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Due to the influence of scatterers around the receiving antenna, the multipath signal in satellite mobile communication systems is correlated with each other which would influence the system performance. There is no systematic standard on the channel modelling of the wideband satellite channel at present, so the study of the modelling of the wideband satellite channel is of great importance. In this paper, firstly we created a multi-beam model which can figure out the antenna gain of the nth component beam. Secondly, we combined the characteristics of multi-beam satellite channel and the distribution of the scatterers, and set up a three-dimension random channel model. This model is more realistic for satellite communication system since it considers the height of scatterers. According to the channel models, we had the formula of spatial correlation coefficient. We used the formula to calculate the relationship between spatial correlation coefficient and the interval of antennas. The result shows that the spatial correlation exists and cannot be ignored while modeling for mobile satellite system.

The development of wideband multimedia service has raised demand of speed and spectrum efficiency of a new generation mobile-satellite communication system. In the condition of limitation of power, it is significant to make use of space resource to increase system performance. Under the influence of the distribution of scatterer near the receiver antenna, channel fading has spatial correlation in mobile-satellite communication system.

Compatible with LTE standard will be a trend for the new generation of mobile-satellite communication system. Because multiple-input multiple-output (MIMO) is an important part of LTE standard, the research of channel spatial correlation has certain reference value.

Currently, the commonly used classical satellite channel models are Loo model, Lutz model, Fontan model etc.

In terms of research regarding channel spatial correlation characteristics, a spatial Rayleigh-fading correlation model for MIMO has been proposed in [

Moreover, Mahmoud developed a geometrical based hyperbolic channel (GBHC) model for macrocells in [

This paper mainly researches spatial correlation of multi-beam channels of mobile satellite system. Different from current spatial correlation research, we create a three-dimension channel model based on stochastic geometric model, which considers the height of scatterers, and deducts spatial correlation coefficient among channels with numeric calculation and analysis.

Satellite multiple beam antenna (MBA) began to develop in the 1970s to 1980s. Single Feed per Beam (SFB) technology was adopted in the early stage. Later, multiple feeds per beam (MFB) technology was employed. Compared with phased-array antenna, feed beam of MBA is more narrow, and stronger. So the MBA has been widely used in satellite mobile communication systems in 1990s.

According to the structure, MBA can be divided to three categories: phased array antenna, reflector antenna and lens antenna. In this paper, we use reflector antenna to create multi-beam model.

As is shown in

According to

where d_{Sn} and d_{Su} are the distance between satellite and component beam center n and user u respectively.

Suppose that ^{th} component beam. The

where _{max,n} is the maximum gain of the n^{th} component beam.

In satellite communication, a signal is fading during propagation. Those fading may cause by environment and various attenuation facts, for instance cloud attenuation, rain attenuation and ionospheric scintillation. Taking into account this paper research mainly discusses spatial correlation, since attenuation facts like cloud attenuation and ionospheric scintillation are stay the same for a long time, we focus on the influence of ground environment near receiver, namely the multipath which arise from scattering, reflection, refraction or diffraction of the radiated energy off scatterers that lie in the environment.

For satellite communication, typically the height of the ground receiver is lower than nearby scatterers. The received signals in the both horizontal and

vertical plane are distributed. While establishing the channel model, we need to consider the height of scatterers, so the traditional two-dimensional geometric channel model no longer applies. Assuming that scatterers are distributed in a right cylinder which has ground receiver as it bottom center, a three-dimension geometry channel model is shown in

For a downlink of satellite communication system, we assume that p and q are the number of satellite antennas, l and m are the number of ground antennas,_{r} and N_{r} are the maximum number of transmitting antenna and receiving antenna. The received signal is given by

where, H(t) is channel impulse response, n(t) is noise.

The received signal includes direct-path and multipath component in satellite communication system. So the channel impulse response is given by

where H_{loS}(t) is impulse response of direct-path, H_{NLoS}(t) is impulse response of multipath. H_{loS}(t) and H_{NLoS}(t) are both N_{T} × N_{R} matrix. K is Rician Index, which describes ratio of direct-path power and multipath power (unit is dB). The value of K depends on angel of elevation from ground receiver to satellite, carrier frequency and environment around receiver. In this paper, since the interval between ground antennas is much small than shadow fading in different states, we

can approximate that received signal shallow fading of two antennas are the same.

