Hindawi Publishing Corporation International Journal of Distributed Sensor Networks Volume 2015, Article ID 928298, 9 pages http://dx.doi.org/10.1155/2015/928298

Research Article Cooperative Transmission for Satellite Wireless Sensor Networks Yuan Lin,1,2 Yuanzhi He,2 and Han Han1,2 1

College of Communication Engineering, PLA UST, Nanjing 210007, China Institute of China Electronic System Engineering Corporation, Beijing 100141, China

2

Correspondence should be addressed to Yuan Lin; [email protected] Received 6 November 2014; Accepted 17 December 2014 Academic Editor: Yan Zhang Copyright © 2015 Yuan Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper presents the performance analysis of wireless sensor networks- (WSNs-) based satellite collocation system as cooperative transmission is applied. A scenario of satellite cluster is considered, where multiple satellites are collocated with each other. Considering that the performance of satellite systems can be improved as the spot beam is split into virtual beams, the optimized system capacity can be expected by applying the geometrical arrangement of the antennas of transmitters and receivers. In the following simulation experiments, the system capacity is investigated as various system configurations are applied. It is found that the optimal value of system capacity exists as expected, and the simulation observations are illustrated as practical limitations are considered.

1. Introduction Technological progress in wireless communications and microelectromechanical systems (MEMSs) have brought about the opportunity of the development of low-power, multifunctional, low-cost, and tiny sensor nodes which can communicate to each other directly. This progress, together with marked advances in the area of microsensors, has allowed inexpensive, energy-efficient, and reliable sensors with wireless networking capabilities to become a reality. The development of such devices has given rise to the increasingly popular concept of wireless sensor networks (WSNs) [1]. This network consists of a large number of nodes, which have sensing, processing, and communicating capabilities and perform human-unattended information collection [2], which has been the subject of extensive studies [3–5]. Nowadays, various kinds of WSNs-based application networks are attracting more and more attentions, such as smart grids [6], smart home [7], and e-health [8]. recently, wireless sensor network market also represents an interesting and potentially huge revenue stream for the satellite industry. The reason is that terrestrial network currently covers only 10% of the world and has created a need to switch toward satellite networks which would help to cover the remaining 90% of the

world, making it the most attractive aspect of satellite sensor connectivity. In recent years, the research of combing wireless sensor network with satellite communication represents a good opportunity [9–11]. The wireless sensor satellite communication market comprises services such as environmental and habitat monitoring, satellite remote sensing for ocean research, and structural health monitoring. These services can make use of the backward satellite link capacity for the transmission of telemetry data, requiring only a small fraction of capacity in the forward direction. In order to improve the capacity and spectral efficiency of satellite sensor network, the construction of multiple input multiple output (MIMO) systems is very promising especially with regard to satellite transmission. This is mainly due to two reasons: on the one hand, there is a rising demand for transmission bandwidth; on the other hand, the usable frequency spectrum of available bandwidth becomes short and particularly expensive. However, it is difficult for satellites to employ MIMO techniques directly on the existing satellite platform, due to the constraints from satellite’s size or hardware implementation. Compared to traditional MIMO systems, cooperative communication does not need multiple antennas at terminal devices and therefore significantly reduces the implemental

