Amplitude and Phase Adaptive Nulling with a Genetic Algorithm for Array Antennas Le Quang Thao, Nguyen Ngoc Dinh, Dam Trung Thong Radio Physics Department, Physics Faculty Hanoi University of Science, VNU Hanoi, Vietnam thaolq@vnu.edu.vn Tel: 84.4.858.2254 Mobile: 84.983.712.941 Abstract - This paper researchs an efficient by using the genetic algorithm apply in amplitude and phase to adaptive nulling for phase array antennas A genetic algorithm adjusts some of the least significant bits of the beam steering phase shifters and amplitude weights in order to minimize the total output power and place nulling in the jammes Using a few bits for nulling speeds convergence of the algorithm and limits pattern distortions Various results are presented to show the advantages of this approach Keywords: phase array antenna, genetic algorithm, adaptive nulling I INTRODUCTION Almost radar system while the frequency spectrum becomes more crowded, they become more vulnerable to interference When the mainbeam gain times the desired signal is less than the sidelobe gain times the interference signal, the desired signal is overwhelmed by the interference A smart or adaptive antenna is one alternative for recovering desirable signals A smart antenna adapts its receive and/or transmit pattern characteristics in order to improve the antenna’s performance It may place a null in the direction of an interference source or steer the mainbeam in the direction of a desired signal At least two different antennas constitute a smart antenna, they known as an antenna array The amplitude and phase of the received signals are weighted and summed in such a way as to meet some desired performance expectation MIMO (multiple input /multiple output) communications systems have adaptive transmit and receive antennas Adaptive nulling complements the low sidelobe antenna by placing nulls in a few low sidelobes to reject the strongest interfering sources Almost adaptive algorithm possesses some of these characteristics, but none of them meets all the characteristics, as a result, they not find the optimum weights to reject the interference at hand Some common adaptive algorithms include Least Mean Square Algorithm and Howells-Applebaum adaptive processor, and examples can be found in references [1] and [2] These methods are very fast but the difficulties mentioned prohibit their widespread use, particularly for arrays with more than a handful of elements settings in order to reduce the total output power from the array [3] and [4] These algorithms are cheap to implement because they use the existing array architecture without expensive additions, such as adjustable amplitude weights or more receivers Their drawbacks include slow convergence and possibly high pattern distortions This class has two approaches The fisrt approach to phase only nulling is to use a random search algorithm [5] Random search algorithms check a small number of all possible phase settings in search of the minimum output power The search space for the current algorithm iteration can be narrowed around the regions of the best weights of the previous iteration A second approach forms an approximate numerical gradient and uses a steepest descent algorithm to find the minimum output power [6] This approach has been implemented experimentally but is slow and gets trapped in local minima As a result, the best phase settings to achieve appropriate nulls are usually not found This paper describes a simple technique suitable for minimizing the total output power and place nulling in interference source by making small adjustments amplitude and phase perturbations at each element of phase arrays antennas The approach combines a genetic algorithm with the hardware limitations of the array to place nulls in the directions of interference with small perturbations to the far field pattern Excellent nulling results are possible for most interference experiment II A Theory of the array antennas A linear array antenna is a group of equally spaced antennas arranged along a line and whose outputs are added together to provide a single output Figure shows a diagram of such an array Mathematically, the array far field pattern is given by: Another class of algorithms adjusts the phase shifter 978-1-4577-0536-6/11/$26.00 ©2011 IEEE THE ARRAY ANTENNA AND THE ADAPTIVE ALGORITHM 1887 N AF = ¦ wn e jΨn n=1 Where: wn = anejĮn : amplitude complex weight at element n Ȍn : phase due to element position and observation direction N: number of elements in the array evolution Genetics is the study of the