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Outage Optimum Routing for Wireless Networks

B. Amiri, H. R. Sadjadpour

Department of Electrical Engineering

University of California, Santa Cruz 95064

JJ Garcia-Luna-Aceves

Department of Computer Engineering

University of California, Santa Cruz 95064

Abstract—A new routing metric for multi-hop wireless ad hoc

networks is presented. The proposed metric is based on the

computation of Signal-to-Noise Ratio (SNR) and minimization

of wireless network outage probability in a fading environment.

This metric improves the Quality-of-Service by reducing dropped

packets. Further, by modeling the network with a Trellis diagram

and then using Viterbi Algorithm to select the best routing path,

we reduce the routing complexity of our approach. Simulation

results demonstrate the improvement achieved by implementa-

tion of this new metric. Performance of the proposed metric

is compared to other commonly used routing metrics such as

Minimum Hop Count (MinHop), Expected Transmission Count

(ETX) and two other SNR-based metrics in both mobile and

stationary networks.

Index Terms—Mobile ad hoc networks, Routing protocols,

Outage Probability, Quality-of-Service, Signal to noise ratio,

Viterbi Algorithm

I. INTRODUCTION

Current high speed wireless communication networks are

used for real-time audio and video applications. For these types

of applications, connection failure is not acceptable to the end

user. Therefore, stability of wireless links is critical. For multi-

hop wireless ad hoc networks, providing route stability is even

more challenging. In these networks, link drop may result in

overall route failure. Therefore, the stability of each link in a

path can be a critical factor. In these networks, where there

are multiple paths between source and destination, finding and

selecting the most reliable path is very essential to the overall

performance of the network.

The network routing process involves two steps: first, as-

signing cost metrics to links and paths and second, distributing

the routing information in the network [1]. Many route dis-

semination techniques [2], [3] have been proposed to address

the second step. Proactive protocols, such as Destination Se-

quenced Distance Vector (DSDV) [4], and reactive protocols,

such as Dynamic Source Routing (DSR) [5] and Ad hoc On

Demand Distance Vector (AODV) [6], are proposed. Most

of these proposed routing techniques consider the number of

hops in a route called MinHop as their cost metric to find

the desired route [2]. Although MinHop offers simplicity and

low communication delay, it may not provide a good quality

of service. In a wireless network, this metric tends to find

paths with long and unstable links which will result in lower

network capacity and reliability.

Lower stability and capacity as two critical disadvantages

of MinHop metric motivated researchers to find cost metrics

which provide better performance. These efforts resulted in

proposing new routing metrics which take into account the

quality of wireless channels [7]–[14]. There has been some

study to compare the performance of these routing techniques.

It is shown that none of these techniques consistently perform

better than others for different network scenarios, such as

stationary or mobile networks [12]. The main reason for this

inconsistency is that most of these proposed routing metrics

are based on intuitive ideas rather than systematic approaches

to calculate an optimum cost metric.

In this paper, we use analytical calculation of outage

probability in wireless networks to find an optimum outage

routing metric for network reliability. This SNR-based routing

metric finds the most stable end-to-end route for wireless data

transmission. In order to reduce the routing complexity, we

model the network as a Trellis diagram and implement the

Viterbi algorithm for routing search.

Finally, we provide simulation results to verify our theoret-

ical findings. Our experiments show that our metric provides

better delivery performance compared to MinHop [5], ETX

[7], [16], MaxMinSNR metric proposed in [9], [13] and the

Average SNR metric proposed in [14] for both stationary and

mobile network scenarios.

II. RELATED WORK

In [7], a routing metric (ETX) is proposed for wireless

networks based on the expected number of transmissions

(including retransmissions) necessary to transmit a packet.

Each node estimates the forward delivery ratio to each of

its neighbors and also receives the corresponding estimate

of the reverse direction. This is done by sending a probe

packet over an initialization time interval before the actual

data transmission. Then, the ETX metric is calculated based

on the inverse of these delivery ratios. It is shown that ETX

outperforms MinHop for stationary fading wireless networks

[12]. One of the problems with ETX, though, is its perfor-

mance in mobile networks. Since probing is completed before

the actual data transmission, ETX may not be an accurate

indicator of the current channel quality [16] and will result

in performance deterioration in mobile networks [12]. As

opposed to ETX, where the metric is calculated before the

real data transmission, our technique will update the routing

metric in a real time manner taking the SNR of the actual

data packets into account. Also, ETX performance in network

scenarios with multiple simultaneous flows is not as good as

in the single flow case [17], which is also a consequence

978-1-4244-9538-2/11/$26.00 c ⃝ 2011 IEEE

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of having separate probing period for metric calculation with

lower network traffic than the actual data transmission.

