1 Introduction

The advancement of wireless multiple-hop technology in recent years has facilitated a promising direction for the ad hoc network [1], in which each node is equipped with a wireless transceiver to share information with other neighboring nodes and, if requisite, route packets via neighboring nodes to destinations that are not within direct communications [2, 3]. The bulk of nodes in an ad hoc network, on the other hand, are typically power-constrained and placed in unsupervised environments where individuals have difficulties replacing or recharging exhausted nodes.

Employing the broadcast aspect of wireless communication, cooperative communication (CC) is an effective approach for combating fading effects by providing spatial diversity by using multiple single radio terminals at the transmitter and/or receiver. Relay nodes retransmit the source's replica of data, which is subsequently combined at the destination for improved decoding of the original data. The CC method boosts network speed, capacity, and reliability by adopting virtual MIMO [4, 5]. Researchers are interested in extending three-stage cooperative communication to large-scale networks due of its effectiveness. However, as the number of neighboring transmission connections grows, there is more interference, which affects network performance even more than direct communication. Electronic devices that implement the IEEE 802.11 network standard [6] can now be fitted with numerous radio terminals at a lower cost thanks to advancements in contemporary wireless technology. Interference can be reduced by allowing neighbor broadcast across multiple orthogonal channels, which increases network capacity [7].

The use of energy is a major concern for MANETs. Many routing protocols, including as flat routing, cluster-based routing, and location-based routing, have been developed to improve the energy efficiency of WSNs. The need for high capacity is quickly growing as a result of high data rate applications, which will increase energy consumption, reduce network lifetime, and reduce network reliability. These issues are addressed by clustering routing methods [8]. One of the most common clustering routing systems is the Low Energy Adaptive Clustering Hierarchy (LEACH). Over the last several years, a variety of improved LEACH routing methods have been developed, concentrating on network topology changed cluster-heads (CHs) selection and network growth [9].

As MANET nodes are battery-powered, energy efficiency is a critical design consideration for the network's long-term viability. When a node's battery runs out, it loses its ability to route network traffic, which reduces the network's lifespan. MANET network lifespan may be extended by either increasing node battery power or lowering total network power usage. Though battery technology has advanced significantly in recent years, it still lags behind semiconductor technology. MANET nodes typically send packets at full power. A packet sent at full power may take fewer hops to reach its destination, but it will reduce channel usage and the node's available energy to a larger extent. At the node level, energy savings can be achieved by lowering the transmission power [9,10,11,12,13]. To save energy, power management-based protocols place as many nodes as feasible into a sleep state. They are, however, more vulnerable to network outages. This is due to the fact that when the nodes go to sleep, the connection may be lost. In [14,15,16,17], a few examples of power management approaches are described. However, the energy consumption and routing in large scale cooperative MANET need to be efficiently addressed. Thus this paper proposes Energy Efficient Multi-hop Cooperative Transmission Protocol for Large Scale Mobile Ad hoc Networks.

The remainder of this paper is prepared as follows. In Sect. 2, Literature survey is presented in detail. Our proposed Energy-efficient hybrid cooperative routing and optimization of cooperative nodes are presented in Sect. 3. In Sect. 4, we present the simulation results, and finally, we concluded the paper in Sect. 5.

2 Literature Survey

The earlier works may be divided into two groups based on their design goals: the first is aimed to optimize the end-to-end performance of wireless multi-hop transmission, and the second is designed to maximize the network lifespan. There have been several attempts to improve the end-to-end performance of wireless multi-hop transmission. The goal of minimizing total energy routing (MTE) [18] is to discover the least total energy non-cooperative route possible, which can be accomplished using a conventional shortest path method like Dijkstra or Bellman-Ford. In cooperation along the minimum energy non-cooperative path CAN-l [19], the packet is collaboratively sent to the next-hop node by the last l nodes along the aforementioned non-cooperative path. Progressive cooperative routing PC-l, like CAN-l, merged the previous l nodes into a single node before updating the shortest path from the combined node to the destination node.

Based on the non-cooperative approach, cooperative cluster-based routing (CwR) [20] added the ‘recruiting-and-transmitting' phase, and the cooperative model was comparable to the multiple-input–single-output (MISO) scenario. The non-cooperative approach with the least amount of energy was used to create the aforementioned schemes. In reality, when looking for the best end-to-end route, the impact of collaboration on performance should be taken into account. Cooperative shortest path algorithm (CSP) [21] was created using CAN-l to identify the best cooperative shortest path while taking into account the benefits of l-to-1 cooperative transmission. The channel model used in this approach, on the other hand, simply took into account the impact of distance and neglected the fading of the wireless environment.

