Dynamic Beamforming Optimization for Anti-Jamming and Hardware Fault Recovery

1. Dynamic Beamforming Optimization for Anti-Jamming and Hardware Fault Recovery Jonathan Becker Ph.D. Candidate, Electrical and Computer Engineering Carnegie Mellon University Thesis Advisor: Prof. Jason Lohn Thesis Committee: Prof. Ole Mengshoel, Prof. Patrick Tague, Dr. Derek Linden (CTO, X5 Systems, Inc.)

2. About Me Jonathan Becker 15 years of research & industry experience in machine learning, stochastic optimization, antenna design, RFID wireless sensing, and RF / microwave engineering design. 8 papers in the related fields. Carnegie Mellon University / Ph.D. (2009-2014) Advisor: Prof. Jason Lohn University of Southern California / MSEE 2004 Cal Poly San Luis Obispo / BSEE with CS Minor 1999 Work Experience Disney / Wireless Displacement Sensing (2012-2013) EDO / Interference Cancellation Systems (2001-2006) Teradyne / High-bandwidth IC tester interfaces (1999-2001) 2

3. Main Goal The main goal of this research is to develop foundational models of and stochastic algorithms for anti-jamming beamforming in the presence of static and mobile signals and hardware faults. 3

4. Dynamic Beamforming Optimization With Fault Recovery: Motivation Jammer Desired Jammer Wireless Comm. Blocked Array Failure BFFault X X Anti-Jamming Beamforming 4 HW Fault Recovery via Alg.BFFault No HW Redundancy Limited Spectrum BF Volume Constrained X X

5. Fault Tolerance Importance in Anti-Jamming Beamforming 5[1] H.H. Khatib, “Theater wideband communications,” IEEE MILCOM 97 Proceedings, pp. 378-382, 2-5 Nov. 1997. •  Failure to anti-jam can cause a ripple effect down the communication path. •  Reconfiguration of array weights during recovery provides anti-jamming beamforming by definition Array Failure

6. Outline •  Motivation •  Previous Research •  Research Problems and Solutions •  Research Approach •  Experiments and Results •  Conclusion 6

7. Previous Research 7[1] D. Linden. “Optimizing signal strength in-situ using an evolvable antenna system,” NASA/DOD EH Conf., 2002. Reed Relay Switch Feed Point RF Traces GA optimized mainbeam gain by turning switches on and off

8. Previous Beamforming Research •  Haupt used 128 antennas to null one jammer •  Array tuned to signal of interest prior 8 Haupt’s antenna array One bank of attenuators and phase shifters 7 Degrees of Freedom. [1] R. Haupt and H. Southall, “Experimental adaptive nulling with a genetic algorithm,” Microwave Journal, vol. 42, no. 1, pp. 78–89, 1999.

9. Previous Fault Tolerance Research 9 [1] Lee et. al., “A built-in performance-monitoring/fault isolation and correction (PM/FIC) system for active phased arrays, IEEE Transactions on Antennas and Propagation, Nov. 1993. •  8 X 10 antenna active array for radar (mainbeam scanning) •  Injection of external signal for fault detection •  Complex circuitry needed to detect faults & re-tune array Transmission Line Injection Control Circuitry

10. Previous Fault Tolerance Research •  Han et. al. showed GA’s ability to resynthesize beam pattern after transmit/receive module failed 10 J. H. Han, S. H. Lim, and N. H. Myung, “Array antenna TRM failure compensation using adaptively weighted bean pattern mask based on genetic algorithm,” IEEE Antennas and Wireless Propagation Letters, 2012. GA reconfigured weights using pattern mask based fitness function AF = Array Factor

11. Previous Fault Detection Research •  Oliveri et. al. developed a fault detection approach based on Bayesian Compressive Sensing 11 Oliveri et. al., “Reliable Diagnosis of Large Linear Arrays – A Bayesian Compressive Sensing Approach,” IEEE Transactions on Antennas and Propagation, October 2012. ˆf = argmax f P f F( )! " # $ “Difference” field pattern P f F( )= P F f( )P f( ) P F( ) Solve using Bayes Theorem Sparse “failure” vector

