophysiology. In this paper, we introduce generalized analog thresholding (gAT), which achieves millisecond temporal resolution with sampling rates as low as 10 Hz. Consider the torrent of data from a single 1,000-channel MEA, which would generate more than 3 GB/min using standard 30-kHz Nyquist sampling. Recent neural signal processing methods based on compressive sensing still require Nyquist sampling as a first step and use iterative methods to reconstruct spikes. Analog thresholding (AT) remains the best existing alternative, where spike waveforms are passed through an analog comparator and sampled at 1 kHz, with instant spike reconstruction. By generalizing AT, the new method reduces sampling rates another order of magnitude, detects more than one spike per interval, and reconstructs spike width. Unlike compressive sensing, the new method reveals a simple closed-form solution to achieve instant (noniterative) spike reconstruction. The base method is already robust to hardware nonidealities, including realistic quantization error and integration noise. Because it achieves these considerable specifications using hardware-friendly components like integrators and comparators, generalized AT could translate large-scale MEAs into implantable devices for scientific investigation and medical technology. [ABSTRACT FROM AUTHOR]

Highlights: [•] We investigate the modified Colombo–Nyquist rule in satellite gravity recovery. [•] We investigate the influence of ground-track pattern on the gravity solutions. [•] We assess the quality of sub-Nyquist gravity solutions by satellite gravity missions. [•] We employ post-processing tools to deal with high level of noise in the solutions. [ABSTRACT FROM AUTHOR]

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two: Analog compression that narrows down the input bandwidth prior to sampling with commercial devices followed by a nonlinear algorithm that detects the input subspace prior to conventional signal processing. A representative union model of spectrally sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy, and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework. [ABSTRACT FROM PUBLISHER]

Sub-Nyquist sampling technology can ease the conflict between high resolution and wide swath in a synthetic aperture radar (SAR) system. However, the existing sub-Nyquist SAR imposes a constraint on the type of the observed scene and can only reconstruct the scene with small sparsity (i.e., number of significant coefficients). The information channel model of microwave imaging radar based on information theory, in which scene, echo, and the mapping relation between the two correspond to information source, sink, and channel, is built, and noisy-channel coding theorem explains the reason for the aforementioned under this model. To allow the wider application of sub-Nyquist SAR, this paper proposes sub-Nyquist SAR based on pseudo-random space-time modulation. This modulation is the spatial and temporal phase modulation to the traditional SAR raw data and can increase the mutual information of information source and sink so that the scenes with large sparsity can be reconstructed. Simulations of scenes with different sparsity, e.g., an ocean with several ships and urban scenes, were run to verify the validity of our proposed method, and the results show that the scenes with large sparsity can be successfully reconstructed. [ABSTRACT FROM AUTHOR]