Performance Assessment of Satellite-Terrestrial ...

Performance Assessment of Satellite-Terrestrial Relays under Correlated Fading Furqan Jameel+ , Faisal⊥ , M. Asif Ali Haider± , Amir Aziz Butt⊗ Department of Electrical Engineering COMSATS Institute of Information Technology, 44000, Islamabad, Pakistan Email: + [email protected], ⊥ [email protected], ± [email protected], ⊗ [email protected]

Abstract—Relay assisted satellite communication holds the promise to increase the coverage area and enhance the energy efficiency of Land Mobile Satellite (LMS) systems. To this end, this paper focuses on the performance analysis of relay assisted LMS communication. The channel between relays and satellite is subjected to Shadow Rician fading. Moreover, correlated fading environment is assumed between relays and mobile nodes. The satellite adopts Optimal Relay Selection (ORS) strategy to select the best relay out of available set of relays. Furthermore, we evaluate the performance of LMS based on outage probability and provide closed form expression for the said metric. Simulations and analytical results are provided to show the impact of various network parameters on the performance of LMS systems. Index Terms—Land Mobile Satellite (LMS), Optimal Relay Selection (ORS), Shadow Rician fading.

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Transparent Relaying Regenerative Relaying

A. Transparent Relaying

This group of relays forwards the information in a received signal waveform without manipulating them. They usually are equipped with capability of performing non-complex operations such as phase rotation or amplication of Analog signal. As no signal processing is involved during transition, by applying frequency and amplication translation, the analog signals are immediately retransmitted. Following are its subtypes: 1) Amplify and Forward (AF): This is often frequently I. I NTRODUCTION employed method in relays which amplifies the signal received Satellite systems are being used for provisioning of services at relay before retransmission. This method can be at disposal like surveillance, disaster supervision and live broadcasting. over the destination for the amplication purpose to detect the These systems are capable to cover large portions of the land signal properly [4]. while simultaneously achieving high data rates. Despite these 2) Nonlinear-Process and Forward (nLF): It involves nonfeatures, the performance of these systems is largely degraded linear operations on the received analog signal also referred due to the presence of obstacles and fading between satellite to as non-linear AF. It also assists in optimally reducing the and terrestrial users. This poses a difficulty in maintaining Line rate of end-to-end error caused by the amplication of the noise Of Sight (LOS) between satellite and intended receivers [1]. A pertaining to the signal [5]. more reliable solution to tackle this problem is using interme3) Linear-Process and Forward (LF): In this method, linear diate terrestrial relays between satellite and mobile users [2]. phase shifting is performed after amplification of analog These intermediate relays can help to increase the reliability signal. It is usually employed for distributed beam forming and throughput of the system for a given bandwidth or power pertaining to linear phase shifting phenomenon [5]. [3]. In this context, a novel framework namely, Hybrid Satellite Terrestrial Relay Network (HSTRN) was proposed B. Regenerative Relaying in [2]. Before proceeding further, we provide detailed analysis of A relay node of this types manipulates the information the relaying technologies which are being considered for inside the signal waveform upon reception and is usually upcoming wireless communication systems. Conventionally, capable of performing operations that are complex in nature. topology of cellular network is similar to star structure in which Resultantly, the whole relaying operation requires powerful BS is serving as central control point. This central point processing units. This also implies that transparent relays are provides the benefit of simplicity of architecture while generally considered power efficient as compared to regenerproviding good quality of service guarantees. Though, for next ative relays. The methods/ protocols that are most commonly generation networks, this topology also has some glaring flaws used by regenerative relaying include following sub-types: which limit the capacity of the network. This high reliance on a 1) Compress and Forward (CF): This type of relaying central network entity cannot offer energy efficiency and result allows a compressed version of signal that is detected to be in single point of failure. Thus, next generation communication re-encoded for forwarding the transmission [6]. In addition, it systems need to be adjusted to incorporate relays which can necessitates further source coding over signal samples before play a vital role. In literature, plethora of relaying methods have transmitting them and are expected to deliver optimum perforbeen proposed and discussed. Contextually, the taxonomy of mance if relay node lies near destination or it has best channel cooperative relays has been divided in to two broad groups conditions near destination. namely:

2) Estimate and Forward (EF): The relays of this type amplify and then down-converts the signal to baseband. Subsequently, the signal is recovered for a particular modulation order by using an algorithm for signal detection. Finally, the signal estimated, by using a different or similar modulation order, are then retransmitted [7]. 3) Decode and Forward (DF): Unlike the method in transparent relaying, the signal is decoded by relay and then re-encoded before transmission [8]. DF relaying has demonstrated ability to supersede other methods in terms of outage in many application scenarios. From the perspective of relay aided satellite communication, the performance of HSTRN was evaluated for DF and AF relays in [9]. The maximal ratio combining (MRC) was employed at users for combining multipath signals at the receiver and performance analysis was done based on symbol error rate. Asymptotic behavior of Free Space Optical (FSO) along with HSTRN was studied in [10] for AF relays. Authors in [11] considered Multi-Input-Multi-Output (MIMO) relays satellites and expression of outage probability was derived. The authors also presented a comparison between fixed relays and selective relays. In [12], authors analyzed a single hop scenario for multi-antenna satellite communication systems and derived expressions of outage probability and ergodic capacity. The authors in [13] investigated the DF based protocol with satellite relaying. Although above mentioned works have extensively studied and enhanced the performance of satellite terrestrial relay, yet these works assume independent channel between relay and mobile users. Moreover, the performance under Optimal Relay Selection (ORS) for HSTRN is largely unexplored. In this backdrop, this paper focuses on realistic performance analysis of HSTRN by considering correlated fading between relay and terrestrial users. Moreover, we also enhance the performance of HSTRN by performing ORS and deriving closed form expressions of outage probability of the network. The rest of the paper is organized as follows. In Section II, system model is given. Section III, provides performance analysis of HSTRN. In Section IV numerical results are provided. Finally, Section V concludes this work.

First Phase

ℎ

Due to presence of common scatterers around a single relaying node, the link between S to Ri and between Ri to D

ℎ



ℎ









 ℎ

ℎ





ℎ



D

Fig. 1. System Model

experience correlated fading. However, all the relays are placed sufficiently apart such that wireless links among all the relays are assumed to be independently faded. The transmission takes place in two phases by dividing a single block of time into two time slots. During the first phase, S transmits its signal to i-th relay. Let S transmits s signal to i-th relay with power P. Then the signal received at Ri from S, can be written as  ySRi =

P dα SRi

hSRi s + nSRi ,

(1)

where hSRi is the channel amplitude gain between S and the ith relay, nSRi is the Additive White Gaussian Noise (AWGN) at Ri with zero mean and variance N0 , dSRi is the distance between S and i-th relay and α is the path loss exponent. For the second phase, Ri decodes the signal and then reencodes it and transmit over to D. The received signal at D is expressed as  yR i D =

II. S YSTEM M ODEL We consider a downlink Land Mobile Satellite (LMS) system consisting of a geostationary satellite, S, destination D and N intermediate relaying nodes, R = {Ri |i = 1, 2, . . . N } as shown in Figure 1. All relaying nodes along with S and D are assumed be equipped with single antenna and experience Rician Shadow Fading. We assume a block fading model such that fading during a single block is invariant but changes randomly from one block to another [14], [15]. Channel State Information (CSI) of the link from S to Ri and that between Ri to D are known at S for selection of optimal relay.

Satellite (S)

Second Phase

P

hR i D s dα Ri D

+ nR i D ,

(2)

where hRi D is the channel amplitude gain between Ri and D, nRi D is the AWGN at D with zero mean and same variance as N0 , dRi D is the distance between Ri and D. The instantaneous Signal to Noise Ratio (SNR) at Ri and D can be written as γSRi =

|hSRi |2 P dα SRi N0

(3)

γ Ri D =

|hRi D |2 P , dα Ri D N0

(4)

and

respectively. The end to end SNR during one block of time in case of DF relaying is determined by the SNR of the bottleneck link. Hence, the end to end SNR can be represented as  γSRi D = min

|hSRi |2 P |hRi D |2 P , α dα dRi D N0 SRi N0

 .

(5)

III. O UTAGE P ERFORMANCE A NALYSIS OF HSTRN The outage probability of the system is defined as the probability of the event that the instantaneous rate C falls below a specified threshold R > 0 i.e. Pout,i = Pr{Ci < Rs }

(6)

where Ci =

1 log2 (1 + γSRi D ). 2

In case of ORS, the relay with maximum instantaneous rate is selected for reception of message from source and for transmission to destination. Based on this description, the Pout for ORS scheme yields Pout = Pr{max Ci < Rs }