2 complexity and cost, which is widely studied in wireless networks [12, 13]. The performance of cooperative transmission in satellite network is carried out in [14, 15], but only the low earth orbiting satellites scenario is considered. For the scenario of geostationary (GEO) orbiting satellite networks, only the limited numbers of satellites can be supported by the GEO orbit as GEO orbit is one kind of scarce nature resource. Unlike traditional GEO satellite system, multisatellite collocation technology [16], which can allow several satellites running in one GEO orbit window (0.2∘ ), is considered as an available way to use the GEO orbit efficiently. However, it is nowadays widely believed that a high MIMO capacity gain can only be achieved in the rich scattering multipath propagation channel [17]. Contrarily to this impression, in principle, it is possible to form a LOS channel with maximum MIMO multiplexing gain. The main drawback of the satellite cooperative transmission system to be used in satellite sensor networks is found in satellite antenna element spacings, which are too small as several satellites are collocated with each other. In other words, these systems only offered low multiplexing gain coinciding with only a logarithmic rather than a linear increase of the capacity with the used number of antenna elements. In fact, there exist very distinct requirements for the positioning of both the satellite antennas and the ground stations that have to be fulfilled in order to create an orthogonal MIMO channel transfer matrix that offers optimum multiplexing gain. To overcome this problem, for terrestrial antennas system, the optimized antenna setups have been proven to deliver significantly higher channel capacities [18]. Contrarily, with respect to satellite systems, in [19–22], the maximum multiplexing gain of the line-of-sight (LOS) satellite channel is achieved by constructing an orthogonal channel matrix. However, for mathematically manageable results, the analyses are limited to a satellite cooperative transmission system with two satellite antenna elements only, which have to be placed on a single satellite each. In [23], a cooperative transmission scheme and a ground user selection criterion are proposed, but it also limited to the scenario with two satellites and two users. In the multisatellite collocation system, the use of multiple satellites can obviously improve multiplexing gain and spectral efficiency. This paper addresses the optimization of the cooperative transmission channel capacity for a system consisting of 𝑁𝑇 ground satellite terminals and 𝑁𝑆 collocated satellites. Furthermore, we presume a regenerative payload for the satellites, and a communication link is established between each satellite, which could be realized, for example, by a highbandwidth optical link. We proved that maximum MIMO spectral efficiency can be achieved by proper construction of the positions of each antenna on both sides, for satellite terminals and collocated satellites. We also verified that when multiple satellites are used, system capacity can be further improved. The remainder of this paper is organized as follows. The system model and channel model are given in Section 2. In Section 3, we describe a capacity calculation and optimum capacity. The optimization criterion is detailed in Section 4,

International Journal of Distributed Sensor Networks S1

SN𝑆

S2 ···

Ground control station Beam 4 Beam 1

Beam 3 Beam 2

Multibeam

Figure 1: System scenario.

and the performance analysis is given in Section 5. We conclude the paper in Section 6. The superscripts 𝐻 stand for the Hermitian transpose. Upper and lower boldfaced letters are used for matrices and column vectors, respectively. Denote by |𝑥| the absolute value of a scalar 𝑥 or cardinality of 𝑥 if 𝑥 is a set. I is the identity matrix of a certain size implicitly given by the context. We denote by [w1 , w2 , . . . , w𝑁] the concatenation of 𝑁 column vectors; log2 represents the binary logarithm.

2. System and Channel Model 2.1. System Model. A scenario of cooperative collocated satellite system is given in Figure 1, where at least two satellites collocated in one GEO orbit window and multiple users within one spot beam. Here, we suppose that there are 𝑁𝑆 satellites collocated in the GEO orbit and 𝑁𝑇 satellite terminals within one spot beam, each of which is equipped with single antenna. Each satellite is able to generate multibeam. However, for satellite terminals within a spot beam, it can be equivalent to a satellite equipped with only one antenna. Since downlink is quite reasonable and straightforward for GEO satellites to broadcast, in this paper, we mainly focus on uplinks with multiple satellites. The system model is given in Figure 2. As is shown in Figure 2, selected terminals within one beam transmit data to multiple satellites simultaneously with the same frequency and time slot. After receiving the uplink data, satellites forward them to a ground control station. When a satellite terminal has a request for transmitting, the control station

International Journal of Distributed Sensor Networks

3 dominating radio wave propagation mechanism in a satellite channel is formed by the LOS signal component due to its low signal attenuation and multipath signals play a subordinated role. In urban environments, shadowing and blocking cannot be avoided, so, in principle, NLOS signals cannot be ignored. However, an antenna separation of at least half wavelength is commonly satisfied in pure NLOS scenario. Therefore, we restrict ourselves to only consider the LOS signal part and assume in the following a MIMO LOS channel, which is given by

z

Prime meridian

Satellite terminal Equator

y

RT

𝜙T 𝜃T

H (𝑓) = HLOS (𝑓) .

𝜃S,1 𝜃S,n𝑆

RS

Moreover, we assume the channel to be frequency flat if the bandwidth is much smaller than the carrier frequency; that is, 𝐵 ≪ 𝑓. In this case the frequency dependence can be omitted and we have H(𝑓) = H. With the help of the freespace propagation model, each element of channel matrix H is given by [18]

