Performance Analysis of NOMA Integrated Hybrid Satellite Terrestrial Communication System using ML

doi:10.21203/rs.3.rs-1746621/v1

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Performance Analysis of NOMA Integrated Hybrid Satellite Terrestrial Communication System using ML

https://doi.org/10.21203/rs.3.rs-1746621/v1

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The Non Orthogonal Multiple Access (NOMA) is a promising technology for future communication system due to its ability to offer services to multiple users with better connectivity and low latency. The NOMA based Cooperative Relay System (NOMA-CRS) is used to improve the spectral efficiency as compared to conventional Cooperative Relay System (CRS). In this paper, the performance of NOMA over hybrid satellite terrestrial communication system is analyzed over two different fading channels- Shadowed Rician fading channel and Nakagami-m fading channel in two phases of downlink transmission and also derived the expression for end to end Bit Error Rate of proposed model assisted with cooperative relays. The results have shown significant performance with variations in the derived parameters and validated in extensive simulations.

Bit Error Probability (BEP)

Bit Error Rate (BER)

Non Orthogonal Multiple Access (NOMA)

Cooperative Relay System (CRS)

Shadowed Rician (SR) fading

Nakagami-m fading

Successive Interference Cancellation (SIC)

Satellite communication basically refers to any kind of communication link which involves satellite in propagation path of signal to provide services such as data communication, telemetry, navigation, weather forecasting broadcasting and telecommunication. Satellite communication takes place with the help of various multiple access techniques like FDMA, OFDMA CDMA and TDMA. But during the recent years, Non-Orthogonal Multiple Access (NOMA) has been envisioned as one of the most emerging and promising technology due to its massive connectivity, high spectral efficiency and low latency. The basic idea of NOMA is to serve multi users with various applications such as cellular future radio access [2] and 5G communication systems [3]. NOMA is classified into two types namely Power Domain NOMA and Code Domain NOMA. Power domain NOMA (PD-NOMA) performs the multiplexing of different signals in power domain and Code domain NOMA (CD-NOMA) multiplexes the different signals in domain of code. The Power domain NOMA (PD-NOMA) is commonly used in satellite communication because of its various advantages and potentials over CD-NOMA. To make the transmission more reliable, cooperative relays are often integrated with NOMA to analyze the performance [4] and capacity [5]-[6]. The relays used are either half duplex or full duplex [7] depending upon the configuration of the system with any one of the three relay strategies i.e., Decode & Forward (DF) relaying, Amplify & Forward (AF) relaying and Compress & Forward (CF) relaying. The appropriate selection of relay and their strategies are very important for effective transmission as demonstrated in [8]. The performance analysis of NOMA assisted cooperative relay using AF relaying strategy to evaluate outage probability and derive diversity order has been done in [9].

There are different communication channel models such as mobile to mobile communication system [10], terrestrial communication channel, mobile satellite channel [11], land mobile satellite channel [12]-[15] which have been proposed in past studies to investigate the performance and make the transmission efficient using satellite. Another advanced model to mitigate the masking effect during transmission is the hybrid satellite terrestrial network which has been extensively studied and investigated in [16]. The progressive analysis of developed models helped in obtaining the characteristics and measurement statistics [17]-[18]. The transmission process often gets encountered to fading [19] and shadowing [20]. The fading occurs due to multi-path signal propagation and deteriorates the strength of signal transmitted. The statistics of fading with respect to change in atmospheric conditions have been investigated in [21] showing the effect of slow and fast fading of signal during transmission. The applications of various channel models with fading are also estimated in [22]-[23]. There are various distributions proposed to model small scale fading such as Nakagami-m [24], Rayleigh, Hoyt, Weibull etc. Some other new fading models such as Shadowed-Rician (SR) model [25]-[26] have also been proposed in previous studies. The shadowing on the other hand, is the phenomenon which occurs due to presence of obstacles in the path of signal such as buildings, trees, mountains etc. To model shadowing, Gamma distribution and log-normal distribution can be used. In various studies [27]-[30], SR fading model has been extensively used to perform the error performance of NOMA based system and derive the closed form expressions. Another investigative performance of NOMA assisted relay system has been done over Nakagami-m fading in [31]. The analysis of performance of satellite-terrestrial network over the generalized fading channels to obtain the diversity order and derive the expression of error rate has been done in [32]. In addition, the NOMA integrated satellite-terrestrial network has also been studied to analyze the performance in [33]-[34].

