Simultaneous power control and power management algorithm with sectorshaped topology for wireless sensor networks
 Mohsen Nickray^{1},
 Ali AfzaliKusha^{1}Email author and
 Riku Jäntti^{2}
https://doi.org/10.1186/s1363801503559
© Nickray et al.; licensee Springer. 2015
Received: 1 July 2014
Accepted: 8 April 2015
Published: 25 April 2015
Abstract
In this paper, we propose a topology control technique to reduce the energy consumption of wireless sensor networks (WSNs). The technique makes use of both power control and power management methods. The algorithm uses the power management technique to put as many idle nodes as possible into the sleep mode while invoking the power control method to adjust the transmission range of the active nodes. On the contrary to earlier works in which both of these methods were used separately, in this algorithm, they are utilized simultaneously to decide about the sleep nodes and the ranges of active nodes. It is an approximation algorithm which is called simultaneous power control and power management algorithm (SPCPM). The performance bound of this centralized algorithm is determined analytically. Then, to make the proposed method practical for WSNs, a distributed algorithm based on SPCPM is introduced. To assess the efficiency of the proposed algorithm, we compare its average energy consumption with those of three existing topology control algorithms for a sectorbased WSN. The simulation results which were obtained for different numbers of transmitting sensor nodes reveal less average energy consumptions for SPCPM compared to other algorithms.
Keywords
1 Introduction
Recent advances in wireless and electronic technologies have led to the emergence of wireless sensor networks (WSNs) with largescale nodes. They are used in a wide spectrum of applications from industrial and military applications to health and environmental monitoring. In these kinds of networks, different smallsize sensor types are deployed in the area to monitor, e.g., temperature, motion, noise, and seismic activities. A good survey of WSNs is presented in [1] and [2]. The sensors are wireless nodes that transmit the collected data (hop by hop) to a central station called base station or SINK node. Due to critical limitations of the node energy resources (e.g., battery), the nodes should minimize the energy consumption during their computation and communication. Therefore, lowpower algorithms for WSNs are of prime interest. Among different WSN types, sectorshaped networks, where all the nodes send their data to a single base station, are the most common. They have various applications such as health monitoring, data gathering, and surveillance [35]. There have been several research efforts on reducing the overall transmission power of sectorshaped networks [510]. The efforts may be divided into two categories of power control and power management techniques. The key idea of the power control techniques is that instead of transmitting using the maximum power, the nodes in a WSN collaboratively reduce their transmission power by adjusting their transmission range while preserving some required properties (e.g., connectivity) [616]. The power control algorithms focus on reducing the power consumption when the nodes transmit or receive data in transmit and receive modes, respectively. Additionally, WSN nodes have a listen mode in which, while they are idle, they consume energy. The energy is comparable to the energy consumed in the other two modes. To reduce the energy consumption, the radio of the nodes in this mode may be turned off when they are not in use [1720]. Turning off the radios when they are not in use is the basic idea of power management algorithms. Both of these techniques reside in the general category of the topology control algorithms.
It is expected that if these two types of techniques are invoked in coherence with each other in an algorithm, higher energy preservation will be achieved. This may be justified by noting that in this algorithm, the reduction of the energy consumptions of all the transmission, receive, and idle states are considered simultaneously. The energy conservation of wireless sensor networks may be considered as an optimization problem where the energy consumptions of different sources should be minimized. For this problem, each of the power control and power management algorithms may be used. Depending on the network load, one of these algorithms is used for the energy optimization. When the network load is low, the energy consumption of the network is dominated by the energy consumed by nodes in the idle state. For these loads, it is expected that fewer active (awake) nodes with long communication ranges lead to more energy conservation. In these cases, the power management algorithm should have a more determining role. In the cases where the network load is high, more active nodes with short communication ranges provide a better energy efficiency, and hence, the power control algorithm should play a major role in the optimization process. In this work, we propose an algorithm which integrates both of these techniques into one efficient algorithm.
1.1 Our contributions

Its power management technique considers both time and space dimensions.

It makes use of both power management and power control approaches simultaneously without giving any priority to any of them.
