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Minimization of Internally Reflected Power Via Waveform Design in Cognitive MIMO Radar
Abstract
State-of-the-art cognitive MIMO radars maximize the signal-to-interference-plus-noise ratio (SINR) for an extended target of interest by matching the transmitted waveforms to the target impulse response (TIR). Existing methods to match the transmitted waveforms do not consider the problem of internally-reflected power due to the mutual coupling between the transmitting antenna array elements, which results in transmitter inefficiency and possible hardware damage. While the mutual coupling problem in MIMO radars has been handled using microwave techniques heretofore, we herein advocate a signal-processing approach to this problem in cognitive MIMO radars. Specifically, we pro-pose an effective waveform design formalism allowing to jointly maximize the SINR and minimize the reflected power from the transmitting antennas under a TIR matching constraint, while achieving waveform orthogonality in the Doppler domain. Mini-mizing the reflected power is achieved through the incorporation of a regularization term, taking the form of an
-norm, in the objective function of a minimum variance distortionless response criterion. An efficient proximal gradient method is developed to solve the resulting non-smooth optimization problem. Simulations with different TIR distributions and transmitting antenna array sizes show that the proposed waveform design algorithm results in lower active reflection coefficients for the antenna elements than selected benchmarks. Furthermore, our algorithm offers a competitive SINR performance compared to these benchmarks and can cope with the fast-varying TIR.
An analytical load-pull-based design methodology for three-stage Doherty power amplifiers (PAs) is presented and demonstrated. A compact output combiner network, together with the input phase delays, is derived directly from transistor load-pull data and the design requirements. The technique opens up a new design space for three-stage Doherty PAs with reconfigurable high-efficiency power back-off levels. The method is designed to enable high transistor power utilization by maintaining full voltage and current swings of the main and auxiliary amplifier cells. Therefore, a wide efficiency enhancement range can be achieved also with symmetrical devices. As a proof of concept, a 2.14-GHz 30-W three-stage Doherty PA with identical gallium nitride (GaN) HEMT active devices is designed, fabricated, and characterized. The prototype PA is able to linearly reproduce 20-MHz long-term evolution signals with 8.5- and 11.5-dB peak-to-average power ratio (PAPR), providing average efficiencies of 56.6% and 46.8% at an average output power level of 36.8 and 33.8 dBm, respectively. Moreover, an average efficiency as high as 54.5% and an average output power of 36.3 dBm have been measured at an adjacent power leakage ratio of -45.7 dBc for a 100-MHz signal with 8.5 dB of PAPR, after applying digital predistortion linearization.
Adaptive waveform design for cognitive radar in the case of extended target detection under compound-Gaussian (CG) sea clutter is addressed. Based on the CG characteristics of sea clutter, the texture component is employed to characterize the clutter ensemble during each closed-loop feedback and its estimation can be used for the next transmitted waveform design. The resulting waveform design problem is formulated according to the following optimization criterion: maximization of the output signal-to-interference-plus-noise ratio (SINR) for sea clutter suppression, and imposing a further constraint on sidelobes level of the waveform autocorrelation outputs for decreasing the false alarm rate. Numerical results demonstrate the effectiveness of this approach.
Space time adaptive processing (STAP) detects targets by computing adaptive weight vectors for each cell under test
using its covariance matrix, as estimated from surrounding secondary cells. In this context, the non-homogeneity detector (NHD)
excludes the anomalous secondary cells that adversely affect the detection performance. The existing robust NHDs require estimating
the covariance matrix of each secondary cell, which hinders their implementation in modern radars with large-dimensional
range cells. In this paper, we propose a new low-complexity NHD that is suitable for highly correlated clutter environments with both Gaussian and non-Gaussian heavy-tailed distributions. The proposed detector, which is based on the projection depth function from the field of robust statistics, features a nonparametric and covariance-free test statistic. As a result, its computational complexity is much lower than that of current NHDs, such as the widely used normalized adaptive matched filter (NAMF) detector, especially for large-dimensional range cells. In Monte Carlo simulations with different clutter distributions and radar system configurations, the proposed detector shows a comparable performance to that of NAMF. The low complexity and robust performance of the new detector make it particularly attractive for real time applications.