A relay node of each cooperative connection was carefully selected in relay selection-based cooperative routing (CC-OPT) [22] and power efficient location-based cooperative routing (PELCR) [23] from nodes in the intermediate area between the transmitter and the receiver. However, rather than a fixed number, the number of cooperative nodes should be determined by the actual neighbors. Minimum-energy cooperative routing (MECR) [24] presented a probabilistic cooperative routing to discover the network's minimum-energy route under a link reliability restriction, but it is centralized and has a high computational complexity.

In [25], the authors have proposed a virtual cooperative MIMO transmission mechanism and obtained an analytical expression for the optimal number of cooperative nodes for two-stage cooperative networks. A low complexity cooperative routing algorithm was proposed in [26] and presented an optimal power allocation strategy. To minimize the network energy, the authors in [27] have proposed routing algorithms by enhancing the performance of Physical, MAC, and Network layers. For this, the authors have proposed a cooperative automatic repeat request (ARQ) mechanism at the MAC layer. A cooperative routing algorithm based on Quality of Service was presented in [28], to minimize energy consumption. But all the aforementioned authors considered the network, where all the nodes are equipped with a single radio terminal.

The authors in [29] have proposed an opportunistic cooperative packet transmission (OCPT) scheme for multi-hop cooperative networks. In OCPT, before the transmission, a cluster head selects the transmitter and receivers to form MIMO. Because of multiple transmitters and receivers in each hop, the energy utilization of the network is considerably high. A two-stage cooperative routing strategy was proposed in [30] to enhance energy efficiency and network lifetime. Therefore this work has considered the effect of cooperation into link cost evaluation, and then obtains the optimal path based on link cost. But to obtain the best possible path, this scheme needs to evaluate the effect of cooperation and update link cost periodically.

In [31], the performance evaluation of the Rayleigh and Weibull fading channels with the best technology for relay selection for the non-regenerative wireless cooperative network. Yet, a few larger relay nodes which diminish the accuracy of the analytical design and unwanted resource usage. An asymptotically optimum solution is created by converting the original problem into a fixed stage number equivalent Finite-Horizon Markov Decision process (MDP) in [32]. A modern method is then introduced to solve the dimensionality burden, which offers empirical representations of estimated value functions. For the case where these data are unclear, a reinforcement learning algorithm is suggested. In addition, this function often includes energy consumption. [33] carry out a multi stage transfer to improve spectrum effectiveness in wireless information fusion. Often, the core network and the wireless link provide high pressure if many users request the same data.

Sadeghzadeh et al. [34] suggested a plan for physical layer protection in downlink massive MIMO system wireless connection, a systemized block diagonalization precoding that use the Artificial Noise (AN) strategy. However, the packet error rate power (PER), maximization of the confidentiality rate, or compliance with such service quality metrics are not regulated. A new Optimum Power Assignment Method (OPA) is presented in [35] to improve the cooperative Wireless Network's instantaneous secrecy limit. Nonetheless, a low convergence rate and an ineffective solution is attained by this method. [36] described horizontally as two separate homogeneous Possion Point processes (PPPs), the permissible destination and eavesdropper are dispersed, and each UAV is located just above its respective permissible destination for effective secrecy transmission. However, these terthe terms used in it are all too complex mathematically for intuition. From the aforementioned issues, it is essential to develop a new technique of routing algorithms for energy consumption in a cooperative network.

3 Hybrid Multi-hop Cooperative Routing Algorithm

In recent years, collaboration on wireless networks was becoming increasingly attractive since the particularly severe channel impairments resulting from multi-way diffusion could be alleviated. To further enhance structure and performance, the MANET and co-operative transmissions (shown in Fig. 1) are used. However, energy consumption for MANETs is a crucial issue. Due to applications of high data rate, the demand for high capacity is increasingly growing, which in turn increase energy utilization, reduce the lifespan of the network. Mobile ad hoc networks are the purest form of decentralized systems and thus place numerous challenges on cooperative communication. As a result, much ad hoc research on the network has focused on investigating fundamental algorithms for routing and clustering. Specialized protocols for embedded nodes have been built to diminish the process's energy utilization as well as to hit the entire system with high probability in the shortest possible time. Thus there is a great need to develop a new routing algorithm to reduce energy consumption.

