Showing papers in "IEEE Transactions on Aerospace and Electronic Systems in 2019"

A mmWave Automotive Joint Radar-Communications System

Abstract: We propose a millimeter-wave joint radar-communications (JRC) system comprising a bi-static automotive radar and vehicle-to-vehicle communications. We study the applicability of known phase-modulated-continuous-wave (PMCW) and orthogonal-frequency-division-multiple-access waveforms for bi-static-JRC. In both cases, we design multiplexing strategies to ensure the parameter identifiability, derive JRC statistical bounds and numerically demonstrate superior performance of proposed low-complexity JRC super-resolution algorithms over conventional two-dimensional fast Fourier transform/MUltiple SIgnal Classification.

Dual-Function MIMO Radar Communications System Design Via Sparse Array Optimization

Abstract: Spectrum congestion and competition over frequency bandwidth could be alleviated by deploying dual-function radar-communications systems, where the radar platform presents itself as a system of opportunity to secondary communication functions. In this paper, we propose a new technique for communication information embedding into the emission of multiple-input multiple-output (MIMO) radar using sparse antenna array configurations. The phases induced by antenna displacements in a sensor array are unique, which makes array configuration feasible for symbol embedding. We also exploit the fact that in a MIMO radar system, the association of independent waveforms with the transmit antennas can change over different pulse repetition periods without impacting the radar functionality. We show that by reconfiguring sparse transmit array through antenna selection and reordering waveform-antenna pairing, a data rate of megabits per second can be achieved for a moderate number of transmit antennas. To counteract practical implementation issues, we propose a regularized antenna-selection-based signaling scheme. The possible data rate is analyzed and the symbol/bit error rates are derived. Simulation examples are provided for performance evaluations and to demonstrate the effectiveness of proposed dual-function radar-communication techniques.

Fixed-Time Attitude Tracking Control for Spacecraft With Input Quantization

Abstract: This paper investigates the fixed-time attitude tracking control problem for rigid spacecraft with input quantization and external disturbances. A novel fixed-time disturbance observer is designed to estimate unknown disturbances. By using adding a power integrator technique, a fixed-time controller is constructed, which can guarantee system states converge to a neighborhood of origin in fixed time. The parameter of quantizer can be coarsely chosen. Finally, simulation results are employed to demonstrate the effectiveness of the developed control scheme.

Performance Limits of Cognitive-Uplink FSS and Terrestrial FS for Ka-Band

Abstract: This paper investigates the performance limits of cognitive-uplink fixed satellite service (FSS) and terrestrial fixed service (FS) operating in the range 27.5–29.5 GHz for Ka-band. In light of standard recommendations from the International Telecommunications Union and a rain-fading channel model, we analyze the interference level at the FS receiver by considering statistical properties of the channel, propagation losses, and antenna patterns. By employing the interference constraint criterion at the FS, an analytical expression for the capacity of the cognitive-uplink FSS is derived, which is useful in understanding the limits in performance and the potential application of the considered coexistence scenario. Simulations are carried out to verify the theoretical derivations and highlight the impact of key parameters on the performance limits.

Constrained Waveform Design for Colocated MIMO Radar With Uncertain Steering Matrices

Abstract: This paper deals with the robust waveform design of multiple-input multiple-output radar to improve target detectability embedded in signal-dependent interferences. Two iterative algorithms with ensuring convergence properties are introduced to maximize the worst case signal-to-interference-plus-noise ratio (SINR) over steering matrix mismatches under the constant modulus and similarity constraints. Each iteration of the proposed algorithms splits the high-dimensional problem into multiple one dimensional problems, to which the optimal solutions can be found in polynomial times. Numerical examples are provided to assess the capabilities of the proposed techniques in comparison with the existing methods in terms of the SINR and the computational times for both the continuous and discrete phase cases of the probing signal.