inheritance and variation of biological traits Manipulation of the forces behind genetics is found in breeding animals and genetic engineering Evolution is closely intertwined with genetics It results in genetic changes through natural selection, genetic drift, mutation, and migration Genetics and evolution result in a population that is adapted to succeed in its environment In other words, the population is optimized for its environment Figure Diagram of a phase array antennas In order to minimize total output power, which consists of the interference signal and possibly the desired signal, without sacrificing the desired signal requires the antenna to place nulls in the sidelobes and not the mainbeam It’s reasonable to assume that the desired signal enters the mainbeam and the interference enters the sidelobes Large phase shifts are required to place a null in the mainbeam Large reductions in the amplitude weights are required in order to reduce the mainbeam Consequently, if only small amplitude and phase perturbations are allowed, then a null can’t be placed in the mainbeam but can be placed in the sidelobes Lower sidelobes require smaller perturbations to the weights in order to place the null Using only a few least significant bits (LSBs) of the digital phase shifter and attenuator bits prevents the GA from placing nulls in the mainbeam The algorithm has the following steps as showed in figure Create an initial population Evaluate the fitness of each population member Invoke natural selection Select population members for mating Generate offspring Mutate selected members of the population Terminate run or go to step III EXPERIMENT RESULTS We consider with a 20 element adaptive linear array with elements spaced half a wavelength apart Assume the amplitude and phase weights have bits quantization If the only source enters the mainbeam, then the adaptive algorithm tries to reduce the mainbeam in order to reduce the total output power Figure shows the mainbeam reduction when 0-4 least significant bits (LSBs) in the amplitude weights are used for nulling Zero bits corresponds to the quiescent pattern A maximum reduction of dB is possible using bits of amplitude The adaptive algorithm is based on a genetic algorithm and uses a limited number of bits of the digital phase shifters and a few least significant attenator bits in amplitude weights A genetic algorithm is a computer program that finds an optimum solution by simulating evolution in nature In this application the phase shifter settings evolve until the antenna pattern has nulls in the directions of jammers and amplitude weights setting reduce the meanbeam A genetic algorithm was chosen for this application because it is an efficient method to perform a search of a very large, discrete space of phase settings to achieve the minimum output power of the array A genetic algorithm (GA) offers an alternative to traditional local search algorithms It is an optimization algorithm inspired by the well known biological processes of genetics and 1888 35 P ow er (dB ) B Theory of the adaptive algorithm Amplitude and phase adaptive nulling algorithm modifies the quantized phase and amlitude weights based on the total output power of the array If no interference is present, then the algorithm tries to minimize the desired signal To prevent desired signal degradation, the algorithm should only be turned on when the desired signal becomes swamped by the interference or the nulling phase shifts and amplitudes weights should be small This potential problem is discussed in more detail in the next section The disadvantages of the phase-only algorithms make them unlikely candidates for use with antenna arrays This section presents a method that is as fast as the beam space algorithm, doesn’t easily get stuck in local minima, and limits pattern distortion Figure Genetic algorithm flowchart 28 21 -90 -60 -30 Theta (degree) 30 60 90 Figure Mainbeam reduction depend on amplitude weight In contrast, Figure shows the mainbeam reduction when 0-4 LSBs least in the phase weights are used for nulling Using 1-3 LSBs results in very little perturbation to the mainbeam Unlike amplitude-only nulling, phase-only nulling causes beam squint Also, bits of phase had more effects on the mainbeam than did bits of amplitude This experiment demonstrates that adaptive nulling with the LSBs would not cause significant degradation to the mainbeam 35 Item Value Crossover probability Pc 50% Mutation probability Pm 10% Convergence of the algorithm is shown in Figure Generation represents the