A New Model of the Lifetime of Wireless Sensor Networks in Sea Water Communications

In this paper we present a new model for the lifetime of wireless sensor networks used for sea water communications. The new model for power communications takes into consideration parameters such as power consumption for the active mode, power consumption for the sleep mode, power consumption for the transient mode, transmission period, transient mode duration, sleep mode duration, and active mode duration. The power communications model is incorporated in the life time model of wireless sensor networks. The life time model takes into consideration several parameters such as the total number of sensors, network size, percentage of sink nodes, location of sensors, the mobility of sensors, power consumption when nodes move and the power consumption of communications. The new model for power consumption in communications shows more accurate results about the lifetime of the sensor network in comparison with previously published results.


Definition of Network Lifetime
There are two network lifetime metrics that introduced in literature based on definitions in the previous sections. Both metrics depict the network lifetime in seconds. The metrics probably become most expressive when used together.
(1) The first metric gives the accumulated network lifetime Z a as the sum of all times that ζ (t) is fulfilled, stopping only when the criterion is not fulfilled for longer than Δ t sd seconds.
(2) The second metric, the total network lifetime Z t , gives the first point in time when the liveliness criterion is lost for a longer period than the service disruption tolerance Δ t sd .

Wireless Sensor Networks
In this section we present a new model for the power consumption of the communications in wireless sensor networks. The model is based on the work of Cui et. al. [18].

Energy Consumed in Communications
In this model, the total energy consumed in communications is given by Equation (1): E =P on T on + P sp T sp + P tr T tr =(P t + P c0 )T on + P sp T sp + P tr T tr (1) The following parameters are used in the calculation of Equation (1): 1. P on power consumption value for the active mode 2. P sp power consumption value for the sleep mode 3. P tr power consumption value for the transient mode 4. the transmission period: T is given by T = T tr + T on + T sp .

International Journal of Computer Engineering Science (IJCES)
Volume 2 Issue 9 (September 2012) ISSN : 2250:3439 https://sites.google.com/site/ijcesjournal http://www.ijces.com/ 5 5. T tr is the transient mode duration, which is equal to the frequency synthesizer settling time (the start-up process of the mixer and PA is fast enough to be neglected), 6. T sp is the sleep mode duration, 7. T on is the active mode time for the transceiver such that T on ≤ T , where T on is a parameter to optimize, 8. The active mode power P on comprises the transmission signal power P t and the circuit power consumption P c0 in the whole signal path. 9. P c0 consists of the mixer power consumption P mix , the frequency synthesizer power consumption P syn , the LNA power consumption P LNA , the active filter power consumption P filt at the transmitter, the active filter power consumption P filr at the receiver, the IFA power consumption P IFA , the DAC power consumption P DAC , the ADC power consumption P ADC , and the PA power consumption P amp 10.
P amp = αP t and α = ξ/η − 1 with η the drain efficiency [11] of the RF PA and ξ the peak-average ratio (PAR), which is dependent on the modulation scheme and the associated constellation size.

11.
Since P on = max{P on , P tr , P sp }, the peak-power constraints are given by: P ont =P t + P amp + P ct = (1+α)P t + P ct ≤ P maxt P onr =P cr ≤ P maxr 12. P ct = P mix + P syn + P filt +P DAC and P cr =P mix +P syn + P LNA + P filr + P IFA + P ADC denote the circuit power consumption (excluding the PA power consumption) in the active mode at the transmitter and the receiver, respectively.

13.
The start-up time for other circuit blocks is negligible compared to that of the frequency synthesizers. 14.
Given (1) and (2), and the fact that P sp = 0and P tr ≈ 2P syn , the energy consumption per information bit E a = E/L is given by 15.

Under water Signal Propagation
The signal propagation in water depends on the path loss in water. Received power as a function of transmitted signal, path loss and antenna gain at the receiver end is given from Friis equation as shown in Equation 2 [19]. (2) where P t is the transmit power, G r and G t are the gains of the receiver and transmitter antenna, L Pathloss is the path loss in water.
The path loss is shown in Equation 3 [20].
is the path loss in air and given by: where d is the distance between transmitter and receiver in meter, f is the operating frequency in Hertz and c is the velocity of light in air in meter per second.
is the path loss due to changing in medium and given by [19]: where λ 0 is the signal wavelength in air and calculated (λ 0 =c/f) and λ is the wave factor and given by (λ=2π/β) and β is the phase shifting constant and calculated as shown in Equation 6.
where ′ and ′′ are the real and imaginary parts of the complex dielectric constant is the path loss due to attenuation in medium and given by: where α is the attenuation constant and calculated as shown in Equation 8:

International Journal of Computer Engineering Science (IJCES)
Volume 2 Issue 9 (September 2012) ISSN : 2250:3439 https://sites.google.com/site/ijcesjournal http://www.ijces.com/ The reflection from the surface and bottom depends on reflection coefficient at the interface between water and air and between water and sand. The reflection coefficient is given by Equation 9 [20].
where ρ 1 and ρ 2 are the density of the first and second medium respectively and v 1 and v 2 are the wave velocity in both mediums.
The reflection loss from the surface and from the bottom is L ref and shown in Equation 10.

log
where is calculated as shown below: where r is the reflected path length, |Г|and are the amplitude and phase of the reflection coefficient respectively and Δ(r) is the difference between r and d.
where r can be calculated as follow:

Simulation Results
The following parameters values are used in the simulation carried in this paper:

Energy Consumption for Sea Water
In Figure

Scenario Number 1
In this scenario the following parameters are considered:        In order to examine the validity of our model, we have tested it for many lifetime scenarios. In this paper we are presenting five of these scenarios. The following parameters are used: total number of sensors, network size as defined by its width and length, and the percentage of sink sensors. In each scenario, we have evaluated both the total power in the network over the life cycle, number of dead sensors over the life The results presented in this paper show the importance of such a simulator from the designer perspective. The model can be used as a design tool as well as a research tool to evaluate the network performance. In the future, we would expect to extend the work presented in this model to include other parameters and modes of operations for underwater and underground wireless sensor networks.