With the advancement of intelligent technologies, Artificial Intelligence (AI) has emerges as a potential tool for providing ubiquitous services and solving numerous complex problems in different fields like communication, wireless technology, medicine, smart home, satellite communication etc. AI is classified into three sub-classes- Machine Learning (ML), Reinforcement Learning (RL) and Deep Learning (DL). ML is basically the branch of AI which teaches the machine to imitate human mind to provide solution to the problems with the help of algorithms. While RL is a type of ML technique where a cost/reward is awarded to the trained machine on correct behavior and penalty is charged on wrong attempts. And DL is a ML technique based on Artificial Neural Network (ANN) to solve the problems. All the three branches of AI are very useful in innumerable applications. In [40], a detailed review of AI for satellite communication has been presented and discussed various features, future scopes and state of art algorithms of AI in existing as well as emerging fields. It is shown in recent studies that with the help of ML algorithms, the successful results can be achieved in diverse applications such as satellite communication, wireless communication, channel modelling, network traffic forecasting, anti-jamming, wireless network design [41] and satellite-terrestrial networking [42]. The intelligent antenna pointing integrated satellite- ground communication system with improved efficiency using ML algorithms has also been proposed in [43]. The adaptability and other applications of ML algorithms in real world satellite operations for communications with reduced complex computation and desirable results have been presented in [44] with the related security approaches in [45].

In this paper, we analyze the approximated closed form expression of bit error probability (BEP) of NOMA integrated hybrid Satellite-Terrestrial communication system using power allocation and power sharing techniques, shaping parameters and spread parameters. The concept of using ML with NOMA to derive the closed form error expression has not been presented in previous literature work. Also, it is not easy to obtain the maximum value and insight of the proposed system by observing the complex expressions, therefore, we investigate the bit error performance of the NOMA integrated hybrid Satellite-Terrestrial communication system using elevation angle. With the help of suitable range of elevation angle, wide area for downlink transmission can be covered to analyze the performance statistics. This paper is organized into five sections. An introduction to the paper and the related literature survey is presented in Section I. The section II contains the system model and its detailed description. Numerical results showing the effect of different parameters involved over end to end BEP are shown in Section III. The Section IV includes the useful conclusions of the paper. The final section V is an Appendix section containing the related definitions and formulations.

In this paper, the system contains a Cooperative Relay node, a source (S) node and a destination (D) node. The source is a satellite and the destination is an earth station. The relay is a half duplex relay, present at the earth. Each of these units are well equipped with a single antenna for downlink transmission. Considering the cost of maintenance, ease to use and gain in the practical cases, single antenna is employed in the system. There are two types of channels links present in the system namely satellite channel link and terrestrial channel link. The link between source and destination as well as between source and relay is satellite channel link which is assumed to follow Shadowed Rician distribution [15] while the terrestrial channel link is present between relay and destination, assuming to follow Nakagami- m distribution [24],[31].

