User grouping for NOMA-based sensor nodes for improved outage probability and throughput

Over the recent years, the utilization of wireless sensor networks (WSNs) in many fields is gaining attention for a variety of uses, e.g., monitoring, measuring, sensing, etc. in agriculture, industry, smart cities, medical care, etc. [1,2,3]. The inclusion of WSN has an advantage of adapting to the existing architecture that can be utilized without requiring additional costs of equipment and wiring (WSNs operate on radio except the backbone network), and they have additional advantage of fast connection and cloud. The WSN suffers from the data transmission problems when the larger number of devices generates massive amount of data [4]. The non-orthogonal multiple access (NOMA) technique is considered as an option that address this issue of massive amount of data and connectivity requirement in both downlink and uplink transmissions [5,6,7]. Multiple users can be supported while using the same time and frequency resources. This study focuses on creating a ground-based LoRa network that will eventually connect to a satellite [8]. However, LoRaWAN networks have a problem with collisions when there are many devices trying to send data at once. This is especially problematic in crowded areas like cities. To fix this, we suggest a new method called Energy efficiency (EE)-LoRa. EE-LoRa helps LoRaWAN networks use less energy by choosing the right spreading factor and controlling the power of the gateways [9].

When a sensor node communicates with its relay or sink [10], it consumes maximum power at that time while operating in WSNs. The coverage area of sensor nodes is limited to adjacent nodes in WSNs; therefore, they rely on relay(s) to transfer information to sink node(s), which are located at farther distance. The WSNs when used for agriculture purpose are divided into different clusters in a way to cover the whole farm and reduce complexity, which makes the sensor nodes to connect with nodes in their own cluster only. Furthermore, in order to reduce consumption of energy consumption, the sensor nodes can be synchronized to transmit data at a predefined interval of time [10, 11]. NOMA is one of the key techniques for 5G and beyond next generation due to its capability to meet the demand of high rate and massive connectivity in both downlink and uplinks transmissions [12,13,14,15,16]. As compared to traditional orthogonal multiple access (OMA), it can provide support to more users while using the same time and frequency elements. The support to relaying provided by NOMA makes it more suitable candidate for WSNs. NOMA utilizes amplify-and-forward (AF) and decode-and-forward (DF) relaying system transmissions for cooperative communication, which can achieve astounding gain in the ergodic sum rate [17, 18].

The problems in WSNs can be used with the transition techniques combined with NOMA. Gomez et al. [19] used the uplink NOMA model with two users while using the DF relay for communication with base station. This study gives an in-depth system analysis by providing the formulas on throughput and system probability while adjusting SNR and transmitted power.

The remainder of this study is as follows. System model is given in Section 2.

In this model, a relaying system is used for uplink of the WSN as shown in Figure 1. The system consists of M sensor clusters, consists of N sensor nodes, and has R relay nodes and a sink. Consider a sensor cluster is denoted by m_i,1 ≤ i ≤ M, a sensor node in a cluster i is denoted by n_ij,1 ≤ j ≤ N, and a relay used by j^th sensor node in i^th cluster is denoted by r_k,1 ≤ k ≤ K. Two sensor nodes from two nearby clusters will do user grouping depending on their channel quality, and the relays are simple AF relays that forward it to the sink node. The sensor nodes in each cluster, relay, and sink can work only in half duplex mode.

Figure 1:

Outage probability compared with the relay power for varying power levels of near and far users.

The signals from paired sensor nodes n_ij and n_i+1,j+1 utilize the superposition principle of NOMA as follows:

Phase 1: Sensor nodes n_ij and n_i+1,j+1 send signals x_i,j and x_i+1,j+1 to the selected relay r_k in the first half of transmission block time (T) i.e. T2 \left( {{T \over 2}} \right) .

