Ambiguity function for distributed MIMO radar systems

Current generation radars employ a first order approximation to compensate the frequency shift due to target's velocity. This approach is inadequate when high velocity targets are considered; however, real targets do not possess such high velocities. For that reason, this research analyzes how the increment of the Time-Bandwidth (TBW) product and the target velocity would impact the analysis of radar signals when a first order approximation is implemented to compensate the Doppler shift. The common approach to improved resolution and performance of radar system is to increase the time-bandwidth product of the transmitted signal. The problem of using the first order approximation to compensate the Doppler is that it is limited only to the first two terms of a power series expansion of a full Doppler compensation. As a consequence, an increment on the target's velocity or the time-bandwidth product of the transmitted signal will result in a significant error at the output of the matched filter. On this research a Linear FM (chirp) signal with a large TBW is considered as the transmitted signal. First, to observe the effects of increasing the time-bandwidth product and target velocity the received signal is modeled using a full Doppler compensation and a first order approximation. Second, each signal is applied to the input of one matched filter in which the transmitted signal is used as a reference. Finally, the outputs from both matched filters are analyzed in order to observe the effects of using the first order approximation to model the Doppler induced on the reflected signal. This analysis was performed assuming that the target was moving at a constant velocity. By increasing the time-bandwidth product of the transmitted signal the output of both matched filters are compared and analyzed to observe the differences between modeling the reflected signal using the first order compensation and the full Doppler compensation. The simulation results showed that, by increasing the time-bandwidth product of the transmitted signal the output of the matched filter using the first order approximation deviates significantly with respect to the matched filter that contains the signal modeled using the full Doppler compensation. From these results it is concluded that a dramatic increase in time-bandwidth product of the received signal, results in a significant error at the output of the matched filter if the first order approximation is used to model the reflected signal instead of the Full Doppler compensation.

Range, radial velocity, and acceleration MLE using frequency modulation coded LFM pulse train

