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Detecting the number of signals (NOS) is a fundamental problem in array processing. However, most existing methods have a computational complexity of $O(M^3)$ , where M is the number of sensors. In this paper we propose a fast detection algorithm with a complexity of $O(DM^2)$ , where D is the number of signals. Different from the conventional approaches that depend on the eigenvalues of the sample covariance matrix (SCM), the proposed method is based on the Ritz values --- the eigenvalues of the projected SCM in Krylov subspace. We first present a scheme to construct the Krylov subspace via the Lanczos tridiagonalization. Then we prove that the first D Ritz values are equal to the $D$ signal eigenvalues. Furthermore, if the Krylov subspace has a dimension greater than D, the minimum Ritz value (MRV) converges to the noise power. Therefore, we can detect the NOS by comparing the MRV with a threshold determined by the noise power. Because the proposed algorithm does not perform eigenvalue decomposition, it has a simple implementation structure. Moreover, by using the Sylvester's law of inertia, the Ritz values do not need to be computed either. Simulation results show that the proposed algorithm outperforms the existing methods under the conditions of small sample size and low signal-to-noise ratio.

In this letter, we investigate the impact of channel correlation and line-of-sight (LOS) on the performance of spectrum sensing, focusing on energy detection (ED) with estimated noise power and the sphericity test (ST). We derive the expected value and variance of the test statistic for ED with estimated noise power, showing that detection probability decreases with channel correlation but increases with LOS propagation. For the ST, we show that detection improves with increased LOS, but the effects of correlation are complex. Depending on the system parameters correlation can improve or degrade detection performance. The analysis is corroborated by means of simulations for correlated Rayleigh, Ricean and ray-based channel models. Finally, we leverage these results to investigate the performance of the recently proposed mixture detector (MD).

The noises embedded in signals will degrade the signal processing quality. Traditional denoising algorithms might not work in practical systems since the statistical characteristics of noises might not be learned. To address this issue, we propose an efficient residual shrinkage convolutional neural network (RSCNN) aided denoiser based on the principle of the domain transformation, shrinking and inverse transforming operations conducted by the traditional denoiser. The proposed RSCNN is composed by the batch normalization layer, domain transformation layers, the shrinkage module and inverse transformation layers, wherein transformation layers consist of convolutional layers and the nonlinear activation function. Moreover, we propose a thresholds learning subnetwork to automatically determine the thresholds, so as to enhance noise suppressing performances. Furthermore, we compose the data set by preprocessing the received signals, and design the loss function according to different denoising requirements. To validate the efficiency and universality of the RSCNN aided denoiser, we apply the proposed RSCNN denoiser to three different application scenarios, including the modulation recognition, detection and decoding. After the offline training, at the online deployment stage, we utilize the RSCNN denoiser to reduce the noise power and improve the signal to noise ratios. Simulation results demonstrate that the proposed intelligent denoiser can efficiently improve the signal processing capabilities to achieve higher modulation recognition accuracy, better detection and decoding performances with lower complexity than benchmark schemes.

This paper presents a detailed examination of fluctuating input noise power levels on the analog to digital convertor (ADC) sampling hardware of the NASA CYGNSS instruments and the associated impacts on the level 1 NBRCS estimation performance. The impact of external noise variations on both the CYGNSS science and navigation channels are quantified with respect to how the fluctuating received power impacts the low level ADC sampling distribution and subsequent NBRCS estimation. This work demonstrates that there are clear quantifiable geo-spatially dependent noise variations linked to GNSS space based augmentation systems (notably QZSS and WAAS) and that these additional noise sources significantly alter the digital sampling distribution of the CYGNSS instruments, actively degrading the level 1 NBRCS estimation if not corrected. A derivation of the theoretical correction for both the science and navigation channel ADC sampling variations is presented which is later tuned based on empirical performance metrics in an effort to minimize the induced calibration errors. The impacts of the enhancements outlined in this work on CYGNSS level 1 calibration are evaluated using 1 year of observations before and after the digital sampling corrections, using model ECMWF wind and Wavewatch III MSS surface validation data sets.

This letter proposes a novel method to implement calibration-free wavelength modulation spectroscopy (CF-WMS) with enhanced sensing sensitivity and accuracy. Compared with traditional 1f-normalized CF-WMS implementation, the proposed method is derived, for the first time, from the power spectral density (PSD) spectrum of transmitted laser. This novel derivation enables estimation of noise power, thus enhancing of sensing sensitivity and retrieval accuracy of gas parameters, particularly in noisy environment. The proposed method is validated by both numerical simulation and condition-controlled experiment, indicating improvement of the detection limit of gas parameters by a factor of 2.64 compared to the traditional method.