The Fig-1 shows block diagram of the system model for downlink transmission. The dotted line shows the satellite channel link and the darker line shows terrestrial channel link. For better efficiency, NOMA is applied for two consecutive symbols s₁ and s₂ to be transmitted simultaneously with an assumption that symbols s₂ contains more information than symbols s₁. NOMA uses the concept of using superposition coding principle at transmitter and Successive Interference Cancellation (SIC) at the relay. It is assumed that the SIC implemented at relay is perfect to avoid interference. This strict assumption should be relaxed considering the nature of wireless communications. Then, using the superposition coded symbol conveyed to destination and relay, the received signal in the first phase of transmission can be given from [1] as

$$y=\sqrt {{P_s}} (\sqrt \alpha {s_1}+\sqrt {(1 - \alpha )} {s_2}){h_z}+{W_z}$$

Where ${h_z}$is flat fading channel coefficient with z = sd,sr,rd and are source to destination, source to relay and relay to destination respectively and $\alpha$ is the power allocation coefficient and assumed to be less than 0.5. ${P_s}$ is the transmit power of source. ${W_z}$ denotes additive white Gaussian noise with variance ${N_0}$. ${s_1}$ and ${s_2}$ are the two symbols that are transmitted simultaneously. In the first phase of transmission, symbol ${s_2}$ is detected by relay and destination while symbol ${s_1}$ is treated as noise. To detect the ${s_1}$ symbol, relay uses SIC to estimate ${\hat {s}_1}$ and forward it to the destination in second phase and is given from [1] as

$${y_{rd}}=\sqrt {{P_r}} {\hat {s}_1}{h_{srd}}+{W_{rd}}$$

where ${P_r}$ denotes the transmit power of relay. The Eq. (2) shows that symbol ${s_1}$ is detected by the destination based on ${y_{rd}}$. We want to obtain the total Bit Error Probability (BEP) of the NOMA-CRS, therefore, according to the law of probability, the average Bit error probability (ABEP) of the NOMA CRS with symbols ${s_1}$and ${s_2}$ can be given as

$${P_{e2e}}(e)=\frac{{{P_{{s_1}}}(e)+{P_{{s_2}}}(e)}}{2}$$

Where ${P_{{s_1}}}(e)$ and ${P_{{s_2}}}(e)$ are the BEPs of symbols ${s_1}$ and ${s_2}$ respectively. Since only symbol ${s_2}$is transmitted to the destination in first phase and symbol ${s_1}$ is detected as noise therefore, the BEP for symbol ${s_2}$ appears same as the BEP of far end user in downlink NOMA transmission which is dependent on constellation pairs chosen. Thus, the conditional BEP of the far end user in NOMA given in [1] is used as.

$${P_{{s_2}}}(e|{\gamma _{sd}})=\sum\limits_{{i=1}}^{M} {{P_i}Q(\sqrt {2{\upsilon _i}{\rho _s}{\gamma _{sd}}} )}$$

where ${\rho _s}={P_s}/{N_0}$and ${\gamma _z}=|{h_z}{|^2}$. The coefficients ${P_i}$, M and ${\nu _i}$ vary according to the chosen constellation pair for symbols ${s_1}$and ${s_2}$. If the chosen constellation pair is BPSK then as given in [1], ${\upsilon _i}=1 \mp 2(\sqrt {(\alpha ) - {{(\alpha )}^2}} )$, ${P_i}$= 0.5 and M = 2. Since the satellite channel links are supposed to follow Shadowed Rician fading in first phase therefore, we can express the SR fading distribution for symbol ${s_2}$as given in [15] and [29] and with the help of Eq. (4) as

$$P_{{{s_2}}}^{{sd}}(e)=\int\limits_{0}^{\infty } {\sum\limits_{{i=1}}^{M} {{P_i}Q} } \sqrt {2{\upsilon _i}{\rho _s}{\gamma _{sd}}} {\alpha _i}{e^{ - {\beta _i}x}}{}_{1}{F_1}({m_i};1;{\delta _i}x)dx$$

where ${}_{1}{F_1}$ denotes confluent hypergeometric function given in [35], [36] and ${m_i}$ is the shaping parameter of the Shadowed Rician (SR) fading distribution with i = 0,1 and the other parameters are given in [32] as follows.