Fractional-Order Fuzzy Sliding Mode Control for the Deployment of Tethered Satellite System Under Input Saturation

Abstract: In this paper, a novel fractional-order fuzzy sliding mode control strategy is developed to realize the deployment of the tethered satellite system (TSS) with input saturation. The considered TSS is modeled as an underactuated system. By decoupling the underactuated system into two subsystems, a fractional-order and a constrained integer-order sliding surfaces are designed for the actuated and unactuated subsystems, respectively. Then, a new hybrid sliding manifold is obtained by coupling the two subsliding surfaces. Adaptive fuzzy algorithm is used to regulate the coupling coefficient in the newly proposed hybrid sliding manifold in order to procure satisfactory performance. Meanwhile, the saturation nonlinearity of control input is also considered. The asymptotic stability of the closed-loop system is demonstrated theoretically. With the existence of fractional order, the presented controller can perform faster and more smooth tether deployment when compared with conventional ones. Finally, the effectiveness and superiority of the proposed control approach are validated by illustrative simulations.

Robust Beamforming Design for Sum Secrecy Rate Maximization in Multibeam Satellite Systems

Abstract: This letter investigates the secure transmission optimization in a multibeam satellite downlink network with multiple eavesdroppers, where each legitimate user is wiretapped by a corresponding eavesdropper. Our design objective is to maximize the sum secrecy rate of the multibeam satellite network in the presence of imperfect channel state information (CSI) of eavesdroppers, while guaranteeing the total transmit power constraint on-board the satellite. Due to the nonconvexity and intractability resulting from the eavesdroppers’ CSI uncertainty, a robust beamforming scheme is proposed to transform the initial optimization problem into a convex framework by jointly applying the Taylor expansion, S-Procedure, and Cauchy–Schwarz inequality. Meanwhile, an iterative algorithm is introduced to obtain the optimal solution. Finally, the validity and superiority of the proposed scheme are confirmed through comparisons with the existing nonrobust and perfect CSI approaches.

DNN Transfer Learning From Diversified Micro-Doppler for Motion Classification

Abstract: Recently, deep neural networks (DNNs) have been the subject of intense research for the classification of radio frequency signals, such as synthetic aperture radar imagery or micro-Doppler signatures. However, a fundamental challenge is the typically small amount of data available due to the high costs and resources required for measurements. Small datasets limit the depth of DNNs implementable, and limit performance. In this work, a novel method for generating diversified radar micro-Doppler signatures using Kinect-based motion capture simulations is proposed as a training database for transfer learning with DNNs. In particular, it is shown that together with residual learning, the proposed DivNet approach allows for the construction of DNNs and offers improved performance in comparison to transfer learning from optical imagery. Furthermore, it is shown that initializing the network using diversified synthetic micro-Doppler signatures enables not only robust performance for previously unseen target profiles, but also class generalization. Results are presented for 7-class and 11-class human activity recognition scenarios using a 4-GHz continuous wave software-defined radar.

Classification, Denoising, and Deinterleaving of Pulse Streams With Recurrent Neural Networks

Abstract: Pulse streams of many emitters have flexible features and complicated patterns. They can hardly be identified or further processed from a statistical perspective. In this paper, we introduce recurrent neural networks (RNNs) to mine and exploit long-term temporal patterns in streams and solve problems of sequential pattern classification, denoising, and deinterleaving of pulse streams. RNNs mine temporal patterns from previously collected streams of certain classes via supervised learning. The learned patterns are stored in the trained RNNs, which can then be used to recognize patterns-of-interest in testing streams and categorize them to different classes, and also predict features of upcoming pulses based on features of preceding ones. As predicted features contain sufficient information for distinguishing between pulses-of-interest and noises or interfering pulses, they are then used to solve problems of denoising and deinterleaving of noise-contaminated and aliasing streams. Detailed introductions of the methods, together with explanative simulation results, are presented to describe the procedures and behaviors of the RNNs in solving the aimed problems. Statistical results are provided to show satisfying performances of the proposed methods.