Sn𝑆

x S1

GEO orbit

· ·· Collocated satellites

H𝑚𝑛 = 𝑎𝑚𝑛 exp (−𝑗2𝜋𝑓

Figure 2: System model. Table 1: Parameters of satellite system. Parameter Value

EIRP 69.3 dBW

(𝐺 − 𝑇) 2.4 dBK

𝐵 5 MHz

𝐿 209.3 dB

allocate a specific frequency and time slot to multiple selected users (for the sake of simplicity, only two satellite terminals are considered for cooperation). The system characteristics and parameters are given in Table 1. Where EIRP is the effective isotropic radiated power, 𝐺 − 𝑇 is the logarithm ratio of figure of merit, 𝐵 is the transmission bandwidth, and 𝐿 is path loss, with carrier frequency 𝑓 = 18 GHz. Using the parameters of Table 1, for the SNR at the satellite, we obtain SNR = EIRP + (𝐺 − 𝑇) − 𝐿 − 𝐾 − 𝐵 = 24 dB,

(1)

where 𝐾 and 𝐵 are the logarithmic value of the Boltzmann constant and uplink bandwidth, respectively. It is assumed here that SNR is constant and identical for each pair of TxRx antennae, and it includes all the gains of the link budget, except for the LOS path loss, which has been incorporated into the channel matrix. 2.2. Channel Model. The frequency selective MIMO satelite channel H(𝑓) consists of a LOS signal part HLOS (𝑓) and a second part H𝑁LOS (𝑓), which is formed by multipath signal. The channel model is described as [24] √

𝐾 1 (𝑓) , H (𝑓) + √ H 𝐾 + 1 LOS 𝐾 + 1 𝑁LOS

(3)

(2)

where 𝐾 denotes the Ricean 𝐾-factor, which is defined as the power of the LOS signal component divided by the power of the multipath parts. Unlike terrestrial mobile scenario, the

𝑟𝑚𝑛 ), 𝑐0

(4)

where 𝑐0 is being the speed of light in free space and 𝑟𝑚𝑛 is being the distance from the 𝑚th satellite terminal to the 𝑛th satellite antenna. The term 𝑎𝑚𝑛 = (𝑐0 /4𝜋𝑓𝑟𝑚𝑛 ) exp(𝑗𝜙) is the complex envelope, for which 𝜙 = 0 will be assumed in the following, as it is a phase angle common to every channel entry. We also assume that the magnitude of the channel gain is approximately constant for each couple of transmit and receive antenna, as the distance from the user antenna to the satellite is much larger than the distance between each terminal; that is, 𝑎𝑚𝑛 ≈ 𝑎.

3. MIMO Capacity 3.1. Channel Capacity. In the scenario of conventional satellite communication networks, with the help of Shannon theory, the capacity of a single-input-single-output (SISO) system is given by 󵄨2 󵄨 (5) 𝐶SISO = log2 (1 + 𝜌 󵄨󵄨󵄨ℎSISO 󵄨󵄨󵄨 ) , where ℎSISO is the channel gain between the satellite terminal and the satellite and 𝜌 denotes the SNR at the transmitter. However, in a scenario of cooperative transmission, the system can be treated as a virtual distributed MIMO. If the transmit symbols are independent, identically distributed (i.i.d.) Gaussion random variables and the channel state information (CSI) are unknown to the transmitter; the time invariance spectral efficiency of a frequency-flat time invariance MIMO transmission channel without a relay is calculated according to the Telatar’s well-known equation [25] 𝐶MIMO = log2 [det (I𝑁𝑇 + 𝜌HH𝐻)] ,

(6)

where the transmit symbols are realizations of uncorrelated independent, identically distributed (i.i.d) Gaussian random variables. The ratio 𝜌, which incorporates all the gains of the link budget except the LOS path loss, is calculated as 𝜌 = 10(SNR+𝐿)/10 .

(7)

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3.2. Optimum Capacity. We define the square matrix Q with eigenvalues 𝛾𝑖 as follows [20]: 𝐻 {H H, 𝑁𝑆 ≥ 𝑁𝑇 , Q={ HH𝐻, 𝑁𝑆 < 𝑁𝑇 . {

(8) uT

Then, the maximum spectral efficiency is achieved when all eigenvalues of 𝑄 are identical; that is, 𝛾𝑖 = |𝑎|2 max{𝑁𝑆 , 𝑁𝑇 } (𝑖 = 1, 2, . . . , min{𝑁𝑆 , 𝑁𝑇 }). In this case we obtain an optimum eigenvalue profile and an orthogonal channel transfer matrix. Then, the spectral efficiency also obtains its optimum value which is given by 𝐶opt = min {𝑁𝑆 , 𝑁𝑇 } log2 (1 + 𝜌 |𝑎|2 max {𝑁𝑆 , 𝑁𝑇 }) .