13. Research Problems in Anti-Jamming Beamforming Research problems: 1.  Signal directions often time-varying and unknown a priori, so canonical beamforming techniques used with Radar arrays not applicable. 2.  How to search a large, combinatorial parameter space with multimodal fitness landscape? 3.  How well do stochastic algorithms adapt to mobile signals? •  Available frequency spectrum is a scarce resource. •  Increased interference will occur as the wireless spectrum saturates. •  Antenna arrays used to focus electromagnetic energy on a desired signal of interest & minimize energy towards interfering signals Goal: Perform anti-jamming in presence of static & mobile signals 13 BF X X Anti-Jamming Beamforming

14. Fault Recovery Research Problems Research problems: 1.  Recovery from hardware failures and localized faults in the array 2.  How do stochastic algorithms treat hardware faults vs. mobile signals? 3.  What happens if a hardware component fails before algorithmic convergence? After convergence? •  Hardware redundancy addresses antenna array reliability at expense of more volume, mass, cost. •  Volume, mass, and cost constraints create lack of hardware redundancy. •  Faulted hardware components cause loss of anti-jamming functionality. Goal: Perform HW fault recovery with stochastic algorithms Fault Recovery BF X X Fault 14

15. Anti-Jamming Beamforming Arrays 15 Shape radiation pattern using multiple antennas and hardware amplitude / phase weights Null shifted to 30°

16. Stochastic Search Algorithms 16 Approach Features Drawbacks Least Mean Squares Adaptive feedback Local search with poor multi-modal performance Conjugate Gradient Method Searches parameter space using conjugate directions Signal directions needed, poor multi-modal performance, O(N2) Genetic Algorithms Population based global search Run-time is problem dependent Simulated Annealing Evaluates solutions sequentially Convergence is cooling schedule dependent

18. Triallelic Diploid Genetic Algorithm 18 SINROut tn,p !" #$= PS,Out tn,p !" #$ Pj,Out tn,p !" #$+ No j=1 J ∑ Fitness Function: SINR = Signal to Interference and Noise Ratio

19. Simple Genetic Algorithm 19 SINROut tn,p !" #$= PS,Out tn,p !" #$ Pj,Out tn,p !" #$+ No j=1 J ∑ Fitness Function: SINR = Signal to Interference and Noise Ratio

20. Simulated Annealing Block Diagram 20 SINROut tn[ ]= PS,Out tn[ ] Pj,Out tn[ ]+ No j=1 J ∑ Fitness Function:

21. Hill Climbing Block Diagram 21 SINROut tn[ ]= PS,Out tn[ ] Pj,Out tn[ ]+ No j=1 J ∑ Fitness Function:

22. Wireless Channel Model 22 Symbol Meaning J Number jammers Q Number reflections N Number antennas •  Array creates single weighted sum of signals and reflections •  Signal directions unknown a priori •  Sum of signals and multipath reflections should not exceed number of antennas in the array •  Array response calculation important for simulation fidelity N antennas Antenna Array Response

23. Array Factor Model of Antenna Arrays P(R,θ,ϕ) •  Models antennas as infinitesimal dipoles •  Far-field computation in O(N) time •  Ignores antenna mutual coupling and reflections off objects near antennas 23 AF θ,φ( )= ˆaiejβaR⋅di i=1 N ∑ ˆai = aie− jψi ai ∈ ℜ and 0 < ai ≤1 ψi ∈ ℜ and 0 ≤ ψ < 2π Complex array weights Element Positions Spherical Unit Vector