Distributed Adaptive Attitude Control for Networked Underactuated Flexible Spacecraft

Abstract: This paper studies the distributed adaptive control of a team of underactuated flexible spacecraft under a leader–follower architecture with the measurements of the rigid bodies only. By treating the flexible spacecraft as an underactuated Lagrange system, an adaptive control strategy is proposed with the feedback of the generalized coordinates, velocities, and accelerations of the rigid bodies. Then, an extended state observer is introduced to design a distributed adaptive controller without the measurement of the generalized accelerations.

Real-Time Optimal Control for Spacecraft Orbit Transfer via Multiscale Deep Neural Networks

Abstract: This study is motivated by the requirement of on-board trajectory optimization with guaranteed convergence and real-time performance for optimal spacecraft orbit transfers. To this end, a real-time optimal control approach is proposed using deep learning technologies to obtain minimum-time trajectories of solar sail spacecraft for orbit transfer missions. First, the minimum-time two-dimensional orbit transfer problem is solved by an indirect method, and the costate normalization technique is introduced to increase the probability of finding the optimal solutions. Second, by making novel use of deep learning technologies, three deep neural networks are designed and trained offline by the obtained optimal solutions to generate the guidance commands in real time during flight. Consequently, the long-standing difficulty of on-board trajectory generation is resolved. Then, an interactive network training strategy is presented to increase the success rate of finding optima by supplying good initial guesses for the indirect method. Moreover, a multiscale network cooperation strategy is designed to deal with the recognition deficiency of deep neural networks (DNNs) with small input values, which helps achieve highly precise control of terminal orbit insertion. Numerical simulations are given to substantiate the efficiency of these techniques, and illustrate the effectiveness and robustness of the proposed DNN-based trajectory control for future on-board applications.

Fusing Deep Learning and Sparse Coding for SAR ATR

Abstract: We propose a multimodal and multidiscipline data fusion strategy appropriate for automatic target recognition (ATR) on synthetic aperture radar imagery. Our architecture fuses a proposed clustered version of the AlexNet convolutional neural network with sparse coding theory that is extended to facilitate an adaptive elastic net optimization concept. Evaluation on the MSTAR dataset yields the highest ATR performance reported yet, which is 99.33% and 99.86% for the three- and ten-class problems, respectively.

Radar Data Cube Processing for Human Activity Recognition Using Multisubspace Learning

Abstract: In recent years, radar has been employed as a fall detector because of its effective sensing capabilities and penetration through walls. In this paper, we introduce a multilinear subspace human activity recognition scheme that exploits the three radar signal variables: slow-time, fast-time, and Doppler frequency. The proposed approach attempts to find the optimum subspaces that minimize the reconstruction error for different modes of the radar data cube. A comprehensive analysis of the optimization considerations is performed, such as initialization, number of projections, and convergence of the algorithms. Finally, a boosting scheme is proposed combining the unsupervised multilinear principal component analysis (PCA) with the supervised methods of linear discriminant analysis and shallow neural networks. Experimental results based on real radar data obtained from multiple subjects, different locations, and aspect angles (0 $^{\circ }$ , 30 $^{\circ }$ , 45 $^{\circ }$ , 60 $^{\circ }$ , and 90 $^{\circ }$ ) demonstrate that the proposed algorithm yields the highest overall classification accuracy among spectrogram-based methods including predefined physical features, one- and two-dimensional PCA and convolutional neural networks.

