Reliable lowenergy group formation for infrastructureless public safety networks
 Seonik Seong^{1},
 Illsoo Sohn^{2},
 Sunghyun Choi^{1} and
 Kwang Bok Lee^{1}Email author
https://doi.org/10.1186/s136380160644y
© Seong et al. 2016
Received: 12 November 2015
Accepted: 21 May 2016
Published: 7 July 2016
Abstract
In this paper, we study an infrastructureless public safety network (IPSN) where energy efficiency and reliability are critical requirements in the absence of cellular infrastructure, i.e., base stations and wired backbone lines. We formulate the IPSN group formation as a clustering problem. A subset of user equipments (UEs), called group owners (GOs), are chosen to serve as virtual base stations, and each nonGO UE, referred to as group member, is associated with a GO as its member. We propose a novel clustering algorithm in the framework of affinity propagation, which is a stateoftheart messagepassing technique with a graphical model approach developed in the machine learning field. Unlike conventional clustering approaches, the proposed clustering algorithm minimizes the total energy consumption while guaranteeing link reliability by adjusting the number of GOs. Simulation results verify that the IPSN optimized by the proposed clustering algorithm reduces the total energy consumption of the network by up to 31 % compared to the conventional clustering approaches.
Keywords
1 Introduction
A public safety network (PSN) has been developed as a special class of wireless communication network that aims to save lives and prevent property damage. PSNs have evolved separately from commercial wireless networks satisfying various requirements and regulatory issues associated with them [1, 2]. With growing needs for the transmission of multimedia data, existing voicecentric PSN technologies are facing hurdles in fulfilling the demand for high capacity and different types of services. Missioncritical requirements for PSNs include the guaranteed dissemination of emergency information such as alarm texts, images, and videos of disasters even in the absence (or destruction) of cellular infrastructure [3].
Many research projects have been launched to meet the missioncritical requirement of PSN, e.g., Aerial Base Station with Opportunistic Links for Unexpected & TEmporary events (ABSOLUTE), Alert for All (Alert4All), Mobile Alert InformAtion system using satellites (MAIA) [4]. The research projects include the emergency communications using satellite communications, aerial eNodeBs, and terrestrial radio access technologies. The approaches take advantages of inherent broadcasting and resilience with respect to Earth damages for disseminations of alert messages. In this paper, we limit our interests to terrestrial radio access technologies, e.g., LongTerm Evolution (LTE), TErrestrial Trunked RAdio (TETRA), TETRAPOL, and Digital Mobile Radio (DMR), because PSNs should be operational even in the lowclass user equipments (UEs) that are lacking in satellite communication functionalities.
In this paper, we focus on two critical goals to organize groups for PSNs: energy efficiency and reliability. IPSNs should minimize energy consumption of UEs to maximize the survival time of the networks. In addition, IPSNs should guarantee reliable communications. In order to guarantee reliable communications, any pair of UEs should be connected through qualified links only considering wireless coverage. These goals are extremely important in IPSNs, as failing to meet the goals could directly lead to losses of lives or property. To resolve the challenges, we formulate a constrained clustering problem for group formation of IPSNs considering both energy efficiency and reliability. Our formulation becomes a mixedinteger programming which requires a combinatorial optimization. We propose a lowcomplexity clustering algorithm to solve this problem. As will be discussed in detail in the next section, existing techniques are not efficient enough to provide a satisfactory solution to the problem, thus motivating us to introduce affinity propagation (AP) [12], a stateoftheart messagepassing technique. AP has been proven to be a very efficient tool for various types of optimization problems in communication networks [13–15]. The proposed clustering algorithm based on the AP framework efficiently minimizes the total energy consumption of IPSNs while guaranteeing reliable communications.

IPSN organization: We formulate the IPSN group formation as a constrained clustering problem. Unlike the conventional clustering problems studied in the literature, our clustering formulation minimizes energy consumption while guaranteeing reliable communications. This requires a computationally demanding optimization.

Lowcomplexity algorithm: We propose a lowcomplexity clustering algorithm for the constrained clustering problem in the AP framework. The proposed clustering algorithm iteratively performs AP to determine the number of clusters adaptively. In addition, we present how to determine the initial parameters to reduce the number of required iterations and improve the convergence speed.

Energysaving performance: Our simulation results verify that the proposed clustering algorithm reduces the total energy consumption in the network by up to 31 % compared to the conventional clustering algorithms. Note that such energy saving is achieved while guaranteeing reliable communication in the network.