24. Method of Moments (MOM) Model of Antenna Arrays •  Models antennas as combination of small wire segments •  Mutual coupling included in calculation of far-field radiation patterns •  Ignores reflections off objects near antennas 24 Fields calculated in O(N3) time. Goal: Given known port excitations, solve integral equations to calculate currents on each wire Solution: Divide each wire into segments and estimate unknown currents as sum of weighted basis functions Segmentation on N antennas ˆI = ˆZ! " # $ −1 ˆV Result: Ultimately obtain vector equations of form Post-processing: Calculate far-fields D. B. Davidson, Computational Electromagnetics for RF and Microwave Engineering, 2nd ed. New York, NY: Cambridge University Press, 2011 Matrix Inversion

25. Antenna Arrays with Nearby Objects •  Physical arrays include metallic objects near antennas •  Incorporate reflections into MOM by including metallic objects in model •  Model objects as Perfect Electric Conducting (PEC) planes 25Fields calculated in O(N3) time.

26. Optimal Array Weights with Mutual Coupling Compensation 26 MC −1 âM,opt = MC −1 âAF,opt âAF,opt Inverse of Coupling Matrix MC found using MOM compared to array factor calculation Optimized weights using Array Factor calculations Coupling compensated optimized weights [1] T. Zhang and W. Ser, “Robust beampattern synthesis for antenna arrays with mutual coupling effect,” IEEE Transactions on Antennas and Propagation, vol. 59, no. 8, pp. 2889–2895, 2011 [2] P. J. Bevelacqua, “Antenna arrays: Performance limits and geometry optimization,” Ph.D. dissertation, Arizona State University, May 2008. [3] M. Joler, “Self-recoverable antenna arrays,” IET Microwaves Antennas Propagation, vol. 6, no. 14, pp. 1608–1615, 2012.

27. Optimal Array Weights with Mutual Coupling and Hardware Reflection Compensation 27 MCR −1 âMR,opt = MCR −1 âAF,opt âAF,opt Inverse of Coupling Matrix New Method: Hardware reflections compensation not discussed in literature Optimized weights using Array Factor Coupling + Reflection compensated optimized weights MR −1 âMR,opt = MR −1 âM,opt âM,opt Inverse of Reflection Matrix Coupling + Reflection compensated optimized weights MCR = MC MR MOM output

28. Equivalence of Stochastic Algorithms with Different Antenna Array Models 28 Need to calculate an inverse matrix for each transformation Most Reliable but O(N3)Least Reliable but O(N) Solution: Calculate in O(N) timeˆaMR

29. WIPL-D / AntNet Integration 29 Array Layout Input File WIPL-D AntNet ˆVSAlg ∝ ˆaAlg ∈ CN×1 Beamformed Fields [1] D.S. Weile and D.S. Linden, “AntNet: A fast network analysis add-on for WIPL-D, 27th International Review of Progress in Applied Computational Electromagnetics, March 2011 ˆVSnom = 1 ∈ ℜN×1 O(N3) O(N) Simulate Once Run Multiple Times (Saved in file) Chosen by Algorithm Nominal Port Far Fields & S/Y/Z matrices

30. HFSS and MOM Models of Array 30 •  HFSS = High Frequency Structure Simulator •  HFSS is based on the Finite Element Method (FEM) •  Divides structure into small tetrahedra with boundary conditions •  MOM: divides wires into small segments, planes into small triangles FEM (HFSS) MOM (WIPL-D)

31. Comparison of HFSS and WIPL-D to in-Situ Measurements 31 •  Good agreement between simulations and in-situ measurements •  Good agreement in jammer directions •  Extra nulls via nonlinear hardware effects not captured by HFSS & MOM HFSS results similar to WIPL results in both cases

32. Diagnosis Model for Hardware Fault Detection 32 Problem: Events overlap making it insufficient to diagnose what caused the algorithm to fail in anti-jamming by tracking the fitness function alone. Solution: Add array weight tracking to understand why the algorithm failed.