${\alpha _i}=0.5{(\frac{{2{b_i}{m_i}}}{{2{b_i}{m_i}+{\Omega _i}}})^{{m_i}}}/{b_i}$ ; ${\beta _i}=\frac{{0.5}}{{{b_i}}}$ ; ${\delta _i}=\frac{{0.5{b_i}}}{{2{b_i}^{2}{m_i}+{b_i}{\Omega _i}}}$

The parameter ${\Omega _i}$ denotes average power of the LOS component and $2{b_i}$ denotes the average power of multi-path component. The range of shaping parameter ${m_i}$ varies from 0 to $\infty$. Now for calculating BEP, the approximated Q function [39] is used and given as

$$Q(x)=\frac{1}{{12}}{e^{\frac{{ - {x^2}}}{2}}}+\frac{1}{4}{e^{\frac{{ - 2{x^2}}}{3}}}$$

Now, the Eq. (5) can be rewritten with the help of Eq. (6) and properties of hypergeometric function [36], [37] to obtain the BEP of symbol ${s_2}$ as follows

$$P_{{{s_2}}}^{{sd}}(e)=\frac{1}{{12}}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}})+\frac{1}{4}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}})$$

While, the symbols ${s_1}$ are detected in the initial phase of transmission at relay and forwarded to the destination in next phase. The detection is erroneous in both the phases but are totally independent. So, with the help of law of total probability, the BEP of symbol ${s_1}$ is

$${P_{{s_1}}}(e)=P_{{{s_1}}}^{{sr}}(e)[1 - P_{{{s_1}}}^{{rd}}(e)]+[1 - P_{{{s_1}}}^{{sr}}(e)]P_{{{s_1}}}^{{rd}}(e)$$

where$P_{{{s_1}}}^{{sr}}(e)$ and $P_{{{s_1}}}^{{rd}}(e)$ are BEPs of symbol ${s_1}$ from source to relay in very first phase and relay to destination in the second phase respectively. The second phase transmission is not encountered with interference so, the transmission from relay to destination becomes easier to obtain the BEP of symbol ${s_1}$. For BPSK, the conditional probability of ${s_1}$ is given with the help of [1] as

$${P_{{s_1}}}^{{rd}}(e|{\gamma _{rd}})=Q\sqrt {2{\rho _r}{\gamma _{rd}}}$$

Where ${\rho _r}={P_r}/{N_0}$. The use of SIC resulted in detection of symbols ${s_1}$ where Nakagami-m fading distribution is assumed to have followed. Therefore, the BEP of symbol ${s_1}$ from [1] can be given as follows

$$P_{{{s_1}}}^{{rd}}(e)=\frac{1}{{2\sqrt \pi }}\frac{{\sqrt P }}{{{{(1+P)}^{{m_{rd}}+0.5}}}}\frac{{\Gamma ({m_{rd}}+0.5)}}{{\Gamma ({m_{rd}}+1)}}{}_{2}{F_1}(1;{m_{rd}}+0.5;{m_{rd}}+1;\frac{1}{{1+P}})$$

Where $P=\frac{{{\rho _r}{\Omega _{rd}}}}{{{m_{rd}}}}$. The Eq. (10) is applicable when ${m_{rd}}$ is non integer while for integer values, the equation from [1] is given as under

$$P_{{{s_1}}}^{{rd}}(e)=\frac{1}{2}[1 - {\mu ^2}(P)\sum\limits_{{j=0}}^{{{m_{rd}} - 1}} {\left( {_{j}^{{2j}}} \right)} {(\frac{{1 - {\mu ^2}(P)}}{4})^j}]$$

