An Analytical Model for Energy Efficiency of Error ... - Semantic Scholar
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
An analytical model for energy efficiency of error control schemes in sensor networks João H. Kleinschmidt, Walter C. Borelli School of Electrical and Computer Engineering State University of Campinas FEEC - UNICAMP {joaohk,borelli}@dt.fee.unicamp.br
Abstract - This paper analyzes the energy efficiency of wireless sensor networks using different error control schemes. An analytical model is presented to evaluate the energy efficiency in Nakagami-m fading channels. The model is applied to error control schemes of Bluetooth technology. Some custom error control schemes and adaptive techniques using different FEC and ARQ strategies are analyzed. Performance results are obtained through analysis for networks with different number of hops and fading channel conditions.
I. INTRODUCTION
Marcelo E. Pellenz Graduate Program in Computer Science Pontifical Catholic University of Paraná PPGIA - PUCPR [email protected]
Some techniques of error control for wireless sensor networks are discussed in Section II. In Section III the analytical model to evaluate the energy efficiency is described and Section IV shows the Bluetooth error control schemes and the adaptation of the analytical model for Bluetooth technology. Section V presents performance results obtained for different scenarios of Bluetooth-based sensor networks. Finally, Section VI gives the final considerations and conclusions. II. ERROR CONTROL SCHEMES FOR WIRELESS SENSOR
The recent advances in wireless communications and digital electronics led to the implementation of low power and low cost wireless sensors. These devices can be grouped to form a sensor network [1]. Energy constraints are the driving factors in the design of wireless sensor networks. The wireless radio channel is time varying and can have high bit error rates. In order to improve the reliability of the data sent in the wireless channel, some techniques can be employed, such as automatic repeat request (ARQ) and forward error correction (FEC). Although an error control strategy improves the reliability of a packet, the energy consumed due to the transmission of the additional bits in these coded schemes contributes to increase the energy consumption. Some authors have studied the problem of energy consumption for some error control schemes in wireless sensor networks [2], [3], [4], [5], [6]. In [2] and [3] the energy efficiency of different error control techniques was evaluated for sensor networks with a commercial radio transceiver using an analytical model. The reliability and energy consumption were analyzed in [4] using simulation for sensor networks without any specific technology or channel model. In [5] and [6] the energy consumption and reliability of Bluetooth error control strategies were studied in a Rayleigh fading channel using simulation. This paper presents an analytical model to evaluate the energy efficiency of error control schemes of wireless sensor networks in Nakagami-m fading channels. This model can be used in different sensor network technologies, such as the IEEE 802.15 standards. In this work it is applied to Bluetooth technology using the different error control schemes of the specification and the custom and adaptive error control schemes presented in [5] and [6]. The performance results are obtained for various sensor networks scenarios with different number of hops and channel conditions.
NETWORKS
In order to improve the reliability of the data sent in the wireless channel, techniques such as automatic repeat request (ARQ) and forward error correction (FEC) can be employed [7]. FEC employs error correcting codes to combat bit errors by adding redundancy (parity bits) to information packets. The receiver uses the parity bits to detect and correct errors. FEC techniques are associated with unnecessary overhead that increases energy consumption when the channel is relatively error free. In ARQ techniques only error detection capability is provided; the receiver requests to the transmitter the retransmission of the packets received in error. Usually an ARQ scheme uses Cyclic Redundancy Check (CRC) codes for error detection. At the receiver, the CRC code verifies the packet. If it detects errors, the node asks a retransmission for the transmitter (negative acknowledgement). If the reception is correct, a positive acknowledgement is sent to the transmitter node. Hybrid ARQ schemes can be developed using the combination of FEC and ARQ schemes. Some typical error control techniques for wireless networks are discussed in [6]. The energy consumption of these schemes is very important. Although a strong error control can correct many errors, the energy consumed may be too high for an energy constrained sensor network. Using the same error control scheme for the whole network could be a good choice in some cases, but not always. Sometimes it is needed to apply the best error control available, while in other cases less error control should be used. Thus, an adaptive scheme that changes the error control technique may be developed. In order to apply an adaptive scheme in a sensor network it was used an approach similar to the proposed in [4] and [5]. To use and adaptive error control
1-4244-0353-7/07/$25.00 ©2007 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
scheme, a mechanism has to be designed to judge the importance of a packet and then choosing an appropriate error control scheme. The importance of a packet is evaluated using the multihop principle, as shown in Fig. 1. The choice of error control technique shall be based on the number of hops the packet traveled within the sensor network. If a sensor node has to send a data packet to the sink node, before the packet reaches its destination it may travel through some other nodes of the network. If the packet gets lost at the first hop, only the energy to send the packet from a sensor to a specific node is lost. If the packet is corrupted after few more hops, much more energy will be spent to transmit the packet through the network. In this sense, a packet is more important if it travels through more nodes in the network, and consequently, more energy is being consumed. An adaptive scheme might use stronger error control techniques for packets that travel more hops and weaker error control for packets with fewer hops. Some adaptive schemes are presented in Section IV. n
2 dn
...