PREFACE. CONTRIBUTORS. 1 MIMO Radar - Diversity Means Superiority (Jian Li and Petre Stoica). 1.1 Introduction. 1.2 Problem Formulation. 1.3 Parameter Identifiability. 1.4 Nonparametric Adaptive Techniques for Parameter Estimation. 1.5 Parametric Techniques for Parameter Estimation. 1.6 Transmit Beampattern Designs. 1.7 Conclusions. Appendix IA Generalized Likelihood Ratio Test. Appendix 1B Lemma and Proof. Acknowledgments. References. 2 MIMO Radar: Concepts, Performance Enhancements, and Applications (Keith W. Forsythe and Daniel W. Bliss). 2.1 Introduction. 2.2 Notation. 2.3 MIMO Radar Virtual Aperture. 2.4 MIMO Radar in Clutter-Free Environments. 2.5 Optimality of MIMO Radar for Detection. 2.6 MIMO Radar with Moving Targets in Clutter: GMTI Radars. 2.7 Summary. Appendix 2A A Localization Principle. Appendix 2B Bounds on R(N). Appendix 2C An Operator Norm Inequality. Appendix 2D Negligible Terms. Appendix 2E Bound on Eigenvalues. Appendix 2F Some Inner Products. Appendix 2G An Invariant Inner Product. Appendix 2H Kronecker and Tensor Products. Acknowledgments. References. 3 Generalized MIMO Radar Ambiguity Functions (Geoffrey San Antonio, Daniel R. Fuhrmann, and Frank C. Robey). 3.1 Introduction. 3.2 Background. 3.3 MIMO Signal Model. 3.4 MIMO Parametric Channel Model. 3.5 MIMO Ambiguity Function. 3.6 Results and Examples. 3.7 Conclusion. References. 4 Performance Bounds and Techniques for Target Localization Using MIMO Radars (Joseph Tabrikian). 4.1 Introduction. 4.2 Problem Formulation. 4.3 Properties. 4.4 Target Localization. 4.5 Performance Lower Bound for Target Localization. 4.6 Simulation Results. 4.7 Discussion and Conclusions. Appendix 4A Log-Likelihood Derivation. Appendix 4B Transmit-Receive Pattern Derivation. Appendix 4C Fisher Information Matrix Derivation. References. 5 Adaptive Signal Design For MIMO Radars (Benjamin Friedlander). 5.1 Introduction. 5.2 Problem Formulation. 5.3 Estimation. 5.4 Detection. 5.5 MIMO Radar and Phased Arrays. Appendix 5A Theoretical SINR Calculation. References. 6 MIMO Radar Spacetime Adaptive Processing and Signal Design (Chun-Yang Chen and P. P. Vaidyanathan). 6.1 Introduction. 6.2 The Virtual Array Concept. 6.3 Spacetime Adaptive Processing in MIMO Radar. 6.4 Clutter Subspace in MIMO Radar. 6.5 New STAP Method for MIMO Radar. 6.6 Numerical Examples. 6.7 Signal Design of the STAP Radar System. 6.8 Conclusions. Acknowledgments. References. 7 Slow-Time MIMO SpaceTime Adaptive Processing (Vito F. Mecca, Dinesh Ramakrishnan, Frank C. Robey, and Jeffrey L. Krolik). 7.1 Introduction. 7.2 SIMO Radar Modeling and Processing. 7.3 Slow-Time MIMO Radar Modeling. 7.4 Slow-Time MIMO Radar Processing. 7.5 OTHr Propagation and Clutter Model. 7.6 Simulations Examples. 7.7 Conclusion. Acknowledgment. References. 8 MIMO as a Distributed Radar System (H. D. Griffiths, C. J. Baker, P. F. Sammartino, and M. Rangaswamy). 8.1 Introduction. 8.2 Systems. 8.3 Performance. 8.4 Conclusions. Acknowledgment. References. 9 Concepts and Applications of A MIMO Radar System with Widely Separated Antennas (Hana Godrich, Alexander M. Haimovich, and Rick S. Blum). 9.1 Background. 9.2 MIMO Radar Concept. 9.3 NonCoherent MIMO Radar Applications. 9.4 Coherent MIMO Radar Applications. 9.5 Chapter Summary. Appendix 9A Deriving the FIM. Appendix 9B Deriving the CRLB on the Location Estimate Error. Appendix 9C MLE of Time Delays - Error Statistics. Appendix 9D Deriving the Lowest GDOP for Special Cases. Acknowledgments. References. 10 SpaceTime Coding for MIMO Radar (Antonio De Maio and Marco Lops). 10.1 Introduction. 10.2 System Model. 10.3 Detection In MIMO Radars. 10.4 Spacetime Code Design. 10.5 The Interplay Between STC and Detection Performance. 10.6 Numerical Results. 10.7 Adaptive Implementation. 10.8 Conclusions. Acknowledgment. References. INDEX.

The most important radar system performance is determining the range-velocity of the detected target. This performance is obtained from processing an ambiguity-function (AF) between signals from target reflections and radar radiation signals. Selection of the appropriate waveform transmitted by the radar is a key factor in supporting high resolution radar performance in the AF. There are many waveforms that have been studied in radar systems, especially for multi-antenna radars, i.e., subarray-MIMO (SMIMO) radar which can form phased array (PA) and MIMO radars simultaneously, in the form of linear-frequency-modulated (LFM) signals. In this paper, we examine the use of LFM waveforms combined with SMIMO radar to produce plots of three-dimensional AF as a function of time delay and Doppler shift. The results of the comparison with the Hadamard signal determine the effectiveness of the observed AF performance on parameters such as magnitude, range-velocity resolution, peak sidelobe level ratio, and integrated sidelobe ratio by taking into account the factors of the number of Tx antennas on the PA radar and the number of Tx subarrays on the MIMO radar. The evaluation results of the SMIMO radar configuration (M = 6) with the number of Tx-Rx antenna elements the being 8 provide the best mainlobe magnitude, sidelobe magnitude, range resolution, velocity resolution, PSLR, and ISLR of AF LFM signals compared to conventional radars are 235.2dB, 7.54dB, 37.5m, 75km/s, 29.89dB, and 29.8dB, respectively. Meanwhile, the LFM signal is far superior to the Hadamard signal which has PSLR and ISLR 1.16dB and -3.36dB, respectively.

