Network lifetime The lifetime of any network depends on the power dissipated. Using relaying rather than direct transmission extends the lifetime, as well as giving frequency reuse benefits. Let ES be the energy needed to sense a bit, ER that to receive a bit and ET that to transmit a bit over some distance

d. Assume second order power loss with the distance

d. The parameters associated with the node energy are as follows: 11 represents the energy consumed by transmitter electronics per bit, 2

accounts for the energy dissipated in the transmit op-amp, 12 is the energy consumed by the receiver electronics per bit and 3 is the energy cost of sensing a bit.

(a) Model ET, ER, and ES in terms of the alpha parameters. (Note the 2 depends on the propagation loss.)

(b) If the relay rate is r b/s, what is the power consumed by a relay, Prel? The function of a relay is to receive data and then to transmit them x meters further. Denote 11þ12 by 1. Assume the values for 1 and 2 are 180 nJ/
bit and 10 (pJ/bit)/m2 respectively.

(c) If P1 relays are introduced between S and T as illustrated in Figure10.6, what is the overall rate of dissipation, Plink?

(d) We are given that there are P1 relays between S and T and the distance separating the two ends is D. Calculate the set of hop distances between the relays that will minimize Plink.

(e) Let the point source radius be dS and distance to the fusion center from the source be dF. Evaluate the minimum energy dissipated in the entire network.
Use PlinkðDÞ ð2D ffiffiffiffiffiffiffiffiffiffi 12 p 12Þr:

(f) For the deployment of N sensor nodes, the active lifetime is bounded by:
L NE= f2ðdF dSÞ ffiffiffiffiffiffiffiffiffiffi 12 p ½ 12 þ 3gr:
Calculate the initial energy, E, in each node needed to support the maximum lifetime of 185 days for the deployment of 100 nodes. The fusion center is 40m from the source and the source radius is 3 m. Assume the relay rate to be 15 b/s and that the cost of relaying data dominates.

Transcribed Image Text:

S d d2 dp-1 dp 2 P-2 P-1 T D Figure 10.6 Communication relays. A 2 B 0.25 1.5 4 S D 2 2 F E 0.5 Figure 10.7 Minimum energy path.