The rest of the paper is organized as follows. In Section 2, we briefly review the related works while Section 3 describes the network topology along with the energy model which is used in our study. In Section 4, we use an example to show the dependency of the minimum energy consumption to the network data traffic. In Section 5, we describe the proposed centralized Simultaneous Power Control and Power Management (SPCPM) algorithm in detail and compare its efficiency with similar techniques reported in the literature. Section 6 is devoted to the distributed SPCPM, and its performance is compared to those of existing techniques. Finally, the paper is concluded in Section 7.
2 Related works
In this section, we briefly review some of the previous works in the area of energy preservation of WSNs. These may be classified into two categories of power control and power management algorithms. The features of the algorithms are discussed while the main difference of our approach compared to these works is described at the end of the section.
2.1 Power control
Power control algorithms adjust the transmission power without adversely affecting desirable properties of the network (e.g., connectivity). Several empirical studies show that existing topology control solutions, which use static transmission power, transmission range, and link quality, might not be effective in the physical world (see, e.g., [21,22]). The authors in [22] propose a selective singlerelay cooperative scheme, combining selectiverelaycooperative communication with physical layer power control. Based on the medium access control (MAC) layer RTSCTS signaling, a set of potential relays compute individually the required transmission power to participate in the cooperative communication. Based on the theory of stochastic fictitious play (SFP), a reinforcement learning algorithm to schedule each node’s power level is proposed in [23]. Also, a transmission power self optimization (TPSO) technique is presented in [24]. It basically consists of an algorithm able to guarantee the connectivity as well as an equally high Quality of Service (QoS) concentrating on the efficiency of WSNs, while optimizing the necessary transmission for data communication in each node.
In the scheme proposed in [11], a node chooses its next node for relaying the information based on minimizing the total energy consumption for the whole transmission. It was shown that the network was strongly connected when every node had links only to those nodes that were within its enclosure defined by a relay region. In [12], the authors suggested two centralized algorithms to minimize the maximal power used per node while maintaining the connectivity of the network. Narayanaswamy et al. [14] and Kumar and Kawadia [15] propose algorithms to maintain network connectivity using a minimal transmission power. The authors in [16] proposed a minimum spanning tree (MST)based topology control scheme which keeps the network connectivity and has bounded node degrees [16]. For detailed surveys on the power control techniques in WSNs, one may see, e.g., [2527].
2.2 Power management
Power management algorithms focus on turning off the radios of the nodes which are not in use. There are two basic approaches, namely, schedulingbased [17], [18] and backbonebased sleep management [13,20]. In [28], a systematic and comprehensive survey of the power management schemes is presented. In the schedulingbased approaches, nodes turn on their radios only in scheduled slots. Backbonebased sleep management can improve network performance by maintaining a backbone composed of a small number of active nodes, while scheduling the other nodes to be active for small periods of time to conserve energy. From another aspect, the techniques may be divided based on the dimension that they use for the power management. The dimensions include node (e.g., [29]) or time (e.g., [13,20]). The approaches based on the node dimension, such as geographical adaptive fidelity (GAF) [29], mainly focus on detecting redundant nodes which can be turned off. In this algorithm, the network is divided into small square grids whose sizes are equal and fixed. All the nodes in a grid have the same routing role where at any time only one node is active and all the other nodes are in the sleep mode. The sleeping nodes periodically switch to the listen mode to guarantee that in each grid at least one node stays on. The algorithms based on the time dimension concentrate only on detecting the time when the nodes are idle and can be turned off [13,20]. In SPAN [13], a subset of nodes is adaptively selected to form a multihop forwarding backbone. The subset nodes, called coordinators, carry all the traffic of the network causing the energies of the other nodes which are in the sleep mode to be conserved. A technique, which is called STEM, defines two ‘transfer’ and ‘monitoring’ states for the nodes [20]. The approach is based on the fact that most of the time the sensor network is only monitoring its environment, waiting for an event to happen. In this state, the nodes can be asleep and the radio can be off. When an event is detected, the node becomes awake, changing its state to the transfer state.