(9)

This optimal capacity is also the upper bound we try to obtain in the following. Considering that the channel matrix is related with the distances between the satellite terminals and the satellites, so those path lengths are the degrees of freedom, which can be exploited to adjust the channel entries so that the eigenvalues of 𝑄 are equal, and thus min{𝑁𝑆 , 𝑁𝑇 } identical eigenvalues are generated. On the contrary, if the channel matrix is rank deficient, the so-called keyhole effect and the lower bound of the spectral efficiency are achieved. 3.3. Cooperative Gain. In practice, if the LOS channel is not orthogonal for all satellites and satellite terminals, the capacity of cooperative system may not be better than that of noncooperative system. Therefore, following the definition given in [23], we define the cooperative gain generated by the cooperative transmission as follows: 𝐺=

𝑅co , 𝑅nco

(10)

where 𝑅co and 𝑅nco are the achievable transmission rate of the cooperative and noncooperative system, respectively. It is well known that the capacity denotes the spectral efficiency of a system, so the achievable transmission rate of cooperative and noncooperative system can be given by 𝑅nco = 𝑁𝑇 𝑓nco 𝐶SISO , 𝑅co = 𝑓co 𝐶MIMO ,

Satellite terminal 1

Figure 3: Geometrical description of two satellite terminals.

satellite terminals. The geometrical description of satellite terminals is given in Figure 3, where the center of the satellite terminals has longitude 𝜃𝑇 and latitude 𝜙𝑇 on the Earth surface, while the position of each satellite is given by longitude 𝜃𝑆,𝑛𝑆 , for 𝑛𝑆 = 1, 2, . . . , 𝑁𝑆 . Define 𝑅𝑇 and 𝑅𝑆 as the mean Earth radius and the radius of the geostationary orbit, respectively. Then, the position vector of the center of two satellite terminals in Cartesian coordinates is given by 𝑥𝑇 = 𝑅𝑇 cos 𝜙𝑇 cos 𝜃𝑇 𝛼𝑇 = ( 𝑦𝑇 = 𝑅𝑇 cos 𝜙𝑇 sin 𝜃𝑇 ) .

(13)

𝑧𝑇 = 𝑅𝑇 sin 𝜙𝑇 Then, we define the angle between a tangent in the eastwest direction and the direction of two arbitrary satellite terminals is denoted by 𝑢𝑇 ∈ {−180∘ ≤ 𝛿𝑇 ≤ 180∘ }, and the position vectors of two satellite terminals are given by 𝛼𝑇,𝑛𝑇 𝑥𝑇,𝑛𝑇 = 𝑥𝑇 − 𝑝𝑛𝑇 (sin 𝜃𝑇 cos 𝑢𝑇 + sin 𝜙𝑇 cos 𝜃𝑇 sin 𝑢𝑇 ) = (𝑦𝑇,𝑛𝑇 = 𝑦𝑇 + 𝑝𝑛𝑇 (cos 𝜃𝑇 cos 𝑢𝑇 − sin 𝜙𝑇 sin 𝜃𝑇 sin 𝑢𝑇 )) ,

(11)

(14)

where 𝑝𝑛𝑇 = ±(1/2)𝑑𝑇 . For each of the satellites, we may define 𝑥𝑆,𝑛𝑆 = 𝑅𝑆 cos 𝜃𝑆,𝑛𝑆 𝛽𝑆,𝑛𝑆 = ( 𝑦𝑆,𝑛𝑆 = 𝑅𝑆 sin 𝜃𝑆,𝑛𝑠 ) .

𝑓 𝐶 𝑅co = co MIMO 𝑅nco 𝑁𝑇 𝑓nco 𝐶SISO

𝑓co log2 {det (I𝑁𝑇 + 𝜌HH𝐻)} = 󵄨2 . 󵄨 𝑁𝑇 𝑓nco log2 (1 + 𝜌 󵄨󵄨󵄨ℎSISO 󵄨󵄨󵄨 )

East

West

𝑧𝑇,𝑛𝑇 = 𝑧𝑇 + 𝑝𝑛𝑇 cos 𝜙𝑇 sin 𝑢𝑇

where 𝑓nco and 𝑓co are the bandwidth of the noncooperative and the cooperative system, respectively. 𝑁𝑇 is the number of satellite terminals. From (5), (6), and (11), we can obtain 𝐺=