This paper addresses the waveform design problem of cognitive radar for extended target estimation in the presence of signal-dependent clutter, subject to a peak-to-average power ratio (PAR) constraint. Owing to this kind of constraint and the convolution operation of the waveform in the time domain, the formulated optimization problem for maximizing the mutual information (MI) between the target and the received signal is a complex non-convex problem. To this end, an efficient waveform design method based on minimization–maximization (MM) technique is proposed. First, by using the MM approach, the original non-convex problem is converted to a convex problem concerning the matrix variable. Then a trick is used for replacing the matrix variable with the vector variable by utilizing the properties of the Toeplitz matrix. Based on this, the optimization problem can be solved efficiently combined with the nearest neighbor method. Finally, an acceleration scheme is used to improve the convergence speed of the proposed method. The simulation results illustrate that the proposed method is superior to the existing methods in terms of estimation performance when designing the constrained waveform.
Ship detection in the maritime domain is best performed with radar due to its ability to surveil wide areas and operate in almost any weather condition or time of day. Many common detection schemes require an accurate model of the amplitude distribution of radar echoes backscattered by the ocean surface. This paper presents a review of select amplitude distributions from the literature and their ability to represent data from several different radar systems operating from 1 GHz to 10 GHz. These include the K distribution, arguably the most popular model from the literature as well as the Pareto, K+Rayleigh, and the trimodal discrete (3MD) distributions. The models are evaluated with radar data collected from a ground-based bistatic radar system and two experimental airborne radars. These data sets cover a wide range of frequencies (L-, S-, and X-band), and different collection geometries and sea conditions. To guide the selection of the most appropriate model, two goodness of fit metrics are used, the Bhattacharyya distance which measures the overall distribution error and the threshold error which quantifies mismatch in the distribution tail. Together, they allow a quantitative evaluation of each distribution to accurately model radar sea clutter for the purpose of radar ship detection.
Multiple-input multiple-output (MIMO) ground moving target indication (GMTI) radar has been studied recently because of its excellent performance. In this paper, a general signal model is established for the MIMO GMTI radar with both fast-time and slow-time waveforms. The general signal model can be used to evaluate the performance of the MIMO GMTI radar with arbitrary waveforms such as the ideal orthogonal, code division multiple access (CDMA), frequency-division multiple access (FDMA), time division multiple access (TDMA), and Doppler division multiple access (DDMA) waveforms. We proposed a range-compensation method to eliminate the range-dependence of the FDMA waveforms. The simulation results indicate that the improved performance of FDMA waveforms is achieved utilizing the range-compensation method.
A new scheme based on Kalman filtering to optimize the waveforms of an adaptive multi-antenna radar system for target impulse response (TIR) estimation is presented. This work aims to improve the performance of TIR estimation by making use of the temporal correlation between successive received signals, and minimize the mean square error (MSE) of TIR estimation. The waveform design approach is based upon constant learning from the target feature at the receiver. Under the multiple antennas scenario, a dynamic feedback loop control system is established to real-time monitor the change in the target features extracted form received signals. The transmitter adapts its transmitted waveform to suit the time-invariant environment. Finally, the simulation results show that, as compared with the waveform design method based on the MAP criterion, the proposed waveform design algorithm is able to improve the performance of TIR estimation for extended targets with multiple iterations, and has a relatively lower level of complexity.
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider exchanging less memory usage for more processing time in order to enable the computation of the inverse which otherwise would be prohibitive. We propose a new algorithm to compute the inverse of block partitioned matrices with a reduced memory footprint. The algorithm works recursively to invert one block of a k × k block matrix M, with k ≥ 2, based on the successive splitting of M. It computes one block of the inverse at a time, in order to limit memory usage during the entire processing. Experimental results show that, despite increasing computational complexity, matrices that otherwise would exceed the memory-usage limit can be inverted using this technique.