1
sink d1
...
D
The wireless channel is modeled using the Nakagami fading. When m → ∞ , it converges to the AWGN channel and for m=1 is the Rayleigh fading. Using m1 fading intensities more and less severe than Rayleigh are obtained, respectively. The Nakagami probability density function is given by: γ m mγ m−1 exp − , for γ ≥ 0 f (γ ) = (3) m Γ(m)γ γ where γ is the average received SNR and γ is the instantaneous SNR. The packet error probabilities can be evaluated using equation (3) in (1) and (2). It is being assumed that the propagation conditions between the transmitter and the receiver are the same in both directions. The probability of a packet being successfully received at the receiver node is the probability of success of the packet at forward and reverse channels: (4) PA = (1 − PER f )(1 − PERr )
Thus, the packet error probability for ARQ packets is: (5) PER = 1 − [(1 − PER f )(1 − PER r )] The probability of a packet being successfully received at the sink node for packets without ARQ is: (6) Pnarq = (1 − PER f ) H where H is the total number of hops. Let n be the number of retransmissions of ARQ packets. Assuming perfect error detection of a CRC code and infinite retransmissions, the probability that a packet arrives correctly at the sink node is:
Figure 1. Multihop sensor network
III. ANALYTICAL MODEL
∞
In this section it is presented an analytical model to evaluate the energy efficiency of different error control schemes in multihop wireless sensor networks. A received packet is not accepted whenever any of the bits of a packet is received with error (in non-coded systems). Thus, the packet error probability of the forward channel, PERf, and reverse, PERr (for ARQ systems) can be defined as: ∞
[
]
PER f = 1 − ∫ f (γ f ) 1 − p (γ f ) dγ 0
∞
b
PER r = 1 − ∫ f (γ r )[1 − p (γ r )] dγ r 0
b
f
(1)
(2)
where b is the size of the packet in bits, f(γf) and f(γr) are the probability density functions and γf and γr are the signal-tonoise ratio (SNR) of the forward and reverse channels, respectively. The variable p(γ f ) is the bit error probability of the forward channel and p(γ r ) is the bit error probability of the reverse channel. The forward channel is used to send data packets and the reverse channel indicates the success or not of a packet transmission (for ARQ systems). The bit error probabilities p(γ f ) and p(γ r ) can be evaluated using an expression of symbol error probability of the modulation used in the sensor network. The modulation type used in a sensor network depends on the wireless technology (Bluetooth, IEEE 802.15.4, etc.). When channel coding is used, such as block or convolutional codes, the packet error rates PERf and PERr are evaluated in a different manner. Some examples are given in Section IV.
