Principles of Waveform Diversity and Design
2: Department of Electrical Engineering and Computer Science, University of Kansas, KS, USA
This is the first book to discuss current and future applications of waveform diversity and design in subjects such as radar and sonar, communications systems, passive sensing, and many other technologies. Waveform diversity allows researchers and system designers to optimize electromagnetic and acoustic systems for sensing, communications, electronic warfare or combinations thereof. This book enables solutions to problems, explaining how each system performs its own particular function, as well as how it is affected by other systems and how those other systems may likewise be affected. It is an excellent standalone introduction to waveform diversity and design, which takes a high potential technology area and makes it visible to other researchers, as well as young engineers.
Inspec keywords: remote sensing; diversity reception; chaotic communication; waveform analysis; radio spectrum management
Other keywords: distributed aperture sensing; long-range active sensing; remote sensing; matched illumination; spectrum management; waveform design; chaotic waveforms; waveform diversity paradigms; multimission systems; distributed aperture communications; imaging
Subjects: Communication system theory; General electrical engineering topics; Geophysical techniques and equipment; Legislation, frequency allocation and spectrum pollution; Radio links and equipment; Mathematical analysis
- Book DOI: 10.1049/SBRA023E
- Chapter DOI: 10.1049/SBRA023E
- ISBN: 9781891121951
- e-ISBN: 9781613531501
- Format: PDF
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Front Matter
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0 Introduction: A Short History of Waveform Diversity
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The purpose of this chapter is to provide a contextual setting for the waveform diversity (WD) activities of the past several years (2002-2009), as well as to provide a summary of the history of WD and its evolution over this short period. Also, the authors wish to apologize in advance for the radar-centricity of the ensuing discussion, as radar is our source of inspiration and the sensor of choice in our research communities. This bias notwithstanding, we hope the reader will bear with us, because the discussion and underlying mathematics cuts across all scientific and engineering disciplines where information is conveyed by waves.
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Section A: Waveform Diversity Paradigms
1 Diversity Strategies: Lessons from Natural Systems
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The behaviour and performance of echolocating bats in terms of detecting, locating, tracking and capturing prey have been investigated. The most significant key aspects for their autonomous navigation in terms of waveform diversity are identified: the design of the transmitted waveforms; and their dynamic adjustments as a function of flight trajectory. This dynamic transmission of diverse waveforms is evident through the wide range of frequency modulations used by different bat species (CF, LFM, HFM) and the number of different parameters required for undertaking particular tasks. The abilities to change the bandwidth of the transmitted call within a feeding buzz sequence, to reduce the illuminating frequency, and to modify the pulse repetition interval, call intensity and pulse length are undoubtedly signs of important waveform diversity design which may provide insights into the development of more reliable autonomous systems. It should also be noted that this analysis has only considered transmitted calls; whereas, of course, the real information will be embedded in the received calls. Additionally, the received calls are processed via two ears (receivers). These aspects will be the subject of future studies.
2 Distributed and Layered Sensing
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In this chapter, we discuss the electromagnetic compatibility (EMC) issues that must be addressed and understood as part of the development of a futuristic intelligence, surveillance, and reconnaissance concept utilizing Distributed and Layered Sensing waveform diverse systems. These systems involve the innovative integration of cutting edge technologies such as: knowledge-based signal processing, robotics, wireless networking, waveform diversity, the semantic web, advanced computer architectures, and supporting software languages. This concept is projected as an autonomous constellation of air, space, and ground vehicles that would offer a robust paradigm to build toward future deployments. The goal is to develop waveform-time-space adaptive processing algorithms for distributed apertures that could reduce EMC issues.
3 Waveform Diversity and Sensors as Robots in Advanced Military Systems
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Multistatic ambiguity function is a performance measure that may be used for selecting waveforms for neutralizing the distortion affects of some difficult bistatic triangles. Simulations and experiments should be performed to develop the necessary rules for choosing the proper waveforms for their potential use in a Sensors as Robots proof of concept demonstration of the work presented.
4 Implications of Diversity from a Sensing Point of View
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The objective of this chapter is to illustrate that the influence of diversity in the regeneration of species is quite different from the effect of diversity in a vector wireless environment. Diversity in a regenerative environment is always welcome and often provides variety, the often desired spice of life. However, diversity from an electrical engineering standpoint is quite different, as the vectors representing a desired outcome may add or subtract, resulting in a final form that can be beyond any common sense expectation and that cannot be anticipated a priori unless the environment is clearly defined. This situation is primarily true for electromagnetic sensing. Examples are presented to compare the principles of physics with the conventional wisdoms of established myths held by most wireless practitioners. One area of recent notoriety in the wireless community is the multiple-input multiple-output (MIMO) system and the associated misinterpretation and misrepresentation of the various metrics often used to illustrate MIMO's superiority over conventional systems. Just like the vector problem when the quantities of interest add in phase, one gets superior performance; however, when they subtract, the performance can be very bad. Clearly, one cannot average good and bad behaviors, because each piece of datum is equally important-like transmitting one's bank balance over wireless where each digit has to be accurate and an average value really has no significance.
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Section B: Applications. Part I: Multi-mission Systems
5 An Evolutionary Algorithm Approach to Simultaneous Multi-Mission Radar Waveform Design
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The simulation results although preliminary illustrate an increase in fitness for two experimental simulation scenarios. Each scenario incorporates multiple objectives to be optimized which are dictated by the mission or missions of interest. The relatively small initial population size and the number of generations allowed to evolve were dictated by computing and time constraints. Current investigations are applying the four objective functions presented herein to a single simulated scenario. Additional degrees of freedom of the waveform parameter space are also being investigated and simulated. These incremental advances will be reported in future forums on waveform diversity and design. The presented technique to the design of diverse waveforms shows promise and will continue to become more practical as computing resources increase in power and affordability.
6 Interlacing of Non-Uniform Doppler Waveforms and Metric Space Geometry of Negative Curvature
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In this chapter an advanced Doppler processing technique has been proposed, based on covariance matrix CFAR, that is itself based on an innovative mathematical tool (information geometry and geometry of Bruhat-Tits metric space) that provides explicit equations for computing: the robust distance between covariance matrices, the geometric mean of two covariance matrices, and Karcher's barycenter of N covariance matrices.Use of metric space and negative curvature space in place of normed and flat space to manipulate Hermitian positive definite covariance matrices could drastically improve the performance of classical signal processing algorithms, and improve the robustness of Doppler processing for sparse Doppler waveforms (based on regular non-uniform Doppler bursts).
7 Evolutionary Algorithms Based Sparse Spectrum Waveform Optimization
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This chapter presents a technique to determine a suite of 'optimal' waveforms (in the Pareto sense) for a single platform radar system performing multiple radar missions simultaneously. The authors contend that a waveform suite can be determined by applying the Strength Pareto Evolutionary Algorithm 2 (SPEA2) developed by Zitzler et al. to find waveform parameters that successfully realize a set of objectives particular to a variety of radar missions. The objectives to be optimized are dictated by the missions of interest. The mapping of these objective functions to actual radar performance parameters is used in the SPEA2 algorithm to determine how best to perform multiple radar missions simultaneously, such as ground moving target indication (GMTI), airborne moving-target indication (AMTI), synthetic aperture radar (SAR) imaging, etc. using a single radar system. This chapter introduces the concept of using an evolutionary computational approach to design optimal waveforms for a diverse set of radar missions. Results are presented for a scaled multi-mission multi-objective function scenario to illustrate the potential of the proposed methodology.