Satellite terminal 2

dT 2

(15)

𝑧𝑆,𝑛𝑆 = 0 (12)

4. Optimum Criterion 4.1. Geometrical Description. The principle of Mercator projection is used to obtain the positions of the satellites and

Thus, the distance between the 𝑛th terminal and the 𝑚th satellite is given as 𝑟𝑚𝑛 = ‖𝛼𝑇,𝑛 − 𝛽𝑆,𝑚 ‖. Thanks to the approximation on the magnitude of the channel gain given by (4), it is actually shown that the phase relations between the channel matrix entries are the only degrees of freedom to modify the properties of the channel. As explained in Section 3.2, by imposing the eigenvalues of Q to be equal, a criterion on these phase relations which allows

International Journal of Distributed Sensor Networks

5

maximizing the system capacity for a 𝑁𝑇 × 2 MIMO channel was proposed in [20]. The most general formulation of this criterion, which can be used as a starting point for the present work, can be described as 𝑟𝑘,1 − 𝑟𝑘,2 + 𝑟𝑙,2 − 𝑟𝑙,1 = V (𝑘 − 𝑙)

𝑐0 , 𝑁𝑆 𝑓

(16)

where 𝑘, 𝑙 ∈ {1, 2, . . . , 𝑁𝑆 } and 𝑟𝑛𝑆 ,𝑛𝑇 is the distance between the 𝑛𝑇 th transmit antenna to the 𝑛𝑆 th satellite receive antenna. The parameter V ∈ 𝑍 is indivisible by 𝑁𝑆 , and the possible configurations satisfying the condition have actually an angle periodicity of 2𝜋. As a second step, we look for the expression of the length 𝑟𝑛𝑆 ,𝑛𝑇 . We first express the distance vector between the terminal antenna 𝑛𝑇 and the satellite antenna 𝑛𝑆 as a Euclidean norm, following the notation introduced before as 2

2

2 . 𝑟𝑛𝑆 ,𝑛𝑇 = √ (𝑥𝑇,𝑛𝑇 − 𝑥𝑆,𝑛𝑇 ) + (𝑦𝑇,𝑛𝑇 − 𝑦𝑆,𝑛𝑇 ) + 𝑧𝑇,𝑛 𝑇

(17)

Inserting the position vector of 𝛼𝑇,𝑛𝑇 and 𝛽𝑆,𝑛𝑆 and after a number of mathematical manipulations involving trigonometrical theorems, we obtain 𝑟𝑛𝑆 ,𝑛𝑇 = [𝑅𝑆2 + 𝑅𝑇2 − 2𝑅𝑆 𝑅𝑇 cos 𝜙𝑇 cos (𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ) + 2𝑅𝑆 𝑝𝑛𝑇 (cos 𝑢𝑇 sin (𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ))

(18)

+ sin 𝑢𝑇 cos (𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ) sin 𝜙𝑇 + 𝑝𝑛2𝑇 ]

1/2

.

couple of (𝑘, 𝑙) can be treated as 2-satellite pairs, and optimizing this result is equivalent to the joint optimization of these 𝑁𝑆 (𝑁𝑆 − 1) satellite pairs which compose the chosen ones from collocated satellite system. Assume that the positions of satellites are given; in order to simplify (21), we first review the degree of freedom in the optimization of the position of two satellite terminals: (1) the number of transmit antenna 𝑁𝑇 , (2) the distance 𝑑𝑇 between two cooperative satellite terminals within one spot beam, (3) the direction angle 𝑢𝑇 . Assuming that 𝑁𝑇 is given, then we try to find the values of distance 𝑑𝑇 and angle 𝛿𝑇 to maximize the system capacity. Next, we reformulate (21) to separate the dependency on those two parameters. Whereas the dependency on distance 𝑑𝑇 is already evident, we reformulate 𝑐𝑛𝑆 as 𝑐𝑛𝑆 = 𝑅𝑆 (𝐺𝑛1𝑆 cos 𝑢𝑇 + 𝐺𝑛2𝑆 sin 𝑢𝑇 ) ,

where the coefficients 𝐺𝑛1𝑆 = 2 sin(𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ) and 𝐺𝑛2𝑆 = 2 cos(𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ) sin 𝜙𝑇 include parameters related to the positions of each satellite and the centre of two terminals, independent of the two optimization parameters. We then insert (22) into (21), after assuming the following definition for ease of notation as 𝐴 𝑘𝑙 =