[
Parq = ∑ (1 − PER f )(1 − PER r ) n=0
]
H +n
=1
(7)
The probability of n retransmissions is the product of failure in the n-1 transmissions and the probability of success at the nth transmission: (8) p N [n] = (1 − PER )( PER ) n −1 Thus, equation (9) is used to evaluate the average number of retransmissions N in one hop: ∞
N = ∑ p N [n ] × n
(9)
n =1
The number of packets that arrive with error at the sink node can be defined for the packets without ARQ as the product of the total number of transmitted packets npac and the probability that the packet arrives with error at the sink node: (10) n error = (1 − Pnarq ) × n pac Considering the same assumptions of equation (7), none of the ARQ packets is received with errors and thus nerror = 0: (11) nerror = (1 − Parq ) × n pac = 0 The reliability R is given by the percentage of the sent packets that arrive correctly at the sink node and it may be evaluated as: (12) R = [(n pac − nerror ) / n pac ] Since no specific hardware is being used, the energy consumption is expressed only in normalized terms. The energy considered are the energies spent in the communication (transmission and reception) and the decoding process. The encoding energies are assumed to be negligible. This
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
assumption is reasonable for asynchronous codes, where the decoding process is more complex than coding. It is considered the same model of [4] and [5], where the reception of a determined number of bits consumes approximately 75 per cent of the energy spent to transmit the same number of bits. The minimum energy consumed Emin for H hops is evaluated for packets without error control: (13) E min = H × n pac × (n bits + nbits × 0.75 ) where nbits is the total number of bits of a packet. The total energy consumed E in a sensor network for packets without ARQ and without CRC is the total number of bits transmitted and received and the decoding energy per packet Edec: (14) E = H × n pac × (nbits + nbits × 0.75 + E dec ) where nbits is the total number of bits of a packet, including the parity bits of the code used in the packet. If no channel code is used, Edec=0. For the packets with ARQ, the energy E is the total number of bits transmitted and received, including retransmissions: E = H × n pac × N × [nbits + nack + (nbits + nack )0.75 + Edec ] (15) where nack is the total number of bits of the return packet. In order to evaluate the energy E for packets without ARQ and with CRC the average number of hops has to be computed. The probability that a packet achieves h hops is the product of success in the h-1 hops and the probability of failure in the hth hop, if h
An analytical model for energy efficiency of error control schemes in sensor networks João H. Kleinschmidt, Walter C. Borelli School of Electrical and Computer Engineering State University of Campinas FEEC - UNICAMP {joaohk,borelli}@dt.fee.unicamp.br
Abstract - This paper analyzes the energy efficiency of wireless sensor networks using different error control schemes. An analytical model is presented to evaluate the energy efficiency in Nakagami-m fading channels. The model is applied to error control schemes of Bluetooth technology. Some custom error control schemes and adaptive techniques using different FEC and ARQ strategies are analyzed. Performance results are obtained through analysis for networks with different number of hops and fading channel conditions.
I. INTRODUCTION
Marcelo E. Pellenz Graduate Program in Computer Science Pontifical Catholic University of Paraná PPGIA - PUCPR [email protected]
Some techniques of error control for wireless sensor networks are discussed in Section II. In Section III the analytical model to evaluate the energy efficiency is described and Section IV shows the Bluetooth error control schemes and the adaptation of the analytical model for Bluetooth technology. Section V presents performance results obtained for different scenarios of Bluetooth-based sensor networks. Finally, Section VI gives the final considerations and conclusions. II. ERROR CONTROL SCHEMES FOR WIRELESS SENSOR
The recent advances in wireless communications and digital electronics led to the implementation of low power and low cost wireless sensors. These devices can be grouped to form a sensor network [1]. Energy constraints are the driving factors in the design of wireless sensor networks. The wireless radio channel is time varying and can have high bit error rates. In order to improve the reliability of the data sent in the wireless channel, some techniques can be employed, such as automatic repeat request (ARQ) and forward error correction (FEC). Although an error control strategy improves the reliability of a packet, the energy consumed due to the transmission of the additional bits in these coded schemes contributes to increase the energy consumption. Some authors have studied the problem of energy consumption for some error control schemes in wireless sensor networks [2], [3], [4], [5], [6]. In [2] and [3] the energy efficiency of different error control techniques was evaluated for sensor networks with a commercial radio transceiver using an analytical model. The reliability and energy consumption were analyzed in [4] using simulation for sensor networks without any specific technology or channel model. In [5] and [6] the energy consumption and reliability of Bluetooth error control strategies were studied in a Rayleigh fading channel using simulation. This paper presents an analytical model to evaluate the energy efficiency of error control schemes of wireless sensor networks in Nakagami-m fading channels. This model can be used in different sensor network technologies, such as the IEEE 802.15 standards. In this work it is applied to Bluetooth technology using the different error control schemes of the specification and the custom and adaptive error control schemes presented in [5] and [6]. The performance results are obtained for various sensor networks scenarios with different number of hops and channel conditions.
