Spiral Array Design with Particle Swarm Optimization

Rilin Chen, Pengxiao Teng, Yichun Yang

Key laboratory of noise and vibration research Institute of Acoustics, Chinese Academy of Sciences

Beijing, China chenrl@mail.ioa.ac.cn

AbstractIn this paper, a novel optimization method based on the particle swarm optimization (PSO) algorithm for the array design is proposed. The PSO is introduced to search for the optimal microphone distribution on the Archimedes spiral line with the minimum sidelobe level and the narrow mainlobe width. Numerical simulation show the better performance of the array reconfiguration designed by means of PSO algorithm. Experime-nts in the semi-anechoic room demonstrate the effectiveness of the proposed scheme.

Keywords- spiral Array;PSO; microphone distribution;

I. INTRODUCTION Recent studies of microphone arrays embraced a wide

range of applications, including multimedia communication, speech recognition, video conference system, mobile robot and falut source localization [1]. Beamforming of planar microph-one array overlapped with the video image, which is regarded as acoustic imaging or acoustic camera [2], is an established technique for efficient and accurate noise source localization and measurement. Performance of planar arrays is determined by many parameters, such as the number of microphones, array design (microphone distribution), and the aperture of array. It is desired to optimize microphone distribution that fulfill specific requirements, like the mainlobe width (MLW) and the sidelobe level (SLL) which will affect the accuracy of localization and measurement by the arrays. On the condition of the same number of microphones and the same aperture of arrays, array configuration design is the dominant factor for the performance. Therefore, searching for the best microphone distribution is an important work to acquire optimal performance.

In array design process, the objective function and constraint condition are always nonlinear and nondifferentiab-le. Therefore, heuristic methods, like genetic algorithm (GA) [3] and particle swarm optimization (PSO) [4, 5] are often adopted to solve these problems. GA is very efficient at exploring the entire search space, but it is relatively poor in finding the precise local optimal solution in the region where the algorithm converges. Particle swarm optimization is similar in some ways to genetic algorithms, but is much easier to understand and implement and can find much precise solution. Particle swarm optimization which was developed by Kenney and Eberhart originated in studies of the social behavior of birds flocking and fish schooling in their search for food [6] when the researchers realized that their simulation algorithms

possessed an optimizing process. During the optimization process of PSO, members of this population are flying according to their previous flying experience, including their individual and the swarm experience. It is accomplished by adjusting their decision parameters toward the two best solution Pbest that is the best individual found so far by that individual, and Gbest that is the best individual previously by the population.

So, particle swarm optimization is desired to optimize the array design. In common, many researches are based on the rectangular grid by making some grid point on or off to accomplish a new reconfiguration of microphones. The present work is to find the best array design on the Archimedes spiral line, which clearly showed its advantage that is able to keep much greater performance [7].

The structure of this paper is as follows: In Section , the beampattern formula is described. In Section , the particle swarm optimization approach for array design is presented in detail. In Section , data simulations and results are presented and discussed. Finally, conclusions are given in Section .

II. BEAMPATTERN FORMULA Beampattern reflects the spatial localization accuracy and

separation ability of a microphone planar array. The mainlobe width shows its separation ability for different sources. The narrower the mainlobe is, the stronger the spatial separation ability is. If the mainlobe width is too wide, the array will not be able to separate multi-sources. The sidelobe level indicates the interference rejection capability of arrays. The sidelobe of lower level will increase its anti-interference ability.

Figure 1. Model of incident plane wave

Y

X

Plane wave

P4

P3

P5

P2 P1

Z

In Fig. 1, there is incident plane wave to the spiral array (z=0), so the time delay relative to the physical center of the array is as follows:

mmt c =

kp (1)

where c is the sound speed; pm is the position vector of the microphone m; k is the wavenumber.

sin cossin sin

cos

x

y

z

uuu

=

k = (2)

where (, ) is the direction of the incident plane wave. The beampattern of the spiral array can be expressed as:

( ) 21

1,

Tm

Mj f c

i

B f eM

=

= p kk (3) where f is the frequency of the incident plane wave and M is the number of microphones. Without loss of generality, it is assumed that =90 which make uz=0. The wavenumber (2) will be simplified to

x

y

uu

=

k (4)

where -1ux1, -1uy1. The mainlobe width of the beampattern is expressed as:

( ), 2MLW fd

=k (5)

where is the wavelength of incident plane wave;

d is the aperture of the spiral array; is the correction factor of aperture equivalent. The sidelobe level can be written as:

( )( )

( ), 2 2

, max ,MLW f

SSL f B f