Study on 3D Spatial Wireless Channel Improvement of MIMO Based Satellite System

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Study on 3D Spatial Wireless Channel Improvement of MIMO

Based Satellite System

Zarina yasmin J

, C.Arunachalaperumal

, DR. C. Arun

1,2

S.A. Engineering College, chennai

3 _{RMK college of Engineering and Technology, Chennai}

Abstract —In this paper a 3D channel model for wireless communication is studied. Also this paper enlightens the difficulties of the analysis of 3D channel model as there are several geometric parameters are required to perform the analytical correlations and to see how the channel depends on those parameters. The reason for preferring MIMO systems which is based on information theory point of view is that it takes no extra cost concerning transmit power or bandwidth The advantage of MIMO systems is that, it provides 1)high gain 2)high directivity 3) space and multi user diversity gain

4)spatial multiplexing gain 5) array and coding

gain,6)interference reduction .The 3D spatial channel model provides insight into spatial aspects of MIMO communication systems. The analytical correlation functions are used to compare the rate of MIMO & SIMO systems. It is noticed that the 3D model supports any arbitrary antenna array configuration as well as any distribution of scatters. In satellite systems significant rate gain can be obtained by the distributed MIMO systems.

Keywords — MIMO, 3D channel model, geometric parameters, spatial correlation, flat fading, distributed MIMO.

I. INTRODUCTION

The advantage of employing the MIMO technology in satellite communication is, it will advance the overall diversity gain, capacity of the system and interference diminution. In SIMO (single input and multiple outputs) technology, the multiple antenna arrays is used at receiver in order to minimize the error and optimize the data speed. SIMO technology finds wide applications in digital television (DTV), Wireless local area networks (WLANs), metropolitan area networks (MANs), and mobile communications. SIMO is also, known as diversity reception, has been used by military, commercial, amateur, and shortwave radio operators at frequencies below 30 MHz since the First World War.

MIMO overcomes the disadvantage of SIMO, because MIMO provide improvements in both channel robustness as well as channel throughput.

Optimizing the trade-off between array gain, diversity gain and multiplexing gain is a highly active research area and beginning to gain strength in standardization for cellular, indoor and fixed wireless access environments. Different data is transmitted simultaneously from each antenna element at the same time and frequency. Advanced receiver algorithms are able to separate each channel because the scattered environment causes these channels to be partially orthogonal; this orthogonality is a random variable as the channel parameters are fluid and hence capacity is also a random variable.

II. SIMOAND MIMO

In a receive diversity SIMO (single input multiple output) case, when the receiver uses Optimum combining (maximum ratio combining), the capacity can be given by

When using selection diversity, where the strongest channel is selected, the capacity is given by

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III. 3DSPATIAL CHANNEL MODEL

Consider a MIMO system with Q transmit antennas located at positions xq, q = 1, 2, . . .,Q from a transmitter origin and P receiver antennas located at positions zp, p = 1, 2, . . . , P from a receiver origin, within balls of radius rT and rR respectively, as shown in Fig. We assume that scatters are distributed outside the balls of radii rTS (> rT) and Rrs (> rR). Thus, the wireless channel has three spatial regions, namely, scattering free balls encompassing transmit antennas and receiver antennas, and the rest of the space assumed to be a complex scattering media. We assume that the surface of scattering free ball is in the far field of either receiver or transmitter origin. In this paper, we only consider flat fading channel environment Where propagation delay is always less than the symbol period. Our attention is aimed to understand fading due to spatial effects rather than temporal effects. Let u = [u1, u2, . . . , uQ]_ be the vector of baseband transmitted signals from the Q transmitters during a signaling interval, A(_φ,_ϕ) is the complex gain of a signal leaving from the transmitter-scattering-free ball at an angle _φ (unit vector) and entering the receiver-scattering-free ball at an angle _ϕ (unit vector), v = [v1, v2, . . . , vP ]_, be the vector of baseband received signal during a signaling interval, and n = [n1, n2, . . . , nP ]_, be the vector of noise at the receiver antennas where

[・]_ denotes the vector transpose. Then we can write v = Hu+ n,

Where H is a P × Q channel matrix with the (p, q) element given by

Where k 2π/λ is the wave number, λ the wavelength, dΩ(_φ) and dΩ (_ϕ) are surface elements of the unit sphere Ω.

src: Characterization of 3D Spatial Wireless Channels

IV. THREE-DIMENSIONAL CHANNEL MODEL

Due to channel reciprocity, we only describe the downlink case. All the satellite antennas are referred to as transmit antennas; while the ground station antennas are referred to as receive antennas. Both LOS and multipath components are taken into account. We consider nT

transmit antennas, which may belong to different satellites, and nR receive antennas, which belong to one ground

station in the center of a scatterer ring. The relative locations of satellites, the ground station, and the scatterer ring are shown in Figure. Following notations are used throughout the paper.