The remainder of the paper is organized as follows. Section 2 describes the related work in comparison with our work. The system model and the problem formulation are described in Section 3. In Section 4, we propose a novel clustering algorithm in the AP framework. In Section 5, how to determine the initial parameter p ^{(1)} is presented to reduce the number of iterations required by the proposed clustering algorithm. We show the simulation results of the proposed clustering algorithm in Section 6. Finally, Section 7 concludes the paper.
Frequently used notations
Notation  Definition 

N  Number of UEs 
\({\mathcal {V}}\)  Set of GOs 
\({\mathcal {N}}_{j}\)  Set of GMs associated with GO j 
d _{ ij }  Distance between UE i and UE j 
r _{1}  Maximum range for reliable intragroup link 
r _{2}  Maximum range for reliable intergroup link 
w(d _{ ij })  Power consumption for the transmission between GO j and UE i 
\(\bar {w}\)  Power consumption for the management of each group 
s(i,j)  Similarity of UE i to UE j 
2 Related work
2.1 Energyminimizing network formation
The previous studies have investigated minimizing the total energy of the network in wireless sensor networks (WSNs) [16–21]. In WSNs, lowenergy adaptive clustering hierarchycentralized (LEACHC) [18] proposed a pioneering idea, which minimizes the total energy consumption of the network using a clustered hierarchy. In LEACHC, simulated annealingbased optimization algorithm [22] is adopted for cluster formation. Several improvements have been proposed to enhance LEACHC by considering residual energy [19], a reclustering frequency [20], and solar cells [21]. In [23–25], LEACHC has been improved by replacing simulated annealing with Kmeans clustering [26], which has been proved to be efficient for most clustering tasks in machine learning fields.
Recent studies have developed network formation techniques based on the game theory [27–32]. Among various studies exploiting coalition game for communications networks, the study in [27] proposed a hybrid homogeneous LEACH protocol (HHOLEACH) to minimize energy consumption of the network. As described in its name, HHOLEACH is based on LEACH in minimizing energy consumption. However, the connectivity constraints are not considered in [27] like other studies that have enhanced LEACH.
2.2 Reliable network formation using CDS
Network formation under connectivity constraint has been focusing on connected dominating set (CDS) [33–36]. In graph theory, CDS is defined as a connected subgraph of a graph to which every vertex not belonging to the CDS is adjacent. For the last two decades, various algorithms such as Guha and Khuller’s algorithm and Ruan’s algorithm have been developed for various types of CDS constructions [37, 38]. In ad hoc networks, a CDS is used to select a wireless backbone network guaranteeing reliable connection for routing and control [33–36]. Vertices and edges in a graph represent the set of nodes and the set of links in ad hoc network, respectively. Whether any pair of nodes are adjacent to each other or not (that is, whether two vertices are connected by an edge in a graph) depends on the distance between them.
2.3 Limitations of previous approaches
The aforementioned studies cannot be directly applied to IPSNs because they focus on either minimizing the total energy consumption or guaranteeing reliable connection. Clustering algorithms that minimize total energy consumption do not consider connectivity constraints for reliable communication between UEs. On the other hand, minimization of total energy consumption of a network is not considered in the CDSbased network formation techniques. Thus, we propose a new network formation scheme for IPSN considering both minimizing total energy consumption and guaranteeing reliable communications.
3 System model and problem formulation
3.1 Channel model and network structure
To organize a reliable clustered hierarchy for an IPSN, two different transmission ranges for reliable links are considered depending on the link types. The transmission range for intragroup links is r _{1}=f(P _{1},γ _{1}), where P _{1} and γ _{1} are maximum transmit power for intergroup links and SNR threshold for intragroup links, respectively. The transmission range for intergroup links is r _{2}=f(P _{2},γ _{2}), where P _{2} and γ _{2} are the maximum transmit power for intergroup links and SNR threshold for intergroup links, respectively. Normally, higher transmit power, lowerorder modulation, and lowercode rate are required for intergroup links of a wireless backbone, implying that r _{1}≤r _{2} [11].