Where $\mu (P)=\sqrt {\frac{P}{{1+P}}}$. In the first phase of transmission, the relay received the superimposed signal for which SIC is employed therefore, the propagation of error during SIC should be considered in the analysis and closed form derivation of BEP. To detect symbol ${s_1}$ the symbol ${s_2}$ should be detected first and the detected symbol ${\hat {s}_2}$ should be subtracted from the received signal. For the analysis, both the erroneous and correct SIC of symbol ${s_2}$ should be taken into consideration. Since the satellite channel link is supposed to follow the Shadowed Rician fading therefore, the conditional BEP of ${s_1}$ symbols in first phase of downlink transmission from [1] can be given as

$${P_{{s_1}}}(e|{\gamma _{sr}})=\sum\limits_{{i=1}}^{N} {{\eta _i}Q\sqrt {2{V_i}{\rho _s}{\gamma _{sr}}} }$$

Where ${V_i}$, N and ${\eta _i}$ varies with modulation pairs and for BPSK from [1], ${\eta _i}$ = 0.5 [2,–1, 1, 1,–1], N = 5 and the roots values are ${V_i}=[\alpha ,1 \pm 2\sqrt {\alpha - {\alpha ^2}} ,4 - 3\alpha \pm 4\sqrt {\alpha - {\alpha ^2}} ]$. Now, with the help of approximated Q function given in Eq. (6) and the conditional BEP of Eq. (12), the BEP for symbol ${s_1}$ is evaluated and given as

$$P_{{{s_1}}}^{{sr}}(e)=\frac{1}{{12}}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{{V_i}{\rho _s}+{\beta _{isr}}}})+\frac{1}{4}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}})$$

Where the parameters ${\alpha _{isr}}$ and ${\beta _{isr}}$ are defined in the similar way as ${\alpha _i}$ and ${\beta _i}$. ${m_{sr}}$ is the shaping parameter. Now, end to end bit error probability (BEP) of the system can be evaluated by substituting the Eq. (10) and Eq. (13) in Eq. (8) and the obtained result and Eq. (7) in Eq. (3), we get final Eq. (A) for non-integer values of ${m_{rd}}$ as given below

${P_{e2e}}(e)=\frac{1}{2}[[\frac{1}{{12}}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{{V_i}{\rho _s}+{\beta _{isr}}}})+\frac{1}{4}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}})] \times$ \(\begin{gathered} [1 - \frac{1}{{2\sqrt \pi }}\frac{{\sqrt P }}{{{{(1+P)}^{{m_{rd}}+0.5}}}}\frac{{\Gamma ({m_{rd}}+0.5)}}{{\Gamma ({m_{rd}}+1)}}{}_{2}{F_1}(1;{m_{rd}}+0.5;{m_{rd}}+1;\frac{1}{{1+P}})]+ \hfill \\ [\frac{1}{{2\sqrt \pi }}\frac{{\sqrt P }}{{{{(1+P)}^{{m_{rd}}+0.5}}}}\frac{{\Gamma ({m_{rd}}+0.5)}}{{\Gamma ({m_{rd}}+1)}}{}_{2}{F_1}(1;{m_{rd}}+0.5;{m_{rd}}+1;\frac{1}{{1+P}})] \times \hfill \\ [1 - \frac{1}{{12}}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}) - \frac{1}{4}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}})]+ \hfill \\ [\frac{1}{{12}}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}})+\frac{1}{4}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}})]] \hfill \\ \end{gathered}\)

And for the integer values of ${m_{rd}}$, the end to end bit error probability (BEP) of the system can be calculated by substituting the Eq. (11) and Eq. (13) in Eq. (8) and the obtained result and Eq. (7) in Eq. (3), we get final Eq. (B) as follows