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a sparse constrained tensor optimization problem. The optimality conditions are characterized based on the sparse constrained optimization theory. By dropping the sparsity constraint, we show that the resulting relaxation problem can recover the global minimizer of the original problem. The critical step in solving the original problem is to identify the location of nonzero entries (referred as support set) in a global minimizer. Inspired by such observations, we penalize the equality constraints and apply the quadratic penalty method to solve the relaxation problem. Under reasonable assumptions, we show that the support set of the global minimizer in hypergraph matching problem can be correctly identified when the number of iterations is sufficiently large. A projected gradient method is applied as a subsolver to solve the quadratic penalty subproblem. Numerical results demonstrate that the exact recovery of support set indeed happens, and the proposed algorithms are efficient in terms of both accuracy and speed.
Radar waveform design is of great importance for radar system performances and has drawn considerable attention recently. Constant modulus is an important waveform design consideration, both from the point of view of hardware realization and to allow for full utilization of the transmitter's power. In this paper, we consider the problem of constant-modulus waveform design for extended target detection with prior information about the extended target and clutter. At first, we propose an arbitrary-phase unimodular waveform design method via joint transmitter-receiver optimization. We exploit a semi-definite relaxation technique to transform an intractable non-convex problem into a convex problem, which can then be efficiently solved. Furthermore, quadrature phase shift keying waveform is designed, which is easier to implement than arbitrary-phase waveforms. Numerical results demonstrate the effectiveness of the proposed methods.
Learning according to the structural risk minimization principle can be naturally expressed as an Ivanov regularization problem. Vapnik himself pointed out this connection, when deriving an actual learning algorithm from this principle, like the well-known support vector machine, but quickly suggested to resort to a Tikhonov regularization schema, instead. This was, at that time, the best choice because the corresponding optimization problem is easier to solve and in any case, under certain hypothesis, the solutions obtained by the two approaches coincide. On the other hand, recent advances in learning theory clearly show that the Ivanov regularization scheme allows a more effective control of the learning hypothesis space and, therefore, of the generalization ability of the selected hypothesis. We prove in this paper the equivalence between the Ivanov and Tikhonov approaches and, for the sake of completeness, their connection to Morozov regularization, which has been show to be useful when effective estimation of the noise in the data is available. We also show that this equivalence is valid under milder conditions on the loss function with respect to Vapnik’s original proposal. These results allows us to derive several methods for performing SRM learning according to an Ivanov or Morozov regularization scheme, but using Tikhonov-based solvers, which have been thoroughly studied in the last decades and for which very efficient implementations have been proposed.
In cognitive radar systems, a closed-loop feedback is formed by the transmitter, environment, and receiver. Then, the transmit waveform can be optimised to improve the radar estimation performance. Unlike existing works that only consider single target with temporally correlated characteristic, waveform design for multiple extended targets is investigated in this study. The authors propose a Kalman filtering (KF)-based method to exploit the temporal correlation of target scattering coefficients (TSCs) and improve the corresponding estimation performance. Additionally, for the targets of both closed and separated in range, a novel optimisation problem is established to design the transmit waveform and minimise the mean square error of estimated TSC at each KF iteration, where an additional weight vector is introduced to achieve a trade-offamong different targets. Since the optimisation problem is non-convex and cannot be solved efficiently, a two-step method is proposed to convert it into a convex problem, which can be solved by an optimisation toolbox such as CVX. Simulation results demonstrate that the joint method of waveform design outperforms the existing methods in TSC estimation for both separated and closed targets, and offers much more flexibility.
Classification in large-scale data is a key problem in big data domain. The theory of compressive sensing enables the recovery of a sparse signal from a small set of linear, random projections which provides a compressive classification method operating directly on the compressed data without reconstructing for big data. In this paper, we collected the compressed vowel /a:/ and /i:/ voice signals using compressive sensing for throat polyp detection. The throat polyp prediction procedure based on wavelet packet transform and support vector machine intelligent algorithm was deduced. The experiments for throat polyp prediction with the proposed classification algorithm were carried out. The results showed that the correct rate of prediction was stable under different number of samples and different random measurement matrices.