(7)

i∈N

By exploiting the independence of wireless links among all the relays, we obtain

Pout =

N 

Pr{Ci < Rs } =

i=1

N 

mSR

mSRi i (1 + KSRi ) fγSRi (γSRi ) = γ¯SRi (KSRi + mSRi )mSRi   (1 + KSRi )γSRi × exp − γ¯SRi   KSRi (1 + KSRi ) γSRi × 1 F1 mSRi , 1; KSRi + mSRi γ¯SRi (12) where mSRi is the shadowing factor and KSRi is the Rician K factor which is the ratio of total power of line of sight components to the total power of multipath components. Also, 1 F1 (.) is the confluent hypergeometric function. Then using (12) we have mSR  ∞ mSRi i (1 + KSRi ) Pr{γSRi > 22Rs − 1} = ¯ (K + mSRi )mSRi 22Rs −1 γ   SRi SRi  (1 + KSRi )γSRi KSRi (1 + KSRi ) × exp − 1 F1 mSRi , 1; γ¯SRi KSRi + mSRi  γSRi × (13) dγSRi γ¯SRi

After some mathematical manipulations and with the help of [16] we get  Pr{γSRi > 22Rs − 1} = 1 − KSRi (22Rs − 1)Φ2 1 − mSRi mSR

Pout,i .

(8)

, mSRi ; 2; −

i=1

mSRi i (22Rs − 1) (22Rs − 1) ; γ¯SRi γ¯SRi (KSRi + mSRi )mSRi

 (14)

Using (6), we get where Φ2 (.) is the bivariate confluent hypergeometric function. Using similar approach, we can obtain

Pout,i = Pr{log2 (1 + γSRi D ) < 2Rs } = Pr{γSRi D < 22Rs − 1}

(9)

Replacing 5 in 9 yields

 Pr{γRi D > 22Rs − 1} = 1 − KRi D (22Rs − 1)Φ2 1 − mRi D mR

2Rs

Pout,i = Pr{min(γSRi , γRi D ) < 2

− 1}

(10)

Using order statistics, above expression can be simplified as Pout,i = 2 − Pr{γSRi > 22Rs − 1} − Pr{γRi D > 22Rs − 1} − Pr{γSRi < 22Rs − 1, γRi D < 22Rs − 1}

(11)

Let us first calculate Pr{γSRi > 22Rs − 1} in (11). The Probability Density Function (PDF) of γSRi is given as

, mRi D ; 2; −

mRi Di (22Rs − 1) (22Rs − 1) ; γ¯Ri D γ¯Ri D (KRi D + mRi D )mRi D D

 (15)

Now we derive the expression for Pr{γSRi < 22Rs − 1, γRi D < 22Rs − 1}. Without loss of generality and for tractability of analysis we assume mRi D = mSRi = m, KRi D = KSRi = K and γ¯Ri D = γ¯SRi = γ¯ throughout this paper. Since both γSRi and γRi D are correlated therefore we use bivariate PDF expression of Shadowed Rician fading for random variables Y and Z which is given as [17]



 (22Rs − 1) mm (22Rs − 1) ; Pout,i = K(2 − 1)Φ2 1 − m, m; 2; − + K(22Rs − 1) γ¯ γ¯ (K + m)m   mρ 2(1 + K)( mρ+K )m  ∞ (22Rs − 1) mm (22Rs − 1) ; x − × Φ2 1 − m, m; 2; − γ¯ γ¯ (K + m)m γ¯ ρ 0  2  2 2(1+K) 2(22Rs −1)(1+K)     x γ¯ (1−ρ)  + γ ¯ (1−ρ) K(1 + K) 2 (1 + K)x2 + x × 1 − exp × exp − γ¯ ρ γ¯ ρ(ρm + K) 2     

2 ∞ ∞ k 2j+k

(1 + K) (22Rs − 1) 1 1 × x x (22Rs − 1) j!Γ(j + k + 1) γ¯ (1 − ρ) k=0 j=0     ∞ k

m−1 (−1)k K(1 + K) 2 − x × dx k k! γ¯ ρ(ρm + K) 2Rs

(16)

k=0



mρ mρ+K

Substituting (14), (15) and (19) in (11) we get

m

 y2 + z2 fY,Z (y,z) = 6 yz exp − 2 σ ρ(1 − ρ)2 σ (1 − ρ)      ∞ 2yx (1 + ρ) 2 x I0 × x exp − 2 σ ρ(1 − ρ) σ 2 (1 − ρ) 0     2zx K 2 x × I0 m; 1; dx, F 1 1 σ 2 (1 − ρ) σ 2 ρ(ρm + K) (17) 8



where I0 (.) is the Bessel function of first kind and zero order. The Cumulative Distribution Function (CDF) of bivariate Shadowed Rician fading for random variables Y and Z which is obtained as  y  z   fY,Z (y, z)dzdy (18) FY,Z (Y < y , Z < z ) = 0





