1. Introduction
Satellite systems are nowadays widely used in many diverse applications such as navigation, mobile communication, broadcasting, and disaster relief. So their proper functioning in many possible scenarios is very important from both users’ and service providers’ points of view. Due to increase in population density (especially in city centers), tall/wide buildings/structures and narrow streets/roads are very common at the present time. This results in for line-of-sight (LOS) communication difficult to be maintained because of shadowing and obstacles between satellite and terrestrial user [1]-[2]. This is also referred to as masking when LOS is lost between satellite and terrestrial user and it severely affects the indoor users being served by mobile satellite systems or in case of low satellite elevation angles.
A number of performance evaluations have been done by taking the above mentioned masking effect into consideration, especially for hybrid satellite-terrestrial cooperative networks (HSTCNs) [1]-[2]. Being one of the earliest performance analysis works, [3] gives the outage probability and the symbol error rate (SER) performance of HSTCN with multiple relays using a variable gain amplify-and-forward (AF) protocol. The average SER of the fixed gain AF HSTCN with generalized (Nakagami-m) fading channels has been derived in [4]. The channel between the satellite and terrestrial nodes (relay/destination) in [3] and [4] is assumed to follow the shadowed Rice land mobile satellite (LMS) model [5]. Different aspects of HSTCN have been studied in [6]-[9]. The outage performance of a HSTCN is analytically calculated in [10], where satellite links are assumed to suffer from shadowed Rice fading, while the terrestrial channel suffers from Nakagami-m fading. In [11], authors derive the exact outage probability of a HSTCN, where selective decode-and-forward (DF) protocol is implemented between the satellite and a terrestrial node, and a selection of the best relay terminal is performed. A slightly same system model of [11] is used in [12] to study the symbol error probability performance of a HSTCN, where in [12] no direct path from satellite to terrestrial (destination) node exists. In [13], authors investigate the performance of AF relaying in a hybrid satellite-terrestrial free space optical cooperative link with no direct connection between satellite and ground user. The use of multiple antennas (at relay & destination) in hybrid satellite-terrestrial cooperative system is considered in [14]. An approximate closed-form performance analysis of maximal ratio combining (MRC) in LMS channel of [5] is provided in [15]. The performance results of MRC over correlated κ−μ shadowed fading channels are obtained in [16].
All of the above mentioned papers have significantly increased our knowledge of performance analysis of HSTCN, however they have concentrated on ideal case without co-channel interference (CCI). The assumption of no CCI is unrealistic nowadays due to the deployment of many wireless standards, and increased practice of reusing the spectrum resource as much as possible in traditional wireless networks causes interference at relay/destination [17]-[20]. Different from the previous research, recently in [21] the effect of CCI on SER of HSTCN has been investigated. In [21], DF protocol is assumed at the terrestrial relay and the destination is corrupted by multiple CCI, both the satellite-destination and satellite-relay links undergo the shadowed Rice fading while the relay-destination link follows Rayleigh fading.
As we have mentioned above with the exception of [21], the effects of multiple CCI on the performance of dual-hop HSTCN have not been investigated in the open literature. Specifically, we note that the performance analysis of three node AF based hybrid satellite-terrestrial relay network (HSTRN), with either single CCI or multiple CCI at the relay has not been done yet. As a result, in this paper, for hybrid satellite-terrestrial cooperative system, we analyze the average SER of M-PSK-modulated dual-hop fixed gain AF relay system with multiple interferers at the relay. We study a network with no direct connection between source (satellite) and destination (terrestrial mobile user), where a relay (terrestrial) forwards the source message to the destination. The direct link between satellite and destination is unavailable due to the following propagation impairments: the blocking of signals produced by large obstacles (shadowing), severe attenuation (path loss) and multipath fading. The above mentioned wireless propagation effects are most common in satellite to terrestrial radio links, that is why we study the relay network having no direct link from satellite to terrestrial receiver. We consider generalized fading channels where the source-relay (satellite-earth) link follows the shadowed Rice LMS model; and the relay-destination and interferers-relay links follow Nakagami-m fading. The system model proposed here is particularly applicable to frequency-division relay systems [22]-[23], where the relay and destination nodes experience different interference patterns. Also, the system model considered here is strongly motivated by the fact that multi-access relay techniques deal with many sources (satellites), which use the same relay in order to deliver their data to a single destination [24]. We derive the exact moment generating function (MGF) of the proposed network, based on the derived MGF the average SER of the considered relay network is obtained. Extensive performance analysis in the presence of multiple interferers for M-PSK modulation is done based on the expressions developed in the paper.
The remainder of this paper is organized as follows. Section 2 gives the detailed system model of considered dual-hop relay network. Section 3 details the performance analysis of the proposed system model. Specifically, MGF of the cooperative link is derived and, based on this exact MGF analytical expression for SER of the cooperative link is given. Section 4 presents the detailed numerical results. Finally, Section 5 concludes this paper.