In this paper we develop proximal methods for statistical learning. Proximal
point algorithms are useful for optimisation in machine learning and statistics
for obtaining solutions with composite objective functions. Our approach
exploits a generalised Moreau envelope and closed form solutions of proximal
operators to develop novel proximal algorithms. We illustrate our methodology
with regularized logistic and poisson regression and provide solutions for
non-convex bridge penalties and fused lasso norms. We also provide a survey of
convergence of non-descent algorithms with acceleration. Finally, we provide
directions for future research.
We introduce the Lipschitz derivative or the L-derivative of a locally Lipschitz complex map: it is a Scott continuous, compact and convex set-valued map that extends the classical derivative to the bigger class of locally Lipschitz maps and allows an extension of the fundamental theorem of calculus and a new generalisation of Cauchy–Riemann equations to these maps, which form a continuous Scott domain. We show that a complex Lipschitz map is analytic in an open set if and only if its L-derivative is a singleton at all points in the open set. The calculus of the L-derivative for sum, product and composition of maps is derived. The notion of contour integration is extended to Scott continuous, non-empty compact, convex valued functions on the complex plane, and by using the L-derivative, the fundamental theorem of contour integration is extended to these functions.
Waveform design is studied for a cognitive multiple-input multiple-output (MIMO) radar system faced with a combination of additive Gaussian noise and signal dependent clutter. The linear frequency modulation (LFM) signals are employed as transmitted waveforms. Based on the sensed statistics of the target and clutter-plus-noise, assuming the LFM waveforms transmitted at different transmitters can have different starting frequencies and bandwidths, these waveform parameters are designed to maximize the signal-to-clutter-plus-noise ratio at the receiver of the cognitive MIMO radar system. The constraints of the allowable range of operating frequency and total transmit energy are considered. We show that in the tested examples, the designed waveforms are nonorthogonal which leads to superior performance compared with that of the frequency spread LFM waveforms commonly used in the traditional MIMO radar systems.
Max-norm regularizer has been extensively studied in the last decade as it
promotes a low rank estimation of the underlying data. However, max-norm
regularized problems are typically formulated and solved in a batch manner,
which prevents it from processing big data due to possible memory bottleneck.
In this paper, we propose an online algorithm for solving max-norm regularized
problems that is scalable to large problems. Particularly, we consider the
matrix decomposition problem as an example, although our analysis can also be
applied in other problems such as matrix completion. The key technique in our
algorithm is to reformulate the max-norm into a matrix factorization form,
consisting of a basis component and a coefficients one. In this way, we can
solve the optimal basis and coefficients alternatively. We prove that the basis
produced by our algorithm converges to a stationary point asymptotically.
Experiments demonstrate encouraging results for the effectiveness and
robustness of our algorithm.
This paper describes two applications suited to the particular characteristics of MIMO radar. We provide a brief description of the MIMO radars which could meet these applications and present a detailed analysis of two candidate waveform types suited to these applications. Each of the waveform types are shown to have different characteristics that make them better suited to one application area over the other.
This article presents an orthogonal load-modulated balanced amplifier designed to mitigate the effects of the load mismatch on the power-added efficiency and output power of the amplifier. This is achieved by electronically adjusting the ratio between the two input signals of the power amplifier (PA) (in phase and amplitude) and the reactive termination at the output nominally isolated port. The mode of operation of the PA is described using a theoretical analysis that highlights the role of the different tuning parameters and is confirmed by simulations using a simplified transistor model. The design and characterization under load mismatch of a prototype PA, working in the 1.6–3.2 GHz band are described and the experimental results compared to those of an analogous balanced PA, where it is shown that the orthogonal balanced amplifier is able to increase substantially the mismatch region on which a given target performance is achieved.
Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective. It covers proximal methods, block-coordinate descent, reweighted ?2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provides an extensive set of experiments to compare various algorithms from a computational point of view. The presentation of Optimization with Sparsity-Inducing Penalties is essentially based on existing literature, but the process of constructing a general framework leads naturally to new results, connections and points of view. It is an ideal reference on the topic for anyone working in machine learning and related areas.