Fig. 1
figure 1

Cooperative communication

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Therefore, we proposed a novel hybrid multi-hop cooperative routing algorithm for large scale cooperative networks is proposed by combining clustering and location-based routing strategies in this paper. When a flow request arrives, the network divided into clusters via cluster heads. The formation of cluster considers various metrics which includes link Signal to Noise Ratio (SNR), relative distance, and relative mobility. After forming the cluster, one of the nodes in this is selected as a cluster head based on its location. Further, we optimize the number of transmitters and receivers in every hop; and obtain an optimal quantity of cooperative relays in every hop to reduce the end-to-end energy utilization. It is shown in Fig. 2.

Fig. 2
figure 2

Hybrid multi-hop cooperative routing algorithm

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3.1 Large Scale Cooperative MANET

Large Scale Cooperative Mobile Ad hoc Network (LC-MANET) consider as a network, where N nodes are uniformly distributed over an area of LxL m2, as shown in Fig. 3. Every node in the network is assumed to be self-organized and employs the Decode and Forward (DAF) relay protocol. We consider that every node in the network contains M radio terminals; a power control mechanism, which changes the power transmitted based on the distance. R and r denote the transmission coverage area and transmission radius, respectively and Ri is the nodes in the transmission region of node i (Ni) which can communicate directly with a probability of error (Pe) lower than or equivalent to a predefined threshold.

Assume that, all the nodes in LC-MANET are equipped with encoding and decoding capabilities, ideal channel evaluation and synchronization; and Maximum Likelihood (ML) detection at the destination. We consider the channel between nodes is Rayleigh fading. Let a node i broadcasts the information X, which can be successfully decoded by another node \(j \in R_{i}\). The received information (yi) at node j is given by [37]:

$$y_{i} = \sqrt P h_{ij} X + \zeta_{j}$$
(1)

where \(h_{ij}\) represents the channel coefficient between nodes i and j designated as complex Gaussian random variable i.e., \(\left| {h_{ij} } \right|^{2} = \mu_{ij}^{2} d_{ij}^{ - 4} ;\,\;\mu_{ij}^{2} \;{\text{and}}\;\,d_{ij}\) are the variance and distance between i and j; X represents the compressed encoded data transmitted by node \(i\,\;{\text{and}}\;\,\zeta_{j}\) represents zero-mean additive Gaussian noise with the variance \(\sigma^{2}\).

Every node can obtain its location using GPS and neighbor nodes location by exchanging beacon signals periodically (i.e., for every β sec). Based on these beacon signals, every node obtains parameters like link Signal to Noise Ratio (SNR), distance, and relative velocity. The link SNR between node p and node q is evaluated as

$$\zeta_{q} = \frac{{P\left| {h_{pq} } \right|^{2} }}{{\sigma_{q}^{2} }}$$
(2)

Depending on the SNR value, node p measures the relative distance to the node q as:

$$\delta d_{pq} = \left( {\frac{{P\delta_{pq} }}{{\sigma_{q} \delta \zeta_{pq} }}} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$4$}}}}$$
(3)

where \(\delta \zeta\) is the relative SNR, it is obtained as

$$\frac{1}{{\delta \zeta_{pq} }} = \left| {\frac{1}{{\zeta_{p}^{{t_{2} }} }} - \frac{1}{{\zeta_{q}^{{t_{1} }} }}} \right|$$
(4)

and \(t_{2} - t_{1} = \beta\) The relative velocity of the nodes can be given as:

$$\delta v_{pq} = \frac{{\delta d_{pq} }}{\beta }{\text{m/sec}}$$
(5)

After the cluster has been created, with the SNR then one of the nodes in this is chosen as a cluster head based on its position. The following section explains the routing algorithm.

Fig. 3
figure 3

Large scale cooperative MANET

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3.2 Energy-Efficient Hybrid Cooperative Routing Mechanism

We first describe the proposed energy-aware hybrid cooperative routing scheme for LC-MANET and then the optimization of cooperative nodes to minimize energy consumption in this section.