2.3 Unified power control and power management algorithm
Comparison between the previous works and proposed algorithm in this work
3 Network topology and energy model
3.1 Network topology
3.2 Energy model
4 Illustrating example
In Figure 2 part a, we have plotted E_{1}, E_{2}, and E_{3} versus different packet sizes of the source node. The results have been obtained assuming L_{MAX}, R, E_{r}, E_{id}, E_{e}, E_{s}, and α to be 500 bytes, 400 m, 0.01 nj/bit/m^{2}, 50 nj/bit, 50 nj/bit, 12.5 pj/bit, and 2, respectively [34]. As the figure shows, when the network load is low, e.g., the packet size is 25 bytes, the minimum energy consumption will be achieved if the third scenario is used. In this scenario, the node A transmits data directly to the SINK node with the maximum transmission range while the other nodes are in the sleep state. When the network load is high, e.g., the packet size is more than 150 bytes, the first scenario will preserve energy more. For the medium range of traffic, e.g., the packet size of 80 bytes, the second scenario will lead to the minimum energy consumption.
As this example shows, when the network load is low, the energy consumption of the network is dominated by the idle energy. Therefore, scheduling more nodes to be in the sleep mode (power management task) with a long transmission range for the active nodes (power control task) will preserve more energy. When the load is high, the transmit energy dominates the energy consumption of the network. For this case, scheduling more nodes in the active mode with short transmission ranges will preserve more energy. Since the nodes B, C, and D first should receive the data and then relay it, they can have, at most, one half of the active period for receiving the packet and the other half of the period for transmitting the packet. Therefore, L ≤ L_{MAX}/2 or L/L_{MAX} ≤ 1/2. For this reason, in the case of the example discussed in Figure 2, we assumed L_{MAX} = 500 bytes × 8 bits = 4,000 bits and hence we plotted the energy consumptions versus L in the range of 50 to 2,000 bits.
We use the ratio L/L_{MAX} to denote the proportion of the network cycle time that is used by a node to transmit its data. This notation is only valid when the transmission rate is constant for all the nodes. Otherwise, L/L_{MAX} should be replaced by node transmission time divided by the network cycle period.
5 Proposed algorithm
5.1 Problem definition
Here, the first summation in the first line is performed on all the nodes (v) that the node u transmit packet to them, and the second summation is performed on all the nodes (v’) which they transmit to the node u. The average energy consumption of the node u is the weighted average of the transmit, receive, and idle energy consumptions. Also, since the energy dissipation of the node in the sleep state is very small, it has been ignored in the calculations [30].
From the above formulation, we can see that each node has a fixed cost of W _{ c }. Also, for each edge (u,v), the cost is W _{ v }(u,v) which is independent from the packet size. The packet size (proportional to the traffic load) has been entered in the calculation using a data fraction factor denoted by f _{ i }.
5.2 Centralized SPCPM
In this section, we introduce an approximation algorithm called SPCPM to maximize the energy preservation of a sectorshaped wireless sensor network. In this algorithm, based on a combined cost function, the algorithm decides about the state of nodes and the transmission range of the active nodes simultaneously.
5.2.1 A. Algorithm description
Let us describe the algorithm whose pseudo code is given in Algorithm 1. The input of the algorithm is the network ψ(α,R,N,k), and its output is the subnet graph G’(V’,E’) where V’ is the set of active nodes and E’ is the set of the links between the active nodes. In step (1), we describe the network using the graph G(V,E). To generate the graph G, for each node u, we should consider all possible routes that connect u to the SINK node. In SPCPM, we only consider transmission scenarios where the hops with about equal distances (in terms of the number of hops) are included. Figure 1 shows all the routes which may be used by SPCPM to transmit data from the node A to the SINK node. In scenario 1, 2, and 3, the node A transmits data by a 4hop, 2hop, and 1hop transmission while communication scenarios like A → B → SINK and A → D → SINK are excluded. For some nodes (nodes with an odd annulus numbers), using equal hop distances may not be possible which in these cases, one of the hop distances will become one hop smaller than the others. For example, the node B in Figure 1, may take the route B → C → SINK in a twohop scenario. As will be discussed in Section 6, the assumption of equal hop distances does not considerably affect the efficacy of the algorithm.
As an example, consider the network of ψ(α,R,64,8). For this network, the number of transmission scenarios for a node in annulus 7 is 4 where the numbers of hops for these four scenarios will be 7, 4, 2, and 1. Considering sce(2), the sequence of hops identified by the annulus number are 7 (the source node), 5,3, 1, and 0 (the SINK node) (sce(2) = 4).
After finding the shortest path for the iteration i, we set the state of all the nodes on this path to active. The output of SPCPM is the set of all the shortest paths found for all the iterations and the set of all the active nodes (G’(V’,E’)). It is apparent that the nodes which are not selected as active remain in the sleep state.