NETWORKS
In order to improve the reliability of the data sent in the wireless channel, techniques such as automatic repeat request (ARQ) and forward error correction (FEC) can be employed [7]. FEC employs error correcting codes to combat bit errors by adding redundancy (parity bits) to information packets. The receiver uses the parity bits to detect and correct errors. FEC techniques are associated with unnecessary overhead that increases energy consumption when the channel is relatively error free. In ARQ techniques only error detection capability is provided; the receiver requests to the transmitter the retransmission of the packets received in error. Usually an ARQ scheme uses Cyclic Redundancy Check (CRC) codes for error detection. At the receiver, the CRC code verifies the packet. If it detects errors, the node asks a retransmission for the transmitter (negative acknowledgement). If the reception is correct, a positive acknowledgement is sent to the transmitter node. Hybrid ARQ schemes can be developed using the combination of FEC and ARQ schemes. Some typical error control techniques for wireless networks are discussed in [6]. The energy consumption of these schemes is very important. Although a strong error control can correct many errors, the energy consumed may be too high for an energy constrained sensor network. Using the same error control scheme for the whole network could be a good choice in some cases, but not always. Sometimes it is needed to apply the best error control available, while in other cases less error control should be used. Thus, an adaptive scheme that changes the error control technique may be developed. In order to apply an adaptive scheme in a sensor network it was used an approach similar to the proposed in [4] and [5]. To use and adaptive error control
1-4244-0353-7/07/$25.00 ©2007 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
scheme, a mechanism has to be designed to judge the importance of a packet and then choosing an appropriate error control scheme. The importance of a packet is evaluated using the multihop principle, as shown in Fig. 1. The choice of error control technique shall be based on the number of hops the packet traveled within the sensor network. If a sensor node has to send a data packet to the sink node, before the packet reaches its destination it may travel through some other nodes of the network. If the packet gets lost at the first hop, only the energy to send the packet from a sensor to a specific node is lost. If the packet is corrupted after few more hops, much more energy will be spent to transmit the packet through the network. In this sense, a packet is more important if it travels through more nodes in the network, and consequently, more energy is being consumed. An adaptive scheme might use stronger error control techniques for packets that travel more hops and weaker error control for packets with fewer hops. Some adaptive schemes are presented in Section IV. n
2 dn
...
1
sink d1
...
