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Frequency Diverse Array Receiver Architectures A thesis submitted in partial fulﬁllment of the requirements for the degree of Master of Science in Engineering by Aaron M. Jones Department of Electrical Engineering and Computer Science B.S. Engineering Physics, Wright State University, 2007 2011 Wright State University

Wright State University SCHOOL OF GRADUATE STUDIES I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPER- VISION BY Aaron M. Jones ENTITLED Frequency Diverse Array Receiver Architectures BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering. November 18, 2011 Brian D. Rigling, Ph.D. Thesis Director Kefu Xue, Ph.D. Department Chair of Electrical Engineering Committee on Final Examination Brian D. Rigling, Ph.D. Fred Garber, Ph.D. Douglas T. Petkie, Ph.D. Andrew Hsu, Ph.D. Dean, Graduate School

ABSTRACT Jones, Aaron M., M.S.Egr, Department of Electrical Engineering and Computer Science, Wright State University, 2011. Frequency Diverse Array Receiver Architectures. Typical radar systems are limited to energy distribution characteristics that are range indepen- dent. However, operators are generally interested in obtaining information at particular ranges and discarding elsewhere. It seems appropriate then to attempt to put energy solely at the range(s) of interest, thus minimizing exposure to clutter, jammers and other range-dependent interferences sources. The frequency diverse array (FDA) can provide a mechanism to achieve range-dependent beamforming and the spatial energy distribution properties are investigated on transmit and receive for different architectures herein. While simpliﬁed FDA receive architectures have been explored, they exclude the return signals from transmitters that are not frequency matched. This practice neglects practical consideration in receiver implementation and has motivated research to formulate a design that includes all fre- quencies. We present several receiver architectures for a uniform linear FDA, and compare the processing chain and spatial patterns in order to formulate an argument for the most efﬁcient design to maximize gain on target. It may also be desirable to beamsteer in higher dimensionalities than a linear array affords, thus, the transmit and receive concept is extended to a generic planar array. This new architecture allows 3-D beamsteering in angle and range while maintaining practicality. The spatial patterns that arise are extremely unique and afford the radar designer an additional degree of freedom to develop operational strategy. The ability to simultaneously acquire, track, image and protect assets is a requirement of future ﬁelded systems. The FDA architecture intrinsically covers multiple diversity domains and, there- fore, naturally lends it self to a multi-mission, multi-mode radar scheme. A multiple beam technique that uses coding is suggested to advance this notion. iii

List of Symbols Chapter 1 F DA ST AP LF M frequency diverse array space-time, adaptive processing linear frequency modulation Chapter 2 SAR GM T I U LA φ R c ∆f LP I M IM O HM P AR Chapter 3 synthetic aperture radar ground, moving-target indicator uniform linear array apparent scan angle range speed of light linear frequency step low probability of intercept multiple-input, multiple-output hybrid MIMO phased array radar CW t d λmin fn fc N sn Rn θo α s λc ωf ωo CF F D SN R rm M h∗ v∗ β∗ y∗ Hm m m m continuous wave time inter-element spacing minimum wavelength set of transmit frequencies from a linear array carrier frequency number of elements in the array transmit signal from each element range from each element to a target location angle off boresight of target transmit beam-weighting factor composite transmit signal wavelength of carrier frequency π∆f πd λc constant frequency frequency diverse signal-to-noise ratio received signal at each element number of receive elements ﬁlter for receive architecture * ﬁltered received signal at each element for architecture * receive beam-weighting at each element for architecture * composite received signal for architecture * ﬁlter bank for each receive element iv

Chapter 4 dy dx fnm ∆fx ∆fy N M P Q ypq Chapter 5 fln Fl ∆fl L cl fs T C Y-axis inter-element spacing X-axis inter-element spacing transmit frequency for the nm element frequency offset along X-axis frequency offset along Y-axis number of elements along X-axis number of elements along Y-axis receive element along X-axis receive element along Y-axis receive signal at each element set of transmit frequencies for each beam and element carrier frequency for each beam offset frequency for each beam number of beams orthogonal code sequence for each beam code sampling rate length of code integration amplitude scaling factor v