βk: elevation angle of kth transmit antenna; hk: height of kth transmit antenna;

ϕk: direction angle of kth transmit antenna;

fDk : Doppler spread frequency caused by the movement of kth transmit antenna;

ρp: distance from the pth receive antenna to the center of the scatterer ring;

θp: angle of the pth receive antenna; ξ: angle of the ground station moving speed;

fD: Doppler spread frequency caused by the movement of The ground station;

λ: carrier wavelength;

N: total number of the scatterers on the ring; a: radius of the scatterer ring;

angle of the nth scatterer scn on the ring ( = 2πn/N); φn: initial phase shift of the nth scatterer.

A. Line of sight (LOS) component

The LOS components of the channel coefficient between the kth transmit antenna and the pth receive antenna (t) is given below. The distance between the

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where the approximation is based on the fact that the distance from the transmit antenna to the center of the scatterer ring is far greater than the distance from the receive antennas to the center of the scatterer ring ( ).The corresponding channel matrix entry is

Here we assume that the received signal at each ground station antenna has the same unitary power strength and only differs in phase caused by different length of propagation path, because the receive antennas are relatively close to each other, and the attenuation of the signal from different satellites can be normalized into their transmit powers.

V. MULTIPATH SIGNAL COMPONENT

We consider the multipath component and the corresponding channel matrix entries. Similar to the 2-D multipath fading channel model proposed , a scatterer ring is placed around the ground station to model the multipath environment. The scatterers are assumed to be uniformly distributed on the ring, and each scatterer has an independent, uniformly distributed initial phase over [-π,π] Summing signals bounced from the scatters, the multipath component of the channel coefficient between the kth transmit antenna and the pth receive antenna is

Where N is the number of scatterers φ(Sa) kn = −2πskn/λ; skn is the distance between kth transmit antenna and the nth scatterer; φ(GS)pn = −2πLpn/λ; Lpn is the distance between pth receive antenna and nth scatterer. When N approaches infinity, the distribution of cpk(t) converges to Gaussian because of the uniformly distributed initial phase.

1) Transmit Antenna Correlation (2-D Scatterer Ring Case):

In the following, we derive the correlation between two channel coefficients of two arbitrary satellite antennas and one ground station antenna. Without loss of generality, the two satellite antennas are indexed by subscript 1 and 2 and the ground station antenna index is omitted.

The channel coefficients are

Let Δφ(Sa) n be the phase difference caused by the propagation path length difference from nth scatterer to two transmit antennas, then Δφ(Sa) n = φ(Sa) 1n −φ(Sa) 2n = −2π(s1n−s2n)/λ. The distance between the ith transmit

antenna and the nth scatterer sin is

For typical cases of wireless communication between satellite and ground station, hi >> a always holds. Thus it can be simplified to

Define and

Then the path length difference from nth scatterer to the

two transmit antennas is

Define projected distance

and

above equation

becomes Which can be used to calculate and eventually the correlation

function

Proposition 1. Assuming N → ∞, the cross-correlation between two transmit antennas for the 2-D scatterer ring case can be shown to be

Where J0(・) is the Bessel function of the first kind of order zero. Under following conditions, the correlation of multipath components between two transmit antennas can be parameterized by A12, instead of all the geometric

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If the ground station is not moving, then by Proposition 1, the correlation is

The norm of the correlation is |Rc1c2| = |J0 (2π λ aA12)|,

which is solely determined by A12. When A12 is small, the

correlation between the two transmit antennas’ multipath components is high. As shown in Figure 1, the physical meaning of A12 is the distance between v1and v2, the

projections of two transmit antennas’ unit length direction vectors d1 and d2. Thus, we call it ―projected distance‖, and

it indicates how close the directions of these two transmit antennas are. Since high correlation leads to decreasing of the rate, this parameter is useful for Distributed MIMO system rate evaluation.

2) Transmit Antenna Correlation (3-D Scatterer Ring Case):

Here we assume that the scatterers are uniformly distributed on the 3-D scatterer ring in the shape of a cylinder. This is useful for an urban area. For a scatterer

scnm, its direction angle is αn = 2πn/N, n = 1, 2, ・・・,

N, and its height is hRm = hL + (hH − hL) , m = 1, 2, ・

・・ ,M, where hL and hH are corresponding to bottom and

top of the scatterer ring . Thus the total number of scatterers is NM. Considering of the phase difference brought by the height of the scatterers, Proposition 1 can be extended to the 3-D version.

Proposition 2. Assuming N → ∞ and M → ∞, the cross correlation between two transmit antennas for the 3-D scatterer ring case is

The cross-correlation function for the 3-D case only differ in a phase shift and in the sinc function part compared to 2-D case. The projected distance again plays an essential role in determining the value of the cross-correlation function. But it should be noticed that the sinc function part can reduce the correlation even if the projected distance is small.

3) Transmit and Receive Antenna Correlation:

Finally we consider the correlation between any two entries of the channel matrix.

For the 2-D scatterer ring case, since we assume all the receive antennas are near the center of the scatterer ring and the distances between them are far smaller than the radius it’s reasonable to assume that the two

arbitrary receive antennas are symmetric with respect to the center of the scatterer ring. Let the line connecting the two receive antennas be the Y-axis. For arbitrary receive antennas p and q and transmit antennas k and l, assume coordinates of the first receive antenna in the XYZ-axes is and coordinates of the second one is

.