8 Intra-Pulse Radar-Embedded Communications
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Embedding communications information into radar backscatter on an intra-pulse basis may provide a substantial increase in data-rate relative to previous inter-pulse approaches that necessitate possibly hundreds of pulses. A mathematical framework has been developed to model the reception of anintra-pulse modulated signal in the presence of ambient backscatter and noise. Three approaches to design the set of embedded communications waveforms have been devised that provide different degrees of communication error performance and intercept probability. Coupling with appropriate cancellation of the backscatter interference on receive facilitates a communication paradigm that can be made very difficult to intercept while providing data rates on the order of bits-per-pulse.
9 Waveform Design for Joint Digital Beamforming Radar and MIMO Communications Operability
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In this chapter a unique waveform design concept has been presented that allows for simultaneously performing both digital beamforming radar and MIMO communication operations including dedicated multiple antenna techniques. The starting point of the waveform design has been a standard phase-coded communication signal. A coding scheme employing pseudo-random codes has been developed that allows for simultaneous operation of both applications even in multi-user environments under the condition that codes with quasi-ideal properties are available.
10 A Transform Domain Communication and Jamming Waveform
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A multi-function waveform has been shown with the ability to communicate, avoid the spectrum of friendly users, and jam the spectrum of enemy users. The TDJCS waveform's communication performance is not affected by the amplitude of the jamming. The jamming severely degrades the performance of the enemy communication system and causes a slight degradation in the friendly system as the J/S is raised.
11 Optimal Space-Time Transmit Signals for Multi-Mode Radar
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The development of true space-time transmit signals has been shown to significantly improve the efficacy of communications systems, and there is every reason to believe that similar results are possible for radar sensors as well. The problem is how to construct an effective space-time transmit signal for radar applications. It was demonstrated that by expanding a general space-time transmit function as a superposition of orthogonal basis functions, the problem is simplified to finding an optimal transmit data vector. This allows for the direct implementation of linear algebraic techniques (e.g., eigen analysis) for determining solutions for many optimality criteria and likewise allows for direct implementation of iterative and search techniques. Moreover, this structure allows for optimal solutions to be found for any radar mode (e.g., SAR, GMTI) hybrid mode by simply classifying measurement subspaces as either target or clutter.
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Section B: Applications. Part II: Long-Range Active Sensing
12 Waveform Diversity and Adaptive Signal Processing to Improve SBR GMTI Performance Degraded by MEO Antenna Mechanical Distortions
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This paper studied the use of novel waveforms, adaptive RF transmit and STAP receive compensation techniques to overcome the limitations to MEO space-based radar GMTI detection, caused by both clutter range ambiguities enhanced by the earth's rotation, and antenna mechanical distortions. Both very large phased array and cylindrical reflector antennas were considered and it was demonstrated that the deleterious effects of these phenomena were greatly mitigated by the use of quadratic phase modulation waveforms, adaptive RF subarray phase shift compensation and STAP true target steering vector correction. Subsequent research investigated RF column phase shift corrections on distorted reflectors in conjunction with QPMW and STAP that resulted in a 2-3:1 improvement in GMTI MDV and NDBZW detection.
13 Multidimensional Waveform Encoding for Spaceborne Synthetic Aperture Radar Remote Sensing
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This chapter presents a novel fully active digital beamforming technique for radar remote sensing that is based on the concept of multidimensional waveform encoding on transmit. In contrast to the aforementioned techniques, the full area of the antenna aperture is used for both the transmission and the reception of radar pulses. This enables an improved SAR imaging performance while relying on the well established transmit/receive (T/R) module technology. The mandatory expansion of the antenna beam width for wide area illumination is achieved by an innovative spatiotemporal modulation of each transmitted radar pulse. The modulation introduces angular waveform diversity in the transmitted signal and provides, thereby, in the recorded radar echoes additional information about the spatial scatterer distribution. The multidimensional waveform encoding is hence the natural complement to digital beamforming on receive, and the combination of both techniques enables a wealth of new SAR imaging modes that significantly increase the performance, flexibility, and adaptability of future radar systems and missions.
14 Time Reversed Over-The-Horizon Radar
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Time reversal can play a significant role in improving the performance of current sky-wave high-frequency over-the-horizon-radar (HF OTHR), especially with respect to real-time monitoring and compensation of ionospheric turbulence. Also, multipath interference arising from an HF OTHR environment can significantly increase resolution and the signal-to-clutter-ratio. Furthermore, the proposed double-pass time-reversal EVA method incorporated into active beam steering has the potential to provide high-resolution radar imaging. Currently, a test site is being built between the Chesapeake Bay Detachment (CBD) and Tilghman Island in Maryland to prove the concepts of the proposed system.
15 Issues with Orthogonal Waveform Use in MIMO HF OTH Radars
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Current operational HF over-the-horizon (OTH) radars are now accepted as effective and comparatively low-cost wide-area surveillance sensors. They are routinely used to provide air and surface situational awareness over vast regions of land and sea. The technology in, and performance of, these current generation radars is impressive, however, there are many advanced concepts yet to be realized in operational systems. Future OTHR are expected to deliver dramatically improved capability in every performance dimension. While all facets of OTHR systems are being re-considered, in this chapter, we concentrate on one aspect of the transmit sub-system.
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Section B: Applications. Part III: Distributed Aperture Sensing
16 Waveform Diversity and Signal Processing Strategies in Multistatic Radar Systems
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This chapter is organized as follows. In Section 2 we define a multistatic radar system that will be analyzed. Section 3 provides an overview of the multistatic ambiguity function. In Section 4 we relate the multistatic ambiguity function with different performance measures for multistatic radar systems. In Section 5 an optimal multistatic receiver in the Neyman-Pearson sense is presented. In Section 6 we demonstrate through several simulation examples how the multistatic ambiguity function can be used for waveform selection and development of signal processing strategies in multistatic radar systems. Finally, in Section 7 we provide concluding remarks.
17 A Framework for Optimal Code Design for MIMO Radar
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This chapter has derived a simple maximum likelihood receiver for MIMO radar systems with unitary space-time codes and explicit transmitter beamforming. The transmitter codes are chosen to maximise the Fisher information associated with the MIMO model. An gradient projection algorithm has been proposed to solve this constrained optimisation problem.
18 Space-Time Adaptive Processing for Frequency-Diverse Distributed Aperture Radars
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In this chapter a distributed array of radar apertures is consider to determine the presence of a target within a chosen region of space. The overall detection capability is limited by interference. This interference may be caused by the radar signal itself, e.g., clutter or by electronic counter-measures (ECM) such as jamming. The interference is far stronger than any potential target signal and, therefore, traditional non-adaptive techniques are inadequate for reliable detection. Unlike a traditional array of co-located sensors, each element in the distributed aperture can transmit at its own center frequency. This allows for each element in the aperture to process the signals over transmissions independently and without mutual interference.