3.2 Problem formulation
In a groupbased hierarchy in IPSN, reliable communication between any pair of UEs can be guaranteed by two connectivity conditions, namely, intragroup connectivity and intergroup connectivity. Intragroup connectivity condition implies that each GO should be in the communication range of all GMs associated with it. This condition can be represented as \(d_{ij}\leq r_{1}, ~\forall j\in \mathcal {V}, ~\forall i\in \mathcal {N}_{j}\). Intergroup connectivity condition implies that any GO should not be isolated from the network of GOs. For the mathematical representation of intergroup connectivity, we define the intergroup adjacency matrix \(\mathcal {C}\) and the intergroup connectivity matrix \(\mathcal {A}\). Matrix \(\mathcal {C}\) is an L×L matrix whose (l,l ^{′}) entry is one when the distance between the lth GO and the l ^{′}th GO is less than r _{2}, and is zero otherwise, where \(L=\mathcal {V}\). Matrix \(\mathcal {A}\) is an L×L matrix which is defined as \(\phantom {\dot {i}\!}\mathcal {A}=\sum _{k=1}^{L1} \mathcal {C}^{k}\). The (l,l ^{′}) entry of \(\mathcal {C}^{k}\) is greater than zero if the lth GO and the l ^{′}th GO are connected via k reliable intergroup links, and is zero otherwise. Thus, \(a_{ll'}>0\phantom {\dot {i}\!}\) means that the lth GO and the l ^{′}th GO are connected via one or multiple intergroup reliable links, where \(a_{ll'}\phantom {\dot {i}\!}\) is the (l,l ^{′}) entry of \(\mathcal {A}\). Then, intergroup connectivity condition can be represented as \(\phantom {\dot {i}\!}a_{ll'}>0,~\forall ~l,l'\in \{1,2,\ldots,L\}\) such that l≠l ^{′}.
where (5a) represents the minimization of the total energy consumption through the determination of \(\mathcal {V}\), and \(\mathcal {N}_{j}\)’s, (5b) denotes the connectivity constraints C _{1} for intragroup connectivity, and (5c) denotes the connectivity constraints C _{2} for intergroup connectivity. Note that the clustering problem for minimizing the sum of the energy consumption without any constraints is known to be an NPhard problem [40]. In addition to this problem, our formulation includes complicated integer constraints to guarantee reliability. This is very challenging, and none of the previous study investigates an efficient solution. To this end, we develop a novel lowcomplexity algorithm by introducing AP framework.
4 Constrained clustering algorithm for IPSN
First, we present some background with regard to the AP framework. Secondly, we embed the optimization problem (5) into the AP framework through similarity modeling. Finally, we develop a lowcomplexity clustering algorithm for IPSNs.
4.1 Preliminaries: affinity propagation
AP is a stateoftheart clustering algorithm developed in computer science based on a messagepassing algorithm [12, 41]. It was originally proposed to find a set of representative data points (or exemplars) to partition a set of data points into subsets of data points. AP has various advantages. First, it outperforms existing clustering algorithms, i.e., Kmeans clustering and simulated annealing. Secondly, AP provides a deterministic result, unlike other clustering algorithms whose performance depends on the choice of the initial point. Thirdly, AP can be adapted to various complicated problems owing to its flexibility.
if j ^{⋆}≠i. UE i itself becomes a GO if j ^{⋆}=i.
The overall computational complexity of affinity propagation increases as \(\mathcal {O}(N \bar N t_{\text {max}})\), where \(\bar N\) denotes the average number of UEs adjacent to a UE and t _{max} denotes the maximum number of iterations. Decades of iterations are enough to converge in AP [15, 42] and the convergence properties and proofs are discussed in depth in [15, 42]. Another advantage of this approach is that the computational load of affinity propagation can be implemented in a distributed fashion using multicore processors [43]. Although the renewal periods of clusters depend on the mobility patterns of UEs, clusters organized by the proposed algorithm are expected to be maintained for a few minutes without a renewal of the clusters. Considering that the proposed clustering algorithm is performed on a longterm time scale, the computation cost for the proposed clustering algorithm is manageable.
4.2 Similarity modeling
where p takes a value that is less than zero. If UE j is not eligible to become a potential GO due to its high mobility, low residual energy, or UE type, it is precluded by setting s(j,j) to −∞.