5.2.2 B. SPCPM algorithm analysis
In this section, we study the complexity of SPCPM and also obtain the approximation ratio of the algorithm. The proposed problem in this work was defined in Equation (7). The problem is finding the minimumweight Steiner tree in the graph G(V, E) with the weight g _{ i } given by Equation (12). Here, E and V are the sets of edges and nodes in G, respectively. Finding the minimumweight Steiner tree is an NPhard problem (see, e.g.,) [35]. We used the SPCPM algorithm to solve the problem. Assuming equal hop distances, the complexity of SPCPM becomes O(S.logE.logV) where S, E, and V are the numbers of sources, edges, and nodes in G, respectively. In the case of considering all possible routes, the complexity increases to O(S.logE.logV) (see Equations (8)(9)).
Theorem: The approximation ratio of the algorithm SPCPM is not greater than: \( \frac{\leftS\right\times \leftK\right}{\leftV\hbox{'}\right} \).
Therefore, the approximation ratio of SPCPM, in the worst case, is \( \frac{\leftS\right\times \leftK\right}{\leftV\hbox{'}\right} \).
5.3 Performance evaluation
To evaluate the effectiveness of the proposed algorithm, we have compared it with three other algorithms. They included the algorithms Transmission Power Minimum Spanning Tree (TMST) [10], Transmission power Shortest Path Tree (TSPT) [36], and Minimum Power Configuration (MPC) [30]. All the algorithms were implemented in MATLAB. The first two algorithms are basic topology control methods while the last algorithm is similar to the SPCPM technique considering the minimization of both idle and transmit/receive energies. The TMST algorithm finds the minimum spanning tree of the network where each edge is weighed by the transmission power of the transmitting node. The TSPT technique finds the shortest path tree of the network when each edge is weighted by the transmission power. In the MPC algorithm which is more efficient compared to the two previous ones, each edge is weighted by a combination of the transmission and idle powers of the node. The parameters L_{MAX}, R, E_{r}, E_{id}, E_{e}, and E_{s} in our simulation were assumed to be 500 bytes, 400 m, 0.01 nj/bit/m^{2}, 50 nj/bit, 50 nj/bit, and 12.5 pj/bit, respectively [34]. We assumed that 100 nodes were randomly distributed in the sectorshaped area with R = 800 m and α = π/4.
6 Distributed SPCPM
In this section, the design and implementation of the distributed form of SPCPM are discussed. This distributed algorithm is based on destinationsequenced distancevector (DSDV) method [37] which is a shortest path algorithm widely used in the literature. DSDV is based on a distributed implementation of the BellmanFord shortest path algorithm [38]. A node in DSDV advertises its current routing cost to the SINK (distance to the SINK node) by broadcasting update messages (control packets). Having received the messages, each node sets the neighbor with the minimum cost as its parent. The routing table for this node also is formed based on the broadcasted update messages where the table is periodically broadcasted to other nodes. In our work, we used an improved DSDV technique where the modifications (compared to the conventional one [37]) were described in [3941]. Examples of these improvements include avoiding DSDV extra traffic using incremental updates and implementing multipath routing.
An example of a routing table for a node in distributed SPCPM
Data fraction  Cell number/annulus number  Cost  Sequence number 

f _{ i } < 0.1  3/2  5  100 
0.1 < f _{ i } < 0.3  1/4  4  20 
f _{ i } > 0.3  1/7  6  41 
It should be noted that when a new source node with a new data flow appears in the network, the data fraction (f _{ i }) for some nodes may change. This change may cause the next hop for some nodes to alter too (see Table 2). In addition, the appearance of a new flow may activate a node previously running in the sleep mode. This reduces the cost of transmitting data for the neighboring nodes of the newly activated node. Therefore, the routing tables should be updated. The transmission costs are calculated from Equation (12). In addition to the appearance of a new data flow, the disappearance of an existing flow may also require a route update. In such a case, the active nodes on the routing path for this flow may switch to the sleep mode after some timeout. Another case where the routing tables should be updated is when a source node changes its data rate (significantly). This again changes the data fraction of some nodes and hence the routing tables should be updates. When the workload of the network is dynamic, multiple rounds of route updates may be initiated at the same time, resulting in high network contention. In the DSDV technique, to reduce the overhead of route updates in such a case, the SINK can include several default data rates in its initial route updates, based on the estimation of source rates.