𝐺𝑙1 𝐺𝑘1 − , 𝑠𝑙 𝑠𝑘

𝐵𝑘𝑙 =

𝐺𝑙2 𝐺𝑘2 − , 𝑠𝑙 𝑠𝑘

𝐶𝑘𝑙 =

2 (𝑘 − 𝑙) 𝑐0 . 𝑅𝑆 𝑁𝑆 𝑓

Two auxiliary quantities are now introduced as 𝑠𝑛𝑆 =

√𝑅𝑆2

+

𝑅𝑇2

− 2𝑅𝑆 𝑅𝑇 cos 𝜙𝑇 cos (𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ),

𝑐𝑛𝑆 = 2𝑅𝑆 [cos 𝑢𝑇 sin (𝜃𝑇 − 𝜃𝑆,𝑛𝑆 )

(19)

+ sin 𝑢𝑇 cos (𝜃𝑇 − 𝜃𝑆,𝑛𝑆 ) sin 𝜙𝑇 ] .

𝑟𝑛𝑆 ,𝑛𝑇 ≈ 𝑠𝑛𝑆 +

2𝑠𝑛𝑆

≈ 𝑠𝑛𝑆 + 𝑝𝑛𝑇

𝑐𝑛𝑆 2𝑠𝑛𝑆

.

(20)

This result may be inserted into (16), and we have 𝑑𝑇 (

𝑐𝑙 𝑐 (𝑘 − 𝑙) 𝑐0 − 𝑘 )=V . 2𝑠𝑙 2𝑠𝑘 𝑁𝑆 𝑓

(23)

Then, the optimization equation becomes

Now, we apply a first order Taylor series expansion as a good approximation of the square root √1 + 𝑎 ≈ 1 + 𝑎/2; we have [20] 𝑝𝑛𝑇 𝑐𝑛𝑆 + 𝑝𝑛2𝑇

(22)

(21)

A comparison with this result for the equation obtained in [20] clearly shows that this time the optimization criterion keeps the dependence on the difference between 𝑘 and 𝑙, while, in [20], this dependence disappeared; thanks to it, only consider two satellites, and the optimization of the positions of both satellites and terminals became independent of the choice of 𝑘 and 𝑙. However, the term (𝑘−𝑙) shows that different solutions exist, considering the particular couple of antenna elements chosen for the optimization. In other words, each

𝑑𝑇 (𝐴 𝑘𝑙 cos 𝑢𝑇 + 𝐵𝑘𝑙 sin 𝑢𝑇 ) = V ⋅ 𝐶𝑘𝑙 .

(24)

Now, we have one equation for each couple of (𝑘, 𝑙), for 𝑘 ≠ 𝑙. Actually, (24) describes a nonlinear system which contains 𝑁𝑆 (𝑁𝑆 − 1) equations, where parameter V gives a further degree of freedom for each equation of the system. Although we can assume that approximate solutions may be found in the least squares sense to deal with an overdetermined system, it is still impossible to give a closedform expression for an exact solution of the system, for the chosen values of distance 𝑑𝑇 and angle 𝑢𝑇 that would ensure full achievement of the optimal system capacity. For this reason, we continue our analysis through numerical simulations, which will be shown in the following section.

5. Simulation Results In this section, we present performance results through numerical simulations, where two satellite terminals and multiple collocated satellites are considered.

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International Journal of Distributed Sensor Networks 30

10

50

0 ∘

uT ( )

5

0

10

20

30

40

50

dT (m)

−50 −100 −150 −200 4

Figure 5: System capacity computed by numerical simulations for 𝑁𝑆 = 3 and 𝑓 = 18 GHz.

Three satellites with cooperation Three satellites without cooperation One satellite without cooperation

95

Table 2: Parameters of simulation. 𝜃𝑇 12∘

𝜙𝑇 52∘

𝜃𝑆,2 12∘

C/Copt (%)

100

Figure 4: Achievable rate for three satellites with cooperation, noncooperative satellites and one big satellite for 𝑁𝑇 = 2, 𝑢𝑇 = 0∘ , and 𝑓 = 18 GHz.