Phase 2: In the second half T2 \left( {{T \over 2}} \right) of the period, the selected relay receives the superimposed signal, amplifies it, and forward it to the sink. The sink then uses successive interference cancellation (SIC) to detect the individual signals x_i,j and x_i+1,j+1 from nodes n_ij and n_i+1,j+1, respectively.

Mathematically,

In phase 1

The superposition signal received at selected r_k will be (1) ykrec=αi,jPi,jhi,jkxi,j+αi+1,j+1Pi+1,j+1hi+1,j+1kxi+1,j+1+nk y_k^{{\rm{rec}}} = \sqrt {\left( {{\alpha _{i,j}}{P_{i,j}}} \right)} h_{i,j}^k{x_{i,j}} + \sqrt {\left( {{\alpha _{i + 1,j + 1}}{P_{i + 1,j + 1}}} \right)} h_{i + 1,j + 1}^k{x_{i + 1,j + 1}} + {n_k} where α_i,j + α_i+1,j+1 = 1, α_i,j, α_i+1,j+1 denotes the power coefficients of sensor nodes, hi,jk h_{i,j}^k , hi+1,j+1k h_{i + 1,j + 1}^k denotes the Rayleigh fading channel coefficient of links between sensor nodes and relays, and n_k denotes AWGN noise with mean equals to zero and variance of σ². The Rayleigh fading is used as it is a reasonable model to consider the ionospheric and tropospheric signal propagation while including effect of buildings and objects in the urban environment.

In Phase 2: By employing AF at relay r_k, the transmitted signal will be (2) yktrans=Gkykrec y_k^{{\rm{trans}}} = {G_k}y_k^{{\rm{rec}}} where Gk=Pkαi,jPi,jhi,jk2+αi+1,j+1Pi+1,j+1hi+1,j+1k2+σ2, {G_k} = \sqrt {{{{P_k}} \over {{\alpha _{i,j}}{P_{i,j}}{{\left( {h_{i,j}^k} \right)}^2} + {\alpha _{i + 1,j + 1}}{P_{i + 1,j + 1}}{{\left( {h_{i + 1,j + 1}^k} \right)}^2} + {\sigma ^2}}}} , , and P_k = transmission power of relay r_k.

The received signal at sink will be (3) ys=Gkyktranshsd+ns {y_s} = {{{G_k}y_k^{{\rm{trans}}}{h_s}} \over {\sqrt d }} + {n_s} where h_s denotes the Rayleigh fading channel coefficient of links between the relay and the sink, d is the Euclidean distance between the relay and the sink, and n_k denotes AWGN noise with mean equals to zero and variance of σ².

SIC can be applied to a user pair effectively when one user is the near user and another is the far user, assuming that n_ij is the near user and n_i+1,j+1 is the far user. Using SIC, the n_ij signal will be detected first due to better channel conditions, and its signal will be subtracted from the overall signal to detect the n_i+1,j+1 signal. The instantaneous SINR for the detection of signal x_i,j is (4) SINRxi,j=αi,jPi,jGk2hi,jk2hs2Gk2αi+1,j+1Pi+1,j+1hi+1,j+1k2+σ2hs2+σ2d {\rm{SIN}}{{\rm{R}}_{{x_{i,j}}}} = {{{\alpha _{i,j}}{P_{i,j}}G_k^2{{\left( {h_{i,j}^k} \right)}^2}{{\left( {{h_s}} \right)}^2}} \over {\left( {G_k^2\left( {{\alpha _{i + 1,j + 1}}{P_{i + 1,j + 1}}} \right){{\left( {h_{i + 1,j + 1}^k} \right)}^2} + {\sigma ^2}} \right){{\left( {{h_s}} \right)}^2} + {\sigma ^2}d}} (5) SINRxi+1,j+1=αi+1,j+1Pi+1,j+1Pkhi+1,j+1k2hs2dαi,jPi,jhi,jk2+dαi+1,j+1Pi+1,j+1hi+1,j+1k2+Pkhi,jk2+σ2d {\rm{SIN}}{{\rm{R}}_{{x_{i + 1,j + 1}}}} = {{{\alpha _{i + 1,j + 1}}{P_{i + 1,j + 1}}{P_k}{{\left( {h_{i + 1,j + 1}^k} \right)}^2}{{\left( {{h_s}} \right)}^2}} \over {d\left( {{\alpha _{i,j}}{P_{i,j}}} \right){{\left( {h_{i,j}^k} \right)}^2} + d\left( {{\alpha _{i + 1,j + 1}}{P_{i + 1,j + 1}}} \right){{\left( {h_{i + 1,j + 1}^k} \right)}^2} + {P_k}{{\left( {h_{i,j}^k} \right)}^2} + {\sigma ^2}d}}