D
The wireless channel is modeled using the Nakagami fading. When m → ∞ , it converges to the AWGN channel and for m=1 is the Rayleigh fading. Using m1 fading intensities more and less severe than Rayleigh are obtained, respectively. The Nakagami probability density function is given by: γ m mγ m−1 exp − , for γ ≥ 0 f (γ ) = (3) m Γ(m)γ γ where γ is the average received SNR and γ is the instantaneous SNR. The packet error probabilities can be evaluated using equation (3) in (1) and (2). It is being assumed that the propagation conditions between the transmitter and the receiver are the same in both directions. The probability of a packet being successfully received at the receiver node is the probability of success of the packet at forward and reverse channels: (4) PA = (1 − PER f )(1 − PERr )
Thus, the packet error probability for ARQ packets is: (5) PER = 1 − [(1 − PER f )(1 − PER r )] The probability of a packet being successfully received at the sink node for packets without ARQ is: (6) Pnarq = (1 − PER f ) H where H is the total number of hops. Let n be the number of retransmissions of ARQ packets. Assuming perfect error detection of a CRC code and infinite retransmissions, the probability that a packet arrives correctly at the sink node is:
Figure 1. Multihop sensor network
III. ANALYTICAL MODEL
∞
In this section it is presented an analytical model to evaluate the energy efficiency of different error control schemes in multihop wireless sensor networks. A received packet is not accepted whenever any of the bits of a packet is received with error (in non-coded systems). Thus, the packet error probability of the forward channel, PERf, and reverse, PERr (for ARQ systems) can be defined as: ∞
[
]
PER f = 1 − ∫ f (γ f ) 1 − p (γ f ) dγ 0
∞
b
PER r = 1 − ∫ f (γ r )[1 − p (γ r )] dγ r 0
b
f
(1)
(2)
where b is the size of the packet in bits, f(γf) and f(γr) are the probability density functions and γf and γr are the signal-tonoise ratio (SNR) of the forward and reverse channels, respectively. The variable p(γ f ) is the bit error probability of the forward channel and p(γ r ) is the bit error probability of the reverse channel. The forward channel is used to send data packets and the reverse channel indicates the success or not of a packet transmission (for ARQ systems). The bit error probabilities p(γ f ) and p(γ r ) can be evaluated using an expression of symbol error probability of the modulation used in the sensor network. The modulation type used in a sensor network depends on the wireless technology (Bluetooth, IEEE 802.15.4, etc.). When channel coding is used, such as block or convolutional codes, the packet error rates PERf and PERr are evaluated in a different manner. Some examples are given in Section IV.
[
Parq = ∑ (1 − PER f )(1 − PER r ) n=0
]
H +n
=1
(7)
The probability of n retransmissions is the product of failure in the n-1 transmissions and the probability of success at the nth transmission: (8) p N [n] = (1 − PER )( PER ) n −1 Thus, equation (9) is used to evaluate the average number of retransmissions N in one hop: ∞
N = ∑ p N [n ] × n
(9)
n =1
The number of packets that arrive with error at the sink node can be defined for the packets without ARQ as the product of the total number of transmitted packets npac and the probability that the packet arrives with error at the sink node: (10) n error = (1 − Pnarq ) × n pac Considering the same assumptions of equation (7), none of the ARQ packets is received with errors and thus nerror = 0: (11) nerror = (1 − Parq ) × n pac = 0 The reliability R is given by the percentage of the sent packets that arrive correctly at the sink node and it may be evaluated as: (12) R = [(n pac − nerror ) / n pac ] Since no specific hardware is being used, the energy consumption is expressed only in normalized terms. The energy considered are the energies spent in the communication (transmission and reception) and the decoding process. The encoding energies are assumed to be negligible. This
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
assumption is reasonable for asynchronous codes, where the decoding process is more complex than coding. It is considered the same model of [4] and [5], where the reception of a determined number of bits consumes approximately 75 per cent of the energy spent to transmit the same number of bits. The minimum energy consumed Emin for H hops is evaluated for packets without error control: (13) E min = H × n pac × (n bits + nbits × 0.75 ) where nbits is the total number of bits of a packet. The total energy consumed E in a sensor network for packets without ARQ and without CRC is the total number of bits transmitted and received and the decoding energy per packet Edec: (14) E = H × n pac × (nbits + nbits × 0.75 + E dec ) where nbits is the total number of bits of a packet, including the parity bits of the code used in the packet. If no channel code is used, Edec=0. For the packets with ARQ, the energy E is the total number of bits transmitted and received, including retransmissions: E = H × n pac × N × [nbits + nack + (nbits + nack )0.75 + Edec ] (15) where nack is the total number of bits of the return packet. In order to evaluate the energy E for packets without ARQ and with CRC the average number of hops has to be computed. The probability that a packet achieves h hops is the product of success in the h-1 hops and the probability of failure in the hth hop, if h
