ENERGY OPTIMIZATION IN MULTIHOP WIRELESS EMBEDDED AND SENSOR NETWORKS Zach Shelby, Carlos Pomalaza-R´aez, Jussi Haapola Centre for Wireless Communications, University of Oulu, Finland,
[email protected]
Abstract - This paper provides an analytical model for the study of energy consumption in multihop wireless embedded and sensor networks. The nodes in this type of network are battery-powered and as such they must be extremely frugal with their energy budget. The networks usually have a large number of nodes whose deployment and topology is application dependent. Low-power optimization techniques developed for conventional ad hoc networks are not sufficient as they do not properly address particular features of embedded and sensor networks. It is not enough to reduce overall energy consumption, it is also important to maximize the lifetime of the entire network, that is, maintain full network connectivity for as long as possible. This paper considers different multihop scenarios to compute the energy per bit, efficiency and the energy consumed by individual nodes and the network as a whole. The analysis uses a detailed model for the energy consumed by the radio at each node. Multihop topologies with equidistant and optimal node spacing are studied. Numerical computations illustrate the effects of packet routing. These results show that using a simple multihop message relay strategy is not always a good procedure to extend a network’s lifetime. Depending on the radio hardware characteristics and on the topology, direct relay to a sink or a routing mechanism that bypasses intermediate nodes can be, in some cases, the recommended procedure. Keywords - multihop, energy efficiency, embedded, sensor networks, routing I. I NTRODUCTION Conventional ad hoc networks can be considered as a loose collection of mobile nodes that are capable of communicating with each other without the aid of any established infrastructure or centralized administration. In recent years the rapid advancements in various areas of technology such as low-cost, low-power micro electro-mechanical systems have led to the evolution from traditional ad hoc networks to wireless embedded networks (WENs) for a variety of applications. A wireless sensor network (WSN) is a specialized type of WEN. A typical WSN node has applicationoriented sensing technology as well as the computation and networking components of a conventional ad hoc network node [1]. The small size and low cost of a WSN node facilitates the use of networks with a very large number of
nodes in a variety of commercial and military applications [2]. There are however fundamental differences between a conventional ad hoc network and a WEN (or a WSN). These differences include: • A very large number of nodes, often on the order of thousands • Low data rates • Each node has a limited amount of energy which in many applications is impossible to replace or recharge • Broadcast communications are more common than point-to-point due to the large number of nodes • Nodes usually do not have a global ID such as an IP address • Security, both physical and at the communication level, is more limited than in conventional networks The limited amount of energy at each node directly affects the lifetime of the network and therefore energy consumption has been a very important design consideration for the protocols and algorithms developed for WENs [3]–[5]. Almost all of this reported work deals with networks that have identical nodes, e.g. nodes with the same sensing, communication, computation, and power capabilities. A study where the architecture is heterogeneous can be found in [6]. Since the conservation of energy is paramount for WENs most of the reported work has concentrated on energy efficient MAC and routing algorithms. Usually the proposed techniques have been extensions and modifications of ideas that were developed and proven to be successful for conventional ad hoc networks. As mentioned above conventional ad hoc networks have substantial differences from WENs. These differences are not just limited power and a large number of nodes, two of the main design considerations that have been used extensively to modify the protocols already developed for ad hoc networks. The deployment and topology of most WENs is such that a natural mode of communication is to use multihop protocols. The goal is to reduce not just the overall energy consumption but also to maximize the lifetime of the entire network, i.e., maintain full network connectivity for as long as possible. This paper extends the work of previous studies such as the ones described in [7]–[9]. The energy consumption of different multihop scenarios is analyzed and optimized. This study uses a detailed model for the energy consumed by each node’s radio and analyzes topologies with equidistant node separation and with optimal spacing.
power derived in [10] we can derive multihop energy per payload bit from (1) with
Fig. 1. d n n
d 1
...
2
1
r
Fig. 2.
; @ @ ;
Radio energy consumption model.
sink
Linear multihop model with equal hop distances.
