Comparison of Data-driven Link Estimation

Methods in Low-power Wireless Networks

Hongwei Zhang Lifeng Sang Anish Arora

From sensor networks to cyber-physical systems (CPS)

Sensing, networking, and computing

tightly coupled with the physical world

Automotive

Alternative energy grid

Industrial monitoring and control

Wireless networks as carriers of

mission-critical sensing and control

information

Stringent requirements on predictable

QoS such as reliability and latency

Dynamic wireless links

Link estimation becomes a basic element of routing in wireless networks.

0 2 4 6 8 10 12 140

20

40

60

80

100

distance (meter)

pack

et d

eliv

ery

rate

(%

)

0 50 100 150 200 250 30075

80

85

90

95

100

time seriespa

cket

del

iver

y ra

te (

%)

5.5 meters

(2 secs)

transitional region (unstable & unreliable)

Why not beacon-based link estimation?

Sampling error due to traffic-induced interference

Unicast ETX in different traffic/interference scenarios

Sampling error due to temporal link correlation

2 4 6 8 10 12

-80

-60

-40

-20

0

distance (meter)

diffe

renc

e in

del

iver

y ra

te (

%)

d = 0d = 0.01d = 0.04d = 0.07d = 0.1d = 0.4d = 0.7d = 1

mean reliability of each unicast-

physical-transmission minus that

of broadcast

Errors in estimating unicast ETX via broadcast

reliability: estimated unicast ETX minus actual

unicast ETX and then divided by actual

unicast ETX

Data-driven link estimation

Unicast MAC feedback

{NTi}: # of physical transmissions for the i-th unicast

As a simple, low cost mechanism to address the

sampling errors of beacon-based link estimation

Two representative methods for estimating ETX

L-NT uses aggregate unicast feedback {NTi}

represents SPEED, LOF, CARP

L-ETX uses derived information for individual unicast-physical-

transmission

represents four-bit-estimation, EAR, NADV, MintRoute

EWMA{NTi} ETX

PDRcalculation

{NTi} {PDRj}EWMA

PDR1/PDR

ETX

Won’t L-NT and L-ETX behave the same?

Accuracy of EWMA estimators

Given {xi: i = 1, 2, …} where xi is a random variable with

mean and variance 2, the EWMA estimator for is

Degree of estimation error (DEk) for using estimator

,...3,2 ,10 ,)1(1

11

kxyy

xy

kkk

ky

COV[xi

]

DEk is approximately proportional to COV[xi].

1

12])[( 122

,...,1

k

kxx

k

yEDE k

Relative accuracy in L-NT and L-ETX

where P0 is the failure probability of a unicast-physical-

transmission, and W is the window size for calculating PDRj;

COV[NTi] > COV[PDRj] if (which generally holds), thus

DEk(L-NT) > DEk(PDR)

)1(

PDRCOV ,NTCOV0

0

j0i PW

PP

L-ETX tends to be more accurate than L-NT in estimating link ETX.

DEk(L-ETX)

01

1

PW

Can we experimentally verify the analytical

results?

Testbed based link-level experimentation

We use Mica2 motes that are deployed in a 147 grid

Focus on links of the middle row

Interferers randomly distributed in the rest 6 rows, with 7 motes on each row

on average; interfering traffic is controlled by the probability d of generating

a packet at an arbitrary time

L-NT vs. L-ETX: when d = 0.1

Estimated ETX values in L-NT and L-ETX for a link 9.15 meters (i.e., 30

feet) long

2 4 6 8 10 120

0.5

1

1.5

distance (meter)

CO

V

L-NTPDR

COV[NTi] vs. COV[PDRj]

Variants of L-NT and L-ETX

Variant/stabilized L-NT: L-WNT

L-NADV (variant of L-ETX): estimate PER instead of PDR

L-NT vs. L-ETX: forwarders used

Method Forwarder Percentage(%)

Cost ratio

L-NT

5

6

7

8

10

0.1

4.14

7.17

21.26

67.33

2.3

1.3

1.5

1.3

1

L-ETX

6

7

8

10

5.91

0.2

5.1

88.79

1.3

1.5

1.3

1

Implications for routing behaviors?

Testbed based routing experiments

Convergecast routing in a 77 grid A node at one corner as the sink

Other 48 nodes as sources generating packets based on the event traffic

trace from “A Line in the Sand”

sink

L-NT vs. L-ETX: routing performance

Event reliabilityNumber of transmissions

per packet received

L-NT L-WNT L-ETX L-NADV0

5

10

15

20

Num

Tx

Seemingly similar methods may differ significantly in routing

behaviors (e.g., stability, optimality, and energy efficiency)

L-NT vs. L-ETX: routing stability

Two consecutiveroutes (%)

L-NT L-WNT L-ETX L-NADV

Same 36.55 42 99.94 99.97

Diff. routes but

samehop count

17.08 11.18 0.03 0.03

Increased hop

count

23.96 24.19 0.03 0

Decreased hop

count

22.41 22.63 0 0

Other experimental results

Related data-driven protocols

L-ETX-geo, L-ETX

Periodic traffic, other event traffic load

Sparser network

Random network

Network throughput

Concluding remarks

Two seemingly methods L-ETX and L-NT differ

significantly in routing performance

Variability of parameters being estimated significantly

affects the reliability, stability, latency, and energy

efficiency of data-driven link estimation and routing

Future work

Other metrics (e.g., RT oriented)

Opportunistic routing and biased-link-sampling

Backup slides

Traffic pattern affects temporal link correlation

Autocorrelation tends to decrease, especially for smaller lags, as interference load

increases, partly due to increased randomization as a result of random traffic

0 20 40 60 80

0

0.2

0.4

0.6

0.8

h

(h)

d = 0d = 0.01d = 0.04d = 0.07d = 0.1d = 0.4d = 0.7d = 1

2 4 6 8 10 12

0

0.5

1

1.5

Link length (meter) (

4)

d = 0d = 0.01d = 0.04d = 0.07d = 0.1d = 0.4d = 0.7d = 1

Autocorrelation coefficient for a

link of length 9.15 meters (i.e.,

30 feet)

Autocorrelation coefficient for

lag 4

Beacon-based vs. data-driven routing

Event reliability Number of transmissions per packet received

ETX RNP L-ETX0

1

2

3

4

5

6

Num

Tx