19 A Novel Waveform Diversity Model for Distributed Aperture Radars with Consideration on Environment Non-Stationarity
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This chapter discusses the benefit of the joint use of distributed aperture radars and waveform diversity in conjunction with space-time adaptive processing. The interference is modeled as a sum of noise and clutter; the clutter contribution, basically due to chaff cloud, is, in turn, modeled as the sum of several low power interference sources as done for airborne radar, however, here, each source has a range dependent contribution. A well known problem in bistatic radar is that clutter Doppler center is range dependent due to the relative motion between antennas and interference source. This dependency significantly degrades the achievable performance of the receiver and must be taken in account for effective clutter suppression.
20 Waveform Concepts and Design for Weather Radar Network
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Doppler weather radar has been a valuable tool for quantitative precipitation estimation. The received signal for volume targets composed of precipitation particles was described briefly. A short summary of the relation between the backscattering covariance matrix and the received signal covariance matrix that defines the basis of waveform diversity and agility for dual-polarization weather radars was presented. Weather radar observables are estimated from the received signal that is affected by many factors. The challenges associated with designing waveforms that provide reliable estimates of the weather radar observables were presented. The challenges include range-velocity ambiguity, ground clutter suppression, and sensitivity. In addition, these challenges are augmented when the operating frequencies are changed to attenuating frequencies such as X-band. Unlike hard target radars, the cause of attenuation is also the target that is being observed. Higher frequency radars are essential for large scale deployment of distributed collaborative systems. This chapter addressed various waveforms designed to mitigate specific challenges.
21 Waveform Time-Frequency Characterization for Dynamically Configured Sensor Systems
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In this work, a waveform agile sensing method for the target tracking problem has been described. By dynamically selecting the transmitted waveform from a generalized FM chirp signal library with different phase functions and chirp parameters, the tracker can improve the performance dramatically. The waveform design algorithm is based on the myopic optimization of a cost function, which is the predicted mean squared error. The cost function is approximated using the CRLB combined with unscented transformation. Then the generalized FM phase function and the corresponding parameters are configured according to a grid search over all the phase function candidates and allowable parameter values. Due to the nonlinearity of the measurement model in the tracking system, particle filtering is applied to track the state of the target. This approach was demonstrated by tracking a target moving in a 2-D cluttered environment with two active sensors. The simulation results showed that the mean squared error of the tracking was dramatically reduced by adaptively adjusting the transmitted signal.
22 The Role of Coherence in Waveform Design
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We have shown the role of coherence in waveform design in determining the performance of a sensing system by incorporating the degrees of freedom afforded by new waveform design strategies. Using this approach, we were able to use coherence properties generated by the waveform and aperture to derive an analytic bound on the Generalized Likelihood ratio test that is commonly used in many sensor systems. Thus coherence allows a means of determining a fundamental bound on system performance.
23 Image Formation and Waveform Design for Distributed Apertures in Multipath via Gram-Schmidt Orthogonalization
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In this work, we consider a radar system where the antenna elements are arbitrarily distributed in space with separations of several hundred wavelengths. We call such a radar system a distributed aperture radar system. We assume that the system is operating in a multipathing environment, such as an urban area. We present methods for i) rejecting clutter in transmit processing via preconditioning, ii) designing waveforms to image orthogonal components of target reflectivity, iii) forming target reflection images via matched filtering for sparse distributed aperture arrays. This work generalizes the monostatic radar waveform design method for range-Doppler imaging developed in [1,2] to distributed aperture radar systems. Our approach utilizes Gram-Schmidt orthogonalization (GSO) procedure. The designed waveforms also lead to a filtered-backprojection type reconstruction of the reflectivity function which can be efficiently implemented in a parallel fashion. Although our discussion is focused on radar, the ideas and methods presented in the chapter are applicable to other pulse-echo imaging systems, including sonar, ultrasound and medical microwave imaging. The rest of the chapter is organized as follows. In Section 2, we present a physics based model for scattered field in multi-pathing environment. In Section 3, we present the measurement model for distributed aperture arrays. In Section 4, we derive the preconditioner for clutter rejection. In Section 4, we discuss our waveform design criterion and present our image reconstruction method. We then apply these waveform design and image reconstruction techniques to single transmitterreceiver pair and next apply to distributed aperture arrays. Section 6 concludes our discussion.
24 Characterization of Diversity Approaches for LFM Stretch-Processed Waveforms
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Stretch-processed LFM waveforms are in use in many high-resolution applications such as SAR and ISAR. New processing configurations are being considered that would link multiple LFM radars in a distributed architecture. It is important to understand the interference effects of LFM waveforms, particularly with regard to frequency. This chapter introduces interference regions in range-frequency space as a tool for characterizing LFM interference in a distributed environment.
25 Multi-Waveform Active Sonar Tracking
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Automatic tracking of active sonar data is an important component in the signal and information processing chain that enables effective surveillance performance. Multi-sensor fusion (of which multistatics is a special case) provides additional benefits, provided care is taken in terms of sensor threshold settings, system calibration, and fusion architecture selection. The NURC DMHT enables an optimized selection of processing architecture.
26 A Comparison of Algorithms for MIMO and Netted Radar Systems
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In this chapter we compare three different kinds of radar systems. The first is the classic MIMO case characterized by antennas located far from each other so that they see independent backscatter from a complex target. The second case considers the same radar configuration but this time coherent summation is performed at each receiver in an attempt to maximize the signal-to-noise ratio. We term this netted radar. In the third case we consider an examination of the performance when frequency diversity is substituted for the angle diversity of the first case. This potentially provides a method of achieving the effects of MIMO from a non-distributed aperture. In all three cases the total power available is kept constant such that fair comparisons may be made. Finally we discuss the importance of the role of the target scattering behavior and examine alternative models to that used here. The effect of multipath is also included in the analysis.
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Section B: Applications. Part IV: Distributed Aperture Communications
27 Coherent Initialization Methods for Adaptive MIMO Equalizers
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A coherent initialization approach for DFE filters has been presented and shown to offer a significant improvement when used together with the least mean squares (LMS) algorithm. In summary, new initialization technique has been the following advantages: improves convergence at the start of the training process, enables the simple LMS to work in difficult channel conditions, allows training and tracking with fast changing channel profiles, enables the implementation of a receiver at very low signal to noise ratios and the linear operation of LMS provides better data recovery for error correcting codes. The I-LMS algorithm performs as well as the much more complex RLS algorithm.
28 MIMO Communications Using Offset Modulations
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The use of offset QPSK in a MIMO channel with space-time coding has been demonstrated using OQPSK with the 2 x 1 Alamouti space-time code. It was shown that the desirable orthogonalization properties of the Alamouti space-time code with QPSK do not carry over to the offset case. Unshaped OQPSK and shaped OQPSK were considered. Shaped OQPSK (defined as a CPM) was recast in terms of a memoryless waveform mapper to examine it in the same context as unshaped OQPSK. The basic detector structures for both unshaped and shaped OQPSK are essentially the same, as illustrated in Figure 3. Each detector samples a detection filter output at the bit rate then uses a trellis to account for the memory created by the offset nature of the modulated waveform. The case of differential delays using Alamouti encoded SOQPSK was also explored. The basic detector structure was modified as summarized in Figure 3 (c). The effect on bit error rate performance due to channel gain phase difference, differential delay, timing error, and phase error are explored via simulation and summarized in Figures 12, 14-17. In conclusion, we demonstrated that OQPSK can perform quite well in a space-time coded MIMO channel, although the complexity is significantly higher than when non-offset QPSK is used.
