ATI's Radar Signal Analysis and Processing using MATLAB Technical Training Short Course Sampler

Professional Development Short Course On: Radar Signal Analysis and Processing using MATLAB Instructor: Dr. Andy HarrisonATI Course Schedule: http://www.ATIcourses.com/schedule.htm http://www.aticourses.com/radar_signal_processing.htmATIs Radar Signal Analysis:

www.ATIcourses.comBoost Your Skills 349 Berkshire Drive Riva, Maryland 21140with On-Site Courses Telephone 1-888-501-2100 / (410) 965-8805Tailored to Your Needs Fax (410) 956-5785 Email: ATI@ATIcourses.comThe Applied Technology Institute specializes in training programs for technical professionals. Our courses keep youcurrent in the state-of-the-art technology that is essential to keep your company on the cutting edge in today’s highlycompetitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presentedon-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our trainingincreases effectiveness and productivity. Learn from the proven best.For a Free On-Site Quote Visit Us At: http://www.ATIcourses.com/free_onsite_quote.aspFor Our Current Public Course Schedule Go To: http://www.ATIcourses.com/schedule.htm

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteGlobal Optimization While LMS methods are computationally fast, quantization of the phase will result in errors. Also, it is necessary to have receiver hardware at each element of the phased array as well as an elaborate calibration technique. Global search methods can place very deep nulls in the desired directions, while maintaining the characteristics of the antenna main beam. Since the solution space is predefined by the quantized amplitude and phase coefficients of the particular antenna system, these global methods do not require continuous amplitude and phase shifts. Additionally, these methods deal with the coherent output power of the antenna array and therefore do not require receiver hardware at each element in the antenna array.2

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteOptimization Methods Methods Local Global Conjugate Gradient Random Walk Methods Quasi-Newton Particle Swarm Methods Genetic Simplex Algorithms3

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteOptimization Methods Conjugate Random Genetic Gradient Walk Algorithm Global Optimization Poor Fair GoodDiscontinuous Functions Poor Good Good Non-differentiable Poor Good Good Functions Convergence Rate Good Poor Fair4

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteGenetic Algorithms Genetic Algorithms (GA) are robust, stochastic-based search methods, modeled on the concepts of natural selection. The strong survive to pass on their genes, while the weak are eliminated from the population. Examples  Design of layered material for broadband microwave absorbers.  Extraction of natural resonance modes of radar targets from backscattered response data.  Economics, Ecology, Social Systems, Machine Learning, Chemistry, Physics, etc.5

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTerminology Population – set of trial solutions. Generation – successively created populations. Parent – member of the current generation. Child – member of the next generation. Chromosome – coded form of a trial solution. Fitness – a chromosomes measure of goodness.6

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteChromosome Coding GAs operate on a coding of the parameters, instead of the parameters themselves. In binary coding, the parameters are each represented by a finite- length binary string. Chromosomes are the combination of all the encoded parameters. (A string of ones and zeros) Binary coding yields very simple binary operators. R1 L1 C1 R2 L2 C2 0101 1001 1101 1010 0001 00117

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteGenetic Algorithm Initialize Population Evaluate Fitness Selection of Parents CrossOver and Mutation No No Temp Population Full? Yes Replace Population Evaluate Fitness Termination Criteria Met? Yes End8

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteInitialize Population Random Fill – The initial population is created by filling chromosomes with random numbers. A Priori – Chromosomes in the initial population are created with information about the solution.9

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteParent Selection Proportionate selection – Probability of selecting an individual is a function of the individual’s relative fitness. 1 2 3 4 5 6 7 8 910

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteParent Selection Tournament selection – N individuals are selected at random, the individual with the highest fitness in the sub population is selected. N Parent = Population randomly selected Chromosome chromosomes with best Fitness11

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteCrossover and Mutation The crossover and mutation operations accept the parent chromosomes and generate the children. Many variations of crossover have been developed, with single-point crossover being the simplest. In mutation, an element in the chromosome is randomly selected and changed.12

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteCrossover and Mutation Single Point Crossover Parent 1 a1 a2 a3 a4 a5 b1 b2 b3 b4 b5 Parent 2 Child 1 a1 a2 b3 b4 b5 b1 b2 a3 a4 a5 Child 2 Mutation a1 a2 a3 a4 a5 a6 a7 a1 a2 A3 a4 a5 a6 a713