The Wigner phase space distribution and the Woodward radar ambiguity function have each been optically realized in idealized situations. The realistic performance will be assessed under simulated noise and clutter. A general cross Wigner distribution and cross ambiguity function are also compared as to their advantage in signal analysis. The cross Wigner distribution is a general convolution of non‐zero frequency while the cross ambiguity function is a general correlation of non‐zero frequency. The former is commutative while the latter is not. The significance of this difference is discussed. While the ambiguity function is generally complex, the Wigner distribution is real but not always positive. Both are known to be intermediate signals and are related through a double Fourier transform. However, optical equivalence of one from the other has not been demonstrated. Bartelt et al1 have only produced the even part of the signal whose Wigner distribution is jpositive. Marks et al2 have presented in the noise‐free case the modulus of the ambiguity function, which is known as the ambiguity surface in the radar community. The present extension with noise and clutter provides a better understanding of the optimum condition for signal to noise ratio. Such a comparison study, which takes into account both knowledge of quantum mechanical symmetry and practical experience of radar clutter and noise, turns out to be fruitful.

Integrated sidelobe level(ISL) criterion and the maximal sidelobe level(MSL) criterion are used to design frequency-hopping waveforms based on ambiguity functions respectively in this paper. Some simulation results are given and analyzed. The performance of the proposed algorithm is validated by numerical simulations. Frequency-hopping coding is a kind of orthogonal signals which can be used in radar and sonar systems. And frequency- hopping coding such as Costas arrays (1, 2) has good autocorrelation property. However, for radar and sonar systems, their properties of ambiguity function are mainly considered. In this paper, frequency-hopping waveforms are designed based on ambiguity functions. The results are achieved by minimizing two cost functions which measure the integrated sidelobe level(ISL) and the maximal sidelobe level(MSL) of the autocorrelation function respectively. In this paper, cost functions are defined based on ISL criterion and MSL criterion respectively, and some results are achieved based on genetic algorithm. The remainder of this paper is organized as follows. Section Ⅱ presents the ambiguity function of frequency-hopping waveforms and cost functions designed in this paper, and formulates the problem of designing frequency-hopping waveforms. In section Ⅲ, we introduce the genetic algorithm to optimize frequency-hopping waveforms sets. And design results and their curves of ambiguity functions are presented in Section Ⅳ. Finally, some conclusions are drawn in section Ⅴ.

Over the last decade, research on multistatic radar waveform design has attracted significant consideration among the radar system designers.Among the waveform design techniques, linear frequency modulated waveforms are widely used, but the problem associated with it is range Doppler coupling and complexity in achieving adequate pulse-to-pulse diversity. In this letter, an orthogonal linear frequency modulated (OLFM) waveform has been used as the transmitted waveforms, which has good correlation properties and large time bandwidth product. The ambiguity function (AF), which is the output of the matched filter, is used to analyze the target resolution capabilities of the OLFM waveforms. The mathematical expressions of the AF with OLFM waveforms for the multistatic architecture are represented based on the target fluctuations observed at the receiver. These expressions allow the ambiguity in resolving target position and velocity vectors for any transmitted waveform in the multistatic topology. The normalized cross-correlation value of the LFM waveforms is compared with the OLFM waveforms, which signify the isolation factor between two transmitted waveforms at the receiver. A performance comparison has been made based on the probability of target detection for various multistatic scenarios under numerous signal-to-noise ratio (SNR) conditions.

In this paper we investigate the reason on how the side peaks of ambiguity function are generated, and propose the solution to eliminate the side peaks, the occurrence of side-peak may mask the faint targets echoes at low signal-to-noise ratio (SNR), rendering target localization difficult. By developing cyclostationarity of pilots, we prove that the side peaks care caused by the periodicity of pilots in received OFDM signals, this is quite important in cognitive radio-aided passive correlation localization (CR-PCL). After sensing pilots structure, we get rid of these side peaks from the received targets echoes, therefore, the ambiguity function shows an ideal thumbtack-like ambiguity diagram and super delay-Doppler resolutions are obtained, simulations results verify that the proposed is robust to noise power uncertainty as performing the ambiguity function in a cognitive radio fashion.

