Energy Analysis

1
Energy Analysis

• Charlie Zhong
• August 19, 2002

2
Outline

• Energy analysis
• Application of fix point theorem
• Models and numerical results
• Simulation results

3
Research Goal
Network Layer
neighbors
Link level reliability
Traffic density
Data Link Layer
Modulation
of channels available
Radio Data Rate
Physical Layer
We want to find a combination of algorithms with
lower energy under these constraints.
4
Parameters
Nn
Channel model
Power control
MAC (Ns)
r
Pkt_COL
Error Control (k,M)
Pkt_BER
Nack
N
h
Nch
R
5
The Mega Formula
Average energy per bit per node
EM is average energy spent on maintenance per
cycle PT/PI is TX/RX power TN is average number
of packets per cycle from network R is radio
data rate LN/LOH is the length of info/OH bits
N is number of transmissions EC is average
computation energy per cycle ti is the node idle
time. e.g. receiver duty cycle when no packet has
arrived.
6
Average Transmit Power for Data Transfer

• Power control sets radiated power level
• Efficiency

7
Error Control System View
Probability that data fails
Probability that ACK fails
Pkt_d
Pkt_a
CRCARQ
Channel independent between packets
Probability that either data Or ACK fails
Number of ACKs Nack
Number of transmissions N
8
MAC System View
Number of interferers Nint
Traffic rate lo
Or radius r
MAC
Radio data rate R
Packet size L
Collision rate pkt_COL
9
Collision Rate in Aloha
More accurately,
e.g. data rate
10
Collision Rate in CSMA
Number of hidden terminals Nh
r radius D node density
11
Outline

• Energy analysis
• Application of fix point theorem
• Models and numerical results
• Simulation results

12
A Fixed Point Problem
13
Ordered Set

• pkt belongs to 0,1
• This is a real valued closed set
• It is a fully ordered set (algebraic ordering)
  with bottom 0 and top 1.
• It is also a complete ordered set (CPO) since
  every chain Y in it has lowest upper bound V(Y).
• Every non-decreasing sequence xnin 0,1 is
  bounded, so it has limit x in 0,1.
  Additionally, x is its lowest upper bound.

14
Function

• f is monotonic
• If x1ltx2, f(x1)ltf(x2)
• f is continuous
• For every chain Y in 0,1, V(f(Y))f(V(Y))
• f is continuous gt

15
Fixed Point Theorem

• We need one for algebraic ordered sets
• If X is a CPO with bottom , and f X-gtX is
  continuous,
• Then f has a least fixed point x and we can find
  x constructively by finding the lowest upper
  bound of the chain
• , f(), f(f(), ..

16
Intuitive Way to Look at It
1
f(f(f(0)))
Starting from bottom, monotonically converging
to the least fixed point
f(f(0))
f(0)1-exp(-C) gt 0
For C gt 0
0
17
Ways to Find Fixed Point (1/2)

• Iteration in MATLAB
• Simple, fast
• Scalable to more complicated models
• Simulink model
• Pros intuitive
• Cons slow, internal bugs in close loop, not
  scalable to more complicated models, poor plot
  functionality

18
Ways to Find Fixed Point (2/2)

• Solve equations
• MATLAB solve()
• Slow, no symbolic coefficient, output order not
  specified by user
• Mathematica Solve()
• Pros fast, symbolic coefficient, output order as
  specified
• Cons can not clear previous value, need to
  figure out how to use vector and plot
• Find intersection of f(x) and x

19
Outline

• Energy analysis
• Application of fix point theorem
• Models and numerical results
• Simulation results

20
Model 1

• A little more complicated than the previous model
  used for illustration
• Considers external input of BER
• But ignores ACK, session setup messages for
  simplicity
• Finds only the value of EN
• Single channel MAC (Aloha)
• Supports scalar only

21
Simulink Model
22
Verified by MATLAB Iterations
N
Packet error rate
1000 iterations
23
Model 2

• Considers ACK now
• Still ignores session setup messages
• Supports vector
• Provides the average transmit power for a range
  of traffic density

24
Simulink Model
25
A Break Here

• It is becoming much more difficult to build
  simulink model
• Bugs in Simulink are leading to incorrect results
• Fix point does exist for this model and this has
  been verified by iteratively applying f in MATLAB
  for 1000 times
• MATLAB iteration will be used from now on

26
Model 3

• Considers everything now
• Same has been done to CSMA MAC
• Still single channel
• Parameters used

 
27
Better Accuracy
28
Model 4

• 2 channel MAC
• Session setup messages on one channel
• Data and ACK on the 2nd channel

29
Comparison of MAC
30
Less Traffic ?
31
Packet Loss Rate (1/2)
32
Packet Loss Rate (2/2)
33
Channel Utilization (1/2)
Defined as the ratio of aggregate data rate and
radio data rate
34
Channel Utilization (2/2)
35
Energy Per Useful Bit (1/2)
where
36
Energy Per Useful Bit (2/2)
37
Radio Data Rate (1/4)
38
Radio Data Rate (2/4)
39
Radio Data Rate (3/4)
40
Radio Data Rate (4/4)
41
Number of Transmissions (1/4)
42
Number of Transmissions (2/4)
43
Number of Transmissions (3/4)
44
Number of Transmissions (4/4)
45
Outline

• Energy analysis
• Application of fix point theorem
• Models and numerical results
• Simulation results

46
Purpose of Simulation

• See the effect of inaccurate modeling in the
  following areas
• Retransmission traffic not Poisson distributed
• Channel not independent between packets
• Interaction between retransmissions and collision
  rate
• Timing issues not considered in the modeling so
  far

47
Simulation Setup
24 nodes 1 hour
48
Average Transmit Power
Timeout Data 50ms Control msgs 20ms
Node 0 or 1
49
Packet Loss Rate
Node 0 or 1
50
Statistics
Bursty behavior resulted from receiver being off
51
Appendix
52
Error Control Design

• ARQCRC
• Maximum number transmission M
• Positive acknowledgement

53
Packet Error Rate

• Assume channel impairment is independent of
  collisions

Note increased retransmissions will increase
collision rate
54
Channel Models

• Independent channel model
• For same average BER, this model results in
  higher packet error rate than bursty channel
  model
• Gilbert-Elliott channel model

55
Assumptions for MAC Analysis

• Single channel
• Retransmissions are also Poisson distributed