Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4486 + 2220 = 6706
 Ad Hoc Networks • 4003-543-01/4005-742-01 • Spring Quarter 2007
Course Page

## 4003-543/4005-742 Ad Hoc Networks Module 6. Energy Awareness -- Lecture Notes

Prof. Alan Kaminsky
Rochester Institute of Technology -- Department of Computer Science

• Power ratios
• Power ratio = P1 / P2
• Power ratio in decibels (dB) = 10 log10 (P1 / P2)
• Multiplying and dividing power ratios (linear scale) becomes adding and subtracting power ratios in decibels (logarithmic scale)

• Pt = Transmit (TX) power
• Pr = Receive (RX) power
• Can be expressed as a power ratio in dB by giving a value relative to some standard power level
• dBW: Relative to a power level of 1 watt (W)
• Pt dBW = 10 log10 (Pt W / 1 W)
• Pr dBW = 10 log10 (Pr W / 1 W)

• Path loss
• L = Path loss factor
• Pr = Pt / L
• Pr dBW = Pt dBW - L dB

• Propagation model
• Expresses path loss as a function of transmitter-receiver distance, L(d) dB

• The ground reflection (two-ray) propagation model
• From Theodore S. Rappaport, Wireless Communications: Principles and Practice, 2nd Edition (Prentice Hall, 2002), pages 124-125
• Received signal consists of the sum of two components:
• Direct signal from transmit antenna straight to receive antenna
• Reflected signal from transmit antenna, bounces off the ground, then to receive antenna
• Pr = Pt Gt Gr ht2 hr2 / d4
• Path loss:
• L(d) = d4 / (Gt Gr ht2 hr2)
• Path loss in dB:
• L(d) dB = 40 log10 d - (Gt dB + Gr dB + 20 log10 ht + 20 log10 hr)
• Where:
• L = Path loss (dB)
• d = TX-RX distance (m)
• Gt = TX antenna gain (dB)
• Gr = RX antenna gain (dB)
• ht = TX antenna height (m)
• hr = RX antenna height (m)

• S dBW = The minimum RX power required to reliably receive the transmitted signal
• That is, Pt dBW - L(d) dB >= S dBW
• Solving for d gives dmax, the maximum TX-RX distance
• L(d) dB <= Pt dBW - S dBW
• 40 log10 d - (Gt dB + Gr dB + 20 log10 ht + 20 log10 hr) <= Pt dBW - S dBW
• 40 log10 d <= Pt dBW - S dBW + Gt dB + Gr dB + 20 log10 ht + 20 log10 hr
• log10 d <= (Pt dBW - S dBW + Gt dB + Gr dB + 20 log10 ht + 20 log10 hr) / 40
• d <= 10 ^ ((Pt dBW - S dBW + Gt dB + Gr dB + 20 log10 ht + 20 log10 hr) / 40)
• dmax = 10 ^ ((Pt dBW - S dBW + Gt dB + Gr dB + 20 log10 ht + 20 log10 hr) / 40)

### Topology Control Via Transmit Power

• The transmit power Pt determines dmax

• dmax determines whether two nodes in an ad hoc network are connected

• Therefore, Pt determines the ad hoc network topology

• The ad hoc network topology determines the average number of hops between a randomly chosen source node and a randomly chosen destination node

• The energy needed to send a message across one hop is directly proportional to Pt

• Therefore, Pt determines the average energy needed to send a message

• One way to do energy aware routing is to choose Pt to minimize the average energy needed to send a message

Class AdHocSim01 is a Monte Carlo simulation program for studying transmit power based topology control in an ad hoc network.