Due to the flexibility of the towed line array, shear currents caused by an internal solitary wave (ISW) distort the array shape. This will lead to a mismatch between the conventional target detection algorithm and the array shape, resulting in a significant decline in the performance of the towed line array gain, azimuth resolution, etc. Based on the improved motion model of towed cable constructed by Ablow and Schechter (Ocean Eng, 10: 443–457, 1983), we propose a motion model of the towed line array under an ISW according to the Korteweg-De Vries (KdV) equation and solve the model by finite difference method combined with the Newton iteration method. In addition, the DFT beamforming theory is used to detect the target signal after the array shape distortion compensation to verify the validity of the model. The data analysis shows that the array shape distortion caused by the ISW is mainly affected by the relative position between the array and the ISW, the amplitude of the ISW, the fluid layer density, the fluid layer depth, the towing velocity, the tangential/normal drag coefficient, the elastic modulus, and the towed cable density. The influence of elastic modulus and the towed cable density on array shape distortion can be ignored. The detection results show that the output signal power is about 6 dB higher than the output noise power, and the array gain and azimuth resolution are improved after array shape distortion compensation.

We propose a photonic method for flat spectrum millimeter-wave (mm-wave) noise generation. Specifically, the flat spectrum mm-wave noise is obtained by slicing the broadband ASE optical spectrum into multiple Gaussian-shaped spectra with different central wavelengths, then beating in a wideband photomixer. Our simulation demonstrates that flat spectrum mm-wave noise can be generated in a very large range of frequency of F-band (90-140 GHz) and G-band (140-220 GHz). For the quantitative comparison of the quality of generated mm-wave noise, we define the relative flatness ( $\eta$ ) as the ratio of the generated noise power fluctuation to its average power within a certain frequency range. Our experimental results show that the relative flatness of the generated mm-wave noise is as low as 0.46 (@35 ± 15 GHz).

Modulation identification, a major task of intelligent receivers, is of vital importance for applications in military and civilian fields. In this work, we develop and analyze a blind modulation identification algorithm for two-path successive relaying systems. Analytical expressions for the correlation functions adopted as the basis of the proposed algorithm are derived, and the computational cost of the algorithm is addressed. By taking advantage of the space-time redundancy, we mathematically prove that a group of modulation types exhibits peaks for specific correlation functions while the other group does not. Exploiting this feature, we propose a binary tree hypothesis test for decision-making. A packet length estimator is also introduced as an auxiliary task for the proposed algorithm. The proposed algorithm does not require information about channel coefficients and noise power. The identification performance of the proposed algorithm is evaluated through Monte Carlo simulations under different conditions. Results show that the performance of the proposed algorithm is remarkably better than the traditional algorithms.

This article considers a cyber-physical system with multiple remote state estimation subsystems under denial-of-service (DoS) attack. Suppose that there are multiple distributed estimation systems, in each of which, a sensor monitors the system and sends its local estimation to a remote estimator over one of multiple wireless channels. A DoS attacker emits noise power to jam the wireless channels. A scheduler is installed to dispatch each sensor to transmit information through the specific channel to minimize the total estimation error covariance on account of energy-saving. Whereas, the DoS attacker attempts to jam a channel to realize an opposite objective. With considering interference from other individuals, a multisensor multichannel remote state estimation model is constructed. A myopic policy and a long-term online interaction strategy under varying network environment are investigated and compared by solving a two-player zero-sum game and a Markov game, respectively. Simulations are provided to demonstrate our results.

In this article, we propose a simulation method to investigate the noise mechanism of traveling-wave tube (TWT). Based on the nonlinear theory of Lagrangian description, 1-D noise model is established to analyze the shot noise and the velocity noise of the electron beam in the drift space, which clearly shows that the beam noise propagates along the electron beam with standing wave shape. The shot noise and the velocity noise can be periodically converted into each other along electron beam transmission, which is consistent with the prediction of the classical noise theory developed by Pierce and Danielson (1954). Using the nonlinear beam–wave interaction theory, the evolution process of the shot noise and the velocity noise of the electron beam transforming to the electromagnetic wave in TWT is illustrated. The calculated results show that the input position of the slow wave circuit may affect the noise power spectral density (NPSD) of the device. The proposed method can provide more intuitive and simple images to explain the noise mechanism of TWT.