In our distributed algorithm, we have assumed that either a GPS or GPSless mechanism may be used as a localization technique to obtain the location information of the nodes. In our algorithm, we supposed that each node knew its current location relative to the SINK node. The information is used to configure the network. Due to its importance, the localization (which is not the focus of this paper) is an active area of research (see, e.g., [4246]). For example, the techniques presented in [4446] determine the node location based on the information of the angle of arrival between neighbor nodes. These techniques which are accurate, decentralized, and GPSless may be the better option for being used in conjunction with SPCPM.
6.1 Performance of distributed SPCPM
In order to evaluate the performance of the distributed SPCPM algorithm, we compare it with minimum transmission routing (MTR) [12], distributed minimum power configuration protocol (MPCP) [30], and the original DSDV [37]. A node in MTR chooses the next hop node based on minimizing the expected number of transmissions while considering the same transmission range for all the nodes. The MPCP algorithm is similar to the distributed SPCPM except for the fact that it does not have a cellbased configuration. To generate the results presented in this section, the simulator Prowler was used. Prowler is a Matlabbased network simulator that uses an eventdriven structure. For the physical and MAC layer parameters, we used network parameters described in [47,48]. These parameters are used for the models concerning all levels of the communication channel and application. The nondeterministic nature of the radio propagation is characterized by a probabilistic radio channel model. The radio propagation model determines the strength of a transmitted signal at a particular point of the space. The deterministic part of the propagation function can be any usersupplied function where, in this work, we used the model explained in Subsection 3.2. The fading effect is also modeled by random disturbances. In our simulations, the required transmission power/energy for each node in an active period is estimated based on the distance to the next hop considering the radio environment (including fading). The simulator assumed a continuous adjustment of the transmission power. The same assumption has been considered for implementing all other algorithms in this paper.
For the MAC layer, we have employed a simple CSMA/CA scheme without RTS/CTS, which is based on SMAC. Like [30], as an automatic repeat request (ARQ) mechanism, we retransmit a packet if an acknowledgement is not received after timer preset. The maximum number of retransmissions before dropping a packet is 4. The results were obtained for two sectorshaped configurations. In the first one, a sectorshaped area with R = 400 m which was divided into 4 annuluses and 16 cells where 50 nodes were deployed. In the second configuration, the sectorshaped area had a radius of 800, 8 annuluses, 64 cells, and 200 nodes. The number of sources for these configurations changed from 5 to 25 and 10 to 100, respectively. The data packet size was 120 bytes, and the routing update packets were 40 bytes. For the energy parameters, we assumed the same values as those mentioned in section 4. The simulations were performed for one period of sending report by the WSN sources. It should be noted that in all simulations, to report the energy consumption like in Section 4, we got the sum of the average energy consumption of all network nodes. All the simulation results were obtained by averaging the results of ten simulation runs. We have also shown the corresponding 90% confidence interval for the results.
6.2 Impact of limiting transmission power on SPCPM
6.3 Impact of assumption of equal distance hops on SPCPM
6.4 Impact of SPCPM on energy hole problem
7 Conclusion
In this paper, we proposed a topology control technique to reduce the energy consumption of wireless sensor networks (WSNs) based on simultaneous use of both power control and power management methods. The technique which was called SPCPM minimized the total energy consumption of WSNs. We discussed that none of the power control and power management approaches could optimize the energy consumptions of all the radio states. Also, it was analyzed that in a sectorshaped network, the power control algorithms were effective when the traffic of the network was high while the power management algorithms were effective when traffic was low. We presented an approximation algorithm with a provable performance bound and extended it to a distributed and practical algorithm. The algorithm dynamically updated the routes from the sources to the SINK node based on the data rates in each report period such that the energy preservation was maximized. The efficacy of the proposed algorithm was assessed by comparing its energy consumption, packet delivery rate, endtoend delay, and control message overhead with those of the three other algorithms. The comparisons showed that the SPCPM technique conserved the energy considerably in both centralized and distributed forms. In addition, the packet delivery rate was higher while the endtoend delay and control message overhead were slightly lower in the case of SPCPM.
Declarations
Acknowledgements
We would like to show our gratitude to Mehdi Kamal, Dr, University of Tehran, for sharing his pearls of wisdom with us during the course of this research.
Authors’ Affiliations
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