II. E NERGY C ONSUMPTION M ODEL Power consumption models of the radio in embedded devices must take both transceiver and start-up power consumption into account. The latter actually becomes dominant with small packet sizes and long transition times to receive mode because of frequency synthesizer settle-down. In [7] a model for radio power consumption is given for energy per bit (eb ) as eb = etx + erx +
Edec , ι
(1)
where etx and erx are the transmitter and receiver power consumptions per bit, respectively, Edec is the energy required for decoding a packet, and ι is the payload length in bits. The encoding of data is assumed to be negligible. This model takes the energy needed to transmit a frame from a transmitter to a receiver over a single hop into account as shown in Figure 1. In [7] the model was used over a single hop to optimize frame sizes and coding techniques. In this paper we extend the model for multihop scenarios and different traffic models. III. M ULTIHOP P OWER C ONSUMPTION In this section an analytical model for multihop communications is introduced that takes detailed overheads into account. A linear model is used with variable spacing between nodes assuming a sink node that collects data and is not energy dependent. Energy per bit, energy efficiency and total energy are derived for various traffic cases and node distributions. A. Linear model A similar analysis can be made as in [10] by extending (1) to take the linear multihop scenario shown in Figure 2 into account, assuming optimal power control. Instead of total
eb = (n(ete + eta (r/n)β ) + (n − 1)ere )(1 + +
nEst + (n − 1)(Esr + Edec ) , ι
(α + τ ) ) ι (2)
where ete is the energy per bit needed by the transmitter electronics, ere for the receiver electronics, Est and Esr are startup energies, eta is the power needed to successfully transmit one bit over one meter and β is the path loss exponent. The analysis of multihop power consumption made in [10], [11] assume that perfect power control is used so that the packet error rate is considered to be negligible. In reality this is unrealistic since it is very difficult to fine-tune transmit power, especially in a sensor node, instead a more realistic situation is fixed or very course transmit power control. An extension of the energy efficiency analysis introduced in [7] can be made for the multihop case with η = ηe p a
(3) ι(net + (n − 1)ere ) = k(net + (n − 1)ere ) + nEst + (n − 1)(Esr + Edec ) (4) ∗ (1 − P ER)n .
For this same topology we can also calculate the total energy consumed in the network. Using the same notation as in (2) total multihop energy consumption is EM H = n(k(ete + eta (d)β ) + Est ) + (n − 1)(ker + Esr + Edec ).
(5)
The analysis used to this point has taken an unrealistic traffic assumption into account, that is, only node n (furthest from the sink) transmits data. This was necessary for calculating energy per bit and energy efficiency, which are framecentric metrics. However, in most useful scenarios all nodes will transmit data, we can take that into account by assuming that all nodes have a single frame to transmit towards the sink. Total energy for this scenario is all EM H =
n(n + 1) (k(ete + eta (d)β )) + Est ) 2 n(n − 1) (ker + Esr + Edec ). + 2
(6)
We can compare this multihop case to the single-hop case where each node transmits its frame directly to the sink node, that is, no forwarding is performed. This is calculated as all ESH =
n
(k(ete + eta (id)β ) + Est ).
(7)
i=1
In addition, we can calculate energy consumption from a node-centric point of view, that is, how much power does
and for optimally spaced with β = 2 opt = Elinear
Fig. 3.
Equidistant and optimal spacing.
a particular node n consume. For the multihop case this is calculated as all β EM H (i) = (n − i + 1)(k(ete + eta (d) ) + Est )
+ (n − i)(ker + Esr + Edec ),
(8)
and for the single-hop case as all ESH (i) = k(ete + eta (id)β ) + Est .
(9)
n(n + 1) (kete + Est ) 2 r2 n(n − 1) (ker + Esr + Edec + keta n 1 ). + 2 i=1 i (15)
In addition, weighting can be added between n equidistant and optimal spacing with di = wi r Where i=1 wi = 1. Weighting can be used to search for a desirable energy consumption behavior balanced between nodes close to and far away from the sink which is important for maximizing the lifetime of a network. Weighting can be described with 1 , (16) wi = n ( i=1 (1/(n + 1 − θi)))(n + 1 − θi) where θ takes values between 0 and 1 with θ = 0 corresponding to equal spacing and θ = 1 to optimal.