2. System Model
We consider a hybrid/integrated satellite-terrestrial communication system, where a satellite communicates with a destination node at ground through a relay node located at ground. It is assumed that satellite does not have a direct link to destination node. The communication in the system is divided into two orthogonal phases. In the first phase, the satellite sends its signal to the relay. At relay, the received signal in the presence of n interferers, will be
where h1 is the channel gain between the satellite and the relay; x is the satellite’s transmitted symbol with Es power; h3j is the channel gain between the jth interferer and the relay; yj is the jth interferer’s transmitted symbol with Eij power; n1 is the zero-mean additive white Gaussian noise (AWGN) at relay with variance.
In the second phase, the relay multiplies the received signal1ywith a fixed gain G>0. The amplified signal is forwarded (sent) to the destination. The received signal at destination is given by
where h2 is the channel gain between the relay and the destination, and n2 is AWGN at destination with variance.
The satellite-relay link is assumed to follow the shadowed Rice fading channel with the following probability density function (PDF) [4]-[5]
where Ω1 is the average power of LOS component, 2b1 is the average power of the multipath component, 1F1(a;b;z) is the confluent hypergeometric function [25, Eq. (9.210.1)], and 0≤m1≤∞ is the Nakagami parameter. For m1=0, (3) simplifies to the Rayleigh PDF in (4), while for m1=∞, it reduces to the Rice PDF. In the shadowed Rice model of [5], the scattered component of the received signal follows Rayleigh distribution and LOS component follows a Nakagami-m distribution as follows:
where 2b0 = E[X2] is the average power of the scatter (multipath) component, Γ(·) is the gamma function is the Nakagami parameter, and Ω=E[Y2] is the average power of the LOS component.
The relay-destination link is assumed to follow the Nakagami-m distribution; hence, |h2|2 follows the Gamma distribution [4] as
where and Ω2 denote the shape and scale parameters, respectively, of the relay-destination channel.
The interferer-relay link is assumed to follow the Nakagami-m distribution; hence, |h3j|2 follows the Gamma distribution [4] as
where and Ω3j denote the shape and scale parameters, respectively, of the interferer-relay channel.
3. Performance Analysis
In this section, we will derive the average SER of the system model described in Section 2. We follow the standard MGF based approach [26]. The overall signal-to-interference-plus-noise ratio (SINR) γ can be written [27]-[28], by using (2), as
In case of equal-power interferers (Eij = Ei, for j=1,2,...,n), the step (a) in (8) follows from the use of the following property (summation) of Gamma distribution. When |h3j|2 has a Gamma (m3j, Ω3) distribution for j=1,2,...,n (i.e., all distributions have the same scale parameter Ω3), then,
provided that all |h3j|2 are independent. In case of arbitrarily powered (unequal-power) interferers Ei1≠Ei2≠,...,≠Ein, the step (a) in (8) follows by first applying the scaling property of the Gamma distribution, and then using the summation property of Gamma distribution. The scaling property says that, when |h3j|2▭Gamma(m3j, Ω3j) for j=1,2,...,n, then for any Eij ˃ 0, Eij|h3j|2▭Gamma(m3j, EijΩ3j. Here, for the sake of mathematical tractability and analytical simplicity we assume that Ei1Ω31 = Ei2Ω32 = ,..., EinΩ3n, so that after scaling and summation operations, respectively, the result of the denoted by Ei|h3|2, still follows the Gamma distribution.
Alternatively, (8) can also be written as
On substituting in (9), we finally get
where in (10), is the average signal-to-noise-ratio (SNR), and is the equivalent interference-to-noise-ratio (INR) of interferer-relay links.
3.1 Calculation of the MGF of the Considered System Model
The MGF of the considered system model can be written as
We pick and define the following integral from the above triple-integral:
It can be proved in Appendix I that
Let us now define the following integral from (11) by using I1:
We substitute (13) and (6) in (14), and get the following
By using the method outlined in [4], (15) becomes
where c1 = ⌊m1⌋−1 and e = m1 − ⌊m1⌋ for m1>1; c1=0 and e = m1−1 for m1≤1; and ⌊x⌋ denotes the largest integer not greater than x. By the use of Binomial expansion
in (16), we rewrite (16) as
Now we employ the following approximation (1+x)η≈1+ηx,x<1 (17), and after applying some elementary algebraic operations (for details see Appendix II), we obtain
where,
The MGF of the considered system model can now be written, using (11) and I2, as
By putting (18) in (22), and after rearrangement of integrals and sums, we write the expression for MGF of our proposed system as
In (23)
It can be seen from (24)-(28) that MGF contains finite and infinite integrals, which can be accurately/easily calculated in MATLAB or Mathematica.
3.2 Calculation of SER
The SER of the considered HSTCN for M-PSK constellation is given by [4], [26] as:
where and
Alternatively, the following accurate approximation of (29) can be used from [29]:
where
4. Numerical Results
This section presents the analytical and simulated results of the considered AF based HSTRN scheme using M-PSK modulation over generalized fading channels. We demonstrate the expressions derived in Section 3 using numerical examples and study the effect of interference on the system’s performance. The simulated results are obtained by generating 107 channel realizations for BPSK, QPSK and 8-PSK symbols. It is assumed that relay-destination channel & interference channels follow the Nakagami-m fading with parameters taken from [22]. The satellite-relay LMS channel is varied according to different shadowing conditions. The parameters of the shadowed Rice LMS model are shown in Table 1.