Parameter Value

2

0

(m )

3

1 t

15

op

20

100 95 90 85 80 75 70 65 60 55 200 150 100

d

C/Copt (%)

R (bit/s)

25

90

90

85

80

80

70

75

60

70

50 4

65 2 d

In Figure 4, we display the normalized achievable rate of cooperative and noncooperative system. Here, we assume that three satellites are chosen to communicate with two terminals. The simulation parameters are shown in Table 2, the distance between two satellites are set to 60 km, and the angle 𝑢𝑇 is set to 0∘ . In this figure, three scenarios are taken into consideration: (1) three satellites with cooperation; (2) three satellites without cooperation; (3) one big satellite without cooperation. For cooperative system, the frequency can be reused by two satellite terminals, while, for noncooperative system, frequency division is necessary. Therefore, we set 𝑓co = 2𝑓nco . It is shown that the achievable rate of cooperative system oscillates with a periodicity. For the scenario of three satellites without cooperation, the uplink contains two SIMO channels, while, for the scenario of one big satellite, we set the SNR as 𝜌󸀠 = 3𝜌, and the uplink contains two SISO channels. From this figure, we can see that, with satellite collocation, the achievable rate of both cooperative and noncooperative system is much better than that of one big satellite with high power. Figures 5 and 6 display the contour plot of the calculated system capacity as a function of 𝑑𝑇 and 𝑢𝑇 . Because the distance interval between two satellites is set identically, it is shown in Figure 5 that the near-maximum capacity is achievable in the region by choosing the direction angle near the range of ±180∘ and 0∘ ; that is, when 𝑢𝑇 = 0∘ and 𝑑𝑇 = 1.9 m, we can achieve more than 98% of the optimal capacity. In Figure 6, we observe that (24) describes a straight line on the cartesian plane, whose slope depends on the parameters

T si

0 uT

n(

)

−2 −4 −4

−2

2 0 ) u T os( d Tc

4

60

Figure 6: Polar coordinates representation of the system capacity computed by numerical simulations for 𝑁𝑆 = 3 and 𝑓 = 18 GHz.

𝐴 𝑘𝑙 and 𝐵𝑘𝑙 ; it also shows that we can achieve more than 98% of the optimal capacity when 𝑑𝑇 cos(𝑢𝑇 ) > 1.9 m or 𝑑𝑇 cos(𝑢𝑇 ) < −1.9 m; during this region, 𝑑𝑇 > 1.9 m and 𝑢𝑇 = ±180∘ . In Figure 7, we take into consideration to which degree any deviations from the optimum terminal distance setup will cause degradations of the system capacity. The figure shows that the system capacity 𝐶 changes with the distance between two satellite terminals 𝑑𝑇 for four different directional angle 𝑢𝑇 . It is observed that capacity oscillates with a periodicity in 𝑑𝑇 . Due to the parameters setting of the simulation in which 𝜃𝑇 = 𝜃𝑆,2 ≈ (𝜃𝑆,1 + 𝜃𝑆,3 )/2, given 𝑑𝑇 , system capacity is symmetrical to angle 𝑢𝑇 = 0∘ and has a capacity minimum at 𝑢𝑇 = ±90∘ , so when the angle 𝑢𝑇 is large, system can achieve its optimal capacity even for small terminal distance 𝑑𝑇 and therefore has small 𝑑opt and small periodicity. This figure gives four group curves for 𝑢𝑇 = 0∘ , 30∘ , 60∘ , and 90∘ , respectively. It shows that when 𝑢𝑇 = 90∘ , we can only achieve 55% as percentage of the optimum capacity 𝐶opt ; it is because at this point the condition 𝑟𝑛𝑆 ,1 = 𝑟𝑛𝑆 ,2 , (𝑛𝑠 = 1, 2, . . . , 𝑁𝑆 ) is fulfilled and, therefore, the MIMO channel cannot be optimized at all. This makes the worst-case type

International Journal of Distributed Sensor Networks

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14 C/Copt (%)

100

13

C (bit/s/Hz)

12

80 60 40

11

0

10

1

1.5

2 2.5 dT (m)

3

3.5

4

3

3.5

4

NS = 4

NS = 2 NS = 3

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0

5

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15

20

25

dT (m) ∘

80 60 40

∘

uT = 0 uT = 30∘

C/Copt (%)

100

8 7

0.5

0

0.5

1

uT = 60 uT = 90∘

1.5

2

2.5

dT (m)

Figure 7: System capacity with different 𝑑𝑇 and 𝑢𝑇 for 𝑁𝑆 = 3, 𝑑𝑆 = 60, and 𝑓 = 18 GHz.

dS = 20 km dS = 40 km dS = 60 km

Figure 9: System capacity with different 𝑑𝑇 and 𝑁𝑆 for 𝑑𝑆 = 20 km, 𝑓 = 18 GHz, and 𝑢𝑇 = 0∘ .