Usage: java AdHocSim01 rxsens antgain antheight mintxpower maxtxpower txpowerincr region density trials seed
rxsens = RX sensitivity threshold (dBW)
antgain = TX and RX antenna gain (dB)
antheight = TX and RX antenna height (m)
mintxpower = Minimum TX power (dBW)
maxtxpower = Maximum TX power (dBW)
txpowerincr = TX power increment (dBW)
region = Length of one side of square network region (m)
nodes = Number of nodes
trials = Number of simulation trials for each TX power level
seed = Random seed

The program does the following:

1. Repeat Steps 2-7 for each TX power level from mintxpower to maxtxpower in steps of txpowerincr.

2. Compute dmax = the maximum inter-node distance for connectivity, based on a propagation model (see below).

3. For each TX power level, repeat Steps 4-6 (a simulation trial) trials times.

4. Place nodes nodes at locations chosen uniformly at random within a square area of region x region m.

5. Set up a link between each pair of nodes with an inter-node distance less than or equal to dmax.

6. Choose a random source node and a random destination node. Find the shortest (fewest hops) path from source to destination, or find that there is no path.

7. Over all simulation trials, compute the average path length (hops) and the probability that a path exists between a random source and destination. Let the average energy consumption be the average path length times the TX power level. (The actual energy consumption is directly proportional to this quantity.)

8. Make plots of the average energy consumption, average path length, and path probability versus TX power level.

• Example run
```\$ java AdHocSim01 -94 3 1.5 -20 0 1 2000 100 1000 142857
rxsens      = -94.0 dBW
antgain     = 3.0 dB
antheight   = 1.5 m
mintxpower  = -20.0 dBW
maxtxpower  = 0.0 dBW
txpowerincr = 1.0 dBW
region      = 2000.0 m
nodes       = 100
trials      = 1000
seed        = 142857
txpower (dBW)	dmax (m)	prob	hops	energy (W)
-20.0	150.00000000000003	0.037	2.6486486486486487	0.026486486486486487
-19.0	158.88805877659334	0.049	2.7551020408163267	0.03468467971269645
-18.0	168.3027681452945	0.068	3.0	0.0475467957738334
-17.0	178.27533411555288	0.075	3.8533333333333335	0.07688410787013418
-16.0	188.8388117691252	0.095	3.6842105263157894	0.09254318431877398
-15.0	200.02821482449866	0.154	4.746753246753247	0.15010551750539516
-14.0	211.88063169341314	0.241	5.477178423236515	0.21805040046913549
-13.0	224.43534841416496	0.345	6.214492753623189	0.31146244315851357
-12.0	237.73397886916717	0.45	6.642222222222222	0.4190958894780662
-11.0	251.82060271838415	0.609	7.09688013136289	0.5637252266795311
-10.0	266.74191150583846	0.736	6.6875	0.6687500000000001
-9.0	282.5473634234701	0.835	6.237125748502994	0.7852076101346135
-8.0	299.2893472453319	0.918	5.953159041394335	0.9435121238344208
-7.0	317.0233559754972	0.956	5.203974895397489	1.0383294996830728
-6.0	335.8081707852511	0.976	4.889344262295082	1.2281477511438235
-5.0	355.7060558492484	0.987	4.288753799392097	1.3562230329779887
-4.0	376.78296472643706	0.995	3.993969849246231	1.5900280359593948
-3.0	399.1087589698214	0.995	3.8110552763819094	1.9100522511704687
-2.0	422.75743968966833	0.998	3.5761523046092183	2.2563995615729557
-1.0	447.8073928376941	0.998	3.25250501002004	2.5835565630411
0.0	474.341649025257	1.0	3.105	3.105
```

### Energy Aware Routing

• Minimum energy protocols
• Based on topology control via transmit power
• Set each node's transmit power separately to minimize total energy to transmit a message
• Set every node's transmit power to the same value to minimize total energy to transmit a message

• Takes nodes' battery power levels into account
• Transmitting at a certain power level may drain some nodes' batteries sooner than other nodes, causing the network to fail sooner
• Set each node's transmit power to maximize the time until the network fails because some nodes' batteries are sucked dry

• Power save protocols
• The above assume a node's transmit power can be adjusted
• Some nodes can't do this
• Instead, put nodes into and out of the "sleep" (power save) state on some schedule to reduce energy consumption

 Ad Hoc Networks • 4003-543-01/4005-742-01 • Spring Quarter 2007
Course Page
 Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4486 + 2220 = 6706