Radar Waveform Optimization for Target Parameter Estimation in Cooperative Radar-Communications Systems

Abstract: The coexistence between radar and communications systems has received considerable attention from the research community in the past years. In this paper, a radar waveform design method for target parameter estimation is proposed. Target time delay parameter is used as an example. The case where the two systems are not colocated is considered. Radar waveform optimization is performed using statistical criteria associated with estimation performance, namely Fisher Information (FI) and Cramer–Rao Bound (CRB). Expressions for FI and CRB are analytically derived. Optimization of waveforms is performed by imposing constraints on the total transmitted radar power, constraints on the interference caused to the communications system, as well as constraints on the subcarrier power ratio (SPR) of the radar waveform. The frequency-domain SPR is different than the peak-to-average power ratio, which is computed in time domain. It is shown, using simulation results, that the proposed optimization strategies outperform other strategies in terms of estimation error. It is also shown that the SPR constraint reduces the delay domain ambiguities.

Integration of Spectral Histogram and Level Set for Coastline Detection in SAR Images

Abstract: This study proposed a novel algorithm for coastline detection in single-polarization synthetic aperture radar (SAR) images based on the local spectral histogram (LSH) and the level set method (LSM). The proposed algorithm includes two main steps. In the processing step, a rough land/sea segmentation is done by utilizing a texture-based segmentation using LSH. In the postprocessing step, the region-based LSM is used to refine the previous segmentation and extract the coastline accurately. The level set (LS) function is initialized using the results of LSH segmentation. This prevents the development of spurious contours, becoming trapped in the local minimum, eliminates the manual support, and also speeds up the LS evolution. A hierarchical LS regularization is proposed using two Gaussian kernels, which is compatible with noisy images and able to detect very narrow regions. The proposed algorithm is able to detect a coastline at the full resolution of the input SAR image and is also robust to noise. A criterion to quantify the accuracy of the results was also proposed. The experimental results for a number of real high-resolution single-polarization SAR images demonstrate that the proposed method is robust to noise and efficient for the coastline detection in different coastal and sea environments.

Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion

Abstract: We propose a novel consensus notion, called “partial consensus,” for distributed Gaussian mixture probability hypothesis density fusion based on a decentralized sensor network, in which only highly weighted Gaussian components (GCs) are exchanged and fused across neighbor sensors. It is shown that this not only gains high efficiency in both network communication and fusion computation, but also significantly compensates the effects of clutter and missed detections. Two “conservative” mixture reduction schemes are devised for refining the combined GCs. One is given by pairwise averaging GCs between sensors based on Hungarian assignment and the other merges close GCs for trace minimal, yet, conservative covariance. The close connection of the result to the two approaches, known as covariance union and arithmetic averaging, is unveiled. Simulations based on a sensor network consisting of both linear and nonlinear sensors, have demonstrated the advantage of our approaches over the generalized covariance intersection approach.

Cooperative Aerial–Ground Vehicle Route Planning With Fuel Constraints for Coverage Applications

Abstract: Low-cost unmanned aerial vehicles (UAVs) need multiple refuels to accomplish large area coverage. We propose the use of a mobile ground vehicle (GV), constrained to travel on a given road network, as a refueling station for the UAV. Determining optimal routes for a UAV and GV, and selecting rendezvous locations for refueling to minimize coverage time is NP-hard. We develop a two-stage strategy for coupled route planning for UAV and GV to perform a coverage mission. The first-stage computes refueling sites that ensure reachability of all points of interest by the UAV and feasible routes for both the UAV and GV. In the second stage, mixed-integer linear programming (MILP) based exact methods are developed to plan optimal routes for the UAV and GV. As the problem is NP-Hard, we also develop computationally efficient heuristics that can find good feasible solutions within a given time limit. Extensive simulations are conducted to corroborate the effectiveness of the developed approaches. Field experiments are also performed to verify the performance of the UAV-GV solution.