35 30

dopt (m)

25 20 15 10 5 0 10

20

NS = 2 NS = 3

30

40 dS (km)

50

60

70

NS = 4

Figure 8: Optimal distance 𝑑opt with different 𝑑𝑆 for 𝑓 = 18 GHz and 𝑢𝑇 = 0∘ .

of the channel with respect to the channel multiplexing gain and it is generally referred to as the keyhole channel. Figure 8 shows the value of optimal distance between two satellite terminals 𝑑opt with different satellite interval 𝑑𝑆 and the number of cooperative satellites 𝑁𝑇. For a collocated satellite system within one GEO orbit window, 𝑑𝑆 cannot increase infinitely, so we set 𝑑𝑆 from the range of 10 km to 70 km. It can be observed from Figure 8 that 𝑑opt decrease with the increase of satellite interval 𝑑𝑆 . It also shows that shorter optimal distance is available when we use more satellites, that is, when the interval between two satellites is 40 km and when we choose four and three satellites for

cooperation, the optimal distance is 51% and 33% times shorter than only one satellite are chosen, respectively. Figure 9 shows the increase of the percentage of 𝐶/𝐶opt with terminal distance 𝑑𝑇 , with different satellite interval 𝑑𝑆 and the number of cooperative satellites 𝑁𝑇 , respectively. In this figure, three collocated satellites are considered. It can be observed from the first figure on the top of Figure 9 that the achievable capacity increases with the distance of three collocated satellites. In other words, the required distance between two satellite terminals would be shorter and a better system capacity performance can be achieved with 𝑑𝑆 increases. However, 𝑑𝑆 cannot increase infinitely due to the GEO orbit window of satellite collocation. Note that, for the safety of the satellites, 𝑑𝑆 is not more than 70 km. Therefore, we can use a large 𝑑𝑆 to enhance the system capacity. Another figure which is at the bottom of Figure 9 analyzes the system capacity performance with different 𝑑𝑇 and the number of cooperative satellites 𝑁𝑇 , for 𝑑𝑆 is set to 20 km. It shows that better capacity can be achieved when we use more satellites; that is, when the distance between two terminals is 1.5 m and when we choose four satellites for cooperation, the achievable capacity is 11% and 32% times larger compared to the ones when three and two satellite are chosen, respectively. In practice system, satellite is impossible to maintain absolutely immobile at its defined position. Therefore, a station keeping box is defined, which represents the maximum permitted values of the satellite excursions. For a capacityoptimized system, it is, thus, desirable to guarantee the optimum capacity as long as the satellite stays within this virtual box. Subsequently, we assume typical box dimensions, which are 37.5 km in longitude and latitude and 17.5 km for the eccentricity [26]. We have investigated the effect of satellite drifts in all three dimensions finding significant effects in

8 cases of changes in longitude and latitude with respect to the nominal satellite position. Instead, the eccentricity remains of less relevance for the channel capacity. The capacity degradation is less than 1% of the optimum value 𝐶opt . Hence, station keeping has a negligible impact on the capacity as long as the pointing of the satellite is correct.

6. Conclusions In this paper, we propose a scheme to combine satellite cooperative transmission networks and WSNs. The two sensor devices within one spot beam access a collocated satellite system for data transmission. With the help of cooperative beamforming, each satellite spot beam can be split into multiple virtual beams, by which the capacity can be improved. We present an approach which enables the construction of uplink with two terminals and multiple satellites that can achieve the maximum MIMO spectral efficiency for the case of LOS signal propagation. Maximum multiplexing gain is achieved via an optimized positioning and displacement of the MIMO antenna elements at both sides, which results in an orthogonal MIMO channel transfer matrix. Through simulations, we have confirmed that, for the construction of capacity-optimal MIMO channel transfer matrices, the user is provided with several degrees of freedom for the system design. It shows that capacity increases with the number of cooperative satellites 𝑁𝑆 and satellite interval 𝑑𝑆 , while showing a periodical performance with terminal distance 𝑑𝑇 and angle 𝑢𝑇 . The interdependence and optimization of the design parameters are illustrated, also highlighting practical limitations.

Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment This work was supported by the National Natural Science Foundation of China under Grant no. 61231011.

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