33. Diagnosis Model for Hardware Fault Detection •  H0: Algorithm converged: No Faults, no TVDOAs. •  H1: Algorithm unconverged: No Faults, no TVDOAs. •  H2: Algorithm converged: Faults and/or TVDOAs present. •  H3: Algorithm unconverged: Faults and/or TVDOAs present. 33 Good states Not good states Diagnosis not necessary Diagnosis not possible ∂µa ∂t n( )> 0and ∂µF ∂t n( )> 0 →HW Fault ∂µa ∂t n( )≤ 0and ∂µF ∂t n( )> 0 →TVDOA Assumes fading averaged out

34. Antenna Fault Localization: Array Factor Method AF θ,φ k( )= âiejβaR⋅di i=1 k−1 ∑ + âiejβaR⋅di i=k+1 N ∑ âi = aie− jψi ai ∈ ℜ and 0 < ai ≤1 ψi ∈ ℜ and 0 ≤ ψ < 2π Probability that an antenna fault occurred in branch k: PFault k Failure( )= 1 ξ max xcorr ARF θ,φ k( ), ARM θ,φ( )! " # $ ARF θ,φ k( )=EF θ,φ( )⋅ AF θ,φ k( ) Note :ξ = normalizing factor s.t. 0 ≤ PFault k Failure( )≤1 34 Complex array weights Array Radiated Fields Element Factor Array Factor K = argmax k PFault k Failure( ){ }Assuming 1 fault, most likely fault branch:

35. Antenna Fault Localization with Array Factor Multiple antenna fault detection possible by counting number of faults with more calculations due to possible combinations: PFault k Failure( )= 1 ξ max xcorr ARF θ,φ k( ), ARM θ,φ( )! " # $ Note :ξ = normalizing factor s.t. 0 ≤ PFault k Failure( )≤1 Single fault: K faults: PFault k1,,kK[ ] Failure( )= 1 ξ max xcorr ARF θ,φ k1,,kK[ ]( ), ARM θ,φ( )! " # $ Total AF Correlations = N J ! " # $ % & J=1 N−1 ∑ # Antennas K Total AF Correlations Total AF Corr., 10% Sparsity 4 14 4 8 254 8 16 65534 136 32 > 4 trillion 41448 Total AF Correlations with Sparsity S s.t. S• N!" #$≥1 = N J & ' ( ) * + J=1 S•N!" #$ ∑ 35

36. Antenna Fault Localization: Improvements Pros: •  O(K) for single fault using array factor (AF) •  Useful for small arrays Cons: •  Correlation fidelity questionable since AF neglects mutual coupling –  Higher fidelity requires MOM or FEM at O(N3) cost •  Less useful for modeling damaged components (i.e, stuck-at faults) 36 Solution: Replace AF calculations with AntNet post-processed MOM calculations [1] D.S. Weile and D.S. Linden, “AntNet: A fast network analysis add-on for WIPL-D,” in the 27th International Review of Progress in Applied Computational Electromagnetics, March 2011 ˆV = ˆZ ˆZ + ˆZo( ) −1 ˆVS Eψ θ,φ k( )= Vi i=1 k−1 ∑ Eψ i θ,φ( )+ ViEψ i θ,φ( ) i=k+1 N ∑ , ψ ∈ θ,φ{ } PFault k Failure( )= 1 ξ max xcorr Eψ θ,φ k( ), ARM θ,φ( )! " # $

38. Experiment Setup 38 Port 1 Port 2 VNA VNA = Vector Network Analyzer SOI Jammers SOI = Signal of Interest SOIJam 1Jam 2Jam 3

39. Adaptive Beamforming Array 39 Goal: Show that stochastic algorithms can perform anti- jamming beamforming in the presence of static or mobile signals and hardware faults Step AttenuatorsPhase Shifters Antennas Hardware Controllers Power Combiner

40. Adaptive Beamforming Array in Anechoic Chamber 40 Anechoic chamber approximates free-space conditions (at far end of chamber)

41. Array Diagram and Hardware Settings 41 Att5 (8 dB) Att4 (4 dB) Att3 (2 dB) Att2 (1 dB) Att1 (½ dB) 0 1 0 0 1 Ph5 Ph4 Ph3 Ph2 Ph1 1 1 0 0 1 A21 A31 A41 P2 P3 P4 5 BITS5 BITS5 BITS5 BITS5 BITS5 BITS BIT 30BIT 15BIT 1 Example: 4.5 dB Attenuation out of 15.5 dB max Range: 0 to 360° 11.6° / bit Example: 151° A22 = 0 dB A32 = 0 dB A42 = 0 dB 230 Combinations