Table 1.LMS channel parameters [5]
Fig. 1 shows the average SER versus SNR of the considered HSTRN, for infrequent light shadowing (satellite-relay LMS channel), with multiple values of CCI (-5 dB, 0 dB and 5dB) using different M-PSK modulation schemes: BPSK, QPSK and 8-PSK. It is assumed that = ; and on the x-axis of Fig. 1 (a), Fig. 1 (b) & Fig. 1 (c), SNR denotes ; CCI represents We consider the situation when relay is interfered by three equal-power interferers, i.e., n = 3, and is the CCI caused by each interferer i≤n. The values of total CCI experienced by the source to relay link are selected as: -5 dB, 0 dB and 5dB. Any other appropriate value of CCI could be used by system designer based on specific conditions. Note that our considered system model and analysis deals with the case of arbitrary number of interferers having different transmit powers and channel parameters (already described in Section 3). Here, for simplicity and illustration purposes we consider a most common subset of this case, i.e., multiple equal-power independent interferers. The theoretical SER is plotted by using (30). Fig. 2 presents the average SER versus SNR of the considered HSTRN, for average shadowing (satellite-relay LMS channel), with multiple values of CCI (-5 dB, 0 dB and 5dB) using different M-PSK modulation schemes: BPSK, QPSK and 8-PSK. Fig. 3 illustrates the average SER versus SNR of the considered HSTRN, for frequent heavy shadowing (satellite-relay LMS channel), with multiple values of CCI (-5 dB, 0 dB and 5dB) using different M-PSK modulation schemes: BPSK, QPSK and 8-PSK. The above discussion about values of network parameters for Fig. 1 is also valid for Fig. 2& Fig. 3. We observe from Fig. 1, Fig. 2 & Fig. 3 that simulated SER very closely follows the analytical SER, for all shadowing situations and modulations, considered in the figures; indicating the correctness of the approximations taken and derived analytical formula.
Fig. 1.Average SER versus SNR for M-PSK with CCI in infrequent light shadowing
Fig. 2.Average SER versus SNR for M-PSK with CCI in average shadowing
Fig. 3.Average SER versus SNR for M-PSK with CCI in frequent heavy shadowing
As we can see from Fig. 1, Fig. 2 & Fig. 3, that when CCI at relay increases from -5 dB to +5 dB, there is a notable increase in average SER of the considered system for a given modulation format. We observe that the increase in SER is more prominent for higher-order modulation such as 8-PSK than that of lower-order modulation scheme of BPSK. This can be seen from Fig. 1, Fig. 2 and Fig. 3, e.g., by comparing the curves for 8-PSK and BPSK for the same value of given CCI. The same reasoning is also valid for comparing combinations of 8-PSK/QPSK and QPSK/BPSK. When LMS channel experiences increase in amount of shadowing, as shown by the sequence of Fig. 1, Fig. 2 and Fig. 3, respectively, we notice that the average SER of the HSTRN also increases correspondingly. The reader can view the effect of shadowing on the considered system by comparing the curves for particular modulation with the same given CCI from Fig. 1, Fig. 2 and Fig. 3. We also comment here about the computational time of the expression for MFG in (23) since it contains multiple integrals. We tested in MATLAB that for different SNRs (dB), e.g. {10, 20, 30}, modern personal computer takes approximately 0.2 seconds to calculate (23). The impact of the fading severity of the relay-destination link, namely nakagami m2 parameter, is shown in Fig. 4. The analysis is done for QPSK modulated HSTRN with 0 dB CCI over average shadowed LMS source-relay channel. It can be observed from Fig. 4 that, with the increase in value of m2(decrease in amount or degree of fading), there is a corresponding decrease in SER. The impact of the fading severity of the interferers-relay links, namely nakagami m3 parameter, is shown in Fig. 5. The study is done for QPSK modulated HSTRN with multiple values of m3 amounting to different CCIs over average shadowed LMS source-relay channel. It can be observed from Fig. 5 that, with the increase in value of m3(decrease in amount or degree of fading), there is a corresponding increase in SER. The increase in SER is due to the fact that with decrease in amount or degree of fading, the power of the interferers’ signal increases and so do the resulting CCI caused by it.
Fig. 4.Impact of the fading severity of the relay-destination link
Fig. 5.Impact of the fading severity of the interferers-relay links
5. Conclusion
In this paper, we have investigated the performance of AF based hybrid satellite-terrestrial cooperative system in an interference environment. We have examined the average SER of a HSTRN with multiple interferers at the relay. We have derived the average SER of the considered system under the assumption of generalized fading channels. Our analysis has shown that CCI causes significant degradation in SER performance of AF based hybrid satellite-terrestrial cooperative system. Our results are valuable in understanding how interference at the relay can degrade the overall performance, depending on different channel, interference and network parameters.
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