In a sensor network, the energy consumed by different functions by a sensor, is

Question

In a sensor network, the energy consumed by different functions by a sensor, is as follows. Assume the total number of nodes as M, number of non-cluster nodes as n, the number of cluster heads to be m and the frame size to be B bits. a) Find the power consumption, during a frame time period if sensing and communication is done during every frame, assuming other half nodes are sleeping at that time. b) Find the power consumption in the idle frame when sensing and communication to CH is done in every alternate frame. Remember that power is consumed even in sleeping mode of the cycles, when sensing is not carried out. c) Find the total power consumption m different frames if sensing is done every alternate cycle, while transmission to CH is done every fourth frame.

Explanation / Answer

In the first case, during a frame time period sensing and communication is done with the assumption that when sensing is done communication nodes are in sleeping condition and vice versa.

For for sensing part; net power consumed for 1 bit will be = n*0.5 nJ
For for communication part; net power consumed for 1 bit will be = m*(1000+100) nJ = m*1100 nJ.
So the net power consumed for B bit will be;
(n*0.5 + m*1100)B nJ.

In the second case, sensing and communication is done in every alternative frame. Hence if frame 1 is responsible for sensing then frame 2 will be responsible for communication considering the other nodes are in sleeping.

Therefore, power consumed for 1 bit sensing will be = n*0.5 nJ; whereas for communication part; net power consumed for 1 bit will be = m*(1000+100) nJ = m*1100 nJ.

So the net power consumed for B bit will be in 2 frames;
(n*0.5 + m*1100)B nJ.

Then the power consumption in an average frame will be = (n*0.5 + m*1100)B /2 nJ.

In the third case, sensing is done every alternate cycle, while transimission to CH is done every fourth frame. Hence if frame 1 is responsible for sensing, then again frame 3 will sense and frame 4 will responsible for transmission.
Hence net power consumed will be;
(n*0.5 + n*0.5 + m*1100) for 4 frames;
hence for single frame consumption is (n*0.5 + n*0.5 + m*1100)/4 nJ.
Then for B bit sensing and trnasmission;
power consumption is (n*0.5 + n*0.5 + m*1100)B /4 nJ.

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