29 Hybrid Acquisition of PN Codes Using Order Statistics-Based Detection and Antenna Diversity
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In this chapter, an adaptive hybrid-search PN code acquisition adopting multiple antennas with nonconventional integration has been addressed. The threshold is adaptively varied according to the current environment. The performance of the proposed system has been analyzed and evaluated in Rayleigh fading channels. The obtained results show that the non-conventional integration of multiple-antenna signals enhances the detection performance as well as the mean acquisition time in multipath environments.
30 Improved Space-Time Coding for Multiple Antenna Multicasting
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In this chapter, we consider the problem of transmitting the same copies of information over a wireless channel to a specified subgroup of users that are associated with the transmitter. We assume that the transmitter is equipped with multiple antennas while the users may or may not have multiple antennas. It is observed that when the number of users is small, the max-min beamforming scheme provides some benefit over using OSTBCs. However, as the number of users grows, the performance of this scheme degrades very fast, and at some point, it performs considerably worse than the open-loop OSTBC method. In light of this observation, a MIMO multicasting scheme based on OSTBC precoding is presented.
31 Multi-Beam Free-Space Optical Link Using Space-Time Coding
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In this chapter we will study a FSO MISO system. Section 2 describes the components of single beam and multi-beam FSO communication links. Because spatial correlation among the propagating beams in a MISO link plays a key role in the system performance, this correlation structure must quantified as a function of turbulence strength, beam separation, and propagation distance. We present estimations of the spatial correlation obtained through numerical simulations for a MISO in Section 3. Properly designed multi-beam FSO links can deliver significant improvement in scintillation reduction which manifests in lower bit-error rates. In Section 4 we describe two space-time coding schemes using On-Off Keying (OOK) modulation. The first scheme is based on a spatial repetition code and the second scheme is based on a size-four rate-one ST block code. The latter has been adapted from an orthogonal space-time code proposed for wireless radio-frequency (RF) communications. Adaptation of such codes is mandated by the non-negativity of signals in optical communications. In Section 5 we show that both coding schemes have excellent performance in moderate and stronger turbulence conditions. The simpler repetition scheme, however, shows better performance. This difference is explained at the end of Section 5.
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Section B: Applications. Part V: Remote Sensing
32 Ultra Narrow Band Adaptive Tomographic Algorithm Applied to Measured Continuous Waveform Radar Data
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This chapter addresses the issue of spatial diversity in radar applications. Typically, information concerning ground and air targets is obtained via monostatic radar. Increased information is often equated with increased bandwidth in these radar systems. However, geometric diversity obtained through multistatic radar operations also affords the user the opportunity to obtain additional information concerning threat targets. With the appropriate signal processing, this translates directly into increased probability of detection and reduced probability of false alarm. In the extreme case, only discrete Ultra Narrow Band (UNB) frequencies of operation may be available for both commercial and military applications. With limited spectrum, UNB in the limiting case, the need for geometric diversity becomes imperative. This occurs because the electromagnetic spectrum available for commercial and military radar applications is continuously being eroded, while the need for increased information via radio frequency (RF) detection of threat targets is increasing. In addition, geometric diversity improves target position accuracy and image resolution which would otherwise remain unavailable with monostatic radar.
33 Ultrasound Speckle Reduction in the Complex Wavelet Domain
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Ultrasound is a non-invasive, portable, and low cost imaging modality that offers real-time image formation and has many applications in medicine. Unfortunately, ultrasound images are inherently degraded by a multiplicative noise called speckle that makes further analysis difficult. As a result, a vast number of ultrasound despeckling methods have been introduced. One of the most successful multiscale Bayesian techniques is based on modeling the wavelet coefficients of the logarithmically transformed ultrasound images using a SαS prior. These improvements can be explained by two special characteristics of DTCWT; DTCWT is approximately shift invariant and it has better directional selectivity compared to standard wavelet transforms. Therefore, the DTCWT is proposed as a good candidate for ultrasound despeckling.
34 System-on-Chip RF Sensors for Life and Geo Sciences
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In this chapter we present two innovative contributions derived by the System-on-Chip (SoC) approach combining standard microelectronic technologies with the life and geo-sciences. The former regards a SoC radar sensor for contactless cardiopulmonary monitoring. The latter focuses on a SoC radiometer for temperature remote sensing. For both micro-sensors we report the framework and motivation, theoretical concepts, current results, and the future direction of ongoing research by the authors.
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Section B: Applications. Part VI: Spectrum Management
35 Spectral Sharing with Radar
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This chapter quantifies the effect of interference on radar systems and provides a diverse range of waveform design and processing techniques that allow the mitigation of interference between radars and other service users within a given band and hence allow more users in the finite available bandwidth.
36 Improving Spectrum Use While Maintaining Legacy Compatibility
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As the demand grows for RF communication of information, the technologists will have to contend with existing systems, procedures, equipment, and allocated communication bands. In a few cases, new systems can be developed without legacy constraints. But in many cases, new capability must be added to existing systems in existing allocated bandwidth, and must allow continued operation of the existing equipment. This poses challenges to the system designer requiring clever engineering innovation in addition to mathematical principles of optimum communication of information.
37 Advanced Waveforms for Software Defined Radar (SDR) to Suppress Interfering Channels and Provide Isolation Control
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The radar frequency spectrum is being dramatically affected by the commercial usage of wireless devices such as cell phones and wireless internet access. A new class of radar waveforms is needed in order to maintain the operational capabilities of radar and satisfy the interference requirements of neighboring commercial and military communication systems. The employment of orthogonal frequency techniques in radar systems offers an efficient use of channel bandwidth while optimizing the radar spectrum for, say, improving range resolution. The benefits of orthogonal frequency techniques to future radar designs show the potential of this technology in solving interference problems worldwide.
38 Spectrally Confined Waveforms for Solid-State Transmit Modules
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The allowable transmission spectrum of US Navy radars is being heavily utilized by other services like telecommunication systems which is causing many interference problems between the radars and the non-radar services when the radars operate in a littoral environment. In addition, many Navy radars are being operated in close proximity thereby causing in-band interference between radars. The result is that legacy radars are required to use emission control in many littoral environments, which significantly limits the radars' capability and usefulness. Reducing the spectral spread of the radar emissions can alleviate some of the interference problems, both from in-band radars and from the telecommunication services. The goal of this spectrally clean effort is to develop and implement waveforms that constrain their energy down to a -100 dB level within an instantaneous bandwidth of 20 MHz. The basic cardinal-series sampling expansion is unacceptable because it induces leading and trailing timedomain edges of the pulse that continue for a long time. Moreover, the transmitter would be forced to emit very little energy for long periods of time, thereby reducing the efficiency of a transmit-receive module. However, a significant reduction in the leading and trailing edges has been achieved with the GWS function, but at the cost of increasing the bandwidth and the near-in time sidelobes around the main lobe.