4.3 Proposed clustering algorithm
When an UE detects the disruption of infrastructure, the UE tries to find new clusters of an IPSN to join. If the UE fails to find any available cluster, the UE initiates the procedures to form a clustered hierarchy for an IPSN. To notify the initiation of forming clusters, a floodingbased route discovery can be used, which is well known in distributed network management such as the generation and maintenance of a routing table in ad hoc network [44–46]. The floodingbased route discovery is useful in the disruption scenarios because it is assuming an ad hoc network without infrastructure. A UE initiates the procedures to form a clustered hierarchy by broadcasting an information request (IREQ) packet. Some of UEs receiving the IREQ packet become relay nodes and rebroadcast the IREQ packet. The IREQ packet is rebroadcast for a fixed number of hops. The UEs that received IREQ send an information response (IREP) packet to the source UE of the IREQ packet along the reverse path of the IREQ packet. The IREP contains the identification and location information. The source UE performs the proposed clustering algorithm with the collected UE information. If multiple UEs initiate clustering procedures simultaneously, the UE responsible for performing computation can be decided by the predetermined priority, e.g., the ordering of user identification number. In case of the periodic renewals of clusters, GOs collect UE information of associated GMs and one of GOs collects all the information from GOs to perform the proposed clustering algorithm. After performing the proposed clustering algorithm, the result is delivered to each UE by relaying the result through the selected GOs. According to [44–46], it is known that the signaling overhead of the floodingbased signaling is manageable if it is performed on a longterm time scale as in the proposed clustering algorithm.
The outputs resulting from AP are a set of GOs, \(\mathcal {V}\), and sets of GMs associated with each GO, \(\mathcal {N}_{j}\)’s. The intragroup connectivity is always satisfied for all outputs resulting from AP by our similarity modeling.
where \(\mathcal {V}\) and \(\mathcal {N}_{j}\) denote the set of GOs, and the sets of GMs associated with GO j, resulting from AP with preference p. If the result of AP does not satisfy the intergroup connectivity constraint, the outputs of AP with p are not valid. In such a case, we consider E(p) as ∞. The proposed clustering algorithm finds the value of p minimizing E(p) as described below. Therefore, the final outputs of the proposed clustering algorithm always satisfy the intercluster constraint.
The number of clusters is the key parameter for both total energy consumption and connectivity constraints. As the number of clusters increases, the first term of E(p) decreases and the second term of E(p) increases. If there are too few clusters, the connectivity constraints cannot be satisfied. The proposed clustering algorithm finds the proper number of clusters for the problem (5) by controlling the value of p considering total energy consumption and the connectivity constraints. Finding the optimal value of p is a complicated problem, and we propose an efficient method to find the optimal value of p based on what is known as golden section search [47]. Before beginning the golden section search, the value of preference changes with the moving rate of ρ to obtain the initial search interval of preference value to find the optimal value of p. The search interval of preference value is represented by the preference triplet (ϕ _{min},ϕ _{c},ϕ _{max}). The preference triplet (ϕ _{min},ϕ _{c},ϕ _{max}) consists of the minimum of the search interval ϕ _{min}, the maximum of the search interval ϕ _{max}, and the internal point of the search interval ϕ _{c}. The triplet should satisfy ϕ _{min}<ϕ _{c}<ϕ _{max}, E(ϕ _{min})>E(ϕ _{c}), and E(ϕ _{max})>E(ϕ _{c}). After finding the initial preference triplet, the preference triplet is iteratively updated based on the golden section search to narrow the search interval of preference value by evaluating the total power consumption at a new value in the search interval, namely ϕ. The overall procedure of the proposed clustering algorithm is shown in Algorithm 1, where \(\mathbb {AP}(p)\) represents the optimization via AP with the preference p, and \(\mathbb {GSS}(\phi _{\text {min}},\phi _{\mathrm {c}},\phi,\phi _{\text {max}})\) denotes the updates of the preference triplet and ϕ based on the golden section search.
To find the initial triplet of the preferences, we consider the initial value of p, denoted by p ^{(1)}, and the moving rate of p, denoted as ρ. Initially, AP is performed with the preference of p ^{(1)} and p ^{(2)}, where p ^{(2)}=p ^{(1)} ρ>p ^{(1)}. If E(p ^{(1)})>E(p ^{(2)}) or E(p ^{(1)})=E(p ^{(2)})=∞, AP is iteratively performed by increasing p ^{(m)}=p ^{(1)} ρ ^{ m−1} (m≥3) until finding M such that E(p ^{(M−1)})≤E(p ^{(M)}). The initial triplet of the preferences in this case is (ϕ _{min},ϕ _{c},ϕ _{max})=(p ^{(M−2)},p ^{(M−1)},p ^{(M)}). If E(p ^{(1)})<E(p ^{(2)}), AP is iteratively performed by decreasing p ^{(m)}=p ^{(1)} ρ ^{−(m−2)} (m≥3) until finding M such that E(p ^{(M−1)})≤E(p ^{(M)}). The initial triplet of the preferences in this case is (ϕ _{min},ϕ _{c},ϕ _{max})=(p ^{(M)},p ^{(M−1)},p ^{(M−2)}).