3.2.1 Cooperative Routing Algorithm

If a new flow arrives from source node Ns to destination node Nd, node Ns finds the set of nodes in its transmission coverage region, and measures the metrics; link SNR and relative velocity as mentioned in system model using periodically exchanged beacon signals. Based on measured metrics, the source node forms a cluster and determines the Cluster head (Nh), where \(N_{h} \in R_{s}\). The source node broadcasts the compressed encoded data \(\tilde{X}\) along with destination and cluster head ID.

figure d

It denotes hth hop cluster head and set of cluster nodes as \(N_{h} \;{\text{and}}\;\,V_{h}\) respectively. The (h + 1)th transmission required only when the destination node is not in the range of transmission of \(N_{h}\) i.e.,\(N_{d} \notin R_{{N_{h} }}\). Whenever, the destination node is not in the transmission coverage area of source node, a new cluster formed with the cluster head different from the destination node. The flow diagram of the proposed energy efficient hybrid cooperative routing algorithm is given in Fig. 4.

Fig. 4
figure 4

Flow chart for energy efficient hybrid cooperative routing algorithm

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3.3 Energy Utilization Analysis

In this section, present a cooperative MISO transmission scheme and developed an energy consumption model for a single hop. Based on this model, we obtained an optimal number of cooperative nodes.

The source node (Ns) forms a cluster (as described in Algorithm), and transmit the data in two phases.

3.3.1 Phase I

In the first phase, the data is broadcasted to all the nodes in the cluster. Consider that there are n nodes in the cluster. The average energy utilization for MQAM modulation can be expressed as [38]:

$$E_{{P_{1} }} = \frac{\xi }{\eta }Q_{0} E_{{b,P_{1} }} r^{2} + {\raise0.7ex\hbox{${\left( {P_{tx} + nP_{rx} } \right)}$} \!\mathord{\left/ {\vphantom {{\left( {P_{tx} + nP_{rx} } \right)} {bB}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${bB}$}}$$
(6)

where \(Q_{0} = \frac{{\left( {4\pi } \right)^{2} M_{l} N_{f} }}{{G_{tx} G_{rx} \lambda^{2} }},\;\;\xi = 3\frac{{2^{{{b \mathord{\left/ {\vphantom {b 2}} \right. \kern-\nulldelimiterspace} 2}}} - 1}}{{2^{{{b \mathord{\left/ {\vphantom {b 2}} \right. \kern-\nulldelimiterspace} 2}}} + 1}};\;G_{tx} \;\,{\text{and}}\;G_{rx}\) are the gains of source and destination respectively.

\(M_{l}\) is the link margin, \(N_{f}\) is the receiver noise figure, \(\lambda\) is the carrier wavelength, \(\overline{{E_{{b,P_{1} }} }}\) the average received energy pet bit in phase 1, bis the transmission bit rate, B is the modulation Bandwidth, \(P_{tx} \,\;{\text{and}}\;P_{rx}\) are the transmitter and receiver circuit powers respectively.

The average number of nodes in the cluster is

$$n = \frac{{\pi r^{2} N}}{{L^{2} }}P\left( {\delta v} \right).$$
(7)

After phase 1 broadcast the cluster then it processes phase 2 with n nodes for transmitting the data to the cluster head.

3.3.2 Phase II

In phase 2, n nodes (n − 1 cluster nodes and source node) are used for data transmission to the next-hop cluster head. The average energy consumption can be given by

$$E_{{p_{2} }} = \frac{\xi }{\eta }Q_{0} \overline{{E_{{b,P_{2} }} }} d_{\max }^{2} + {\raise0.7ex\hbox{${\left( {nP_{tx} + P_{rx} } \right)}$} \!\mathord{\left/ {\vphantom {{\left( {nP_{tx} + P_{rx} } \right)} {bB}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${bB}$}}$$
(8)

The average energy consumption per bit of every hop is \(E_{h} = E_{{p_{1} }} + E_{{p_{2} }}\).

The upper bound \(\overline{{E_{{b,P_{2} }} }}\) can be obtained by Chertoff upper bound with several receiving antennas equal to one.

$$\overline{{E_{{b,P_{2} }} }} \le \frac{{2\left( {2^{b} - 1} \right)N_{0} n}}{3b}\left( {\frac{4}{{bP_{e} }}} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}}}$$
(9)

\(\overline{{E_{{b,P_{2} }} }}\) can be obtained by substituting n = 1. By approximation Eq. (9) as equality, we obtained closed-form of expression for the average energy consumption per bit as:

$$E_{h} = C_{b} \left[ {\frac{{C_{e} L^{2} }}{{\pi NP\left( {\delta v} \right)}} + \left( {C_{e} } \right){\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}d_{\max }^{2} } \right]n + C_{p} \left( {n + 1} \right)$$
(10)

where \(C_{b} = \frac{{\xi Q_{0} 2\left( {2^{b} - 1} \right)N_{0} }}{3b\eta },\;C_{e} = \frac{4}{{bP_{e} }}\;{\text{and}}\;\,C_{{_{p} }} = \frac{{P_{tx} + P_{rx} }}{bB}\). According to the proposed algorithm, hthHop cluster head should be in the transmission coverage area of \(\left( {h - 1} \right){\text{th}}\) hop cluster head. Hence the distance among the two cluster heads \(\left( {d_{\max } } \right)\) should be \(d_{\max } \le r\).