The ability of Multiple-Input Multiple-Output (MIMO) radar systems to adapt waveforms across antennas allows flexibility in the transmit beampattern design. In cognitive radar, a popular cost function is to minimize the deviation against an idealized beampattern (which is arrived at with knowledge of the environment). The optimization of the transmit beampattern becomes particularly challenging in the presence of practical constraints on the transmit waveform. One of the hardest of such constraints is the non-convex constant modulus constraint, which has been the subject of much recent work. In a departure from most existing approaches, we develop a solution that involves direct optimization over the non-convex complex circle manifold. That is, we derive a new projection, descent, and retraction (PDR) update strategy that allows for monotonic cost function improvement while maintaining feasibility over the complex circle manifold (constant modulus set). For quadratic cost functions (as is the case with beampattern deviation), we provide analytical guarantees of monotonic cost function improvement along with proof of convergence to a local minima. We evaluate the proposed PDR algorithm against other candidate MIMO beampattern design methods and show that PDR can outperform competing wideband beampattern design methods while being computationally less expensive. Finally, orthogonality across antennas is incorporated in the PDR framework by adding a penalty term to the beampattern cost function. Enabled by orthogonal waveforms, robustness to target direction mismatch is also demonstrated.
We discuss the problem of extended binary phase-shift keying (EBPSK)-modulated radar waveform design in the presence of colored Gaussian disturbance subject to peak-to-average- power ratio and power constraints. The research work aims at improving the target detection and parameter estimation performance with respect to Doppler shifts. We propose an EBPSK coding design algorithm by optimizing the output signal-to-noise ratio (SNR) in correspondence of the unknown target Doppler frequency. Under the same constraints as in the previous problem, we present EBPSK coding cognitive waveform design algorithm by estimating the target scattering coefficients (TSC) based on maximum output SNR criterion. The simulation experimental results showed that extended target detection performances of optimized EBSPK signals are better than those of the unoptimized EBSPK signal. The designed EBPSK signal attains better TSC estimation performance with relatively lower complexity than the EBPSK signal with arbitrary parameters in the cognitive radar system. © 2019 Society of Photo-Optical Instrumentation Engineers (SPIE).
Multiple-input multiple-output (MIMO) radar systems use orthogonal signaling to enable combined transmit and receive beamforming through signal processing on the received signals. Because of the combined role of transmit and receive arrays in this processing for monostatic MIMO radar, mutual coupling present in these arrays impacts the beamforming in a unique way. This paper therefore presents a mathematical model of a MIMO radar with coupled antennas and appropriate radio frequency circuitry. Application of the model to evaluate radar detection of a single target demonstrates that coupling can result in target detection angles that are in error by as much as 12° and increase beamformer response side lobe levels by as much as 8 dB. The results also show that a simple matching network can improve detection performance, particularly when array mutual coupling is high.
In this paper, a novel modified Doherty power amplifier (DPA) that allows for extended output back-off (OBO) range, improved power utilization factor (PUF), and increased peak power over a broad bandwidth is proposed. It starts with an in-depth analysis of the modified DPA circuitry that first revealed the ability to control the impedances seen by the main transistor versus frequency by properly setting the magnitude and phase of the ratio between the peaks of the combining currents. This is then exploited to maximize the peak power and enhance the achievable bandwidth. Furthermore, a complex-to-real output matching network is incorporated in the auxiliary path and its parameters are carefully chosen to produce proper load modulation while satisfying the required peak combining current ratio. For validation purpose, a DPA prototype is designed to operate over the frequency range of 1.35-2.05 GHz with an OBO of 9 dB. Under the continuous-wave excitation, the DPA prototype maintained the drain efficiency (DE) of 52%-55% and 65%-75% at 9-dB OBO and peak power, respectively, over the entire targeted band. In addition, the measured peak power and PUF were about 42 dBm and higher than 0.9, respectively. The linearizability of the DPA prototype using digital predistortion (DPD) with memory was assessed while being driven with a 40-MHz carrier-aggregated signal with a peak-to-average power ratio of 8.9 dB and at an average output power of 33 dBm. When the carrier frequency is swept over the entire band, the measurement revealed an adjacent channel leakage ratio of better than -46.5 dBc after DPD with an average DE of 49.3%-53%.