The update of the preference triplets terminates if ϕ _{max}−ϕ _{min}<εϕ _{c}+ϕ, where ε denotes the termination threshold. The final preference value is p _{r}=ϕ _{c} if E(ϕ)>E(ϕ _{c}), and the final preference value is p _{r}=ϕ if E(ϕ)<E(ϕ _{c}). The final clustering outputs are the \(\mathcal {V}\) and \(\mathcal {N}_{j}\)s resulting from AP with the preference p _{r}.
5 Determination of the initial point
The proposed clustering algorithm is based on iterative updates of the AP solution that requires long processing time and high computational complexity. The required number of iterations of the proposed clustering algorithm depends on the choice of the initial value of preference p ^{(1)}. If the iteration begins with an arbitrary value of p ^{(1)}, the proposed clustering algorithm finds inefficiently the final value of p. To reduce the number of iterations of the proposed clustering algorithm, we determine the p ^{(1)} by estimating the minimum number of clusters, denoted by κ, that satisfies the connectivity constraints.
Then, we determine p ^{(1)} which corresponds to κ via their mathematical relation. We determine the relation between the number of clusters and the value of p in AP by averaging the distribution of the UEs.
Lemma 1.
Proof
See Appendix.
6 Simulation results
Simulation parameters
Parameter  Value 

Area, S  2×2 km 
Path loss exponent, α  4.37 
Transmission loss at d _{0}=1 m, L _{0}  0.068 dB 
Noise power, σ ^{2}  −104 dBm 
Maximum Tx power for intragroup link, P _{1}  23 dBm 
Maximum Tx power for intergroup link, P _{2}  30 dBm 
SNR threshold for intragroup link, γ _{1}  9 dB 
SNR threshold for intergroup link, γ _{2}  3 dB 
Average total power consumption vs the number of iterations
Proposed algorithm (W)  Kmeans clustering (W)  

Number of iterations  100  90  80  70  
Case A  6.8  6.8  6.9  7.1  7.5 
Case B  35.5  36.2  37.7  38.5  41.1 
Case C  8.3  8.4  8.5  8.7  9.3 
Figure 9 shows the average outage probability in the proposed clustering algorithm as a function of the shadowing standard deviation. The proposed clustering algorithm always satisfies the connectivity constraints, and the outage probability equals zero when shadow fading is not considered. As the shadowing standard deviation increases, the outage probability increases. The proposed clustering algorithm can reduce the outage probability by conservative setting in the connectivity constraints. In other words, the outage probability can be reduced if r _{1} and r _{2} are set to smaller values. The conservative setting for reliability results in higher power consumption in the proposed clustering algorithm. The tradeoff between the reliability and the power consumption should be considered in the practical implementations.
Figure 10 shows the average outage probability in the proposed clustering algorithm as a function of time and UE speed, denoted by v. A random walk mobility model [49], which is one of the most employed models used for ad hoc network [50] and sensor network [51], is used in the mobility pattern of UEs. To focus on the impact of mobility in the proposed clustering algorithm, the impact of shadow fading is excluded here. With no mobility of UEs, the outage probability equals zero by the clustering result ensuring the connectivity constraints from the clustering algorithm. As UEs move faster, the outage probability increases fast and the renewal of clusters should be performed more frequently to maintain a reliable hierarchy. However, the renewal of clusters every 10 min is enough to maintain a reliable hierarchy even when v=9 km/h. The outage probability can be reduced by setting r _{1} and r _{2} to smaller values, and the similar tradeoff between the reliability and the power consumption with the fading model exists in the mobility model.
7 Conclusions
A novel clustering algorithm based on affinity propagation is proposed to provision both energy efficiency and reliability in IPSNs. As a key novelty, we embed the optimization problem of IPSNs into the AP framework by means of similarity modeling and proposing an efficient method to find the number of GOs based on the golden section search. The proposed clustering algorithm adaptively determines the number of clusters that minimizes the total energy consumption while satisfying the connectivity constraints. The simulation results have shown that the proposed clustering algorithm considerably outperforms Kmeans clustering, LEACHC, and CDSbased formation in various environments. Future research directions include studies of the impact of UE mobility, heterogeneous traffic patterns, and different device types.
8 Appendix
8.1 Proof of Lemma 1
This completes the proof.
Declarations
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2014R1A2A2A01003637), Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF2015R1D1A1A01057100), and LG Electronics Co. Ltd.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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