39 Non-Interference Limited Multi-Radar Target Detection and Tracking
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This chapter discussed the results of investigations aimed at applying a cooperative multi-sensor approach to enhance the acquisition, tracking, and discrimination of moving targets with low false alarm rate. Multiple radars are assumed to operate together in a non-interference limited manner. A three-fold approach was discussed: (1) applying multi-objective joint optimization algorithms to set limits on the operational parameters of the radars to preclude electromagnetic interference (EMI) based on the Transmission Hyperspace paradigm; (2) measuring and processing radar returns in a shared manner for target feature extraction based on waveform diversity techniques; and (3) employing feature-aided track/fusion algorithms to detect, discriminate, and track real targets from the adversary noise cloud. Computer simulations showed that with the help of simple signal amplitude features obtained from scattering cross section measurements using spatially and frequency diverse radars the overall sensor system can achieve a much better performance for data association and target tracking.
40 Waveform Diversity for Adaptive Radar - An Expert System Approach
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The focus of this chapter is on the design of waveforms for efficient spatial and temporal adaptivity including the focusing of the transmitted energy on a physically-small target, so that it will be possible to synthesize waveforms in the space-time continuum for both monostatic and bistatic applications and so that they can be mission adaptive. The objective is to develop spatially and temporally adaptive sensor technology for application to air, space, and ground systems operating in isolation or in concert with other sensor systems, emphasizing monostatic and bistatic scenarios. This can be achieved with the application of expert system technologies to facilitate the automatic selection of the waveforms in real time and near real time applications based on predefined rules.
41 Electromagnetic Compatibility and Spectrally Cleaner Waveforms
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Radar technology has a number of self-competing interests. For example, a radar must be able to search and track targets by resolving their spatial locations in range and azimuth. Transmitted short-duration pulses, with associated desirable broad bandwidths, allow radars to achieve the high range resolutions necessary to resolve multiple targets in space. However, temporally short pulses and their corresponding fast rise and fall times generate spectral sidelobes that may induce EMI in wireless systems, like WiMAX residing in the 3.4-3.7 GHz band, and other radars in adjacent channels. Waveform diversity techniques and designs, like the NRL Chireix concept, may allow radar performance metrics to be met while permitting conformance to regulatory emission masks like those found in the RSEC. The hypercube concept, while posing many formidable challenges in terms of hardware, signal processing, and networking, may potentially allow future users of the electromagnetic spectrum to coexist without compromising individual performances.
42 Knowledge Base Technologies for Waveform Diversity and Electromagnetic Compatibility
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We have provided an overview of waveform diversity and how it is being studied for communications and radar systems. The deployment of these systems within military platforms has a great potential for causing EM fratricide. There are Semantic Web technologies that can help us manage the EM spectrum within military platforms. However, we will need a paradigm shift in how we develop these intelligent platform systems that can manage waveform diversity devices when deployed with current EM devices on the same or nearby platforms. The EMC area has a new challenge in the integration of waveform diversity devices for the military and commercial worlds. A solution may lie in leveraging the technologies being developed within the artificial intelligence and Semantic Web communities.
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Section C: Waveform Design. Part I: Novel Waveforms
43 Improved Waveforms for Satellite-Borne Precipitation Radar
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This chapter has presented the basis of a continuous nonlinear FM waveform design capable of achieving range sidelobe levels of better than -70 dB, suitable for use with a satellite-borne precipitation radar. The waveform shows good Doppler tolerance, with the low sidelobe performance maintained over the full Doppler bandwidth associated with the antenna footprint. A clear-cut waveform design procedure has been presented that does not require the implementation of numerical optimization procedures. It has been shown that slowly varying phase and amplitude errors in the transmitter and receiver have relatively little effect, but rapidly-varying errors result in paired echo sidelobes whose level can be significant. A closed-loop calibration process is therefore essential to remove the effects of errors in the analog portions of the transmitter and receiver. Reference to the original problem (Figure 1) shows that in fact it is only necessary to have low range sidelobes on one side of the radar point target response. There may therefore be scope in designing a waveform to exploit this, trading sidelobe energy from one side of the response to the other. Some early work on this problem has shown promise [7]. In the context of waveform diversity, the work described in this chapter is an example of an application that demands the generation and processing of very precise waveforms, which is only now becoming practical with high-speed digital circuits with large number of bits. More generally, pulse compression processing giving low range sidelobe performance is required in a number of applications in modern radar systems, so these ideas will find wider application than just meteorological radar. In future years it may be expected that interface between analog and digital parts of a radar will migrate further and further towards the antenna, so techniques of this kind will become easier.
44 Hyperband Radar Waveforms
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This chapter explores the feasibility of a new hyperband radar waveform modulation that decouples the spatial domain beamwidth and associated media propagation issues from the fast time domain impulse response used to determine range and range-rate.
45 Details of the Signal Processing, Simulations and Results from the Norwegian Multistatic Radar DiMuRa
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The signal processing of the Norwegian Multistatic Radar DiMuRa has been presented. The radar uses binary phase coding with a class of binary phase codes with optimal autocorrelation properties. These codes are used to find the range to the target through a correlation process. These codes cannot be used to directly extract the target's velocity. This can, however, be accomplished through a Fourier transform of all the range correlation vectors for each range distance. Results from signal simulation and from a radar trial have been presented in detail.
46 Orthogonal Waveforms for High Resolution Range-Doppler Target Reflectivity Estimation
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The wideband received signal as the affine group Fourier transform of the range-Doppler wideband target reflectivity function evaluated at the transmitted waveform has been described. The approach provides to a framework in which the high resolution target reflectivity function estimation and waveform design problems are jointly addressed. A Wiener filtering method in the Fourier transform of the affine group to suppress clutter has been developed. Then, that Wiener filter use to precondition the transmitted waveforms to reject clutter has been shown. When, only N waveforms are to be transmitted, the optimal waveforms in the MMSE sense becomes the eigenfunctions of the modified Wiener filter corresponding to the largest N eigenvalues.
47 Noise MIMO Radar
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The ability of MIMO radar to measure propagation delays from each transmitter to each receiver allows the concept of the sum co-array, reviewed, to be exploited. The sum co-array allows virtual elements to be synthesized and in some cases this can lead to performance advantages. The relationship of the ES matched filter to the sum co-array is discussed in Section 6 and an interesting example of its application to uniform linear arrays (ULAs) is presented. The cross-spectral matrix approach entails the use of ensemble averages which in practical situations are not realizable and furthermore do not capture the statistical aspects and limitations of using noise waveforms. So finally, in Section 7 statistical techniques are used to derive some theoretical limits on the use of noise waveforms resulting from the use of finite sample sizes and some simulations are presented to illustrate these limitations.
48 Nonlinear Complementary Waveform Sets for Clutter Suppression
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In this chapter we show how waveforms can be constructed which have true complementary behavior when non-linear singnal processing is used at the receiver. We call such waveforms square-complementary, since they have the property that the sum of the squares of their autocorrelations are zero at non-zero lags. In addition, by moving from square-complemtary pairs to square-complemtary quads the complementary behavior can be can be made Doppler tolerant over the range of Doppler shifts normally encountered in radar systems. The remainder of this chapter introduces complementary, square-complementary and mutually orthogonal code sets. Waveform construction via pulse code modulation is discussed, and multiplexing in time and frequency is examined. Applications of complementary coded signals to communications and radar are considered.