This study describes the design of a very compact dual-band-notched ultrawide band (UWB) multiple-input multipleoutput (MIMO) antenna. The main features of the proposed antenna are its compact dimensions and high isolation between the two antenna elements. The UWB performance of the antenna is attained by designing two identical triangular-shaped patch elements, which are designed opposite to each other and connected to a tapered microstrip feedline. The ground plane of the proposed antenna consists of a funnel-shaped patch connected with two triangles at the lower end. In addition, two J-shaped slits are etched in the radiator to get the band rejection characteristics at wireless local area network band from 5.1 to 5.8 GHz and IEEE INSAT/Super-Extended C-band from 6.7 to 7.1 GHz. The designed antenna has the smallest dimension of 26 × 15 × 1.6mm³. Results show that the MIMO antenna has a large impedance bandwidth of 31.9 GHz from 3.1 to 35 GHz. The diversity performance of the proposed antenna is also analysed using different parameters such as envelope correlation coefficient (ECC), diversity gain, total active reflection coefficient and so on. Due to the low mutual coupling of < -24 dB and ECC of < 0.2 across the frequency band this antenna is a good candidate for portable UWB applications.
This letter presents a new approach for balanced power amplifier protection against load mismatch under pulsed-RF operation. The proposed protection mechanism completely eliminates the reflected power under severe mismatch conditions while not affecting nominal operating condition. The concept is based on detection, comparison, and switching technique. The proposed protection circuit offers full protection against open and short at the output. This protection mechanism has been demonstrated on a 10-W X-band power amplifier, intended to be used in space borne radar payloads. The reaction time of the proposed protection mechanism is <100 ns.
In this research article, dielectric resonator based multiple input multiple output (MIMO) antenna system is presented with dual band characteristics. The proposed MIMO antenna includes two symmetrical hybrid radiators. Each hybrid radiator consists of modified annular ring printed line along with cylindrical dielectric resonator antenna (CDRA). Modified annular ring printed line acts as a magnetic dipole and creates two different radiating modes (HEM11δ and TE01δ) in the dielectric resonator. The approach of hybrid antenna (combination of modified annular ring printed line and CDRA) is taken into the account for achieving dual band characteristics. Orthogonally placed antenna elements and a narrow slit in ground plane are used to improve isolation (|S12| < -20 dB) in the entire operating frequency range. The antenna prototype is fabricated and measured for validating the simulated results. The proposed MIMO radiator is operating over two frequency bands i.e. 1.75-2.4 GHz and 3.5-5.5 GHz. Different MIMO diversity performance parameters (ECC, DG, MEG, TARC, and CCL) are also inspected and found within the acceptable limit.
The phrase ‘waveform design and diversity’ refers to an area of radar research that focuses on novel transmission strategies as a way to improve performance in a variety of civil, defense and homeland security applications. Three basic principles are at the core of waveform diversity. First is the principle that any and all knowledge of the operational environment should be exploited in system design and operation. Second is the principle of the fully adaptive system, that is, that the system should respond to dynamic environmental conditions. Third is the principle of measurement diversity as a way to increase system robustness and expand the design trade space. Waveform design and diversity concepts can be found dating back to the mid-twentieth century. However, it has only been in the past decade or so, as academics and practitioners have rushed to exploit recent advances in radar hardware component technology, such as arbitrary waveform generation and linear power amplification, that waveform diversity has become a distinct area of research. The purpose of this book is to survey this burgeoning field in a way that brings together the diverse yet complementary topics that comprise it. The topics covered range from the purely theoretical to the applied, and the treatment of these topics ranges from tutorial explanation to forward-looking research discussions. The topics treated in this book include: classical waveform design and its extensions through information theory, multiple-input multiple-output systems, and the bio-inspired sensing perspective; the exploration of measurement diversity through distributed radar systems, in both cooperative and non-cooperative configurations; the optimal adaptation of the transmit waveform for target detection, tracking, and identification; and more. This representative cross-section of topics provides the reader with a chance to see the three principles of waveform diversity at work, and will hopefully point the way to further advances in this exciting area of research.