For any variable Z_l for exponent distribution, the probability density function (PDF) and cumulative density function (CDF) are calculated as follows: (6) fZlz=1μe−Zμ {f_{{Z_l}}}\left( z \right) = {1 \over \mu }{e^{ - {Z \over \mu }}}

Here, 1μ {1 \over \mu } denotes the decay parameter. (7) FZlz=1−e−Zμ {F_{{Z_l}}}\left( z \right) = 1 - {e^{ - {Z \over \mu }}}

The outage probability for the detection of signals n_ij and n_i+1,j+1is calculated using [20, 21].

For the simulation purpose, Monte Carlo simulation is used to evidence the parameters impact on transmitted power, number of sensor nodes, etc. [20, 21]. The simulation parameters are given.

The outage probability and throughput of the network are compared for different power levels of near and far users, P(10dBm, 10 dBm), P(7.5 dBm, 10 dBm), and P(5 dBm, 10 dBm); the 1st power denotes the power of the near user, and the 2nd power denotes the power of the far user. In Figure 1, the outage probability of near and far users is compared for different power combinations with varying relay powers. The outage probability depends on the SNR ratio of the signal, and from simulations, it is clear that when the relay power increases, the outage probability of both near and far users decreases. Also, when the power of users is high, the outage probability of user signals increases. Even when the near user power is 5 dB, it follows the same trend.

In Figure 2, the throughput of both near and far users is compared for different power combinations explained earlier, and when the power level of near and far users decreases, the throughput of the corresponding user decreases. The throughput compared here is the final throughput at the sink, and the intermediate throughput at the relay is not compared. Decreasing the power of users leads to the decrease in the throughput. When the near user power is 5 dB, the throughput decreases for the near user and increases for the far user.

Figure 2:

Throughput compared with the relay power for varying power levels of near and far users.

In Figures 3 and 4, the outage probability and throughput of the network are compared when the number of nodes increases for increasing the relay power. When the number of nodes increases, interference in a cluster increases due to simultaneous transmission of other users. When the number of near and far users are 4, the outage probability is minimum for both clusters, and when the number of users are 8, the outage probability is higher for near and far users. However, the outage probability decreases for both clusters when the relay power increases from 0 dBm to 20 dBm.

Figure 3:

Outage probability compared with the relay power for different number of nodes in a cluster.

Figure 4:

Outage probability compared with the relay power for different number of nodes in a cluster.

In results of Figure 4, the throughput of both clusters decreases with an increase in the number of nodes.

In this study, the clustered sensor nodes utilize NOMA for the purpose of transmission to the sink node. The LoRa nodes operate mostly in the unlicensed spectrum, and employment of the larger number of LoRa nodes will create scarcity in the number of resources, due to which NOMA is used in this study that allows multiple transmissions in uplink by differentiating them based on their power levels. Due to the limitation of the coverage area of sensor nodes, the cluster’s near and far nodes use relays, and the relay node uses AF on the received signal and transmits it to the sink. The outage probability and the throughput of the network are investigated while varying the transmitted power of the relay and powers of near and far nodes with a variation in the number of nodes in a cluster. When the number of nodes is less, the throughput is higher and the outage probability is less.