Circular Patch Array for Smart Antenna in C-Band

Smart Antennas have recently received increasing for improving the performance of wireless radio systems. The aim of the paper is twofold. One is to design and simulate an antenna array operating in C-band (4–8 GHz) and the other is the design of beamforming algorithm used in smart antenna. In this paper, the first module presents the design of eight circular sector patch elements suitable for beamforming technique in wireless applications. The second module suggests a MP (Matrix Pencil) to accurately estimate the DOA (Direction of Arrival) of the signal of interest, and LMS algorithm for beamforming technique to concentrate the power in the desired direction and nullify the power in the interferer direct ion. The modelling and simulat ion of antenna array is computed using HFSS. The beamforming algorithm is designed in Matlab.


Introduction
The rising importance of wireless communicat ion and mu ltimed ia services is increasing the efforts of design and implementation of novel microstrip patch structures from miniaturized electronic circuits to the antenna arrays [1]. The main advantages of patch antenna [2]: light weight, low cost, planar or conformal and ability of integration with electronic or signal processing circuitry. A detailed study of circular sector patch antenna is presented in [3]. This antenna has interesting dimension, so it can be integrated easily in antenna array.
Recently , Smart antenna [4][5] have received increasing interest for improving the performance of wireless radio systems, their application has been suggested for mobileco mmun icat ions systems, to overco me the prob lem of limited channel bandwidth, satisfying a growing demand for a large nu mber of mobiles on communicat ions channels. However Conventional Antenna systems, which emp loy a single antenna, radiate and receive in formation equally in all direct ions. This omnidirectional radiation leads to the distribution of energy in all direct ions. This Wasted power becomes a potential source of interference for other users or for other base stations in other cells. On The other hand, smart antennas consist of an antenna array, co mbined with signal processing in both space and time, they are capable o f auto matically ch ang ing th e d irection ality o f th eir rad iat io n p atterns in th e res p o ns e to th eir s ig n al environment so they basically attempt to enhance the desired signal power and suppress the interferers by beamforming toward the DOA (direction of arrival) of the desired signal and null steering in the case of the interferences. The smart antenna systems can be divided into two categories. These are: switched beam system, and adaptive arrays. In this paper adaptive arrays are investigated and used for smart antenna model.
The key problem in explo iting the capabilit ies provided by a smart antenna at receiver is in determining the direction of the interfering signals and forming a beam towards the transmitter. The Matrix Pencil algorithm [6][7][8][9] is proposed as a super-resolution parameter estimation technique DOA. Matrix Pencil has some key advantages over the other super-resolution methods for parameter estimation, unlike other techniques, which generally need an estimat ion of the signal covariance matrix, Matrix Pencil deals directly with signal samples and does not require independent data samples. Furthermore, the Matrix Pencil algorith m requires less processing power and executes faster than some other super-resolution methods. One o f the advantages of this technique is that the correlation among the received signals does not have a significant impact on its performances and efficiency. This paper is organized as follow: Design and simulate of circular sector patch elements are presented in section II. In section III, DOA estimation algorith m is developed. Then, the DOA algorith m supplies this informat ion to the beamformer to orient the maximu m of the rad iation pattern toward the SOI (Signal Of Interest) and to reject the interference by placing nulls toward their direction, followed by the conclusion.

Substrate Selection
Most of the microstrip antenna research in the past has emp loyed electrically thin, lo w permittiv ity substrates. Recent interest in millimeter wave systems and miniaturized structure [10], however, has created a need for substrates that are electrically thicker, and/or have high permittiv ity. Increased bandwidth is another reason for interest in electrically thicker substrates. The proposed antennas are designed using the substrate RO3210 (εr = 10.2 tanδ = 0.0035) based on Polytetrafluorel (PTFE) which is widely used because of their electrical and mechanical characteristics [2], minimu m cost and permit to have a miniature antenna with a minimu m loss.

Choice o f Feed ing
The most used feeding mode for patch antenna: Microstrip line, coaxial cable or pro ximity coupling. The feeding microstrip line and coaxial cable feed are easy to implement, however, this type of power generating spurious radiation wh ich affects the radiation pattern. The proximity coupling offer greater bandwidth and better radiation pattern but it's not easy to implement. In this paper we have chosen to feed our antenna via a microstrip line [10]. For the proposed design, the substrate is RO3200 (εr = 10.2), thickness h=0.127 cm. The angle and radius of circular sector patch are respectively α = 90° and a=1cm. Figure 3 shows the architecture of the proposed antenna.

Array Design
A uniform array is defined by uniformly-spaced identical elements of equal magnitude with a linearly progressive phase fro m element to element. Figure 2. Linear phased array [6] It is assumed that each succeeding element has a progressive phase lead current excitation relat ive to the preceding one. An array of identical elements with identical magnitudes and with a progressive phase is called a uniform array.
The AF can be obtained by considering the individual elements as point (isotropic) sources. If the elements are of any other pattern, the total field pattern can be obtained by simp ly multip lying the AF by the normalized field pattern of the individual element [11].
The function ψ is defined as the array phase function and is a function of the element spacing, phase shift, frequency and elevation angle: = + (3) Where β=2π/λ is the phase propagation factor. Studied array will be designed using HFSS. The software enables to compute antenna array radiation patterns and antenna parameters. HFSS models the array radiation pattern by applying an "array factor" to the single element's pattern [12]. Figure 3 present studied arrays with an inter-element distance of 0.6λ and number of element is 4 and 8.    For array of 4 and 8 elements, we got the same curve of single element. So changing number of element didn't impact return loss of antenna.