49 Continuous Coded Waveforms for Noise Radar
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This chapter describes a new class of continuous waveforms for noise radar that can be processed using earlier developed methods for reducing pulse compression sidelobes and equalizing compressed pulses before Doppler filtering. The purpose is to find non-repeating waveforms that are amenable to the proposed processing methods with sufficiently low processing loss. The proposed waveforms are based on codes that modulate sub-pulses which define the bandwidth of the waveform. For constant amplitude waveforms the codes are phase codes and the sub-pulses can consist of rectangular pulses with constant phase or linear phase. The proposed waveforms use many short codes to produce a code with a length that is the product of the shorter code lengths. The resulting long code can be arbitrarily long by introducing new shorter codes iteratively. The code construction is equivalent to many Kronecker products of the shorter code vectors. The codes can be random or deterministic to get a quasi-periodic yet unpredictable waveform.
50 Examples of Ultrawideband Definitions and Waveforms
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In the last fifteen years, the development of ultrawideband (UWB) electromagnetic (EM) systems in communications, radar, and high-power directed energy has been on the rise. In particular, the significant developments in the commercial sector of UWB communications systems and UWB radar for humanitarian de-mining have fueled strong interest in UWB systems and technologies. These developments have led to three similar yet significantly different definitions of UWB by the U.S. Federal Communications Commission (FCC) [1], the International Electrotechnical Commission (IEC) [2], and the U.S. Office of the Secretary of Defense and the Defense Advanced Research Projects Agency (OSD/DARPA) [3]. The differences between these definitions have created much discussion about establishing universal UWB definitions and standards. Consequently, after analyzing the differences and goals of the three categorization schemes, the authors created a new categorization scheme that merges many of the essential features of the earlier schemes in an effort to provide a common basis for discussing UWB waveforms, devices, and systems [4]. In this chapter, this merged scheme is used to compare and contrast a small set of ideal UWB waveforms.
51 Novel Pulse-Sequences Design Enables Multi-User Collision-Avoidance Vehicular Radar
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Our CPSR technique utilizes a novel randomized pulse train composed of a large number of successive pulse sequences randomly selected from a given set interspersed with random gaps instead of a simple train of periodic or staggered pulses. The high performance and interference rejection features of the CPSR technique come from optimum temporal properties of the chosen sequences, high statistical unpredictability of the trains of pulse sequences, and the large number of pulses that are processed in the radar receiver in order to obtain decisions on obstacle presence and range. Sequence trains with thousands of pulses are used thereby increasing the power available for detection and, in comparison with simple pulsed radar systems, improving the system performance with respect to noise and interference rejection. The key operational features of Chaotic Pulse-Sequence Radar can be summarized as follows: Non-coherent radar technology for low-cost, high-volume automotive safety application . Use of specially-engineered randomized pulse sequence trains for modulating pulsed radars . Optimum temporal properties of the sequences provide for high and predictable immunity to interference from similar and dissimilar radar systems or other interferers in uncontrolled multi-user environments . High speed but simple integrating processes in the radar receiver that are tolerant to pulse distortion. The final system includes additional components such as efficient discrimination, ranging of obstacles in road clutter, and temporal tracking.
52 Interactive Least-Squares Costas Waveforms
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This chapter addresses the use of radar waveform optimization in radio frequency interference (RFI) scenarios that include either partial band interference or terrain-scattered interference (hot clutter). Terrain-scattered interference can induce significant coverage losses. Without waveform optimization, the only solution may be to “burn through which will impact the radar time line. Waveform optimization can potentially provide an alternative to this by matching to the target and anti-matching to the interference. Previous noise mitigation techniques result in waveforms with high signal-to-interference-plus-noise ratios (SINRs), but relatively poor waveform properties (specifically, low compressed pulse resolution and non-constant amplitude modulus). This chapter concentrates on the problem of improving these waveform properties while simultaneously maintaining favorable SINRs.
53 Complementary Waveforms for Sidelobe Suppression and Radar Polarimetry
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In this chapter, the focus is on the use and control of degrees of freedom in the radar illumination pattern and presented examples to highlight the value of properly utilizing degrees of freedom. It has been shown that by coordinating the transmission of Golay complementary waveforms in time (or exploiting waveform agility over time) according to carefully designed biphase sequences, and pulse trains whose ambiguity functions have desired properties can be constructed. It has also been shown that by combining Alamouti coding and Golay complementary property unitary polarization-time waveform matrices that make the full polarization scattering matrix of a target available for detection on a pulse-by-pulse basis can be constructed. Looking to the future, unitary waveform matrices as a new illumination paradigm that enables broad waveform adaptability across time, space, frequency and polarization.
54 Frequency-Coded Signals with Low Sidelobes in Central Zone of Autocorrelation Function
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This chapter presents a new class of signals based on frequency coding sequences that may be constructed by means of perfect difference sets. These sequences give rise to frequency-coded signals of a specific structure characterized by nonuniform distribution of the number of subpulses over the frequencies. Such a structure allows achievement of considerably lower sidelobes in the vicinity of the main lobe of the time autocorrelation function relative to those exhibited by Costas signals without using weighting functions. It is clear that unlike the weighting, this approach doesn't result in signal-to-noise ratio degradation although the main lobe broadening still remains. In addition these new signals exhibit thumbtack ambiguity functions with relatively low sidelobes over a wide region of the time-frequency plane. The chapter is organized as follows. In Section 2, the structure of a new class of multifrequency signals is described. Next, a simple algorithm, which employs the fundamental property of perfect difference sets [5], for the design of the frequency coding sequences is considered in Section 3. Section 4 presents some results of analytical and numerical investigation of the autocorrelation and ambiguity functions of the proposed signals.
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Section C: Waveform Design. Part II: Chaotic Waveforms
55 Chaotic Waveforms
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This chapter covers how in principle chaos can meet communications challenges, and the use of chaos to provide signals in both radar and sonar is then considered. For compactness and to establish that results in one domain cross over to the other, the common aspects are dealt with first beginning with an introduction to chaotic signals and terminology. The ability of chaotic radar and sonar to offer improvements in transmitter hardware, covertness, and coverage of the search volume are discussed. Implementation and practical issues arising from the unique properties of chaotic systems are considered and the results of acoustic experiments and trials are given that support prediction from simulation findings. The chapter finishes with a presentation of radar specific issues wherein a unique target adaptive radar architecture and radar applications are discussed. This material was originally presented in four papers published in 2006 at the International Waveform Diversity and Design conference [7], at a workshop on the transmission of Chaotic signals [8], at EuRAD2006 [9], and at the IET Symposium on Waveform Diversity and Design in Communications, Radar and Sonar [10].
56 Chaotic Waveform Diversity and Design: Part I - Motivation
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Chaotic signals are deterministic but appear random and it is these particular features which make chaotic signals potentially useful for secure communication applications. This chapter has identified various types of chaotic systems and provided some of the motivation for their use in chaotic waveform diversity. The remaining two parts of this series address some of the practical issues concerned with chaotic waveform diversity and design.