Machine Learning Methods for Spacecraft Telemetry Mining

Abstract: Spacecrafts are critical systems that have to survive space environment effects. Due to its complexity, these types of systems are designed in a way to mitigate errors and maneuver the critical situations. Spacecraft delivers to the ground operator an abundance data related to system status telemetry; the telemetry parameters are monitored to indicate spacecraft performance. Recently, researchers proposed using Machine Learning (ML)/Telemetry Mining (TM) techniques for telemetry parameters forecasting. Telemetry processing facilitates the data visualization to enable operators understanding the behavior of the satellite in order to reduce failure risks. In this paper, we introduce a comparison between the different machine learning techniques that can be applied for low earth orbit satellite telemetry mining. The techniques are evaluated on the bases of calculating the prediction accuracy using mean error and correlation estimation. We used telemetry data received from Egyptsat-1 satellite including parameters such as battery temperature, power bus voltage and load current. The research summarizes the performance of processing telemetry data using autoregressive integrated moving average (ARIMA), Multilayer Perceptron (MLP), Recurrent Neural Network (RNN), Long Short-Term Memory Recurrent Neural Network (LSTM RNN), Deep Long Short-Term Memory Recurrent Neural Networks (DLSTM RNNs), Gated Recurrent Unit Recurrent Neural Network (GRU RNN), and Deep Gated Recurrent Unit Recurrent Neural Networks (DGRU RNNs).

Avoidance of Time-Varying Radio Frequency Interference With Software-Defined Cognitive Radar

Abstract: Congestion in the RF spectrum is rapidly increasing, which has motivated the need for efficient spectrum sharing techniques. A cognitive radar system has been developed to implement a perception action cycle, for spectrum sharing, in which the RF spectrum is sensed, other RF signals are identified, and the radar frequency band of operation is adapted to avoid interfering signals in the spectrum. The system operates in real time and is capable of coexisting with common communications signals. A system with this capability requires efficient programming that pushes the limits of the technology available. In order to properly test the performance of a radar system designed for this kind of reactive spectrum sharing, a rigorous set of synthetic interference signals is generated and several informative evaluation metrics are defined. Additionally, the system's performance is evaluated with common communications signals such as LTE and GSM. The performance of the system is found to be adequate for avoiding signals that are either varying in frequency or turning on and off at rates on the order of 10 ms.

Deep Learning Based Radio-Signal Identification With Hardware Design

Abstract: This paper proposes a deep learning based intelligent method for detecting and identifying radio signals considering two applications: first, cognitive radar for identifying micro unmanned aerial systems and second, an automated modulation classification scheme for cognitive radio, which can be used for aeronautical communication systems. Our proposed intelligent method is designed of a spectral correlation function based feature extractor and a low-complexity deep belief network classifier with low FPGA logic utilization.

Low-Sidelobe Range-Angle Beamforming With FDA Using Multiple Parameter Optimization

Abstract: In this paper, we propose an equivalent transmit beamforming method in joint range and angle domains at the receiver of the colocated transmit-receive system where frequency diverse array (FDA) acts as transmit antenna. FDA employs a small frequency offset across the array elements and introduces additional degrees-of-freedom in range domain, which can significantly enhance the beamforming flexibility. However, the transmit beampattern of conventional FDA is range-angle-time dependent. In this work, the time-varying problem is first solved by using a series of filters and mixers at the receiver. In the sequel, a subarray-based FDA framework, termed as multisub-FDA, is established and then a range-angle-decoupled equivalent transmit beamforming method is devised based on particle swarm optimization, which incorporates the frequency offset of each subarray and the corresponding weight vector into the optimization problem. With the proposed approach, the array is capable of generating focused beampattern with low sidelobe in both range and angle domains. Numerical results show that the proposed algorithm improves the beamforming performance, range resolution, and sidelobe suppression.

Robust Adaptive Beamforming via Simplified Interference Power Estimation

Abstract: Adaptive beamformer is very sensitive to model mismatch, especially when the signal-of-interest is present in the training data. In this paper, we focus on the topic of robust adaptive beamforming (RAB) based on interference-plus-noise covariance matrix (INCM) reconstruction. First, we analyze the effectiveness of several INCM reconstruction schemes, and particularly analyze the impacts of interference power estimation on RAB. Second, according to the analysis results, we develop a simplified algorithm to estimate the interference powers, and a RAB algorithm based on INCM reconstruction is then presented. Compared with some existing methods, the proposed algorithm simplifies the interference power estimation of INCM reconstruction. Aligned with our analysis, simulation results demonstrate that the overestimation of interference powers hardly degrades the performance of adaptive beamforming, and our proposed algorithm achieves nearly optimal performance across a wide range of signal-to-noise ratios.