42. Multimodal SINR Fitness Landscape 42 Collected from 30 independent in-situ SGA runs with two jammers Multimodal behavior clear with several peaks having SINR ≥ 30 dB

43. Table of Simulations and Experiments Performed Anti-Jamming Fault Recovery (Anti-Jamming) Static Mobile Static Mobile Algorithm 2 jam 3 jam 2 jam 2 jam 3 jam 2 jam SGA S, E S, E S S S S TDGA S, E S S,E S, E S, E S, E SA S, E S, E S S S S HC S S S S S S 43 SGA = Simple Genetic Algorithm TDGA = Triallelic Diploid GA SA = Simulated Annealing HC = Hill Climbing S = Simulation E = In-situ experiments First SecondThird

44. Simulated Anti-Jamming with SGA and TDGA: Two Static Jammers 44 SGA TDGA PerformanceHamming •  TDGA produced better converged SINR values than SGA •  TDGA mean-Hamming distance decayed slower than SGA •  Mean SINR with 95% confidence interval indicate average convergence by 15 generations for both SGA and TDGA

45. In-Situ Anti-Jamming with SGA & TDGA: Two Static Jammers 45 SGA TDGA PerformanceHamming •  In-Situ TDGA produced better minimum converged SINR values than SGA •  Difference between min/max SINR smaller for TDGA than SGA •  Simulated SINR values were conservative compared to in-situ results.

46. SGA and TDGA Radiation Patterns, Simulations and In-Situ Compared: Two Static Jammers 46 SGATDGA Simulation In-Situ Simulation and in-situ radiation patterns are similar at convergence

47. Simulated Anti-Jamming with SA & HCA: Two Static Jammers 47 SA HCA PerformanceRadiation •  SA and HCA obtain similar converged azimuth radiation plots •  Both SA and HCA by chance find ~20 dB SINR solutions early but on average converge much slower than GAs per 95% confidence intervals

48. In-Situ Anti-Jamming with SA: Two Static Jammers 48 PerformanceRadiation •  Average convergence time agrees with simulations. •  Final in-situ SINR values higher than SINR predicted by simulation

49. Anti-Jamming Two Static Jammers: Algorithm Comparison Best Case SINR (dB) In-Situ {Sim} Worst Case SINR (dB) In-Situ {Sim} 95% Conf. Interval (dB) Gauss (Student-t) In-Situ {Sim} Average Converge Time (# Gen / Eval) In-Situ {Sim} SGA 67.8 {27.7} 28.3 {20.7} 3.3 (3.4) {0.65 (0.68)} 15 Gen (3000 Eval) {15 Gen (3000 Eval)} TDGA 55.5 {28.0} 31.1 {22.5} 2.4 (2.5) {0.55 (0.57)} 30 Gen (6200 Eval) {15 Gen (3000 Eval)} SA 48.2 {26.1) 13.8 {21.1} 2.52 (2.62) {0.51 (0.53)} 7800 Eval (39 Gen) {7140 Eval (~36 Gen)} HCA {26.2} {18.2} {0.61 (0.63)} {7140 Eval (~36 Gen)} 49 •  Simulations were conservative in predicting final SINR values •  SGA and TDGA converged to higher SINR values than SA and HCA •  In-Situ 95% confidence intervals were higher than predicted by simulations due to hardware tolerances. •  SA and HCA on average converged slower than SGA and TDGA

50. SGA and TDGA Two Jammer Fault Recovery Performance and Hamming Distance Plots: Simulations 50 SGA TDGA PerformanceHamming •  SGA and TDGA simulations predict recovery, but simulations are conservative. •  Mean Hamming distance for TDGA decays slower than SGA

51. TDGA In-Situ Fault Recovery Performance and Hamming Distance Plots 51 PerformanceHamming •  TDGA in-situ experiments recovered with higher final values than simulations. •  95% confidence intervals indicate TDGA recovered from a fault

52. SGA and TDGA Fault Recovery Azimuth Plots, Simulations 52 SGA TDGA Similar final radiation patterns with conservative fault-recovery predicted.

