# 英文report怎么写 Phased Array Antennas For Mobile Earth

## 2.4 Two element array

Two infinitesimal dipole antennas will be considered, the elements are arranged in a linear horizontal plane, the entire field strength in the far-field region can be found using equation 2.1.

Where and are the respective electric field strengths of elements 1 and 2.

Equation 2.1 Total far field electric field strength of 2 horizontally arranged dipole antennas.

Figure 2.1. two element array with far-field observation

The driving current phase difference between each element is given by Î² and the magnitude of current driving each element is the same across all elements, note this is for the far-field conditions.

From figure 2.2 the far-field, angles and distances can be written as.

This leads to simplifying equation 2.1 which is now written as equation 2.6.

As equation 2.6 indicates the complete field strength of the array is the field strength of a single element which is positioned at the origin, which when multiplied by a value referred to as the array factor (AF) gives the total field strength.

The array factor AF is a very important factor in the design of phased array antennas for the 2 element array it is given by equation 2.7.

The physical separation distance d and excitation phase Î² between each antenna elements control the complete field strength of the array. Therefore the field strength can be determined through what is termed pattern multiplication which is valid where identical antenna elements are used. It is the product of the far-field of a single antenna element, determined at a central reference point, then multiplied with the AF.

The method to find AF for two identical elements can be generalized to for N-elements, the reader is recommended to refer to [6] Balanis 3rd edition chapter 6 for a complete theoretical analysis of phased array antennas.

## 3.1 Introduction

Radio signals transmitted via satellite are subjected to various impairments which may cause the received signal to be attenuated severely. In a mobile satellite link (mobile earth station to satellite or vice versa) signal attenuation is mainly due to the free space loss, shadowing, multipath propagation and signal interference [7].

A phased array antenna will be used to improve the network reception in a multipath channel.

Figure 3.1.mobile earth station system architecture.

## 3.2. Multipath fading and phased array antennas

Previous researchers have proposed an adaptive phased array antenna which is based on a non-linear method, an “on-off” adaptive algorithm to adjust and control the phase angle of driving current at each element in the antenna system in order to control automatically its directivity pattern to enhance the received signal [8].

The algorithm attempts to maximize output power of the array in the estimated direction of the wanted signal.

Figure 3.2. adaptive linear phased array antenna with equally spaced N-elements.

In figure 3.2 the antenna elements are driven with a controllable phase this enables the beam of the antenna to be directed.

If we assume that K narrow-band correlated signals are incident on the array. The complex signal at the ith antenna element can be written as follows:

(3.1)

Where Ak is the complex valued attenuation constant determined by the propagation path, s(t) is the complex envelope ni(t) , is a random Quantity which denotes the thermal noise at the Ith antenna element and Î¦k is the electrical phase between the adjacent antenna elements Which can be written as :

(3.2)

Where Î¦k represents the arrival angle from the broadside of the array, Î» the carrier wavelength and d the inter-element spacing.

As shown in figure, the signal Xi (t) from each element is multiplied by a weighting coefficient wi. The wi (i=1,â€¦N) represents complex variable weights in phase which are controlled under a new adaptive algorithm.