57 Chaotic Waveform Diversity and Design: Part II - Covert Communications
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A covert communication scheme has been described using phase modulation. The phase encoding scheme produces very complex dynamics that appear noise-like, with an approximately uniform PDF and impulsive ACF. Rayleigh amplitude modulation results in a signal similar to noise. BER estimates have been evaluated which indicate comparatively higher levels of Eb/No values for reliable communications. Statistical waveform analysis has been undertaken to provide indications of methods for improving receiver performance at low SNR and a state feedback (SF) architecture has also been proposed.
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Section C: Waveform Design. Part III: Imaging Waveforms
58 Chaotic Waveform Diversity and Design: Part III - Receiver Synchronization
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This chapter discussed the practical aspects of receiver synchronization are provided. Receiver synchronization in a covert communication system employing a noise-like digital phase encoding scheme is discussed and a scheme that enables sample timing and symbol synchronization is proposed. Simulation of a carrier-based covert digital communication scheme using differential phase modulation, demonstrating timing synchronization, is reported.
59 Radar Signal Analysis and Design Using Frequency Modulation of Chaotic Signals
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This chapter presented a theoretical analysis of CBFM signals as well as a sufficient condition for chaotic-based frequency modulated signals to be chaotic. The analysis has been based on Lyapunov exponents. The spectra of chaotic CBFM signals are flat, while the spectra of non-chaotic CBFM signals are non-flat. In radar applications, chaotic signals should not be treated simply as noise signals. This is because changing parameters responsible for producing chaotic signals affects the spectral characteristics of the FM modulated signals. In summary, the proper use of chaotic signals leads to less cost and higher range resolution than noise signals for the application of constant envelope signals in radar.
60 Sparse Stepped-Frequency Waveform Design for Through-the-Wall Radar Imaging
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While the stepped-frequency waveform synthesis for wideband imaging leads to a flexible and simplified implementation of the transmit and receive beamformer, the sparse multi-frequency array with proper frequency selection can obtain reasonable image quality with the same advantages and much less data acquisition time. Random, uniform-random, tapered random, and tapered uniform random reduced frequency selection schemes have been presented for indoor imaging. It is shown that for a single target scene, the uniform-random frequency selection can achieve better image quality, compared to the random frequency selection method, around the target location. For a scene in which multiple targets are close together, uniform-random reduced set of frequencies retains the advantage over random reduction. However, in the presence of other strong targets away from main target cluster, little advantage of uniform random over random remains. In such situations, tapered density of retained frequencies is shown to provide improved image quality.
61 Iterative Technique for System Identification with Adaptive Signal Design
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In this chapter, we again look at applying SNR-based and MI-based waveform design to an M-target ID problem. We first derive expressions for the optimum waveform spectrum under both design metrics, and show how both depend on a function called the spectral variance [2]. The formulation for the SNR-based waveform is different from the one used in [6,7] and uses the unifying spectral variance concept. We then compute a probability-weighted effective spectral variance over the target hypotheses and substitute it into the spectral variance quantity needed for waveform design. Using simulation, we evaluate the efficacy of these waveform strategies in comparison to a wideband pulse. We also consider an iterative procedure where the hypothesis probabilities are updated after each transmission. The updated probabilities can then be used to adapt subsequent waveforms. In the multiple-transmission scheme, sequential hypothesis testing is used to control when the transmissions may cease. It is shown that the number of transmission can be considerably reduced by choosing one of the optimized and adaptable waveform strategies. Furthermore, the relative performance of the waveforms is different under multiple transmissions than it is for a single transmission.
62 Investigation of Non-Traditional Transmit Waveforms for SAR-Based Target Detection
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In this work, two approaches are investigated to improve target detection performance. The two approaches are called the matched waveform and the variable chirp waveform. Both of these approaches are described here and an example is shown for each. The example is based upon data synthetically generated from damped exponential point scatterer data. The relevant metric is based upon the total energy produced for a given target over an appropriate area in an image or image-like product.
63 Time-Reversal Waveform Preconditioning for Clutter Rejection
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In this chapter, we present a time-reversal implementation of a transmit waveform preconditioning scheme for optimal clutter rejection in radar imaging is presented. Waveform preconditioning involves determining a map on the space of transmit waveforms, and then applying this map to the waveforms before transmission. This work applies to antenna arrays with an arbitrary number of transmit and receive elements, and makes no assumptions about the elements being co-located. By our time-reversal implementation we avoid the need to obtain an explicit model for the environment in order to compute the preconditioning operator.
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Section C: Waveform Design. Part IV: Communications
64 Pulse Shapes with Reduced Interference via Optimal Band-Limited Functions
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In this chapter, we focus on the design of pulse shapes for orthogonal frequency division multiplexing (OFDM) systems. As pointed out above, in such systems, mutual orthogonality of the subcarriers alone is not sufficient to ensure ICI-free communications. Thus, recent research effort has been directed towards the design of pulse shapes that possess various other characteristics that are necessary for reliable communication in practical settings. In [3] for instance, soft iterative ICI cancellation in conjunction with pulse shaping has been proposed for low-complexity channel equalization in OFDM systems. Observing that a nearly flat spectral main-lobe generally results in a higher average signal power, and rapid side-lobe attenuation helps contain the magnitude of interference, pulse shapes with such properties have been introduced in [4-7].
65 Waveform Design and Diversity for Shallow Water Environments
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In this chapter, we employ a general signal characterization based on the normal-mode model for shallow water environments that is applicable to a large class of signals. This characterization is based on a frequency domain formulation that can be used with narrowband as well as wideband signals. The normal-mode characterization assumes perfect waveguide conditions, and as a result, it consists of a homogeneous fluid layer with a soft top and rigid bottom. This environment characterization describes a linear time-varying (LTV) dispersive system which can cause different frequencies to be shifted in time by different amounts. Such dispersive signal transformations are specific to the nature of the environment that the signal propagates through, and they can severely limit the performance of underwater acoustic applications such as communications and sonar. In order to improve the performance of these underwater applications, we propose methodologies that exploit dispersion by waveform design and diversity.
66 Capacity Analysis of Spectrally Overlapping Direct-Sequence Spread Spectrum (DSSS) Channels
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As the number of users is increased, performance of the conventional DSSS system becomes an issue. Hence, we proposed a novel approach that can provide a significant increase in the number of users in a given bandwidth over that presently available. The proposed technique is based on division of the entire channel into a number of sub-channels having a smaller bandwidth than the entire channel bandwidth. Analytical results were obtained to estimate the number of users when the channel is divided into smaller bandwidth sub-channels. It is seen from the analytical results and computer simulations that the proposed approach allows more users to be accommodated than is now possible with the conventional single carrier DSSS system.
67 Coexistent Spectrally Modulated, Spectrally Encoded (SMSE) Waveform Design Using Optimization Techniques
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This chapter presents a collective body of work aimed at investigating SMSE waveform design in a coexistent environment using optimization techniques that are commonly employed in the operations research field. For demonstration purposes, a Direct Sequence Spread Spectrum (DSSS) system in an AWGN channel provides the coexistent environment, and Genetic Algorithm (GA) and Response Surface Methodology (RSM) optimization techniques are employed for SMSE waveform optimization.