Detection of GNSS Ionospheric Scintillations Based on Machine Learning Decision Tree

Abstract: This paper proposes a methodology for automatic, accurate, and early detection of amplitude ionospheric scintillation events, based on machine learning algorithms, applied on big sets of 50 Hz postcorrelation data provided by a global navigation satellite system receiver. Experimental results on real data show that this approach can considerably improve traditional methods, reaching a detection accuracy of 98%, very close to human-driven manual classification. Moreover, the detection responsiveness is enhanced, enabling early scintillation alerts.

Universal Kriging for Loran ASF Map Generation

Abstract: After a series of intentional Global Positioning System (GPS) jamming attacks impacted a large area of South Korea, the Ministry of Oceans and Fisheries of South Korea considers long-range navigation (Loran) and enhanced Loran (eLoran) as a maritime backup navigation system. Despite its robustness to signal jamming, the positioning accuracy of Loran/eLoran is lower than that of GPS. Because the signal delay due to the land path, which is called the additional secondary factor (ASF), is the largest unknown component of Loran/eLoran, it is necessary to account for temporal and spatial ASF errors to ensure high accuracy. The generation of ASF maps based on ASF survey data in a service area is the most convenient way to mitigate spatial ASF error, but the quality of ASF maps depends on the applied interpolation algorithm. It is desirable to generate high-quality ASF maps based on ASF measurements at only a few survey points, because extensive ASF surveys are expensive and time consuming and require considerable effort. This paper proposes kriging methods for satisfying this objective and shows their superior performance during a field test in Incheon, Korea. In particular, universal kriging with the proposed drift model showed a better performance than linear interpolation, inverse distance weighing, and ordinary kriging when the test vehicle was close to a coastline. The positioning accuracy with the ASF maps generated by the proposed universal kriging along a 5-km route during the field test was 25.24 m (95%). The land vehicle used for the test experienced significant signal-to-noise ratio (SNR) degradation owing to the noise caused by its engine. A vessel without such SNR degradation is expected to achieve higher accuracy.

Loading Factor Estimation Under Affine Constraints on the Covariance Eigenvalues With Application to Radar Target Detection

Abstract: Maximum likelihood (ML) estimation of the loading factor under affine constraints on the covariance eigenvalues is addressed. Several situations of practical interest for radar are considered, and the corresponding ML solutions to the loading factor estimation problem are derived in closed form. Furthermore, it is shown that the constrained ML problem, the constrained geometric approach, and the constrained problem of mean square error minimization (with respect to the loading factor) all lead to the same solution. At the analysis stage, the effectiveness of the resulting covariance estimators is evaluated in terms of both the signal-to-interference-plus-noise ratio and the receiving beampattern shape and compared with that of other covariance estimation methods available in the literature. Finally, a receiving architecture based on the adaptive matched filter that exploits the new loaded covariance estimators is also considered to assess the benefits of the new strategies in terms of detection probability.

Reciprocal-Filter-Based STAP for Passive Radar on Moving Platforms

Abstract: This paper addresses the problem of clutter cancellation and slowly moving target detection in digital video broadcast-terrestrial-based passive radar systems mounted on moving platforms. First, we show that conventional processing approaches based on the availability of multiple receiving channels might be ineffective in the considered scenarios due to the impossibility to control the employed waveform of opportunity. Therefore, an appropriate space-time adaptive processing scheme is proposed to cope with the Doppler spread clutter returns aiming at ground moving target indication applications. It exploits the benefits of the reciprocal filtering strategy applied at a range compression stage together with a flexible displaced phase center antenna approach. The effectiveness of the proposed scheme is demonstrated via application to a simulated dataset and then tested against experimental data collected by multichannel passive radar on a maritime moving platform.