The average number of nodes in a cluster becomes

$$n \le \frac{{\pi Nd_{\max }^{2} P\left( {\delta v} \right)}}{{L^{2} }}.$$
(11)

where \(P\left( {\delta v} \right)\) the probability of the node having relative mobility difference is less than the threshold. We approximate the optimal value of n to minimize the average energy consumption per bit \(E\left( h \right)\,\;when\;\,d_{\max }^{2} \ge \frac{{nL^{2} }}{{\pi NP\left( {\delta v} \right)}}\) as:

$$\mathop {\min }\limits_{n} \,E_{h} \,s.t.2 \le \frac{{\pi Nd_{\max }^{2} P\left( {\delta v} \right)}}{{L^{2} }}$$
(12)

Otherwise, n = 1 transfers the data in the SISO transmission scheme. We obtain the critical value of a function \(E_{h}\) by differentiating concerning n is:

$$d_{\max }^{2} \left( {C_{e} } \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}}} \left[ {n - 1n\left( {C_{e} } \right)} \right] + \left[ {\frac{{C_{e} L^{2} }}{{\pi NP\left( {\delta v} \right)}} + \frac{{C_{p} }}{{C_{b} }}} \right]_{n = o}$$
(13)

Since the above equation is positive, n should be less than \(\ln \left( {C_{e} } \right)\). Let the positive real-valued solution of the above equation is \(n_{p}\). Then the optimal value of \(E_{h}\) is obtained as:

$$n_{0} = \left\{ {\begin{array}{*{20}c} {\left[ {n_{p} } \right]\,} & {\,if\;2 \le n_{p} \le \frac{{\pi Nd_{\max }^{2} P\left( {\delta v} \right)}}{{L^{2} }}} \\ 2 & {if\;n_{p} < 2} \\ \end{array} } \right.$$
(14)

Thus the proposed routing algorithm reduces the energy consumption with the analysis of multi-hop channels.

4 Results and Discussion

This section clearly explains the feasibility of our proposed method by evaluating and contrasting the experimental results obtained with traditional methods. Specification tools for implementation are given below.

4.1 System Specification

The methodology proposed is described in Sect. 3 above and is analyzed in detail in this section. The suggested approach is applied with the following device specification in the MATLAB work platform.

Platform

MATLAB 2019a

OS

Windows 8

Processor

Intel core i5

RAM

8 GB RAM

4.2 Simulation Results

Simulation analysis of the proposed algorithm is presented in this section. We simulated our algorithm using MATLAB with the parameters listed in Table 1:

Table 1 Parameters for simulation
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Figure 5 demonstrates a network span with the maximum cluster head residual energy, maximum relay node residual energy, maximum path residual energy, and minimal energy transmission of path. Criterion 4 is the longest possible life. As presented in the previous section, the lifetime of the network has been reduced with the increase of energy consumption. Here, the criterian 4 consumes minimum transmission energy for routing, such a way, the network lifespan under criterion 4 has been increased. This implies that criterion 4 is fair and holds a balance of load. Consequently, Criterion 4 is used for the fitness of hybrid multi-hop cooperative routing.

Fig. 5
figure 5

Comparison of four fitness criteria's network lifetimes

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Table 2 demonstrates the network life in which the overall residual energy of CH is 1690, the overall residual energy of the relay node network lifespan is 1800. The network lifetime is 1800, Min. Residual energy of the path. Network life is 1840 with transmitting energy from the path.

Table 2 Network lifetime
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As presented in the proposed routing algorithm, if the destination node is not in the transmission coverage area of the source node, the new cluster has been formed. The time for new cluster formation has been presented in the Fig. 6.