Rad iation Pattern
The radiation pattern of an antenna is important in determining most of the characteristics which include beamdwidth, beam shape, directiv ity and radiated power. Radiat ion pattern is computed using HFSS. So in this section, we trace radiat ion pattern for single element, array of 4 and 8 elements. In figure 5, we traced radiation pattern in E-plan of circular sector antenna. Main lobe is directive and there is no secondary lobe. Figure 6, shows radiation pattern of 4 array element. The main lobe is more directive than single element pattern, but there is more secondary lobe.  It can be observed clearly that the beam widths of all major lobes became narrow and the number of minor lobes increases, when the number of element increases.

Directiv ity and Gain
The directiv ity is a measure of the d irectional properties of an antenna compared to the isotropic antenna. The gain of the antenna directly depends on the radiation efficiency and the directivity of the antenna [11].
The table 1 shows generated gain and directivity for circular sector antenna array for d ifferent nu mber of elements (M = 1; 4; 8). For array with larger the number of elements, the total gain and directivity increase. But we cannot increase number of element to infinite nu mber, it 's important to take in consideration the dimension of array[13].

Smart Antenna
A smart antenna is an antenna array system aided by some smart algorith m designed to adapt to different signal environments. A s mart antenna is an antenna system that can modify its beam pattern or other parameters, by means of internal feedback control while the antenna system is operating.
The basic idea behind s mart antennas is that mult iple antennas processed simultaneously allow static or dynamical spatial processing with fixed antenna topology. The pattern of the antenna in its totality is now depending partly on its geometry but even mo re on the processing of the signals of the antennas individually. Several algorithms have been developed based on different criteria to co mpute the complex weights[14-15].

S t S t S t S t S t
The noise vector by Now if we consider all sources simultaneously, the signal at the mth element will be: And array factor We can now write in matrix notation:

t AS t n t = +
(10) Let's denote the weights of the beamformer as: Where W is called the array weight vector. The total array output will be: Where superscripts T and H, respectively, denote the transpose and complex conjugate transpose of a vector or matrix.

DOA Esti mation
In this paper, we use Matrix Pencil to determinate DOA of signals impinging on smart antenna.
Consider the following ( 1 M L L − × + ) matrix formed using data fro m equation (11): Where L is called the pencil parameter. Now we define two ( M L L − × ) matrices H1 and H2 as: These two matrices can be written as: Where: [ ] Our goal is to estimate the entries of the matrix Z0. Consider the following matrix pencil, Here I is the (d xd) identity matrix. The estimates of zi are, therefore, the generalized eigenvalues of the matrix pair[Y1,Y2] .Once the values of zi are estimated, we can estimate DOA: Where Im[ zi] is the imaginary part of zi.

Adapti ve Beamforming
Using the information supplied by the DOA, the adaptive algorith m co mputes the appropriate complex weights to direct the maximu m radiat ion of the antenna pattern toward the SOI and places nulls toward interferes. The adaptive beamforming algorith m chosen in this project is the LMS for its lo w co mplexity [16][17]. The LM S algorith m is an approximation o f the steepest descent method using an estimator of the gradient instead of the actual value of the gradient. This simp lifies considerably the calculat ions to perform and allows the LMS algorithm to be perfo rmed in real t ime. Based on the array geometry of Figure 8 µ is a step size parameter wh ich is related to the rate of convergence; however, convergence of the w(n) is assured by the following condition: Where λ max is the largest eigenvalue of autocorrelation matrix Rxx o f received signal.

Results Simulations
The simulated system consists of an eight linear arrangement of circular sector antenna array spaced by distance d = 0.6 λ. The received signal arrives at an angle of 50 degrees, interferers arrives at 25 and 80 degrees, the SNR=20 d B. After the antenna array receives all the signals fro m all directions, the DOA algorith m determines the directions of all imp inged signals on antenna array as shown in table 2. Then an adaptive array is simulated in Matlab by using the LMS algorith m. The true array output y(n) is converging to the desired signal d(n). The interferers are cancelled by p lacing nulls in the direction of the interferers. We have chosen step size = 0,01 for our simu lation. After the calculating weights in Matlab simu lation we apply the normalized weights as excitations in the designed antenna array.
The resulting antenna array gain pattern is shown in Figure 9 for three frequencies F1=4.48 GHz, F2=5.27 GHz and F3=7.8GHz using Matlab. Fro m Table 2, Matrix Pencil can accuracy estimate DOA of signals imp inging on array antenna with SNR=20 d B for the three frequencies. Figure 9 g ives good results for three frequencies, the main beam is centred on the direction of desired DOA, the side lobes are at least -30 dB belo w the main beam and Zeros are all belo w -100 dB.    Figures 10-13 show the error between the output and the reference signal over 500 iterat ions for three frequencies, the error decreases much faster, consequently the convergence is reached after about 50 iterations, and the final error is very low.

Conclusions
In this paper, we have presented an antenna array operating in C-band (4-8 GHz), which consists of eight circular sector patch elements. This antenna array has advantage to resonate at three frequencies: 4.48 GHz, 5.27GHz and 7.8 GHz. The design of this antenna was studied and simulated using HFSS. DOA of desired and interferes signals was accurately estimated by Matrix Pencil method. After LM S algorithm was applied to direct the main beam towards the desired signal and form nulls in the directions of interferes, consequently simu lations demonstrate that this antenna is feasible for integration on smart antenna systems.
[13] V.R.Anitha and N.Reddy "Design of an 8x1 square microstrip patch antenna array" International Journal of electronic engineering research Vol .