1. Wireless Sensor Networks Energy Efficiency Issues
Instructor: Carlos Pomalaza-Ráez Fall 2004 University of Oulu, Finland

2. Node Energy Model
A typical node has a sensor system, A/D conversion circuitry, DSP and a radio transceiver. The sensor system is very application dependent. As discussed in the Introduction lecture the node communication components are the ones who consume most of the energy on a typical wireless sensor node. A simple model for a wireless link is shown below

3. Node Energy Model
The energy consumed when sending a packet of m bits over one hop wireless link can be expressed as,
where,
ET = energy used by the transmitter circuitry and power amplifier
ER = energy used by the receiver circuitry
PT = power consumption of the transmitter circuitry
PR = power consumption of the receiver circuitry
Tst = startup time of the transceiver
Eencode = energy used to encode
Edecode = energy used to decode

4. Node Energy Model
Assuming a linear relationship for the energy spent per bit at the transmitter and receiver circuitry ET and ER can be written as,
eTC, eTA, and eRC are hardware dependent parameters and α is the path loss exponent whose value varies from 2 (for free space) to 4 (for multipath channel models). The effect of the transceiver startup time, Tst, will greatly depend of the type of MAC protocol used. To minimize power consumption it is desired to have the transceiver in a sleep mode as much as possible however constantly turning on and off the transceiver also consumes energy to bring it to readiness for transmission or reception.

5. Node Energy Model An explicit expression for eTA can be derived as,
Where,
(S/N)r = minimum required signal to noise ratio at the receiver’s demodulator for an acceptable Eb/N0
NFrx = receiver noise figure
N = thermal noise floor in a 1 Hertz bandwidth (Watts/Hz)
BW = channel noise bandwidth
λ = wavelength in meters
α = path loss exponent
Gant = antenna gain
ηamp = transmitter power efficiency
Rbit = raw bit rate in bits per second

6. Node Energy Model
The expression for eTA can be used for those cases where a particular hardware configuration is being considered. The dependence of eTA on (S/N)r can be made more explicit if we rewrite the previous equation as:
It is important to bring this dependence explicitly since it highlights how eTA and the probability of bit error p are related. p depends on Eb/N0 which in turns depends on (S/N)r. Note that Eb/N0 is independent of the data rate. In order to relate Eb/N0 to (S/N)r, the data rate and the system bandwidth must be taken into account, i.e.,

7. Typical Bandwidth (Null-To-Null)
Node Energy Model
where
Eb = energy required per bit of information
R = system data rate
BT = system bandwidth
γb = signal-to-Noise ratio per bit, i.e., (Eb/N0)
Typical Bandwidths for Various Digital Modulation Methods
Modulation Method
Typical Bandwidth (Null-To-Null)
QPSK, DQPSK
1.0 x Bit Rate
MSK
1.5 x Bit Rate
BPSK, DBPSK, OFSK
2.0 x Bit Rate

8. Node Energy Model Power Scenarios
There are two possible power scenarios:
Variable transmission power. In this case the radio dynamically adjust its transmission power so that (S/N)r is fixed to guarantee a certain level of Eb/N0 at the receiver. The transmission energy per bit is given by,
Since (S/N)r is fixed at the receiver this also means that the probability p of bit error is fixed to the same value for each link.

9. Node Energy Model
Fixed transmission power. In this case the radio uses a fixed power for all transmissions. This case is considered because several commercial radio interfaces have a very limited capability for dynamic power adjustments. In this case is fixed to a certain value (ETA) at the transmitter and the (S/N)r at the receiver will then be,
Since for most practical deployments d is different for each link then (S/N)r will also be different for each link. This translates on a different probability of bit error for wireless hop.

10. Energy Consumption - Multihop Networks
Let’s consider the following linear sensor array
To highlight the energy consumption due only to the actual communication process the energy spent in encoding, decoding, as well as on the transceiver startup is not considered in the analysis that follows.
Let’s initially assume that there is one data packet being relayed from the node farthest from the sink node towards the sink

11. Energy Consumption - Multihop Networks
The total energy consumed by the linear array to relay a packet of m bits from node n to the sink is then,
It then can be shown that Elinear is minimum when all the distances di’s are made equal to D/n, i.e. all the distances are equal.