Disturbance Observer-Based Attitude Control for Spacecraft With Input MRS

Abstract: This paper considers the problem of attitude tracking control for uncertain rigid spacecraft subject to control input magnitude and rate saturation (MRS). First, a smooth input MRS model is proposed. Then, a robust attitude tracking control scheme is designed based on the backstepping and finite-time disturbance observer techniques. Finally, the effectiveness of the control scheme derived here is illustrated by numerical simulations.

DeepTarget: An Automatic Target Recognition Using Deep Convolutional Neural Networks

Abstract: Automatic target recognition (ATR) is an important part for many computer vision applications. Despite the extensive research which has been carried out in this area for many years, there is no ATR system which performs well on all applications. Recently, different object recognition frameworks have been proposed which yield a high performance in baseline databases. However, our experiments showed that they can fail in real-world scenarios, when dealing with a limited number of data samples. In this paper, we propose a new ATR system, based on deep convolutional neural network (DCNN), to detect the targets in forward looking infrared (FLIR) scenes and recognize their classes. In our proposed ATR framework, a fully convolutional network is trained to map the input FLIR imagery data to a fixed stride correspondingly-sized target score map. The potential targets are identified by applying a threshold on the target score map. Finally, the corresponding regions centered at these target points are fed to a DCNN to classify them into different target types while at the same time rejecting the false alarms. The proposed architecture achieves a significantly better performance in comparison with that of the state-of-the-art methods on two large FLIR image databases.

Spatial Spectrum Sharing for Satellite and Terrestrial Communication Networks

Abstract: With the increasing demands on frequency resources, spectrum sharing between the satellite and terrestrial systems becomes prominent, especially when it comes to the millimeter wave (mmWave) bands. In this paper, we propose a general spectrum sharing framework in satellite and terrestrial networks, through analyzing the interference caused by terrestrial cellular systems and nongeostationary (NGEO) systems to geostationary (GEO) systems, respectively, both in the downlink and uplink. Specially, in the spectrum sharing between terrestrial and GEO systems, two scenarios are analyzed. In the first scenario, we consider each base station (BS) equipped with one omnidirectional antenna, and in the second scenario the beamforming scheme is employed at the BSs. In light of the parameters recommended by the standards and recent results presented in the literatures on the mmWave channel model, we calculate the protection area where no cognitive users (terrestrial system or NGEO system) could transmit. The definition of protection area is to guarantee an outage performance for the GEO system. Outside the protection area, the cognitive transmitters may transmit concurrently with GEO systems. Simulations are conducted to verify the effectiveness of the proposed schemes.

Sliding Mode Guidance Law for Impact Time Control Without Explicit Time-to-Go Estimation

Abstract: This paper presents an impact time control guidance law that does not perform explicit time-to-go estimation. In order to satisfy the interception and the desired impact time constraint simultaneously, a sliding surface variable formulated as a sum of the relative range and the desired time-to-go is defined, weighted by two nonzero weighting functions. Then, the achievement of the sliding mode satisfies the following equivalence: The relative range is zero if and only if the elapsed time equals to the desired impact time. It means that both the interception and impact time control can be satisfied at the same time in the sliding mode. The impact time control guidance law is derived to enforce the defined surface variable to the sliding mode. Because the law is designed based on the capture condition without separate time-to-go estimation process, the achievement of the sliding mode always guarantees the interception of the target at the desired impact time. In addition, the proposed law can be applied to an engagement considering nonstationary targets in a straightforward manner because the corresponding time-to-go estimation is not needed. Simulation results demonstrate that the proposed guidance law has better performance in comparison with the existing guidance law, in respect of satisfying the desired impact time constraint against a nonstationary target.