In this study, the authors consider the problem of joint transmit waveform and receive filter design for cognitive radar. The problem is analysed in signal-dependent interference, as well as additive channel noise for an extended target with unknown target impulse response (TIR). To address this problem, an iterative algorithm is employed for target detection by maximising the average signal-to-interference-plus-noise ratio of the received echo on the premise of ensuring the TIR estimation precision. In this method, the transmit waveform and receive filter are optimally determined at each step based on the previous step. In particular, under the same constraint on waveform energy and bandwidth, the Lagrange multiplier method is also considered. Simulation results demonstrate that the proposed iterative algorithm waveform achieves a higher rate of performance significantly compared to Lagrange multiplier algorithm waveform and traditional linear frequency modulated waveform, in terms of estimation accuracy and detection performance.
In Chap. 12, we presented an Active Set Method for solving optimization problems with a nonlinear objective and linear constraints. There we saw that when moving in a linear direction from one feasible point to another, we could keep a subset of the constraints active (or satisfied). This, in general, is not possible for nonlinear constraints, and the development of appropriate algorithms must take this into account.
The orthogonal frequency-division multiplexing (OFDM) chirp waveform has attracted much attention due to its high range resolution, low peak-to-average ratio, and large time-bandwidth product. In its application to multiple-input multiple-output radar, the correlation property of multiple OFDM chirp waveforms should be considered primarily for good detection performance. The simulation results show that high sidelobes exist in correlation functions of the conventional waveforms. In this letter, the reason for high correlation sidelobes is explored first, which is the equal subchirp durations and the same subcarrier bandwidth. Second, two new OFDM chirp waveform diversity design schemes are proposed to suppress the correlation interference. Via designing the various subchirp durations or subcarrier bandwidths specially, the high sidelobes are depressed and the correlation property is improved. Both simulation results and comparisons verify the effectiveness of the proposed methods.
Coherent multiple-input multiple-output (MIMO) radar is capable of forming a specific transmit beam pattern favorable for radar operation, but the transmitted waveforms from different antenna elements need to be orthogonal for coherent beamforming. In this work, an innovative approach is developed for MIMO radar waveform design in space-time domain, rendering MIMO radar able to satisfy transmit beamforming constraint in space-domain as well as the waveform orthogonality requirement in time domain. The approach is validated through simulations.
This paper describes the analysis performed on coherent simultaneously recorded monostatic and bistatic sea clutter data. The data were generated using a networked pulsed radar system, namely, NetRAD. This analysis is completed in both the temporal and Doppler domains, and the parameters characterized are compared between multiple bistatic angles and different polarizations. The K-distribution model is used to assess the variation in the clutter amplitude statistics between multiple bistatic data and the corresponding monostatic data. Key characteristics of the Doppler data, such as the spectrum width, center of gravity (CoG), and variance of the spectral width, are evaluated as a function of bistatic angle allowing novel relationships to be defined. The results conclude that the bistatic Doppler data have a lower K-distribution shape parameter in the majority of bistatic angles compared with the simultaneous monostatic data. In addition, novel trends in the relationship between the clutter spectrum CoG and the clutter intensity are presented.
Professors Cai, Ren and Zhou ought to be congratulated for writing such a wonderful expository paper on optimal estimation of highdimensional covariance and precision matrices. Nearly all optimality results on large matrix estimation were established by the authors (and their coauthors). Thus, they are the most appropriate team to write this much needed review article. My discussion contains three sections. © 2016, Institute of Mathematical Statistics. All rights reserved.
A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or an -norm ball. It can be viewed as a Gauss–Seidel-like variant of Michelot’s variable fixing algorithm; that is, the threshold used to fix the variables is updated after each element is read, instead of waiting for a full reading pass over the list of non-fixed elements. This algorithm is empirically demonstrated to be faster than existing methods.
Waveform design is a pivotal component of the fully adaptive radar construct.