In the model shown in _{m} and R_{l} are the m^{th} and the l^{th} antenna in ground receiver respectively, T_{p} and T_{q} are the p^{th} antenna and the q^{th} antenna in satellite respectively. x − y plane is parallel to horizontal surface, and is perpendicular to OO_{R}. O_{R} is the midpoint of two antennas R_{m }and R_{l }ground projection line. O_{S} is the point of intersection of x axis and y axis and also the midpoint of x − y plane projection line of two antennas T_{p} and T_{q}. O_{T} is the center of transmitting antenna array. H_{S,max} is the maximum height of scatterers distribution. R_{S,max} is the maximum range of scatterer distribution (the maximum radius). _{p} and T_{q} in x − y plane respectively. _{m} R_{l} and x axis. _{m }R_{l} and x − y plane. _{T} and d_{R} is the distance of adjacent antenna on satellite and ground respectively. _{a→b} represent distance of a and b. the distance of _{R} is_{T} is

According to the model, the impulse responses of sub channel from T_{p} to R_{l }can be written as

Since the large number of hypothetical scatterers in the model, let S_{n} be the n^{th} scatterer. Let R_{S,max} and H_{S,max} represent the radius and height of cylinder in the model, namely, the maximum distance and height of scatterers distribution. R_{S(n)} is the distance between O_{R} and S_{n} projection in x-y plane,_{S}_{(n)} is the height of S_{n},^{th} scatterer elevation in scattering path can be approximately shown as^{th} path, which is influenced by S_{n}. In the model, _{S}_{(n)}, H_{S}_{(n)} and

In multi-beam channels of mobile satellite system, the impulse responses of sub _{channel} from T_{p} to R_{l} can be written in terms of (5). Considering the influence from component beam on to received signal, the direct-path component of the channel response can be written as

And multipath component of the channel response can be written as

For the large number of scatterers, according to Central Limit Theorem,

In (6),

In (7), ^{th} multipath component random phase. ^{th} scatterer. K_{pl} represents sub-channel Rician Index from T_{p} to R_{l},

In the early stage of channel research, multi-antenna technology will get a huge channel capacity upgrade in the independent and identically distributed (iid) Rayleigh channel [

where p and q are two transmitting antennas. l and m are two receiving antennas. h_{pl}(t) represents channel response of antenna p to l. In the same way, h_{qm}(t) represents channel response of antenna q to m. E[•] is expectation. ρ_{pl,qm} is correlation coefficient between received signal of antenna l and m.

Since

According to the model shown in

where

Also, the spatial correlation coefficient of multipath component is

Since the large number of scatterers around ground receiver antennas (a larger number N), R_{S}, H_{S} and α_{R}_{ }can replace the discrete variables R_{S(n)}, H_{S(n)} and α_{R,n} as an approximation. (11) can change into integral form

R_{S}, which is the distance of scatterer and ground receiver, can be described by hyperbolic distribution [_{S}, which PDF depends on environment around receiver, is normally described by normal distribution [

When the arrival angle of received signal in x-y plane α_{R} is Laplace distribution, the spatial correlation coefficient of multipath component in the received signal is shown as

where

In this part, the channel spatial correlation coefficient of the signal received by ground antennas is obtained by numeric calculation in multi-beam satellite communication system, which adopt parabolic reflector antenna. All the parameters of simulation are given in

The calculation is on the assumption of

_{T} = 2, n_{R} = 1, the relationship between ground spatial correlation coefficient among three Chinese cities, namely Mohe, Beijing and Shanghai, and the interval of satellite antennas.

As shown in

Take Beijing as example, let K = 4 dB,

Parameter | Description | Value |
---|---|---|

Wavelength | 15 cm | |

f | Focal length | 7.443 m |

D | Diameter of projection plane | 12.5 m |

H | Bias height | 2.607 m |

N | Number of feeds | 37 |

K | Rician Index | 7 dB |

coefficient. With the interval increasing, spatial correlation coefficient showed a decreasing trend, but when the interval is small, the spatial correlation coefficient is still large.

In this paper, considering that the radio transmission feature and the antenna array feature the affection influence the spatial correlation coefficient, we create a 3-demension channel model. According to the model, we derive the spatial correlation coefficient among component beam which received by ground receiver with numeric calculation and analysis. The result shows that spatial correlation coefficient is still large even if the interval of antennas is small. Therefore, the spatial correlation coefficient cannot be ignored in satellite channel research.

This work is supported by the National Natural Science Foundation of China (No.61371073).

Su, Z.M., Fei, X., Cheng, Y.X. and Wu J.J. (2017) Spatial Correlation Characteristics Analysis of Multi-Beam Channels of Mobile Satellite System. Int. J. Communications, Network and System Sciences, 10, 127-137. https://doi.org/10.4236/ijcns.2017.105B012