In this paper, we present a new performance bound for uplink channel estimation (CE) accuracy in the Massive Multiple Input Multiple Output (MIMO) system. The proposed approach is based on noise power calculation after the CE unit in a multi-antenna receiver. We decompose a non-line of sight (NLOS) channel into separate taps and calculate the cross-covariance matrix between them. Then a linear minimum mean squared error (MMSE) method is applied with these taps to estimate residual CE error value for each unique scenario, assuming Gaussian distribution of tap amplitudes and antenna noise. An artificial CE is calculated as a sum of the ideal noiseless channel (pre-defined Quadriga model) and the leftover noise after the optimal estimate. The artificial CE is then utilized in the MIMO detector and decoder units to calculate performance bound. Our method outperforms the accuracy of a well-known Cramer-Rao lower bound (CRLB) due to considering more statistics (number of taps and correlation between them) since performance strongly depends on several channel taps and their power ratio. Additionally, we show that our bound can be obtained from the generalized Bayesian CRLB. Simulation results are presented for the 5G QuaDRiGa 2.0 NLOS channel.

In this article, we present the novel hardware and software architecture of a smart optical force–torque sensor. The proposed configurable, modular, and compact electronics lead to performance characteristics that cannot be reached by currently available sensors: ultra-low noise with average noise power spectral density of 15 nV/ $\sqrt{\text{Hz}}$ over a signal bandwidth of 500 Hz, a resolution of 0.0001% full scale at a 95% confidence level, and a hardware latency of less than 100 $\mu$ s. Performance is achieved by local synchronized oversampling of the sensor's optical transducers and parallel hardware processing of the sensor data using a field-programmable gate array (FPGA). The FPGA's reconfigurability provides for easy customization and updates; for example, by increasing the FPGA system clock rate to a maximum of 160 MHz, latency can be decreased to 50 $\mu$ s, limited by the current analog-to-digital converter. Furthermore, the approach is generic and could be duplicated with other types of transducers. An inertial measurement unit and a temperature sensor are integrated into the sensor electronics for gravity, inertia, and temperature compensations. Two software development kits that allow for the use of the sensor and its integration into the robot operating system have been developed and are discussed.

In this paper, we explore various methods of measuring noise power in RF systems. We discuss some of the systems commonly used to make such measurements, then analyze each system's architecture to obtain the measurement bias and uncertainty for six different combinations of noise models (real and complex noise) and methods of averaging (linear power, magnitude, and logarithmic). Equipped with this knowledge, users can correct for post-measurement biases and determine the number of averages required to yield a desired uncertainty level.

Algorithms of a strapdown inertial orientation system with an inertial measurement module consisting of a three-component gyroscope, accelerometer, and magnetometer are considered. The aim of the work is to improve the algorithms for processing sensor information to ensure the asymptotic stability of the system, tuning for the Schuler period and the low-pass filter with a given bandwidth. The kinematic Poisson equations with positional and integral-positional correction based on the information of accelerometers and magnetometers are considered. The stability and frequency characteristics of the system in relation to the sensor output signals are analyzed. It is shown that the positional correction in each channel does not allow you to adjust the system for the Schuler period. The integral-positional correction allows this adjustment, but in relation to the gyroscope signals, the system is a bandpass filter and does not suppress noise in the bandwidth. The advantages of using positional correction with cross-links in the sense of tuning the frequency characteristics of the system to the Sharper frequency and the third-order low-pass filter are shown. The analysis of the influence of angular velocities confirmed the asymptotic stability of the system with their changes in a given range. The results of mathematical modeling confirmed the compensation of errors in the initial orientation system display, the reduction of noise power in the estimates of the orientation angles in relation to the noise in the sensor signals, and the ability to configure the system for the Schuler period.

Recently, convolutional neural network (CNN)-based channel estimation (CE) for massive multiple-input multiple-output communication systems has achieved remarkable success. However, complexity even needs to be reduced, and robustness can even be improved. Meanwhile, existing methods do not accurately explain which channel features help the denoising of CNNs. In this paper, we first compare the strengths and weaknesses of CNN-based CE in different domains. When complexity is limited, the channel sparsity in the angle-delay domain improves denoising and robustness whereas large noise power and pilot contamination are handled well in the spatial-frequency domain. Thus, we develop a novel network, called dual CNN, to exploit the advantages in the two domains. Furthermore, we introduce an extra neural network, called HyperNet, which learns to detect scenario changes from the same input as the dual CNN. HyperNet updates several parameters adaptively and combines the existing dual CNNs to improve robustness. Experimental results show improved estimation performance for the time-varying scenarios. To further exploit the correlation in the time domain, a recurrent neural network framework is developed, and training strategies are provided to ensure robustness to the changing of temporal correlation. This design improves channel estimation performance but its complexity is still low.