53. TDGA In-Situ Fault Recovery Azimuth Plot 53 [1] J. Becker, J.D. Lohn, and D. Linden, “Towards a self-healing, anti-jamming adaptive beamforming array,” in 2013 IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC), September 2013, pp. 1–4. •  TDGA in-situ pattern showed recovery of anti-jamming function. •  Some SOI gain recovered after the fault. •  Null directed at Jammer 2 (J2) deeper than pre-fault null.

54. Why TDGA Self Heals: An Example 54 Went from High to Low Mean Population Fitness Down Long term genetic memory and +1’s to -1’s dominance allows healing

55. SA and HCA Fault Recovery Performance and Azimuth Radiation Plots: Simulations 55 SA HCA PerformanceRadiation •  Temperature schedules repeated 5 times to allow for fault recovery •  Both SA and HCA showed fault recovery with maximum ~20 dB SINR post-fault

56. Two Static Jammer Fault Recovery: Algorithm Comparison Best Case SINR (dB) post-Fault In-Situ {Sim} Worst Case SINR (dB) post-Fault In-Situ {Sim} 95% Conf. Interval (dB) Gauss (Student-t) In-Situ {Sim} Average Converge Time (# Gen / Eval) In-Situ {Sim} SGA {18.7} {13.4} {0.48 (0.50)} {15 Gen (3000 Eval)} TDGA 47.0 {18.6} 1.12 {13.6} 4.77 (6.74) {0.57 (0.59)} 30 Gen (6200 Eval) {15 Gen (3000 Eval)} SA {20.5} {13.9} {0.60 (0.63)} Repeated Cooling Schedules HCA {20.3} {15.6} {0.43 (0.45) } Repeated Cooling Schedules 56 Fault Condition: two step attenuators in one path set to full values. •  SGA and TDGA simulations produced similar post-fault SINR values •  SA and HCA simulations produced slightly better SINR results than GA •  Algorithm simulations produced similar 95% confidence intervals but TDGA in- situ 95% confidence intervals much larger due to hardware tolerances

57. SGA Tracking Two Jammers from {45°, 200°} to {120°, 300°} 57 •  SGA moves nulls to track the jammers. •  Previous solution sometimes repeated resulting in lower SINR fitness.

58. TDGA Tracking Two Jammers from {45°, 200°} to {120°, 300°} 58 TDGA behaves in fashion similar to SGA.

59. SGA and TDGA Two Mobile Jammers Constantly Moving: Simulations 59 SGA TDGA PerformanceHamming •  SGA and TDGA performance graph follow similar sinusoidal pattern. •  TDGA mean-Hamming distance higher than SGA indicating more diversity in TDGA populations.

60. Azimuth Radiation Plots for SGA and TDGA Two Mobile Jammers Constantly Moving: Simulations 60 SGA TDGA Both SGA and TDGA track both jammers with second jammer having deeper null.

61. Stochastic Algorithms Investigated Name Advantages Disadvantages Simple Genetic Algorithm (SGA) Able to search parameter space in parallel Complexity problem dependent, short-term genetic memory Triallelic Diploid Genetic Algorithm (TDGA) Able to search parameter space in parallel, long-term genetic memory Complexity problem dependent, added step to convert TD strings into binary haploid strings Simulated Annealing (SA) Temperature dependent mutation allows initial exploration of search space with eventual exploitation of solutions Convergence time temperature schedule dependent, 2X slower than GAs Hill Climbing Algorithm (HCA) Simple to implement, finds solutions comparable to GAs and SA Tends to get stuck at local optima, 2X slower than GAs 61