In this paper we consider waveform design for radar space time adaptive
processing (STAP), accounting for the waveform dependence of the clutter
correlation matrix. Due to this dependence, in general, the joint problem of
receiver filter optimization and radar waveform design becomes an intractable,
non-convex optimization problem, Nevertheless, it is however shown to be
individually convex either in the filter or in the waveform variables. We
derive constrained versions of: a) the alternating minimization algorithm, b)
proximal alternating minimization, and c) the constant modulus alternating
minimization, which, at each step, iteratively optimizes either the STAP filter
or the waveform independently. A fast and slow time model permits waveform
design in radar STAP but the primary bottleneck is the computational complexity
of the algorithms.
A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or a l1-norm ball. The algorithm is demonstrated to be faster than existing methods. In addition, a wrong statement in a paper by Duchi et al. is corrected and an adversary sequence for Michelot's algorithm is exhibited, showing that it has quadratic complexity in the worst case.
Choosing a proper waveform is a critical task for the implementation of multiple-input multiple-output (MIMO) radars. In addition to the general requirements for radar waveforms such as good resolution, low sidelobes, etc, MIMO radar waveforms also should possess good orthogonality. In this paper we give a brief overview of MIMO radar waveforms, which are classified into four categories: (1) time division multiple access (TDMA), (2) frequency division multiple access (FDMA), (3) Doppler division multiple access (DDMA), and (4) code division multiple access (CDMA). A special circulating MIMO waveform is also addressed The properties as well as application limitations of different waveforms are analyzed and compared. Some simulations results are also presented to illustrate the respective performance of different waveforms.
A cognitive signal processing system (for example, in radar or sonar) is one that observes and learns from the environment; then uses a dynamic closed-loop feedback mechanism to adapt the illumination waveform so as to provide system performance improvements over traditional systems. Current cognitive radar algorithms are designed only for target impulse responses that are Gaussian distributed to achieve mathematical tractability. Our research generalizes the cognitive radar target classifier to deal effectively with arbitrary non-Gaussian distributed target responses. Given exemplars of target impulse responses, our Bayesian illumination waveform design algorithm requires the ability to draw complex correlated samples from a target distribution specified by both an arbitrary desired probability density function and a desired power spectral density. This capability is realized using kernel density estimation and an extension of a new simple and efficient nonlinear sampling algorithm by Nichols et al. Simulations using non-Gaussian target impulse response waveforms demonstrate very effective target classification performance. We discuss practical issues with the application of the algorithms to real-world problems.
Estimating large covariance and precision matrices are fundamental in modern
multivariate analysis. The problems arise from statistical analysis of large
panel economics and finance data. The covariance matrix reveals marginal
correlations between variables, while the precision matrix encodes conditional
correlations between pairs of variables given the remaining variables. In this
paper, we provide a selective review of several recent developments on
estimating large covariance and precision matrices. We focus on two general
approaches: rank based method and factor model based method. Theories and
applications of both approaches are presented. These methods are expected to be
widely applicable to analysis of economic and financial data.
This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Here, we discuss the many different interpretations of proximal operators and algorithms, describe their connections to many other topics in optimization and applied mathematics, survey some popular algorithms, and provide a large number of examples of proximal operators that commonly arise in practice.
The problem of cognitive radar detecting for range-spread target with unknown target impulse response (TIR) is studied. A detecting algorithm which updates the estimate of TIR and transmitted waveform iteratively is proposed based on track-before-detect method. In the algorithm, the Kalman filter is used to track the range-spread target for estimating the TIR, and the signal-to-noise rate criterion is used to design the transmitted waveform. The simulation results show that if the proposed algorithm is used to detect moving target, the performance of tracking and detecting will be improved when the number of loops increases. And the estimated detecting probability will approach the true detecting probability when the tracking accuracy increases, which would improve the reliability of decision.
In this paper, we consider the problem of waveform design for a multiple-input multiple-output over-the-horizon (MIMO-OTH) radar system corrupted by colored Gaussian noise and signal dependent clutter. The discrete prolate spheroidal (DPS) sequences are applied to construct the waveforms as their band-limited property is suitable for addressing the operational frequency limitations of the MIMO-OTH radar. Optimum waveforms (possibly nonorthogonal) are designed to maximize the target detection performance of the MIMO-OTH radar system under the constraint of fixed total transmitted energy. The effects of the spatial and temporal correlation of the noise are analyzed.