FY,Z (y , z ) =

mρ 2( mρ+K )m 

σ2 ρ  × 1 F1 m; 1;

∞ 0



2

x × Ψ1 × Ψ2 σ2 ρ  x2 dx (19)

x exp −

K σ 2 ρ(ρm + K)



where  Ψy = 1 − exp



( xz¯ )2 + ( yy¯ )2 2



∞  k=0

x¯ y y  z¯

k    x y × Ik z¯ y¯ (20)

and  Ψz = 1 − exp



( xy¯ )2 + ( zz¯ )2 2

(22Rs − 1) − 1) × Φ2 1 − m, m; 2; − γ¯   m 2Rs − 1) m (2 + K(22Rs − 1) × Φ2 1 − m, m; 2 ; γ¯ (K + m)m  mρ 2(1 + K)( mρ+K )m (22Rs − 1) mm (22Rs − 1) ; − ;− γ¯ γ¯ (K + m)m γ¯ ρ      ∞ (1 + K)x2 K(1 + K) 2 x x exp − × 1 F1 m; 1; γ¯ ρ γ¯ ρ(ρm + K) 0 (22) × χ2 dx, Pout,i = K(2

where  2  2 2(1+K) 2(22Rs −1)(1+K)

 x γ¯ (1−ρ) + γ ¯ (1−ρ)

0

After some simplifications and with the help of [17] we obtain



∞  k=0

x¯ z  z y¯

k    x z × . Ik y¯ z¯ (21)

where Ik (.) is the modified Bessel function.



2Rs

χ = 1 − exp  ∞ 

× x k=0

k

1 (22Rs

− 1)

2   2(1 + K) (22Rs − 1) × Ik x γ¯ (1 − ρ) (23)

The above expression can be simplified as (16) on the next page. In (16), Γ(.) is the well-known Gamma function. Now the outage probability can be obtained by straightforward substitution of (16) in (8). IV. N UMERICAL R ESULTS This section discusses the results obtained from the analysis of Section III. Unless mentioned otherwise, the values of parameters for generation of analytical and simulation results are given as: γ¯ = 10 dB, N = 3, K = 5, m = 200, ρ = 0.1 and Rs = 1 bit/sec/Hz. Figure 2 plots the Pout against the increasing values of γ¯ . It can be seen that the outage probability decreases rapidly with the increase in SNR. In contrast we observe that an increase in the threshold Rs causes an increase in Pout . Moreover, it can be seen that the increasing values of Rician K factor

 

Analy. Analy. Analy. Simul. Simul. Simul.

 

Rs = 1 bit/sec/Hz Rs = 2 bit/sec/Hz Rs = 3 bit/sec/Hz Rs = 1 bit/sec/Hz Rs = 2 bit/sec/Hz Rs = 3 bit/sec/Hz



 

Pout

Pout



 





K=10









 







K=5

 

  









γ¯ (dB)





K



Fig. 2. Outage probability against γ ¯.











 

m

Fig. 4. Outage probability against K and m.

 

 



N =1  

 



N =3

 

K

Pout

 

  



N =6

 

 















Rs (bits/sec/Hz)

Analy. Analy. Simul. Simul. 



K=5 K = 10 K=5 K = 10 





  











ρ













Fig. 3. Outage probability against Rs .

Fig. 5. Outage probability against K and ρ.

brings significant reduction in outage probability. Specifically, we note that for γ¯ = 20 dB, the outage probability decreases from 10−2 to 10−3 when K increases from 5 to 10. Figure 3 plots Pout versus Rs for different values of N and K. The outage probability curves show that an increase in the value of Rs increases the outage probability. Here, we also observe that increasing the number of cooperative relays can result into significant reduction of the outage probability. However, it can be seen that the performance gap between two values of K increases when the number of relays are increased from 1 to 6. This shows that significant performance enhancements can be achieved by increasing number of relay for same channel conditions. Figure 4 further elaborates on the impact of wireless channel by plotting outage probability as a function of K and m. In this figure we observe that the increasing values of shadowing parameter m results into prominent reduction in outage probability. In addition to this, we observe that the outage performance of HSTRN is governed by shadowing parameter

m which can result into reduction of outage probability despite any value of K. In figure 5 we illustrate the relationship between outage probability and correlation parameter ρ. It can be seen that the outage probability first decreases and then increases as the ρ increases from 0 to 0.9. The outage probability first decreases due to selection criteria of relay, according to which the relay with best channel condition is chosen. However, as the correlation increases the impact of DF relays, that are placed away from source and near the destination, becomes prominent due to increase in decoding errors at relay. Thus, we observe that despite increase in K, the contours of outage probability follow a bell shape structure. V. C ONCLUSION This article has provided in-depth analysis of the performance of HSTRN under correlated fading. In particular, we derived closed-form expression of outage probability under correlated Rician Shadow fading. We evaluated the impact