\(\begin{gathered} {P_{e2e}}(e)=\frac{1}{2}[[\frac{1}{{12}}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{{V_i}{\rho _s}+{\beta _{isr}}}})+\frac{1}{4}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}})] \times \hfill \\ [\frac{1}{2}+\frac{{{\mu ^2}(P)}}{2}\sum\limits_{{j=0}}^{{{m_{rd}} - 1}} {\left( {_{j}^{{2j}}} \right)} {(\frac{{1 - {\mu ^2}(P)}}{4})^j}]+[\frac{1}{2} - \frac{{{\mu ^2}(P)}}{2}\sum\limits_{{j=0}}^{{{m_{rd}} - 1}} {\left( {_{j}^{{2j}}} \right)} {(\frac{{1 - {\mu ^2}(P)}}{4})^j}] \times \hfill \\ [1 - \frac{1}{{12}}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}) - \frac{1}{4}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}})]+ \hfill \\ [\frac{1}{{12}}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}})+\frac{1}{4}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}})]] \hfill \\ \end{gathered}\)

Thus, it can be seen that the total BEP obtained is the sum of individual BEPs of symbols ${s_1}$ and ${s_2}$. The overall error performance can be further improved by considering the effect of elevation angle. The elevation angle is the angle under which the satellite is observed for fair transmission and reception of signal. The concept of elevation angle is incorporated in our proposed system to improve the transmission by considering Line of Sight between satellite and ground stations (destination and relay). The effect of elevation angle is observed over total Bit Error Probability (BEP). But not all the angles result in successful transmission, therefore only a suitable range defined in [15] and [38] is useful and defined as 20°≤ θ ≤ 80° and the parameters depending on θ are expressed as

$\begin{gathered} {b_0}(\theta )= - 4.7943 \times {10^{ - 8}}{\theta ^3}+5.5784 \times {10^{ - 6}}{\theta ^2} - 2.1344 \times {10^{ - 4}}\theta +3.2710 \times {10^{ - 2}} \hfill \\ m(\theta )=6.3739 \times {10^{ - 5}}{\theta ^3}+5.8533 \times {10^{ - 4}}{\theta ^2} - 1.5973 \times {10^{ - 1}}\theta +3.5156 \hfill \\ \Omega (\theta )=1.4428 \times {10^{ - 5}}{\theta ^3} - 2.3798 \times {10^{ - 3}}{\theta ^2}+1.2702 \times {10^{ - 1}}\theta - 1.4864 \hfill \\ \end{gathered}$

where ${b_0}(\theta )$ is power of multipath component, $m(\theta )$ is shaping parameter and $\Omega (\theta )$ is average power of the LOS component of proposed system as a function of θ. Their effect is observed over derived expression of total BEP of proposed system for integer and non-integer cases shown in the respective plots.

Now, let us consider power sharing coefficient as $\beta$ therefore the total power P’ can be shared as ${P_1}$ = $\beta$ P’ and ${P_2}$ = (1- $\beta$) P'. The function of BEP is given as $F=f(\alpha ,\beta )$ We employed machine learning (ML) algorithm to obtain an appropriate value of $\alpha$ and $\beta$ for better Bit Error Probability (BEP). The training of model is done offline consequently reducing the computational complexity and improving the online implementation. A three tier (input, hidden and output layer), well connected neural network (NN) model is built to obtain effective values of $\alpha$, $\beta$ pair. The neural network used 10 hidden layers to train the model. The ML algorithm that has been used is Levenberg-Marquardt algorithm. The NN model is trained offline with different set of values to predict the appropriate values of the pair. For epoch count of 1000, 12 iterations and 7 validation checks, the performance of the model has been analyzed. The model performed well in training with the performance metrics 2.287e-8 MSE, regression 0.98189 and gradient 8.56e-8. Then, the trained network was tested for different inputs exclusive of training dataset and the test performance metrics otained is 2.2441e-8 MSE, regression 0.9801 and gradient 8.369e-8.

