In the last decade, the use of Wireless Sensor Networks (WSNs) are increased in many fields such as long-term environmental monitoring, tracking objects, military applications, and so on ^{1}. In general, WSNs composed of hundreds and thousands of tiny sensor nodes which can gather various physical data from their surroundings. These resource-constrained limited battery power, low cost, limited processor capacity tiny sensor nodes are deployed in obstacle areas. Then, obtained physical data transferred to the base station through multi-hop communication or directly. Sensor nodes not only collect physical data from their surroundings but also act as routers^{ }^{3, 4.}

A careful design of neighbor discovery algorithms and protocols for energy-efficient ^{5}. Therefore, the neighbor discovery protocols must be energy efficient and must try to minimize the energy consumption in various areas such as overhearing, data collection, idle listening, control packet overhead, and over-emitting. With efficient neighbor discovery protocols, sensor nodes might save a lot of energy to establish a communication path with others ^{6, 7.}

The basic idea behind the neighbor discovery process is to split the time used by sensor nodes over channel access into equal-length time slots, and every node can use one exclusively by one node^{ }^{8}. The fundamental goal of the implemented protocol is to minimize the overall energy consumption by using BIBD symmetric neighbor discovery schedule. In order to reduce energy consumption, the primary function is to schedule the sensor nodes with various radio modes such as active and sleep in consecutive time slots. The minimization of energy consumption can be achieved because sensor devices use different levels of energy at each node ^{9}.

The neighbor discovery process based on BIBD provides or optimal solution in terms of the average case discovery latency of the desired duty cycle. In WSNs, applications are obtaining neighbor nodes information based on BIBD applicable to symmetric strategies. To make BIBD based neighbor discover appropriate to asymmetric environment, the prime number based BIBD developed to design efficient neighbor discovery algorithms. In many WSN applications are desired to work for several months to years without any human intervention. However, resource-constrained sensor nodes in a sensor network may discontinue their operations due to the energy of the node drained out. Therefore, endorsing the lifespan of the network is essential for sensor network functionality.

The neighbor discovery is not one time process, due to the deployment of new nodes, collisions, topology changes, and clock synchronization among nodes need to discover neighbors continuously. In this paper, we propose an energy adaptive-BIBD based neighbor algorithm that adopts both symmetric and asymmetric strategies. The significant contribution in this paper as follows.

This study is the first of its kind to design neighbor discovery by considering the remaining energy of node to construct BIBD based neighbor discovery schedule where they must guarantee the existence of overlapping active slots between any two sensor nodes.

In this work, it is implemented some representative models of the neighbor discovery process in TOSSIM simulation ^{10}. The outputs of our simulation study illustrates that the proposed model significantly over other neighbor discovery algorithms according to energy-efficiency and discovery latency.

There is a vast literature on neighbor discovery algorithms in WSNs and Ad-Hoc networks. Then, this study uses and divides the existing neighbor discover algorithms into the three important modules, such as BIBD-based, Prime number, and Quorum based. The various simulation tools used by researchers to describe models are presented in

Protocol Category | Author | Description, advantages, and disadvantages/ future directions |
---|---|---|

Quorum-based Protocol | Jiang et al. 19 | • Quorum based neighbor discovery derived from an n×n matrix. • It selects one row and one column form the proposed matrix, and assign them to a node discovery schedule. • The chosen column and row then act as active states of a node, and the remaining slots are sleep slots. |

• Simple model for implementation. • Higher efficient. | ||

• Typically, the original Quorum based neighbor discovery protocols are not suitable for asymmetric approaches. | ||

Bakht et al. 20 | • To reduce the problem of the basic Quorum based approach by considering the halve of the Quorum based discovery schedule called searchlight. | |

• It can support both symmetric and asymmetric approaches. • Searchlight has shorter discovery latency and minimum energy consumption because of the half discovery schedule length. | ||

• Not suitable for heterogeneous environments | ||

Chen et al. 11 | • The proposed model called Hedis and Todis to reduce the problem fundamental matrix-based neighbor discovery similar to searchlight. | |

• Simple model for implementation • Low error rate • It can be implemented in both homogeneous and heterogeneous environments. | ||

• It needs more slots, compromises energy efficiency and latency. | ||

Balanced Incomplete Block Design (BIBD) based protocols | Zheng et al. 12 | • The proposed model used a combinatorial structure for block design. • BIBD that designs a sensor device discovery schedule through the block design. |

• The simulation results of BIBD based neighbor discovery produces an optimal solution. | ||

• It is designed for symmetric networks, where sensor nodes have a homogeneous discovery schedule. | ||

