Modelling and Simulation of a Planar Phased Array Antenna for Low Earth Orbit (LEO) Satellite Tracking

S.H. Harding 08040801Department of Computing, London Metropolitan University, Tower Building, North Campus

Abstract

Low earth orbit (LEO) satellites are widely used in the provision of mobile satellite personal communication services (S-PCS) and have become complementary to the terrestrial based cellular providers. LEO S-PCS suffer from some of the link degrading factors that affect cellular systems such as interference and multi-path fading and attempts at increasing system capacity and performance generally require eliminating or mitigating these effects. Antennas used in the handheld units of most LEO S-PCS are usually omni-directional antennas that transmit and receive signals from all directions and are therefore exposed to the effects of fading and interference. A smart antenna system that is capable of reducing these effects is proposed. The phased array antenna has the ability to form very directional beams that can be pointed directly to the satellite and produce nulls in directions of interfering signals. In addition, the main beam of the antenna can be continuously steered to keep track of the satellite.

1. Introduction

Interference from sources such as: terrestrial base stations, other satellite systems operating in the same frequency bands and other users within the same cell sites play a major limiting role on the capacity of satellite personal communications systems and therefore one way to increase capacity is to minimize its effects [1]. The antennas designed for use in most satellite personal communications terminals are usually Omni-directional or wide-angle antennas which usually pick up more echo power than directive antennas [2]. They therefore receive signals from all directions and are

consequently susceptible to multi path fading. Multiple antenna techniques such as diversity and adaptive antenna arrays can be implemented to combat the effects of interference and fading in order to improve the link quality without increasing the transmitted power or bandwidth in wireless communications systems. The several ways and configurations in which multiple antenna systems could be implemented in wireless communications systems are discussed. However, Since it has been projected that the greatest improvements in system capacity still to come in the wireless communications industry will be from the use of the beamforming technique [3], this work aims to investigate the use of a beamforming planar phased array antenna in interference nulling as well as beam pointing in LEO S-PCS. A mathematical model of the planar phased array system is presented and analyzed. A phased array antenna system that is capable of tracking a LEO satellite designed and simulated based on the presented mathematical model.

2. Multiple Antenna Techniques

Receiving multiple copies of the same signal at different times and with different levels of attenuation eventually leads to intersymbol interference (ISI). In addition, under the frequency reuse arrangements of cellular systems, there is bound to be a certain degree of interference between co-channel cells which is termed as co-channel interference. To achieve maximum system capacity and signal-to-noise ratio, all these forms of interference must be kept at their

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absolute minimum [4]. One way of achieving this is through multiple antenna systems whereby increases in channel capacity are attained by exploiting the spatial dimension of the wireless communication link. Diversity, Spatial multiplexing and beamforming phased arrays are three such multiple techniques.

2.1. Diversity

Diversity is one of the most powerful techniques used in combating fading over wireless channels. Fading results in the attenuation of the received signal when the transmitted signal arrives via different paths at the receiver and these multipath signals cancel each other destructively. The diversity technique is implemented using the fact that there is a very low probability that the individual signal paths will each experience the same level of fading. Therefore, it is reasonable to assume that if multiple uncorrelated antennas are used, they will each undergo fading independently of each other. Therefore, an adequate signal level can be achieved by switching or combining between antennas that are not experiencing a fade when other antennas are undergoing this period of fading.

There are several means of ensuring that the multiple antennas are uncorrelated and will ensure independent fading paths. The simplest method is through space diversity in which the multiple transmit or receive antenna elements are separated at a certain distance [5]. Polarization diversity is implemented using two antennas with horizontal and vertical polarization resulting in horizontally and vertically polarized waves [6]. Angle diversity is achieved through the use of directional antennas and is implemented by limiting the receive antenna beamwidth to a certain angle.

2.2. Spatial Multiplexing

Spatial multiplexing is a multiple antenna technique which involves multiplexing

independent data stream in space. In other words, uncoded symbols are transmitted independently over different antennas and at different symbol times [5]. This process is illustrated in Figure 1 in which independent symbols are transmitted over all transmit antennas at every symbol period and received by all receive antennas thus ensuring full diversity gain.

Figure 1: Spatial Multiplexing with Serial Encoding [7]

2.3. Phased Arrays

Phased array antennas are antenna arrays with adjustable phase at each antenna element such that it can be steered to the incoming angle of the strongest multipath component [7].

Figure 2: A Phased array transmitter [8]

They can be used to provide directional antenna gain to both the transmit antenna array as well as the receive antenna array. Phased arrays are sometimes referred to as smart antennas or adaptive antennas. Due to their beamforming capabilities these types of antennas are used to form directional beams that reduce fading and suppress

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interference between users thereby increasing system capacity [9].

3. Phased Array Antenna Modelling

Geometrically, antenna arrays can be configured in a linear, planar or circular arrangement. An N-element linear array is modeled first and the discussion is then focused on planar arrays.

Figure 3: N-element array [10]

The total far-field radiation pattern of the N-element array of identical elements shown in Figure 3 is the product of the field of a single element and the array factor [10]. Therefore,

(1)

The array factor can be expressed as

(2)

(3)

(4)

Where is the distance between the array

elements, the phase difference between

the elements and the wavenumber.

Therefore, the formation and distribution of the array factor can be controlled by prudent selection of the progressive phase between the elements that make up the array.