B. Optimal spacing In [11] it was proven that a characteristic distance can be found minimizing energy used for the multihop scenario where only node n transmits. For the all nodes transmitting case this no longer holds. Instead we can analyze the distribution of di for minimum power consumption in this case. For the all nodes transmitting scenario, total energy consumption is Elinear =
n(n + 1) (kete + Est ) 2 n(n − 1) (ker + Esr + Edec ) + 2 n (n + 1 − i)(di )β . + keta
(10)
i=1
n Minimizing Elinear with the constraint r = i=1 di and taking partial derivatives of L with respect to di and equating to 0 gives ∂L = keta β(n + 1 − i)(di )β−1 − λ = 0 (11) ∂di 1 λ ) β−1 , (12) di = ( keta β(n + 1 − i) n where the value of λ can be obtained using i=1 di = r and replacing it in (12) to compute values for di , the distribution of which can be seen in Figure 3. Thus for β = 2 this is di = n
r
1 i=1 i (n
+ 1 − i)
.
(13)
The total energy for equally spaced nodes can be calculated to be eq = Elinear
n(n + 1) (k(ete + eta (r/n)β ) + Est ) 2 n(n − 1) (ker + Esr + Edec ), + 2
(14)
IV. R ESULTS The results presented in this section were collected using Matlab. All results use parameters for a common 433 MHz radio, the RFM TR1000, running at 19.2 kbps as was used in [7]. Manchester coding is assumed, with a 48 byte payload. Using this model we can compare the use of single-hop vs. multihop communications in low-power networks. The real question is whether transmit energy or receive and startup energy are dominant factors, the former favoring the theory that multihop is always more efficient. However, when accurately taking startup energies and other overheads into account, it can be shown that in most useful cases single-hop techniques are preferred. In Figure 4 energy per useful bit to transmit a single frame is shown dividing a constant total distance over variable numbers of hops. As can be seen, within the range of the radio (about 70 m) single-hop uses less energy. Multiple hops become efficient only when out of range of the radio. It can be seen that eb can be made to scale linearly over distance if the optimal number of hops is always chosen, reinforcing the characteristic distance results reported in [11]. In Figure 5 a similar scenario is used with energy efficiency where channel errors are taken into account. For instance at 50 m a single hop achieves 62% efficiency whereas 5 hops achieves a maximum of 10%. Efficiency exponentially decays if the optimal number of hops is always chosen. Total energy consumption for multihop and single-hop cases can be seen in Figure 6 with the simple traffic model. For up to 15 hops (600 m) single-hop uses less energy than multihop. Figure 7 shows the same comparison with all nodes transmitting. Here energy consumption is an order of magnitude higher and the difference between single-hop and multihop is less, with single-hop being more efficient for up to 13 hops (390 m). Here the multihop case however has problems with network lifetime, that is, nodes close to the sink will die very soon. This is explored in the following.
Total energy over different # of hops, β=2, d=30m 0.7 Multihop Single hop
Energy per bit over different hops, β=3, e = 1e−11
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Fig. 4.
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Fig. 7.
Total energy with all nodes transmitting.
Multihop energy per bit.
Total energy per node, r=1000m, n=20, β=2 Equidistant multihop θ=0.2 θ=0.4 θ=0.6 θ=0.8 Optimal multihop Single hop
0.04
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Multi−hop energy efficiency over different hops counts, β=3 0.7 1 hop 2 hop 3 hop 4 hop 5 hop
Total energy (J)
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Energy efficiency
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Fig. 5.
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Total energy over different # of hops, β=2, d=40m Multihop Single hop
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Using (10) and wi from (16) a comparison of different weighting values from 0 to 1 can be made against the single-hop case. This comparison is made from the nodecentric point of view, that is, how much energy does node n consume. We can see from Figure 8 with a total distance of 1 km using 20 hops, that with multihop nodes closest to the sink use much more energy. This is because these nodes must forward the packets of (20 − n) other nodes to the sink. On the other hand with single-hop higher transmit power is required by nodes far away from the sink. In this case overhead factors (like receive and startup power) are dominant, therefore optimal spacing makes little difference on power consumption. Single-hop is best for up to 10 hops (500 m). Figure 9 looks at a total distance of 10 km where transmission power is then the dominant factor because of large hop distances (500 m/hop). Here we can see the effect of spacing optimization, with θ = 0.8 power consumption can scale quite linearly over n, thus improving the network lifetime. In this case single-hop is useless as the hop distance is very large and the path loss exponent dominates. It can be seen from these results that for cases where
Total energy per node, r=10000m, n=20, β=2
few situations where a simple multihop relay mechanism, by which each node relays packets from a neighbor towards the base station, is the recommended policy. Topologies and relay mechanisms derived from networks that have an energy optimum node separation are not only more energy efficient but also provide for a more graceful degradation of the network as the nodes spend all their energy.