Lee et al. 13 | • To address the problem of symmetric discovery schedule proposed in symmetric-BIBD, combining duty cycle schedules by using OR operation to make it applicable for asymmetric discovery schedule. • Which requires additional active slots | |

• Significantly increases energy consumption. | ||

Lee et al. 14 | • Proposed model Combining duty cycle schedules by using XOR operation. • It also uses additional active slots to address the symmetric discovery schedule. | |

• Increases energy consumption. | ||

Lee et al. 15 | • It supports both symmetric and asymmetric strategies. • It removes additional active slots whenever possible in most of the environments. • The proposed model uses the basic BIBD without additional active slots. • It improved energy efficiency and reduced worst-case latency. • Not effective in route discovery when BIBD blocks are not available for certain duty cycles. | |

Prime number based protocols | Ding et al. 16 | • Chinese Remainder Theorem (CRT) used for cryptography applications and success of this approach worked for constructing discovery schedules for both symmetric and asymmetric strategies in WSNs. |

Dutta et al. 17 | • The proposed protocol is called Disco. Each sensor randomly selects one prime number to construct a discovery schedule. • When two sensor nodes select distinctly prime numbers, if the selected prime numbers are relatively prime, then it guarantees the existence of common active slots between any two nearby nodes. • Improved energy efficiency and latency • Worst-case latency is still high. | |

Kandhalu et al. 18 | • It uses a single prime number to construct a neighbor discovery schedule. • It adds periodic active slots based on the prime number. • Worst-case latency is still high. |

This section is focused on how the BIBD blocks are useful for constructing neighbor discovery in wireless sensor networks, and introduces the node energy estimation for creating neighbor discovery ^{21}. The neighbor discovery in WSN can play a vital role in relaying sensed information from source node to sink node through multi-hop communication. Block designs have many mathematical contexts used in variant fields such as geometry, networking, software testing, and cryptography. Among the block designs, the BIBDs are most suitable for the neighbor discovery algorithm due to their structural properties shown below. Next, we give two definitions of combinatorial block designs ^{22}, and then we define relation with wireless sensor networks.

a)

b)

Balanced Incomplete Block Design is a well-structured optimal block design for many WSN applications ^{8}.

a)

b) Each block contains exactly k-points.

c) Every pair of distinct points is contained in exactly

For illustration, assume that the set X is ^{14}.

Most of the applications composed of hundreds or thousands of sensor nodes, and these nodes can switch between active and sleep to prolong the lifespan of a node. The neighbor discovery is essential to relay data origin to processing node through wireless multi-hop communication. We use a pattern of 0 and 1 to indicate a discovery schedule. Where

^{15}.

For instance, we use

Where

In a single-channel wireless multi-hop communication neighbor discovery is a challenging task due to channel interference, data collisions, and radio interferences. Therefore, sensor nodes may not be able to find any other nodes within their schedule active slots. Sensor node should be repeated discovery schedule and adjust duty cycle length according to the remaining energy. The entire process of WSN broadly classified into three phases, such as deployment, discovery, and communication. After deployment, sensor nodes in the network autonomously obtain nearby node information using the discovery schedule of a node

The Balanced Incomplete Block Design (BIBD) based neighbor discovery techniques an optimal solution for WSNs with symmetric and asymmetric duty cycles ^{15}. For instance, we assume a sensor network environment initially does not know about neighbor discovery schedules. Then any two nearby nodes have different duty cycles at the beginning of network initialization. Assume any sensor nodes such as

Let

The extended block design based on the selected prime number and that is,

For instance, The sensor node

Most of the energy consumption can occur during communication among nodes in the network. The network lifespan can be enlarging long enough to fulfill the application requirement by adapting the minimum energy consumption mechanisms ^{12}. It also crucial for the allocation of a communication channel among nodes; the proposed model satisfies some of the critical factors such as energy-efficiency, collision, and minimum latency in sensor networks. Sensor nodes in networks alternate between active and sleep modes to use on the network activity and requirement ^{13}. The energy consumption problem can be appended due to the number of awake slots in a schedule, and there is a trade-off between the duty cycle and delay. If the number of active slots in schedule increases, then the discovery delay is minimized and vice-versa. The existing symmetric and asymmetric BIBD based neighbor discovery can achieve by constructing a fixed duty cycle schedule over the network lifespan. The adaption of schedule based on the residual energy of node status is beneficial in designing the duty cycle schedule. Lee and Kin proposed a model dynamic phase shift, and Zhang et al. ^{14}Implemented a novel scheduling scheme called traffic adaptive duty cycle strategies for minimizing the energy consumption. These implemented can also avoid the collisions and delay in asynchronous WSNs.