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstitutePopulation Replacement Generational – The GA produces an entirely new generation of children, which then replaces the parent generation. Steady-State – Only a portion of the current generation is replaced by children.14

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteFitness Function The only connection between the physical problem and the GA. The value returned by the fitness function is proportional to the goodness of a trial solution.15

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteGA Optimization Guidelines Population Size: Typically 30 – 100  Large populations enable faster convergence by providing more genetic diversity. Smaller populations yield faster execution, especially for complicated fitness functions. Probability of Crossover: Typically 0.6 – 0.9  Crossover is the primary way a GA searches for new, better solutions. A probability of 0.7 has been found to be optimal for a wide variety of problems. Probability of Mutation: Typically 0.01 – 0.1  The probability of mutation should generally be low. Mutation introduces new genetic material into the search, but tends to push the population’s average fitness away from the optimal value. Replacement Strategy: Generational vs. Steady-State  Steady-state generally converges faster. Lower values of replacement percentage usually converge faster.16

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteParticle Swarm Originated in studies of bird flocking and fish schooling. The potential solutions (Particles) “fly” through the solution space subject to both deterministic and stochastic rules. Particles are pulled toward the local and global best solution with linear attraction forces.17

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology Institute Harmonious FlightThe ability of animal groups—such as this flock of starlings—to shift shape as one, even when theyhave no leader, reflects the genius of collective behavior—something scientists are now tapping to solve human problems.National Geographic 2007 18

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteParticle Swarm Initialize Swarm Evaluate Fitness Update Velocities (Vn) No Update Positions (Xn) Evaluate Fitness Termination Criteria Met? Yes End19

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteInitialize Swarm Random Fill – The initial swarm is created by giving each particle a random position and random velocity. A Priori – Particles in the initial swarm are created with information about the solution.20

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteUpdate Velocities Update the velocity of each particle toward the local and global best position. vn = ω ⋅ vn + κ1 ⋅ rand ⋅ (xlocal best ,n − xn )     + κ 2 ⋅ rand ⋅ (x global best ,n − xn )   Limit the velocity if necessary.    v if vn > vmax , then vn = n vmax vn21

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteUpdate Positions Update position using unit acceleration.    xn = xn + vn Clip position if necessary. if xn ,d > xmax,d , then xn ,d = xmax,d if xn ,d < xmin,d , then xn ,d = xmin,d22

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteParticle Swarm Guidelines ω (Inertia) – Typical values between 0 – 1. This may be allowed to vary randomly for each iteration or decrease with each iteration to encourage local searching at the end of the process. κ1 , κ 2 (Memory & Cooperation) – Can be tuned for the particular problem. Common practice in literature to set both equal in the range 1 – 2.23

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteMATLAB Example Find the minimum of the following function.24

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteMATLAB Example Find the minimum of the follow function.25

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteAntenna Pattern Suppose we want to minimize the antenna gain in a particular direction due to an interfering source (Adaptive Nulling). N M AF (θ , φ ) = ∑∑ I mn e jβ mn e jα mn n =1 m =1 I mn = Amplitude coefficient for each element β mn = Phase shift for each element 2π α mn = [xmn sin θ cos φ + ymn sin θ sin φ ] λ26

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources 16 x 16 element planar array 6 bit phase shifters, 3 bits used for nulling 2 interfering sources located at (θ = 18o, φ = 0o) and (θ = 26o, φ = 90o) 50 Chromosomes / Particles 200 Iterations27

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources Location of Interfering Sources28

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources Genetic Algorithm Particle Swarm Nulls Placed in the Antenna Pattern in the Direction of the Interfering Sources29

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources Interfering Source30

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources Interfering Source31

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources32

Radar Signal Analysis and Processing with MATLAB ♦ Applied Technology InstituteTwo Interfering Sources  Main Beam Loss  1.02 dB (Genetic Algorithm)  1.63 dB (Particle Swarm)  Beamwidth Original GA PS Φ = 0o 3 dB 6.29o 6.30o 6.35o 10 dB 10.48o 10.50o 10.60o Φ = 90o 3 dB 6.29o 6.30o 6.35o 10 dB 10.48o 10.52o 10.59o33

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ATI's Radar Signal Analysis and Processing using MATLAB Technical Training Short Course Sampler

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