12. Energy Consumption - Multihop Networks
It can also be shown that the optimal number of hops is,
where
Note that only depends on the path loss exponent α and on the transceiver hardware dependent parameters. Replacing the of dchar in the expression for Elinear we have,

13. Energy Consumption - Multihop Networks
A more realistic assumption for the linear sensor array is that there is a uniform probability along the array for the occurrence of events. In this case, on the average, each sensor will detect the same number of number of events whose related information need to be relayed towards the sink. Without loss of generality one can assume that each node senses an event at some point in time. This means that sensor i will have to relay (n-i) packets from the upstream sensors plus the transmission of its own packet. The average energy per bit consumption by the linear array is,

14. Energy Consumption - Multihop Networks
Minimizing with constraint is equivalent to minimizing the following expression,
where λ is a Langrage’s multiplier. Taking the partial derivatives of L with respect to di and equating to 0 gives,

15. Energy Consumption - Multihop Networks
The value of λ can be obtained using the condition
Thus for α=2 the values for di are,
For n=10 the next figure shows an equally spaced sensor array and a linear array where the distances are computed using the equation above (α=2)

16. Energy Consumption - Multihop Networks
The farther away sensors consume most of their energy by transmitting through longer distances whereas the closer to the sink sensors consume a large portion of their energy by relaying packets from the upstream sensors towards the sink. The total energy per bit spent by a linear array with equally spaced sensors is
The total energy per bit spent by a linear array with optimum separation and α=2 is,

17. Energy Consumption - Multihop Networks
For eTC= eTR= 50 nJ/bit, eTA= 100 pJ/bit/m2, and α = 2, the total energy consumption per bit for D= 1000 m, as a function of the number of sensors is shown below.

18. Energy Consumption - Multihop Networks
The energy per bit consumed at node i for the linear arrays discussed can be computed using the following equation. It is assumed that each node relays packet from the upstream nodes towards the sink node via the closest downstream neighbor. For simplicity sake only one transmission is used, e.g. no ARQ type mechanism
Energy consumption at each node (n=20, D=1000 m)

19. Error Control – Multihop WSN
For link i assume that the probability of bit error is pi. Assume a packet length of m bits. For the analysis below assume that a Forward Error Correction (FEC) mechanism is being used. Let’s then call plink(i) the probability of receiving a packet with uncorrectable errors. Conventional use of FEC is that a packet is accepted and delivered to the next stage which in this case is to forward it to the next node downstream. The probability of the packet arriving to the sink node with no errors is then:

20. Error Control – Multihop WSN
Let’s assume the case where all the di’s are the same, i.e. di = D/n. Since variable transmission power mode is also being assumed then the probability of bit error for each link is fixed and Pc is,
The value of plink will depend on the received signal to noise ratio as well as on the modulation method used. For noncoherent (envelope or square-law) detector with binary orthogonal FSK signals in a Rayleigh slow fading channel the probability of bit error is
Where is the average signal-to-noise ratio.

21. Error Control – Multihop WSN
Consider a linear code (m, k, d) is being used. For FSK-modulation with non-coherent detection and assuming ideal interleaving the probability of a code word being in error is bounded by
where wi is the weight of the ith code word and M=2k. A simpler bound is:
For the multihop scenario being discussed here plink = PM and the probability of packet error can be written as:

22. Error Control – Multihop WSN
The probability of successful transmission of a single code word is,
Radio parameters used to obtain the results shown in the next slides
Parameter
Value
NFRx
10dB N0
dBm/Hz or 4.17 * J
Rbit
115.2 Kbits 
0.3 m
Gant
-10dB or 0.1
amp
0.2  3 BW
For FSK-modulation, it is assumed to be the same as Rbit
eRC
50nJ/bit
eTC

23. Error Control – Multihop WSN
The expected energy consumption per information bit is defined as:
Parameters for the studied codes are shown in Table below, t is the error correction capability.
Code m k
dmin
Code rate t
Hamming 7 4 3
0.57 1
Golay 23 12
0.52
Shortened Hamming 6
0.5
Extended Golay 24 8

24. Error Control – Multihop WSN
Characteristic distance, dchar, as a function of bit error probability for non-coherent FSK modulation

25. Error Control – Multihop WSN
D = 1000 m

26. Error Control – Multihop WSN
D = 1000 m

27. Error Control – Multihop WSN
D = 1000 m

28. Error Control – Multihop WSN
D = 1000 m

29. Error Control – Multihop WSN
D = 1000 m