62. Results Discussion •  Incorporating physical objects into MOM model of array increased model reliability and fidelity compared to in-situ measurements. •  Need to track both fitness function values and complex weights for a useful diagnostic model to detect faults in non-ideal environments. •  Hardware faults can be localized by correlating in-situ measurements with MOM calculations to provide most-likely faulty antenna branch. •  Showed that stochastic algorithms can perform anti-jamming beamforming with hardware fault recovery –  Simulations gave conservative results in SINR values compared to in-situ measurements –  Simulated Annealing and Hill Climbing Algorithms slower than GAs at anti-jamming static signals. •  GAs able to thwart continuously moving jammers 62

63. Conclusions and Contributions •  New analytical models with experimental results showing that small antenna arrays can thwart interference sources with unknown positions. •  First time demonstration of in-situ optimization with an algorithm dynamically optimizing a beamformer to thwart interference sources with unknown positions, inside of an anechoic chamber. •  First time demonstration of stochastic algorithms that provided recovery from hardware failures and localized faults in the array with reconfiguration of array weights to provide anti-jamming of interference sources having unknown positions. •  Comparison of multiple stochastic algorithms in performing both anti- jamming and hardware fault recovery. •  Showed that stochastic algorithms can be used to continuously track and mitigate interfering signals that continuously move in an additive white Gaussian noise wireless channel. 63

64. Future Work •  Real-time fault recovery and anti-jamming in wireless link •  Wideband 8-antenna array with individual antenna modules 64 PN = Pseudo-random Noise USRP = Universal Software Radio Protocol

65. Selected Publications 1.  J. Lohn, J. M. Becker, and D. Linden, “An evolved anti-jamming adaptive beam-forming network,” Genetic Programming and Evolvable Machines, vol. 12, no. 3, pp. 217–234, 2011. 2.  J. Becker, J. Lohn, and D. Linden, “An anti-jamming beamformer optimized using evolvable hardware,” in Proc. 2011 IEEE Intl. Conf. on Microwaves, Communications, Antennas, and Electronic Systems, IEEE COMCAS 2011, November 2011, pp. 1–5. 3.  J. Becker, J. D. Lohn, and D. Linden, “An in-situ optimized anti-jamming beamformer for mobile signals,” in 2012 IEEE International Symposium on Antennas and Propagation, IEEE APS 2012, July 2012, pp. 1–2. 4.  J. Becker, J. Lohn, and D. Linden, “Evaluation of genetic algorithms in mitigating wireless interference in situ at 2.4 GHz,” in WiOpt 2013 Indoor and Outdoor Small Cells Workshop, May 2013, pp. 1–8. 5.  J. Becker, J. D. Lohn, and D. Linden, “Algorithm comparison for in-situ beamforming,” in 2013 IEEE Intl. Symp. on Antennas and Propagation, IEEE APS 2013, July 2013, pp. 1–2. 6.  J. Becker, J. D. Lohn, and D. Linden, “Towards a self-healing, anti-jamming adaptive beamforming array,” in 2013 IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC), September 2013, pp. 1–4. 65

66. Acknowledgements •  I thank my committee members for their support: –  Professor Jason Lohn –  Professor Ole Mengshoel –  Professor Patrick Tague –  Dr. Derek Linden, CTO X5 Systems Inc. •  I would also like to thank these individuals who assisted me over the years: Prof. Martin Griss, Prof. Bob Iannuchi, Prof. Ted Selker, Dr. James Downey, Dr. Reggie Cooper, Prof. Joshua Griffin, Dr. Matthew Trotter, Prof. Joy Zhang, Prof. Pei Zhang, Prof. Emeritus James Hoburg, Prof. James Bain, Dr. Joey Fernandez, Dr. Faisal Luqman, Dr. Heng-Tze Cheng, Dr. Joel Harley, Jon Smereka •  This research was funded in part by: –  Cylab at Carnegie Mellon University under grant DAAD19-02-1-0389 from the Army Research Office –  The Electrical and Computer Engineering Department at Carnegie Mellon University 66

67. Thank you 67

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