An important tool for assessing a radar's performance is the ambiguity function. On the other hand, many different schemes have been designed for the transmit waveforms of a MIMO radar. For each one, a criterion has been chosen to improve the performace, e.g. achieving better missed detection. In this paper, considering the ambiguity function as the benchmark, we propose a waveform design scheme, which optimizes the ambiguity function of the MIMO radar system.

The presence of many radio frequency illuminators in an area provides an opportunity to be used as a transmission source for a passive radar system called a passive coherent locator (PCL). Unlike the active radar, the passive radar provides advantages such as low cost without an active transmitter, potential for broad range measurements, portable in construction, anti-detectable by active radar or electronic counter measures (ECM), etc. Just like other areas where there are many PCL in Tarakan such as FM radio transmission (RRI), many base-stations (BTS) from 4G-LTE network, digital TV transmission, access-point (AP) from wireless fidelity (WiFi), and so on. This paper will present and analyze all of these PCLs which include predictions of performance and ambiguity function (AF). Performance prediction is related to range detection which provides information about target detection range, radar cross section, and range-velocity resolution. While AF analyzes the transmit waveform of all PCL which gives a limit of resolution to the range and Doppler of adjacent targets. The results of the evaluation and analysis of performance predictions show that FM radio transmission (RRI) has a range and velocity resolution of 1 km and 12 m/s, respectively and the detection range at a maximum SNR of 15 dB is around 4 km. While the results of the AF evaluation on the PCL obtained range and Doppler resolution of around 2.73 km and 500 Hz, respectively.

OF THE DISSERTATION Adaptive OFDM Radar for Target Detection and Tracking by Satyabrata Sen Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, December 2010 Research Advisor: Dr. Arye Nehorai We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing (OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar’s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. ii Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the `1-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose a tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter.

Recently many researchers have turned their interests to Orthogonal Frequency Division Multiplexing (OFDM) signal since its promising features in radar. This paper concerns a novel Synthetic Aperture Radar (SAR) system which employs this OFDM signal. Though the OFDM will bring lots of advantages, the performance may be changed since the signal of SAR is different from conventional ones. To evaluate the change, this paper will give a theoretical analysis and the corresponding simulation results from the viewpoint of ambiguity function. This ambiguity function is equivalent to the role of Point Spread Function (PSF) which is often used in SAR for evaluating resolutions. Comparing to the conventional SAR with LFM signal, it is proved that the resolution of SAR based on OFDM is equivalent to the conventional one or even better. This ambiguity function also provides a principle for selecting various OFDM signals as the transmit signal of SAR.

A multi-frame space-time coding method for the phase-coded signal in MIMO radars

Orthogonal Frequency Division Multiplexing (OFDM) based waveform has been widely used as illuminator of opportunity in passive radar systems. Ambiguity function (AF) of OFDM is shown to be nearly perfect thumbtack shaped except for the undesirable high side lobes in the Doppler dimension. In this paper, we propose a novel filtered OFDM scheme to improve OFDM AF by utilizing Filtered Bank Multi-Carrier (FBMC) prototype filter. We derive the cross ambiguity function (CAF) between OFDM and filtered OFDM. And then we conclude that the weighting network whose power spectrum density decays faster achieves better CAF performance. Simulation results are presented to validate the conclusion. Specifically, FBMC prototype filter is superior to the classical Bartlett and Hanning weighting networks in terms of suppressing OFDM AF's high Doppler side lobes with nearly no cost of Doppler bandwidth.

Frequency diverse array (FDA) radar provides new application capabilities and potentials due to its range-dependent transmit array beampattern. As radar ambiguity function (AF) is an effective tool to analyze the range (time delay) and Doppler resolution characteristics of various radar systems, this paper derives and analyzes the FDA radar AF characteristics in a general way. These characteristics provide some insights into optimal FDA parameters design and are helpful for comparing delay-Doppler performance of the FDA radar with conventional phased-array radar. Furthermore, this paper optimally designs the frequency increments for better FDA radar AF with the simulated annealing algorithm. The optimization object is to minimize undesired range-angle-dependent sidelobes, so that we can focus the transmit beampattern to desired range-angle sections and simultaneously null undesired interferences. All the derived expressions and methods are verified by numerical results. The results also validate that the FDA indeed offers advantages over traditional phased array in delay-Doppler radar applications.