Figure 4: Planar array with M elements along x-axis

and N elements along y-axis [10]

The array factor of a planar array will be established by placing M elements along the x-axis and N elements along the y-axis as illustrated in Figure 4.

The array factor due to the uniform- amplitude M elements placed along the x-axis can be expressed as

(5)

Likewise, the array factor due to the N elements placed along the y-axis is

(6)

The array factor for the entire planar array is given in [11] as

(7)

(8)

(9)

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The main beam of the array factor occurs when .

If the main beam is required and it is to be

pointed along the direction and, then the progressive phase shift

between the elements must be made according to [11]

(10)

(11)

This is the basic operating principle of planar phased array antennas and it demonstrates that the direction of the main beams of both and can be steered by controlling the phase shifts and) between the elements positioned along the x and y axes respectively.

4. L Band LEO Satellite Tracking

In this section an L Band LEO satellite tracking system is designed and analyzed using a program written and implemented in MATLAB. The main objective of the designed tracking system is to enable the pointing of the main beam of the planar phased array antenna to keep track of the LEO satellite’s position. The antenna is designed using microstrip patches as the individual elements of the array.

The specifications of the L band antenna are:

1. Uplink and Downlink Frequency: 1.7 GHz

2. Number of microstrip elements along x axis (M): 20

3. Number of microstrip elements along y axis (N): 20

4. Phase shift between the elements

along x-axis: ) = 0 5. Phase shift between the elements

along x-axis: ) = 06. Spacing between the elements along

x-axis: ) =

7. Spacing between the elements along

x-axis: ) = 8. Directivity: >25 dB9. Side Lobe Level: 13 dB

10. Antenna size ( ⨉ ): 1.76 m ⨉ 1.76 m

The antenna is simulated with the above specifications and the initial result showing the main beam located at and is shown in Figure 5 below. Then the scanning operation of the array is demonstrated by scanning this main beam towards the following coordinates: =

and .

Figure 5: Two-dimensional radiation pattern of the simulated 20-element uniform planar array showing

main beam at and . Inter-element

spacing = = .

The two and three-dimensional radiation pattern of the array factor of the antenna scanned to = and is shown below.

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Figure 6: Two-dimensional radiation pattern of the simulated 20-element uniform planar array showing main

beam at and . Inter-element

spacing = = .

Figure 7: Three-dimensional radiation pattern of the simulated 20-element uniform planar array showing main

beam at and . Inter-element

spacing = = .

Figure 8: 3D spherical plot of the array factor showing location of the main beam in space

5. Conclusions

This paper illustrates the mathematical modeling of phased arrays and uses it to simulate a phased array antenna system capable of tracking a satellite that can be used in a Low Earth Orbit Satellite Personal Communications System. Generally, Satellite-Earth links suffer degradation in signal quality as a result of the signal attenuation due to the long distances involved. In addition, interference and multipath fading serve to provide additional sources of system degradation. The transmit and receive power levels involved in the uplink transmission from the user hand held device to the satellite and the downlink transmission from the satellite to the user device are generally very low to permit exploiting techniques such as increasing the transmission power in order to have an increase in the signal to noise ratio and thus improve the link margin. Therefore, other capacity increasing techniques are required and multi antenna techniques of which phased array antennas are a part of is one such solution. Accordingly, the phased array antenna’s mathematical model is intuitively developed and its beam pointing and tracking capabilities illustrated.

5. References

[1] V.K. Katsambas and J.D. Kanellopoulos, “A model for the estimation of the carrier-to-noise plus total interference ratio between two adjacent dual

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polarized satellite links sharing the same frequency band,” International Journal of Satellite and Communications and Networking, vol. 25, pp. 77-90, 2005.

[2] E. Lutz, “Issues in satellite personal communication systems,” Wireless Networks, vol. 4, Issue 2, pp. 109- 124, 1998.

[3] G.M. Calhoun, “Third Generation Wireless Systems, Volume 1, Post-Shannon Signal Architectures,” Artech House Inc., Boston, 2003.

[4] M. Mouhamadou and P. Vaudon, “Smart Antenna Array Patterns Synthesis: Null Steering and Multi-User Beamforming by Phase Control,”Progress In Electromagnetics Research, PIER 60, pp. 95-106, 2006.

[5] D. Tse and P. Viswanath, “Fundamentals of Wireless Communications,” Cambridge University Press, Cambridge, 2005.

[6] P. Stavroulakis, “Interference Analysis and Reduction for Wireless Systems,” Artech House Inc., Boston, 2003.

[7] A. Goldsmith, “Wireless Communications,” Cambridge University Press, Cambridge, 2005.

[8] http://ocw.mit.edu/OcwWeb/resources/RES-6- 007Spring-2010/ResourceHome/index.htm. Retrieved 12th March, 2010.

[9] T.A. Milligan, “Modern Antenna Design,” 2nd ed., John Wiley, West Sussex, 2005.

[10] C.A. Balanis, “Antenna Theory: Analysis and Design,” 2nd ed., John Wiley, West Sussex, 1997.

[11] A. Canabal, R.P. Jedlicka and A.G. Pino, “Multifunctional phased array antenna design for satellite tracking,” Acta Astronautica, vol. 57, pp. 887- 900, 2005.

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