Let . Since

, we generalize Proposition 1 and 2 to the

correlation between two arbitrary antenna pairs Proposition 3.Letting N →∞, the cross-correlation between two channel coefficients in the 2-D scatterer ring case is

Proposition 4. Letting N → ∞ and M → ∞, the cross correlation between two arbitrary antenna pairs for the 3-D scatterer ring case is

VI. RATE AND CORRELATION

Assuming high speed optical link among the satellites, they can form a distributed MIMO transmitter. The received signal at the ground station is y = Hx+w, where x

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The channel matrix is a linear combination of the LOS component and multipath component as

+

where =[cLOSpk] is the multipath component:

HLOS = [Cpk] is the LOS component; and K is the power ratio between them.We evaluate the information rate assuming no channel state information (CSI) at the transmitter and perfect CSI at the Receiver because of large feedback delay from the receiver to the transmitter. Since the transmitters do not know the correlation of the channel matrix, a strategy that will maximize the minimum average mutual information is suggested in [4] to transmit an

isotropic signal with covariance matrix E[xx†] = InT .

For a specific real scenario, the powers of entries of x should be scaled to reflect the path losses. But for the purpose of illustration in this paper, we assume all transmit antennas have the same distance from the receiver. Under the power constraint , the information rate is

where we have assumed wideband signals so that the phase changes caused by the Doppler shifts are not significant within a symbol period. Then the rate does not depend the Doppler frequency. For narrow band signal, the rate will be studied in future works. The projected distance Aij will determine the performance of the system, since both the cross-correlation function of the multipath component and the phase of the LOS component depend on Aij . For example, if one Aij → 0, the rate will be reduced to the case of nT − 1 satellite antennas.

The projected distance can be used to help the system design:

• For one satellite, one antenna is enough if the ground station antennas are in the same scatterer ring and close to each other. On the other hand, if the ground station antennas have very large separation, like in the case of high speed linked cooperative ground stations at different locations, multiple antennas on one satellite is useful. This fits the design rule in [4] that small-sized antenna arrays can be realized at one link end only at the cost of larger element displacements at the opposite link end.

• The projected distances of the scatterer ring of a ground station can be used to determine when the satellites are worth cooperating. Note that the projected distances are not the same for different scatterer rings at different locations.

If cooperative multiple ground stations at different locations are used, the system will have better performance if the projected distances are large for at least some ground stations.

VII. PERFORMANCE EVALUATION

A scenario involving three one antenna satellites and a ground station with three antennas is considered to show how the projected distances Aij affect the rate of the distributed MIMO satellite system. In the urban area, the multipath signal energy is no longer negligible due to the rich scattering environment,

src: Characterization of 3D Spatial Wireless Channels

K can vary from 3.9~11.9dB in the city .Thus, the simulation parameters are set as K = 7dB, SNR = 10dB, carrier frequency fc = 1.2GHz, symbol period Ts = 50ns, scatterer ring radius a = 20m, number of scatterers N = 64, ground station moving speed and direction vGS = 80km/hr,

ᶓ=3π/5,three ground station antennas location ρ1=ρ2=ρ3=0.3m θ1=0,θ2=2π/3,θ3=4π/3,three LEO satellites

location with respect to scatterer ring h1=900km,β1=π/4,φ1=[0,π],h2=900km,β2=π/4,φ2=0,h3=950k

m.β3=π/3,φ3=π/4.three different cases are

compared:SIMO(1 × 3) system using satellite 1, MIMO(2 × 3) system using satellite 1 and 2, MIMO(3 × 3) system using all three satellites. The locations of the 2nd and 3rd satellites are fixed, while the location of the 1st satellite changes to examine the influence of satellite positions on the rate of different systems.

VIII. CONCLUSION

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The rate gain depends upon the projected distance therefore when we apply this concept in satellite system, the rate gain is good and degradation is possible only when projected distance is very less.

REFERENCES

[1 ] R. Schwarz, A. Knopp, B. Lankl, D. Ogermann, and C. Hofmann,

―Optimum-Capacity MIMO Satellite Broadcast System: Conceptual Design for LOS Channels,‖ Advanced Satellite Mobile Systems, 2008. ASMS2008. 4th, pp. 66–71, Aug. 2008.

[2 ] C. Loo and J. Butterworth, ―Land Mobile Satellite Channel Measurements and Modeling,‖ Proceedings of the IEEE, vol. 86, no. 7, pp. 1442–1463, 1998.

[3 ] T.-A. Chen, M. Fitz, W.-Y. Kuo, M. Zoltowski, and J. Grimm, ―A Spacetime Model for Frequency Nonselective Rayleigh Fading Channels with Applications to Space-time Modems,‖ Selected Areas in Communications, IEEE Journal on, vol. 18, pp. 1175 –1190, jul 2000.

[4 ] D. Shiu, G. Foschini, M. Gans, J. Kahn, etal., ―Fading Correlation and its Effect on the Capacity of Multielement Antenna Systems,‖ IEEE Transactions on Communications, vol. 48, no. 3, pp. 502–513, 2000

[5 ] T. Abhayapala, T. Pollock, and R. Kennedy, ―Characterization of 3D