Fig. 6
figure 6

New cluster formation time

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4.3 Comparison Analysis

In this section we are comparing the lifetime and residual network energies of the EECC (energy-efficient cooperative communication method) sensor nodes [39] and of the HEED (hybrid-energy efficient distributed clustering approach) [41], and SOSAC [Self-Organized and Smart Adaptive Clustering] [40], which are the most common inter cluster routing.

The network lifetime relation is shown in Fig. 7. We compare the lifetimes of the EECC network (use of relay nodes), SOSAC (without relay nodes), and HEED, to claim the legitimacy of the collaborative method of communication.

Fig. 7
figure 7

Comparison of the network lifetime of the proposed algorithm

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Table 3 indicates that the network life time of EECC is about 1,300 while the first node is exhausted and, relative to that of the SOSAC network life, about 1890 after the 20th node has been exhausted. For SOSAC when the first node is drained the lifetime is 1000 and 1700 when the last node is drained. Then for HEED, the first node drained value is 600 and the last node drained value was 1800. However, our proposed work drained the first node the lifetime is 1400 and the last node drained lifetime is 2050 it is greater when compared with the above techniques. The experimentation stated the coordination of the CH and relay nodes, by reducing energy consumption and preserving load balance, intensifies the network's life.

Table 3 Comparison of network lifetime
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Figure 8 shows the comparison graph for the experimentationupon residual energy ratios of various techniques such as EECC (using relay nodes), SOSAC (without relay nodes), and HEED (hybrid-energy efficient distributed clustering approach) with the proposed algorithm.

Fig. 8
figure 8

Experimentation on the residual energy ratios of various techniques

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Table 4 compares EECC, HEED's mean residual energy ratios, which range from 40% (when the first node is exhausted) to 10% (when the twentieth node is exhausted). The HEED ratio is between 70% (when draining the first node) and 25% (when draining the twentieth node). This means that the energy utilization of all EECC sensor nodes is more equal than the energy utilized by HEED.

Table 4 Comparison of residual energy ratio
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The above Fig. 9 depicts the network throughput in which Fig. 9a depicts throughput versus pause time, Fig. 9b plots the throughput versus some nodes, Fig. 9c shows throughput versus CBR connection, and Fig. 9d shows the throughput versus packet size. The compared techniques are ANTC (Adaptive Neighbor-based Topology Control), LFTC (Learning-based Fuzzy-logic Topology Control), and LBTC (Location-Based Topology Control with Sleep Scheduling). Figure 9 demonstrates that the proposed achieved higher throughput. The improvement in network life through an effective power change is attributed to higher efficiency.

Fig. 9
figure 9

Network throughput

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Figure 10 shows the End-to-end Delay versus amount of nodes with the methods like ANTC, LFTC, and LBTC. From Table 5, it is clear that in comparison to LFTC and ANTC, LBTC has a higher end-to—end delay. This is because hop count increases as lower power transmission nodes.

Fig. 10
figure 10

Delay versus number of nodes

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Table 5 Comparison of end-to-end delay
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In order to appraise the overall comparison of our proposed algorithm with the existing system, the following approaches are taken into an account likead hoc on-demand distance vector (AODV) routing algorithm [42], Opportunistic Cooperative Packet Transmission (OCPT) [43].

Figure 11 displays the total number of hops depending on the number of nodes for different routing schemes. The proposed routing scheme needs fewer hops than AODV and OCPT schemes, since the possibility of removing a node from the source also increases with the increase in network node density and transfers the data to the destination with minimal path length i.e., in a minimum number of hops.

Fig. 11
figure 11

Average number of hops

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Figure 12 depicts the comparison of end-to-end energy consumption over the number of nodes for various routing schemes. Since we obtain the optimumamount of cooperative nodes in each hop, the energy consumption of the path will decrease. Our algorithm requires a less number of hops with increased node density; the energy utilization is even minimized by 53.42% as compared to traditional AODV routing algorithms at N = 700 and N = 900.

Fig. 12
figure 12

End-to-end energy consumption

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5 Conclusion

Cooperative communications enable the efficient use of communication resources by allowing communication network nodes or terminals to collaborate in the transmission of information. This paper presented a hybrid multi-hop cooperative routing algorithm for LC-MANET. We combined clustering and location-based strategies to mitigate the mobility effect and reduce the average number of hops. In every hop, we incorporated optimization mechanisms and obtained an optimal number of cooperative nodes by jointly optimizing the number of transmitters and receivers. Implementation outcomes showed that hybrid multi-hop cooperative routing algorithm saves energy utilizationup to 53.42% in contrast with the conventional routingstrategy.