Contents 1 Introduction 1.1 Motivation . . 1.2 Contribution . 1.3 Organization . 2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Range Dependent Transmit Spatial Pattern . . . . . . . . . . . . . . . . . . . . . . 2.2 SAR Using a FDA Conﬁguration . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 FDA in Conjunction with MIMO Radar . . . . . . . . . . . . . . . . . . . . . . . 2.4 Spurious Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Linear Array Receiver Architectures 3.1.1 3.1 FDA Transmit Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FDA Time Dependency Spatial Pattern . . . . . . . . . . . . . . . . . . . 3.2 FDA Received Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Receiver Processing Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Band-limited, Coherent FDA . . . . . . . . . . . . . . . . . . . . . . . . . Full-band, Pseudo-coherent FDA . . . . . . . . . . . . . . . . . . . . . . 3.3.2 3.3.3 Full-band, Coherent FDA . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Planar Array Architectures 4.1 Geometry and Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Planar FDA Transmit Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Transmit Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 4.3 Planar FDA Receive Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial Pattern Snapshots . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Receive Signal Model 4.3.2 Planar Array Spatial Pattern Snapshot 5 Multiple Beam Transmit and Receive with Coding 5.1 Geometry and Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Uncoded Transmit and Receive Signals 5.2.1 Transmit Signal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Receive Signal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Coding Technique . . 6 Conclusions and Future Work vi 1 2 2 3 4 4 5 6 6 8 9 14 14 16 16 17 21 27 28 28 31 33 35 36 39 44 45 46 47 48 53 57

Bibliography 58 vii

List of Figures 3.1 Example of a linear FDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 FDA geometric set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Transmit pattern comparison of CF and FD arrays . . . . . . . . . . . . . . . . . . 3.4 FDA time dependency examination for positive offset . . . . . . . . . . . . . . . . 3.5 FDA time dependency examination for negative offset . . . . . . . . . . . . . . . . 3.6 Band-limited, coherent FDA architecture beamforming chain . . . . . . . . . . . . 3.7 Composite receive pattern for band-limited, coherent FDA architecture . . . . . . . 3.8 Full-band, pseudo-coherent FDA architecture . . . . . . . . . . . . . . . . . . . . 3.9 Composite receive pattern for full-band, pseudo-coherent FDA architecture . . . . 3.10 Beamforming chain for the full-band, coherent FDA architecture . . . . . . . . . . 3.11 Uniform linear array composite receive pattern for full-band, coherent architecture . . . . 4.1 Basic geometric set-up for a planar array . . . . . . . . . . . . . . . . . . . . . . . 4.2 Example of planar array with frequency offsets . . . . . . . . . . . . . . . . . . . 4.3 The 10-dB main beam transmit pattern is shown for a 9 × 9 planar array with (left) frequency diversity (∆fx = 1 kHz, ∆fy = 10 kHz) and (right) constant frequency transmit waveforms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Transmit spatial pattern from a planar array (1) . . . . . . . . . . . . . . . . . . . 4.5 Transmit spatial pattern from a planar array (2) . . . . . . . . . . . . . . . . . . . 4.6 Transmit spatial pattern from a planar array (3) 4.7 Transmit spatial pattern from a planar array (4) . . . . . . . . . . . . . . . . . . . 4.8 Receive beamforming chain of the planar FDA architecture . . . . . . . . . . . . . 4.9 Planar array receive pattern, global view . . . . . . . . . . . . . . . . . . . . . . . 4.10 Planar array receive pattern, side view . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Planar array receive pattern, top view . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Composite receive pattern snapshot for a 9 × 9 FDA for 10-dB beamwidth. . . . . 4.13 Composite receive pattern snapshot for a 9 × 9 FDA for 15-dB beamwidth. . . . . 4.14 Composite receive pattern snapshot for a 9 × 9 FDA for 20-dB beamwidth. . . . . 4.15 Composite receive pattern snapshot for a 9 × 9 FDA for 25-dB beamwidth. . . . . 5.1 Multiple beam scenario and set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Transmit multiple beam spatial pattern comparison . . . . . . . . . . . . . . . . . 5.3 Beamforming chain with ﬁlter structures for two beams. Components include: ﬁlter banks at each element for each beam with a beamsteering mechanism and power combiners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Multiple beam receive patterns with and without crosstalk . . . . . . . . . . . . . 5.5 Multiple beam receive patterns with and with crosstalk . . . . . . . . . . . . . . . . . . . . 10 11 13 15 16 18 19 20 22 23 26 29 30 34 34 35 36 37 38 40 41 41 42 42 43 43 45 48 49 51 52 viii

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