received signals from the quiescent pattern Generation is the best of the initial random population of the GA Performance levels off in about generations 30 28 Null deep (dB) P ower (dB) Definition 21 -100 -80 -40 Theta (degree) 40 80 Figure Mainbeam reduction depend on phase weight We consider the array has bits amplitude and phase weights Two LSBs of the amplitude weights and three of the phase weights are used for nulling [7] show in Figure The desired signal is incident on the peak of the mainbeam and is normalized to 14 or 15 dB One 0dB jammers enter the sidelobes at -300 10 15 20 25 30 Generation 35 40 45 50 Figure Genetic algorithm convergence Sometimes decreasing the null at one jammer location is done at the expense of the null at the other jammer location The total power output decreases monotonically, but the reduction in an individual jammer’s contribution to the total output power can go up or down The output power due to the desired signal remains relatively constant, because the mainbeam remains virtually unperturbed Nulls appear in the array factor at the angles of the jammers as shown in Figure The nulls come at a cost of increased average sidelobe level 16 Initial pattern Optimized pattern 14 -30 degree 12 Power (dB) 10 Figure The least signifi cant bits of the amplitude and phase weights The applied GA parameters are a population size of 20, a chromosome length of 18 bits and a 50% selection rate, uses roulette wheel selection and uniform crossover, and has a mutation rate of 10% This is summarized in Table TABLE I -100 Definition Value Subarray row number N 20 Population size M 20 Gene size P=N-1 Gene bits Q L=PxQ 18 Choromosome bits -80 -60 -40 -20 Theta (degree) 20 40 60 80 100 Figure Null are adaptively placed at -300 DESIGN PARAMETER FOR GA OPTIMIZATION Item The next example has the same array with two 0dB jammers enter the sidelobes at -200 and 200 Nulls appear in the array factor at the angles of the two jammers as shown in Figure 1889 Amplitude and phase adaptive nulling works on existing phased-array antenna designs, unlike signal processing based adaptive arrays that require receivers at every element Its main disadvantage is slow convergence time The genetic algorithm approach amplitude and phase adaptive nulling is significantly faster than the previous approaches of random search and gradient methods Thus, it advances the state of amplitude and phase adaptive nulling 15 - 20 degree Initial pattern Optimized pattern 20 degree P ower (dB ) 10 REFERENCES [1] -100 -80 -60 -40 -20 Theta (degree) 20 40 60 80 [2] 100 Figure Null are adaptively placed at -20 and 20 IV [3] CONCLUSIONS The genetic algorithm performed well for one and two jammers that were : Separated by an angular width of at least one sidelobe and were not symmetric in angular distance about the main beam Both the one or two jammers nulling showed fast convergence, deep nulling capability, and small pattern distortions Using only a few least significant bits and small phase values and amplitude weights for the MSB are keys to the algorithm’s performance Its important advantage is that it is easy to implement on existing phased arrays [4] [5] [6] [7] 1890 R A Monzingo and T W Miller, “Introduction to Adaptive Antennas”, New York: Wiley,1980 R T Compton, “Adaptive Antennas Concepts and Performance”, Englewood Cliffs, NJ: Prentice Hall, 1988 C A Baird and G G Rassweiler, “Adaptive sidelobe nulling using digitally controlled phase-shifters”, IEEE AP Trans 24(5):638–649 (Sept 1976) H Steyskal, “Simple method for pattern nulling by phase perturbation”, IEEE AP-S Trans 31(1):163–166 (Jan 1983) R L Haupt, “Phase-only adaptive nulling with genetic algorithms”, IEEE AP-S Trans 45(5):1009–1015 (June 1997) R L Haupt, “Adaptive nulling in monopulse antennas”, IEEE AP-S Trans 36(2):202–208 (Feb 1988) R L Haupt and Douglas H Werner, “Genetic Algorithms in electromagnetics”, pp 137–141.I A John Wiley & Sons, Inc., Publication 2007. ... signal processing based adaptive arrays that require receivers at every element Its main disadvantage is slow convergence time The genetic algorithm approach amplitude and phase adaptive nulling. .. sidelobes at -200 and 200 Nulls appear in the array factor at the angles of the two jammers as shown in Figure 1889 Amplitude and phase adaptive nulling works on existing phased -array antenna designs,... significantly faster than the previous approaches of random search and gradient methods Thus, it advances the state of amplitude and phase adaptive nulling 15 - 20 degree Initial pattern Optimized pattern