The analytic and simulated results have investigated the approximated closed form of bit error performance of NOMA integrated hybrid satellite-terrestrial communication system using ML with the help of power allocation and power sharing techniques in downlink transmission by varying the derived parameters i.e., power allocation coefficient α, power sharing coefficient 𝛃, shaping parameters ${m_z}({m_i},{m_{rd}},{m_{sr}})$and spread parameters${\Omega _z}({\Omega _i},{\Omega _{rd}})$. The value of power allocation coefficient is kept less than equal to 0.5 for fair reception of the symbols at the destination. Since, the concept of superposition coding is prevalent is NOMA, therefore, one of the symbol has been allotted power coefficient greater than the other symbol and thereby reducing the probability of error propagation between end users. The effect of different shadowing environment is observed over the BEP.

The plot of end to end BEP is shown in Fig-2 is depicting the error performance of our proposed model with variation in parameters $(\alpha ,\beta ,{m_z},{\Omega _z})$ in downlink transmission when m_rd is non integer. The end to end BEP plot for integer cases of m_rd is shown in Fig-3. It can be observed from these two plots that total BEP is much lower and better with smaller values of α and increases with increase in its value. Due to complexities involved in derived expressions, it is difficult to analyze the performance using standard methods, therefore ML based approach is used.

With the help of ML based neural network, the appropriate selection of values of α and 𝛃 pair of the model is achieved for analysis of error performance as shown in Fig-4 and Fig-5 respectively. Increasing their values beyond a range might deteriorates the performance of the system.

The elevation angle θ has also an important role in achieving improved transmission of signal by observing the satellite at a specified range of 20°≤ θ ≤ 80° in Fig-6. From the plot, it can be noticed that as the angle approaches right angle, the transmission gets perturbed, therefore it is kept less than right angle.

The Fig-7 shows the variation in BEP with respect to different values of shaping parameter m_z and it is noticed that transmission improves as the value of m_z increases, resulting in improved BEP.

The Fig-8 shows the plot of theoretical and simulated analysis of our proposed system. All the simulations of this paper are performed in MATLAB.

In this paper, performance of NOMA integrated hybrid satellite-terrestrial communication system is investigated and analyzed using ML and the approximated closed form expression of end to end bit error probability of proposed model is derived for downlink transmission. Based on analysis and simulations in MATLAB, remarkable improvement in Bit Error Probability (BEP) is achieved by varying the derived parameters i.e $\alpha ,\beta ,{m_z},{\Omega _z}$. The performance metrics have been obtained using ML algorithm in proposed neural network model where the training of data is done offline to reduce computational complexity and time. It is concluded from analysis and simulations that the overall performance of proposed model shows improvement with increase in values of shaping parameter over a finite range and smaller values of power allocation coefficient and power sharing coefficient. Also, the BEP is further improved by selecting suitable range of the elevation angle θ. This study can be further extended to achieve optimized performance in various other NOMA assisted systems using AI algorithms.

We consider the approximated Q function and the distribution of Shadowed Rician fading for the evaluation of BEP of symbol ${s_2}$ in first phase and symbol ${s_1}$ in other phase. The approximated Q function from [39] can be given as

$Q(x) \leqslant \frac{1}{4}{e^{ - {x^2}}}+\frac{1}{4}{e^{ - {{\frac{x}{2}}^2}}} \leqslant \frac{1}{2}{e^{ - {{\frac{x}{2}}^2}}}$

or it can be rewritten as

$$Q(x) \leqslant \frac{1}{{12}}{e^{ - {{\frac{x}{2}}^2}}}+\frac{1}{4}{e^{ - {{\frac{{2x}}{3}}^2}}}$$

The distribution of Shadowed Rician fading from [15], [29] is given as

${f_{|h{|^2}}}(x)={\alpha _i}{e^{ - {\beta _i}x}}{}_{1}{F_1}({m_i};1;{\delta _i}x)dx;x>0$

where h is the SR channel link. Now the BEP of symbol ${s_2}$ from source to destination in first phase can be obtained by substituting above two equations in Eq. (5) to get Eq. (C) as follows