Unmanned Aerial Vehicles (UAVs) enabled Aerial Base Stations (UABSs) have been studied widely in future communications. However, there are a series of challenges such as interference management, trajectory design and resource allocation in the scenarios of multi-UAV networks. Besides, different performances among UABSs increase complexity and bring many challenges. In this paper, the joint downlink transmission power control and trajectory design problem in multi-type UABSs communication network is investigated. In order to satisfy the signal to interference plus noise power ratio of users, each UABS needs to adjust its position and transmission power. Based on the interactions among multiple communication links, a non-cooperative Mean-Field-Type Game (MFTG) is proposed to model the joint optimization problem. Then, a Nash equilibrium solution is solved by two steps: first, the users in the given area are clustered to get the initial deployment of the UABSs; second, the Mean-Field Q (MFQ)-learning algorithm is proposed to solve the discrete MFTG problem. Finally, the effectiveness of the approach is verified through the simulations, which simplifies the solution process and effectively reduces the energy consumption of each UABS.

Introduction. Modern digital phased array antenna (DPAA) systems incorporate a large number of identical transceiver modules (TMs). These modules require real-time calibration with a high level of accuracy. In a previous work, we proposed a real-time calibration method for all receiver channels, which is based on the use of a calibration signal (CalSig) of the same frequency spectrum as the reflected signal and modulated in phase and amplitude by BPSK and OOK codes, respectively. This method was found to have a number of advantages over conventional approaches. However, the use of the same CalSig sample for all receiving channels increases the noise power gain at the output of a digital beam-forming unit (DBU). To overcome this limitation, we set out to improve the structure of CalSigs by making them pseudo-orthogonal. As a result, the noise power gain at the DBU output can be significantly reduced compared to that obtained in our previous work.Aim. To propose an improved design of a controlled amplitude modulation code OOK generator, which allows creation of pseudo-orthogonal CalSigs. As a result, the noise power gain at the output will increase insignificantly, thus having no negative effect on the quality of digital beam forming, signal processing and calibration.Materials and methods. Theory of system engineering and technology; theory of digital signal processing; system analysis; mathematical modeling.Results. An improved CalSig for calibrating the receiving channels of TMs was obtained. A structural diagram allowing the formation of pseudo-orthogonal CalSigs was synthesized.Conclusions. We proposed a new approach to improving the structure of signals used for real-time calibrating the DPAA receiving channels. A structural diagram of an amplitude-modulated OOK code generator for pseudo-orthogonal CalSigs was developed.

Recently space communication technology develops rapidly and space chaotic laser communication serves as an excellent scheme to enhance the security of data transmission. To achieve long-distance transmission, Erbium-doped fiber amplifier (EDFA) is used in a space chaotic laser communication system, but this will inevitably bring amplifier spontaneous emission (ASE) noise. In order to investigate the effect of ASE noise, we give a modified bit error rate (BER) calculation model and numerical simulations are conducted based on it. Quantitative results show that most of ASE noise in the system is caused by the EDFA at the receiver rather than the emitter. Apart from this, deeper researches further indicate that ASE noise will induce mismatch. When ASE noise is small, inherent mismatch noise is the main factor causing mismatch. But as ASE noise power becomes larger, mismatch noise will be dominated by external mismatch noise and internal mismatch noise. Our results have a good reference value for the design of space chaotic laser communication systems.

This paper studies the problem of developing an efficient signal sampling framework for distributed blind spectrum sensing, together with the corresponding local cognitive radio (CR) decision and fusion rules. A novel collaborative sampling and binary output (CSBO) generating scheme is proposed to overcome the disadvantage of traditional energy detectors for blind spectrum sensing, in which the signal-to-noise ratio (SNR) and level of noise power at the CRs are unknown and thus the decision threshold of local energy detectors cannot be specified. In designing the fusion rule in conjunction with the proposed CSBO scheme, both fixed-sample-size tests and sequential tests are considered. It is theoretically shown that the proposed CSBO scheme outperforms traditional blind cooperative energy detectors with uniform sampling schemes in terms of its ability to increase the amount of information acquired under a given number of samples. Simulation results confirm the theoretical analyses, and demonstrate that, compared with the fixed-sample-size test, the sequential test requires fewer observations on average to achieve comparable detection performance. The reduction in the expected sample size needed in the sequential CSBO test when compared to the fixed-sample-size CSBO can reach 50% when primary signal is present.