68 Low-Complexity EPS Scheme for PAPR Reduction in OFDM with No Transmission of Side Information
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In this chapter we described a procedure to avoid side information transmission in the EPS scheme proposed in and presented a modification to the receiver. In the original EPS design the side information needs to be transmitted to the receiver in order to identify the erasure pattern selected at the transmitter. We devised a technique to recover the selected erasure pattern from the transmitted data without the need for explicit transmission of side information.
69 UWB-IR Interference Mitigation from Wideband IEEE 802.11a Source Using Frequency Selective Wavelet Packets
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In this chapter we proposed a novel wavelet packet based scheme to reduce the effect of co-existing wideband interference in UWB-IR communication. The emphasis was on the development of maximally frequency selective filter banks derived from a modified Remez exchange algorithm. For the IEEE 802.11a interference, simulation studies showed that the proposed scheme yielded significant BER performance improvements. Further, the performance of the system was found to be determined by the length, transition band, and regularity order of the filter banks.
70 Non-Binary Spread Spectrum Signals with Good Delay-Tracking Features for Satellite Positioning
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Improving time-delay estimation and multipath resistance is one of the most important drivers for designing new satellite signals, together with noise and multiple access interference reduction. This chapter proposes a theoretical analysis for designing new spreading waveforms that can achieve this multiform problem. Following a systematic approach for designing new signal-in-space waveforms has lead to an implementable mathematical optimization problem to improve time delay estimation for the additive white Gaussian noise channel with two-ray multipath (MP) propagation. In this scenario, minimizing the Gabor bandwidth with a constraint on the sidelobe levels is shown to represent an effective optimization criterion for designing spreading signals with higher robustness against MP. Starting from the generic waveform formulation of the signal as a cardinal interpolation of the cardinal sine function, the proposed band-limited non-binary signal represents an effective way to optimize the performance following the Gabor bandwidth analysis.
71 Overlay/Underlay Waveform Design for Enhancing Spectrum Efficiency in Cognitive Radio
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In this chapter, we presented a novel soft decision cognitive radio and dynamic spectrum access paradigm which exploits not only the unused spectrum holes, but also the underused spectrum bands to maximize performance and channel capacity for secondary cognitive users. We reviewed commonly used multi-carrier based enabling waveforms for cognitive radio. We then extended the SMSE framework to generate such overlay, underlay, and hybrid overlay/underlay waveforms to support the soft decision cognitive radio. Performance analysis and simulation results over AWGN and fading channels were then presented to confirm the performance gain of the novel system.
72 Frequency Hopping Waveform Diversity for Time Delay Estimation
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In this work we consider the use of frequency hopping (FH) communications waveforms for TDE. Thus a high dynamic range narrow band receiver may be employed, subject to the complexity of FH acquisition. Adequate time-bandwidth product for TDE can be achieved by processing over multiple hops. We consider each hop to be a narrow band, flat fading channel that is independent from hop to hop. This introduces carrier phase uncertainty for each hop, and the SNR varies over hops as well. There may also be a small unknown carrier frequency offset per hop, and data symbols may be known (e.g., training in a preamble) or unknown (during communications). We consider the case of known carrier frequencies and known data symbols in this work, but the model is general and more complex cases may be studied in future work.
73 Robust Frequency Offset Estimation in OFDM Systems
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In this chapter, 16-ary QAM symbols are referred to as frequency domain symbols and their N-point IFFT is referred to as an OFDM symbol. Our results indicate that combining iterative frequency offset estimation with iterative demodulation and decoding reduces the bit error rate with respect to the SNR. Weighting the reconstructed samples using (19) prevents error propagation when a large number of the decoded bits and reconstructed symbols are in error.
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Section C: Waveform Design. Part V: Matched Illumination
74 Waveform Design for Target Class Discrimination with Closed-Loop Radar
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The basic concepts of cognitive radar and considered the Bayesian framework as an engine for its operation has been summarized in this chapter. Clearly, two critical functions of CR are a probability update function that quantifies the system's understanding and an ability to respond by adapting subsequent transmit waveforms. We applied two waveform strategies to the problem of discriminating an unknown target realization in additive Gaussian noise. The waveforms are based on the SNR and MI criteria. The potential benefits of closed-loop operation are apparent, and we have proposed a diversity-based explanation for the observed performance.
75 Optimal Signal and Jamming Dynamics Embracing Digital Filter Strictures
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The subject of this chapter is the rapid waveform re-design of a transmitted pulse (typically in a radar/sonar or other active pulse detection application), which is in turn countered by a rapid reshaping of a jammer's additive noise transmission. Detection of each received noisy pulse is done by means of the (agile) detection filter that is applied for the currently prevailing pulse and noise situation.
76 Information Theoretic Waveform Design for Tracking Multiple Targets Using Phased Array Radars
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In this chapter we discussed the optimization of multiple waveforms for multiple targets under joint power constraint. This type of waveform design is suitable for unresolved extended targets. We have derived computationally efficient algorithms and presented the result of the optimization in simulations. Further results, as well as design of a single waveform optimized for multiple targets, can be found in [12]. The combination of waveform design and direction-of-arrival estimation is discussed in [13].
77 Polarization Diversity for Detecting Targets in Heavy Inhomogeneous Clutter
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The detection of static or slowly moving targets in heavy-clutter environments is considered a challenging problem, mainly because it is not possible to discriminate the target from the clutter using the Doppler effect. Polarization diversity provides additional information that enhances the detection of targets, particularly under the conditions described above. Detection performance could be further improved if the polarization of the transmitted signal were optimally selected to match the target polarimetric aspects. In this chapter, we present a polarimetric detector that is robust against heavy inhomogeneous clutter; i.e. the detector false-alarm rate is insensitive to changes in the clutter while still maintaining a good probability of detection. Using real data we test its applicability and show its advantages with respect to other polarimetric detectors. Moreover, the test statistic derived from the detector has a well-known distribution that depends on the transmitted waveform parameters. Finally, we propose the selection of the signal polarization that will maximize the target probability of detection.
78 Ambiguity Function Analysis of Adaptive Colored-Noise Radar Waveforms
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Adaptive radar waveforms were designed to be spectrally orthogonal to the received time-varying interference environment. This provides a natural defense against hostile or benign radio frequency interference. An ambiguity function analysis was presented for colored waveforms that graphically illustrates ambiguities, resolution/accuracy of range (time) and Doppler (frequency) estimates, and inherent interference rejection capabilities. Both eigenvector and multistage Wiener filter methods were used to construct such waveforms. The techniques presented illustrate a general methodology for designing adaptive waveforms trading off interference rejection performance, algorithm complexity, sidelobe levels, Doppler tolerance, and ambiguities.
79 Matched Terrain Processing: Possibilities for Waveform Diversity Design
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A technique called matched terrain processing (MTP) is described here that exploits the everincreasing availability of high-resolution geo-spatial databases of the earth's terrain to enhance the capabilities for identification and localization of targets. Waveform diversity design can become the basis for both target and terrain adaptive (not just target adaptive) optimization to enhance the capabilities of MTP further. A proof-of-concept example of the MTP method is provided in this chapter.
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Back Matter
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