Wireless Sensor Networks has a broad range of applications over many fields. WSNs are composed of hundreds or thousands of low cost and tiny sensor nodes and these sensor nodes are mostly battery-powered devices. Sensor nodes deployed for gathering helpful or needed information and transmit them via wireless communication paths from the physical area to the sink node or base station. Once these sensors deployed in unattended area replacement or recharging batteries impossible or a critical task. The communication of these sensor nodes happen either within themselves or else directly with the sink node. Energy efficiency has become a critical issue in WSNs. Therefore, the resource selection and communication need to optimize to enlarge the lifespan of the network.

asynchronous wireless sensor networks. The neighbor discovery process, according to the residual energy, is affecting the sleep latency to balance energy conservation between sensor nodes. Discovery latency described as a sensor node that has data to receive or transmit typically needs to wait for a long duration before actual transmitting or to get the data packet ^{23}. Generally, minimum discovery latency reduces energy utilization. Therefore, it significantly is enlarging the lifespan of a sensor node in the networks. Our proposed model allows every node to construct the discovery schedule based on the residual energy of a node after every neighbor discovery. Following algorithm illustrates proposed block design based neighbor discovery for asynchronous wireless sensor networks

Algorithm: Implementation of Block Design based Neighbor Discovery for Asynchronous WSNs |
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1. Initialize the list of nodes |

2. Initialize the Erem, Etr/re, λ, and Eth Threshold |

3. Procedure to design_Block() //Compute Balanced Incomplete Block Design (BIBD) based schedule |

4. For k ϵ [1, # ListNodes] do |

5. For j ϵ [1, # ListNodes] do |

6. If(gcd(Vk,Vj) == 1) then |

7. k and j are neighbors have common active slot |

8. Else |

Compute new block Prime based schedules for these nodes with common active slot |

9. End if |

10. Erem = Erem – Etr/re // to compute remaining energy of nodes |

11. If (Erem ≤ Eth and Erem != 0) then |

12. design_Block() //nodes need to adjust duty cycle length according to node remaining energy |

To determine the schedule, we consider the discovery duty cycle schedule and residual energy of each node. Let assume a node denotes

Suppose after deployment, each node has maximum energy

Where

Where

In this section, we analyze and evaluate the performance of discovery latency and energy consumption of the proposed model based on energy adaptive neighbor discovery using BIBD. We compare with existing protocols such as Disco, Searchlight, U-Connect, Hedis, and Todis in both symmetric and asymmetric approaches using a simulation tool. The primary goal of the simulation is to handle the practical applications consuming less energy with efficient and faster data delivery. To evaluate the efficiency of the proposed neighbor discovery scheme, we have implemented the proposed model and other earlier neighbor discovery model by using a TOSSIM module ^{10}. The same parameters have been used for all neighbor discovery protocols for simulation.

For the proposed scheme, the simulation approach contains 150 nodes with a transmission range of 50m. The sensor devices are randomly deployed uniformly on the filed of environment of

Name of the parameter | Values |
---|---|

Size of the networks | 500×500 |

Number of sensor nodes | 150 |

Sensing ranging of nodes | 30m |

Initial energy of node | 3.7J |

Network Topology | Random topology |

Channel Access Scheme | CSMA/CA |

Simulation time | 45m |

Initial trigger time | 50s |

Transmission energy | 16mW |

Receive energy | 12mW |

Packet transmission rate | 40 packets/s |

Type of protocol | Hybrid model |

Power intensity | -20dBmto 12dBm |

Neighbor discover protocols | Disco, Searchlight, U-Connect, Hedis and Todis |

For the evaluation and comparison of asymmetric duty cycles, the asymmetric ratio R is defined as

The lifespan of the sensor network is determined by the overall power conservation of sensor devices. The power conservation of sensor devices increases the lifespan of these devices is decreased, and vice-versa. To simulate the impact of the discovery duty cycles on the discovery latency during asymmetric operations, we used different pairs of discovery duty cycles such as

The energy conservation by the sensor nodes decreases curvy linearly, and for duty cycle below

This study introduces a new energy adaptive neighbor discovery protocol based symmetric BIBD for symmetric and asymmetric asynchronous wireless sensor networks. In this proposed model, the features of symmetric and BIBD and Chinese Remainder Theorem are merged to design schemes for asymmetric discovery duty cycles. The major contribution of the proposed system to develop an efficient dynamic duty cycle schedule based on the residual energy of a sensor. Therefore, the proposed strategy anticipates an efficient solution for asymmetric and symmetric discovery schedule problems. As per simulations a result, the performance of the proposed model is significantly smaller energy compared to the other well-defined neighbor discovery protocols, and it can be enlarging the lifespan of the network compared with well-defined protocols.