Electronics And Telecommunication Engineering Project: Sidelobe Reduction In Array Pattern Synthesis Using Genetic Algorithm
This project was based on the theoretical idea of sidelobe level (SLL) reduction. The importance of this technique in communication systems in recent times has been on the rise, as it is one of the most important techniques of digital beamforming. This technique is considered significant as it reduces the effect of interference arriving in the main lobe, which improves the capacity of communication systems. I decided to implement this technique by making use of Genetic Algorithms (GA), in which I used the decimal Single Point linear crossover method. Due to this, I was able to impose constraints on the phases and magnitudes of the complex excitation coefficients. This made the technique implementable in practice through the use of digital phase shifters and digital attenuators.
Project Purpose
The primary purpose of this project was to implement a technique of side lobe level reduction through the use of a genetic algorithm. I chose this project as my submission to the sixth-semester requirement of a mini project, so this was the other purpose behind the development of this project. I aimed to use the decimal single point linear crossover method of genetic algorithms to allow for the representation of array excitation weighing vectors as chromosomes. The algorithm that I intended to use accepted the radiation pattern desired, and then provided the excitation coefficients accordingly to realize this pattern.
Nature of Work Performed
The nature of the work performed in this project was based on and around Electronics and Telecommunication Engineering. It involved the identification of the problem, which was sidelobe level reduction, research, and experimentation to find out the best methods for achieving the goals required. There was also the setting up of the experiment, the analysis of the working of the experimental setup and the results obtained from it, along with the recording of all observations in a tabular format. The observations were also represented by means of some graphs, and MATLAB software was used to write the code required to implement the functionality of the project. To wrap things up, the conclusive statements were derived from the outcomes of the experiment.
People Involved in the Project
I worked on this project in a team of two members, where I was one of them. My teammate was also a student of the Department of Electronics and Telecommunication Engineering at Amity University. The project team was managed by the project mentor, who was one of the professors from the same department. The project mentor kept an eye on the project's advancement by sitting in on the team meetings that were held regularly. Also involved in the project was the Department's Head, Raj Kamal Kapur, to whom the presentation for the project was given, and the report was also signed off by him/ her. I have represented this structure of the project team in the figure given below.
Personal engineering activity
My Input
My contribution to this project was related to the experimentation and the designing of the solution. This required me to carry out some prior research to understand genetic algorithms, as well as the theory behind sidelobe reduction. Once that was done, I drafted a problem statement for this project, which also included the detailed description of the objectives set for the project. I then set up the experiment to carry out the required activities and I determined the design equations for the development of the genetic algorithm which I intended to use for the implementation of the side lobe level reduction technique. I also used MATLAB to simulate the test environment and checked the working of the system, following which I noted the observations obtained.
Research
I decided to start working on the project by studying the problem in detail, first. I, therefore, looked into various resources and books to find content related to sidelobe level reduction. I researched the various methods that can be used for achieving it, and I also carried out an investigation to determine the best method for implementing it in this project. I ended up selecting genetic algorithms, and so I also had to learn about them, including the different techniques of developing genetic algorithms and their various kinds. I studied these concepts by making use of different academic websites, case studies, research papers, etc. and I also consulted the books related to the curriculum of my engineering studies.
Experimental Setup
In this experiment, I decided to use RGA or Real-coded GA, because it made use of floating point number representations for the real variables and did not involve the use of binary encoding and decoding, thereby making it much faster than traditional binary GA. Then, for the setup of the experiment that I intended to conduct for the development of a genetic algorithm for side lobe reduction, I chose a broadside uniform linear array with a uniform spacing. I ensured that the array that I selected was symmetric with respect to the origin and had equal spacing between any and all consecutive elements. I also decided to check that the phase difference between any two given elements was fixed at the value of zero and that the RGA (Real-coded Genetic Algorithm) adjusted the excitation coefficients along with the location of the elements from the centre of the array towards the imposition of deeper nulls in the directions of interference. I also defined a cost function to keep the null and the side lobes at lower levels. In the figure given below, I have defined the geometry of a symmetric element along the Z axis.
This figure above represents my choice for the development of the design equations for the system, namely, a broadside linear antenna array of 2M isotropic radiators. I chose to excite each element by using the same uniform current and I assumed the elements of the array to be equally spaced along the Z-axis and uncoupled. I also assumed that the array's centre corresponded to the origin. The array that I chose was symmetric in terms of the geometry, and the excitation with respect to the centre. And, an array that was made up of identical elements that were also oriented identically had a far-field radiation pattern. This radiation pattern can be expressed as the product of the array factor, and the element pattern. The array factor is unique to every array and is a function of the number of elements present in the array, their arrangement geometrically, their relative spacing, relative phases and relative magnitudes. As the array factor depended on these parameters, and not on the direction characteristics of the radiating elements, I decided to formulate it by the replacement of the actual elements of the array with point/ isotropic sources. The array factor, AF (I, φ, d), was calculated by me for the array represented in the figure, in the azimuth plane (x-y plane) with a symmetric amplitude distribution, by: Here, was the zenith angle that was measured from the broadside direction of the array,d was the spacing between two consecutive elements, and , and k are the wave numbers, with λ = the signal wavelength.
The elements of the array were numbered, from the origin in a symmetric array, from 1 to N/2 and the total number of elements was N. In case of the optimization problem of the null placement in the far field pattern of the array, the array factor at the particular null position had to be less than the reference pattern of the array. In the same way, for the reduction of side lobe problem, the values of the array factor at the peaks of side-lobe had to be less than the reference pattern as well. Therefore, I had to include the array function in the expression for the cost function in order to satisfy this requirement. Then, to introduce the deeper null and reduce the side lobe level, the cost function was minimized with respect to the RGA, given below: Here, m was the maximum number of positions at which null can be imposedAF(nulli) was the array factor value at a particular null positionAFmax was the maximum value of the array factorK was the number of side lobes in the original patternQk was the SLL in dB that was generated by the individual population at a peak point θkand, δ was the value of the desired sidelobe level in dBThen, the function H(k) was defined by me as follows: FNBWcomputed and FNBW(In = 1) were the two beam widths, the first being the computed null beam width in radians for non-uniform excitation for optimal spacing, while the second was for uniform excitation (In = 1) having a uniform spacing between the elements, namely (d = λ/2). I plotted a graph representing the radiation pattern of an antenna's side lobe levels in dB versus its angle of arrival in degrees, and this has been shown below.
Observation and Analysis
After I had come up with the design equations and the necessary computations were done, I moved on to the observation of the working of the system. I carried out this process by taking two examples in which the genetic algorithm was carried out in ten runs, each of 1000 iterations. I also set the CPU time for 100 iterations to be 120 s in the software MATLAB, version 7.12.9.2011a. I used a PC having a processor of 2.13 GHz and a 32-bit operating system. The initial weighing vectors were randomly generated for this example.
I used a broadside linear array having 30 isotropic elements, each of which was equally spaced at the half wavelength. There were six positive excitation amplitude sets in the initial parent population, and I used the method of symmetric excitation. The crossover operation was performed by me on half the chromosomes after I had copied them to the other half in the mirror image format.
Summary
By performing this project, I acquired the invaluable experience of working on practical systems and implementing my academic knowledge in an actual, real-life application. I also enhanced my knowledge of various topics, since I had to conduct a great deal of research when I took up this project. Additionally, I learned how to divide and manage my time, to effectively balance academics as well as the project, and the various phases of the project itself.