${P_{{s_2}}}^{{sd}}(e)=\frac{1}{{12}}\sum\limits_{{i=1}}^{M} {{P_i}{\alpha _i}\int\limits_{0}^{\infty } {{e^{ - x({\nu _i}{\rho _s}+{\beta _i})}}} } {}_{1}{F_1}({m_i};1;{\delta _i}x)dx+\frac{1}{4}\sum\limits_{{i=1}}^{M} {{P_i}{\alpha _i}\int\limits_{0}^{\infty } {{e^{ - x(\frac{4}{3}{\nu _i}{\rho _s}+{\beta _i})}}} } {}_{1}{F_1}({m_i};1;{\delta _i}x)dx$

The above equation can be written as the sum of two terms I₁ and I₂ as

${I_1}=\int\limits_{0}^{\infty } {{e^{ - x({\nu _i}{\rho _s}+{\beta _i})}}} {}_{1}{F_1}({m_i};1;{\delta _i}x)dx$ and ${I_2}=\int\limits_{0}^{\infty } {{e^{ - x(\frac{4}{3}{\nu _i}{\rho _s}+{\beta _i})}}} {}_{1}{F_1}({m_i};1;{\delta _i}x)dx$

Now solving the term I₁ as

${I_1}=\frac{1}{{{\delta _i}}}\int\limits_{0}^{\infty } {{e^{ - \frac{u}{{{\delta _i}}}({\nu _i}{\rho _s}+{\beta _i})}}} {}_{1}{F_1}({m_i};1;u)du$

Now, with the help of following property of hypergeometric function, I₁ can be written as

$\int\limits_{0}^{\infty } {{e^{ - st}}} {}_{p}{F_q}({a_1}....{a_p};{b_1}....{b_q},t)dt=\frac{1}{s}{}_{{p+1}}{F_q}(1,{a_1}....{a_p};{b_1}....{b_q},{s^{ - 1}})$

Now ${I_1}=\frac{1}{{{\delta _i}}}\frac{1}{{\frac{{{\nu _i}{\rho _s}+{\beta _i}}}{{{\delta _i}}}}}{}_{2}{F_1}(1;{m_i};1;\frac{1}{{\frac{{{\nu _i}{\rho _s}+{\beta _i}}}{{{\delta _i}}}}})$

Or, we can write it as

${I_1}=\frac{1}{{{\nu _i}{\rho _s}+{\beta _i}}}{}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{{\nu _i}{\rho _s}+{\beta _i}}})$

Similarly, the expression for I₂ is given as

${I_2}=\frac{1}{{\frac{4}{3}{\nu _i}{\rho _s}+{\beta _i}}}{}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{\frac{4}{3}{\nu _i}{\rho _s}+{\beta _i}}})$

Now, by substituting the values of Eq. (16) and Eq. (17) in Eq. (C), we get

$P_{{{s_2}}}^{{sd}}(e)=\frac{1}{{12}}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{{\upsilon _i}{\rho _s}+{\beta _i}}})+\frac{1}{4}\sum\limits_{{i=1}}^{M} {\frac{{{P_i}{\alpha _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}}} {}_{2}{F_1}(1;{m_i};1;\frac{{{\delta _i}}}{{\frac{4}{3}{\upsilon _i}{\rho _s}+{\beta _i}}})$

In the similar way, the BEP of symbol ${s_1}$ in second phase from relay to destination can be obtained as

$P_{{{s_1}}}^{{sr}}(e)=\frac{1}{{12}}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{{V_i}{\rho _s}+{\beta _{isr}}}})+\frac{1}{4}\sum\limits_{{i=1}}^{N} {\frac{{{\eta _i}{\alpha _{isr}}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}}} {}_{2}{F_1}(1;{m_{sr}};1;\frac{{{\delta _i}}}{{\frac{4}{3}{V_i}{\rho _s}+{\beta _{isr}}}})$

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No competing interests reported.

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Performance Analysis of NOMA Integrated Hybrid Satellite Terrestrial Communication System using ML

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