of Rician K and shadowing factor m on the performance of HSTRN. It was found that the performance gap in terms of outage probability increases with an increase in number of cooperative relays. Moreover, we unveiled that ρ has a dominant impact on outage probability which results in bell shaped contours. Our findings can be of great importance for performance evaluation of HSTRN in correlated fading environments. REFERENCES [1] M. Arti and V. Jain, “Relay selection based hybrid satellite-terrestrial communication systems,” IET Communications, 2017. [2] P. K. Upadhyay and P. K. Sharma, “Max-max user-relay selection scheme in multiuser and multirelay hybrid satellite-terrestrial relay systems,” IEEE Communications Letters, vol. 20, no. 2, pp. 268–271, 2016. [3] K. Guo, B. Zhang, Y. Huang, and D. Guo, “Performance analysis of two-way satellite terrestrial relay networks with hardware impairments,” IEEE Wireless Communications Letters, 2017. [4] J.-C. Lin, H.-K. Chang, M.-L. Ku, and H. V. Poor, “Impact of imperfect source-to-relay csi in amplify-and-forward relay networks,” IEEE Transactions on Vehicular Technology, vol. 66, no. 6, pp. 5056–5069, 2017. [5] M. Iqbal, R. Pudjiastuti et al., “Diversity maximal combining for transparent protocol with cooperative network coding (cnc),” in Asia Pacific Conference on Wireless and Mobile (APWiMob). IEEE, 2016, pp. 30–34. [6] K. Luo, R. H. Gohary, and H. Yanikomeroglu, “Exploiting the n-to1 mapping in compress-and-forward relaying,” IEEE Transactions on Information Theory, vol. 62, no. 1, pp. 290–308, 2016. [7] A. Chakrabarti, A. De Baynast, A. Sabharwal, and B. Aazhang, “Halfduplex estimate-and-forward relaying: bounds and code design,” in Information Theory, 2006 IEEE International Symposium on. IEEE, 2006, pp. 1239–1243. [8] F. Jameel, S. Wyne, and Z. Ding, “Secure communications in three-step two-way energy harvesting df relaying,” IEEE Communications Letters, vol. PP, no. 99, pp. 1–1, 2017. [9] K. An, M. Lin, W.-P. Zhu, Y. Huang, and G. Zheng, “Outage performance of cognitive hybrid satellite–terrestrial networks with interference constraint,” IEEE Transactions on Vehicular Technology, vol. 65, no. 11, pp. 9397–9404, 2016. [10] U. Javed, D. He, and P. Liu, “Performance characterization of a hybrid satellite-terrestrial system with co-channel interference over generalized fading channels,” Sensors, vol. 16, no. 8, p. 1236, 2016. [11] M. Arti, “Channel estimation and detection in satellite communication systems,” IEEE Transactions on Vehicular Technology, vol. 65, no. 12, pp. 10 173–10 179, 2016. [12] K. An, M. Lin, T. Liang, J. Ouyang, and W.-P. Zhu, “On the ergodic capacity of multiple antenna cognitive satellite terrestrial networks,” in Communications (ICC), 2016 IEEE International Conference on. IEEE, 2016, pp. 1–5. [13] J. Zhang, X. Li, I. S. Ansari, Y. Liu, and K. A. Qaraqe, “Performance analysis of dual-hop df satellite relaying over k-amp shadowed fading channels,” in Wireless Communications and Networking Conference (WCNC), 2017 IEEE. IEEE, 2017, pp. 1–6. [14] F. Jameel, S. Wyne, and I. Krikidis, “Secrecy outage for wireless sensor networks,” IEEE Communications Letters, vol. 21, no. 7, pp. 1565–1568, July 2017. [15] F. Jameel and S. Wyne, “Secrecy outage of SWIPT in the presence of cooperating eavesdroppers,” AEU-International Journal of Electronics and Communications, vol. 77, pp. 23–26, 2017. [16] J. F. Paris, “Closed-form expressions for rician shadowed cumulative distribution function,” Electronics Letters, vol. 46, no. 13, pp. 952–953, 2010. [17] J. Lopez-Fernandez, J. F. Paris, and E. Martos-Naya, “Bivariate rician shadowed fading model,” arXiv preprint arXiv:1701.02981, 2017.