Equidistant multihop θ=0.2 θ=0.4 θ=0.6 θ=0.8 Optimal multihop Single hop
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ACKNOWLEDGEMENTS 0.2
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Fig. 9.
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total distance is less than 500 m a single hop is more efficient than multihop for this example technology. The receive and startup power overhead makes multihop an inefficient technique, in addition to increasing the energy drain of nodes close to the sink. If overheads can be reduced with new transceiver technologies multihop becomes more attractive, although only with optimal spacing and when the total distance is out of range for a single-hop. As multihop is necessary for some applications, ways to improve its efficiency should be investigated. In addition, the effect of medium access control should also be considered in a future analysis. V. C ONCLUSION This paper analyzes the energy consumption of multihop wireless embedded and sensor networks. Whereas the size of a deployment area is application dependent these networks usually have a large number of nodes which in some cases requires a multihop mode of communication. The analysis uses a detailed model for the energy consumed by the radio at each node. The paper considers two multihop scenarios and computes the energy per bit, efficiency, the energy consumed by individual nodes, and the energy consumed by the whole network. One scenario assumes equidistant node separation and the other scenario uses a node spacing derived by minimizing the consumption of energy. These results are compared with the case where each node transmits directly to a base or relay station. Numerical results are obtained using the parameters of a common commercially available radio, the RFM TR1000. The results show that depending on the topology, using a simple multihop message relay strategy is not always a good procedure to extend a network’s lifetime. There are many situations where using one hop (direct relay to the sink) is not only simpler but also the most energy efficient without having to worry about loss of network connectivity. Even for networks with equidistant node separation there are very
The authors want to thank their colleagues at the CWC and RWTH Aachen, especially Dr. Petri M¨ah¨onen. This work was performed with funding from the Finnish Defense Forces and TEKES through the WIRSU project. R EFERENCES [1] I. F. Akyildiz et al., “Wireless Sensor Networks: A Survey,” Computer Networks (Elsevier) Journal, pp. 393–422, March 2002. [2] C.-Y. Chong and S. Kumar, “Sensor Networks: Evolution, Opportunities, and Challenges,” in Proc. of the IEEE, vol. 91, no. 8, 2003, pp. 1247–1256. [3] W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “Energy-efficient communication protocol for wireless microsensor networks,” in Proc. of the 33rd ICSS, 2000. [4] A. Goldsmith and S. Wicker, “Design Challenges for Energy-Constrained Ad Hoc Wireless Networks,” IEEE Wireless Communications, pp. 8–27, Aug 2002. [5] C. Guo, L.Z. Zhong, and J.M. Rabaey, “Low Power Distributed MAC for Ad Hoc Sensor Radio Networks,” in IEEE GTC, vol. 5, 2001, pp. 2944–2948. [6] E. Duarte-Melo and M. Liu, “Analysis of Energy Consumption and Lifetime of Heterogeneous Wireless Sensor Networks,” in Proc. of IEEE Globecom, 2002. [7] Sankarasubramaniam, Y., Akyildiz, I.F., and McLaughlin, S.W., “Energy Efficiency based Packet Size Optimization in Wireless Sensor Networks,” in Proc. of SNPA, vol. 38, 2003, pp. 393–422. [8] B. O. Priscilla Chen and E. Callaway, “Energy Efficient System Design with Optimum Transmission Range for Wireless Ad-Hoc Networks,” in Proc. of ICC, vol. 2, 2002, pp. 945–952. [9] C. Schurgers, V. Tsiatsis, S. Ganeriwal, and M.B. Srivastava, “Optimizing Sensor Networks in the EnergyLatency-Density Design Space,” IEEE Transactions on Mobile Computing, vol. 1, no. 1, pp. 70–80, 2002. [10] R. Min, M. Bhardwaj, N. Ickes, A. Wang, and A. Chandrakasan, “The hardware and the network: Total-system strategies for power aware wireless microsensors.” [Online]. Available: citeseer.nj.nec.com/569911.html [11] M. Bhardwaj, A. Chandrakasan, and T. Garnett, “Upper bounds on the lifetime of sensor networks,” in Proc. of IEEE ICC, 2001, pp. 785–790.