In [10], a routing metric based on average Round Trip Time

(RTT) is proposed. In this protocol, the routing is done by

sending probe packets over each channel and measuring the

RTT of the probes. After receiving the packet, each neighbor

responds with an acknowledgment (ACK) containing a time-

stamp to calculate the RTT. RTT is designed for highly loaded

or lossy links. The major drawback of this technique is self-

interference, i.e, route instability due to load-dependence.

When a node has low load, the RTT metric for the links toward

that node is low. Therefore, more paths tend to select that

node as part of their route. This results in higher load on that

node and higher RTT metric, which leads to oscillations and

instability in route selection.

In [12], PktPair protocol is proposed as a modified version

of RTT protocol. This metric is based on measuring the delay

between a pair of back-to-back probes to a neighboring node.

PktPair protocol addresses some of RTT issues (mainly the

self-interference problem) but the performance is poor as a

result of high overhead. In [12], the performance of ETX [7],

RTT [10], PktPair [12] and MinHop are compared. It is shown

that ETX has the best performance in a stationary wireless

network while MinHop demonstrates a better performance

than ETX in mobile cases. Considering these results, we only

select ETX and MinHop among the above four metrics as part

of our performance baseline for simulations.

In addition to the above mentioned metrics, there are some

other proposed routing metrics based on SNR. Incorporating

SNR calculations in the routing metric derivation is a promis-

ing approach, as it addresses the difficulty of defining good and

bad links in wireless networks. Thus, there are many separate

levels of link quality that can be expressed by the SNR. In

[9], a routing strategy is proposed to find the most stable path

in the network, the one with the minimum end-to-end outage

probability. It is assumed that the bottleneck link, i.e., the link

with the minimum SNR, limits the throughput of a path and

an outage can happen only due to a drop in this bottleneck

link. The main drawback of their strategy is that the derived

metric is not composable, i.e., it does not take into account

the performance of all links in the path but only the weakest

one. Nevertheless, failures can also happen in other links.

This is more likely when there are multiple links in a path

with SNR close to the minimum SNR.“Being composable”

is an important property of a routing metric so that the end-

to-end path cost can be easily derived from the individual

link metrics along the path. The metric we propose in this

paper is a composable metric (similar to ETX and RTT) and

takes into account the performance of all links to determine

path performance. Our simulation results demonstrate that this

strategy provides performance improvement compared to other

approaches.

In [13], a very similar approach to [9] is proposed. In this

paper, traditional DSR routing technique is modified so that

the source node selects the route based on the value of the

best of the worst link SNR and Received Power (RP) among

all possible routes. The general performance of this proposed

technique is expected to be similar to [9].

In [14], MinHop and link quality are considered sequen-

tially. First, the path(s) with the minimum number of hops

are extracted. If more than one path is found, then the path

with stronger links, in terms of average SNR, is selected. If the

number of hops is different, no SNR calculations are made and

the path with MinHop will be selected. On the contrary, our

new metric allows comparison of multiple paths with different

number of hops, thus, it is more general and can achieve higher

throughput.

The outage probability model for a network that suffers

from fading was also exploited in [15]. The authors developed

a probabilistic model and studied the relationship between

link reliability, distance between nodes and the transmission

power. Algorithms to find the optimal link were developed by

taking advantage of route diversity. The emphasis of this work

was on the trade-off between reliability and end-to-end power

consumption, whereas we focus on the computation of the best

path with minimum outage probability.

III. METRIC DERIVATION

This paper considers maximizing path reliability as the main

criterion in route selection for wireless ad hoc networks and

our goal is to find a routing cost metric to minimize the outage

probability. In addition, a good routing metric for practical

applications should be simple and composable.

We first start by calculating the link outage probability. In a

Rayleigh fading environment, the channel gain can be modeled

as a complex Gaussian random variable with zero mean and

variance σ2

two Gaussian random variables X and Y , Z =

and Z2are Rayleigh and exponentially distributed respectively.

The transmit power is and the received signal power will be

exponentially distributed with mean σ2

white Gaussian noise with variance N0/2 per complex dimen-

sion is added to the received signal. With a finite bandwidth

of B Hz and transmit power of PT, the average received SNR,

¯ γm, including path loss and shadowing is

mper complex dimension [18]. Note that for any

√X2+ Y2

m. Further, an additive

¯ γm= σ2

m

PT

BN0.

(1)

The outage probability of link m in path i can be calculated

as

Pi

out,m= P(γi

m< γth) = 1 − P(γi

m≥ γth),

(2)

where γth is the SNR threshold required to support system

desired data rate. For an exponentially distributed received

SNR, this probability is given by

Pi

out,m= 1 − exp(−γth

γi

m

).

(3)

Eq. (3) shows link outage probability as a function of SNR.

The next step is to calculate path outage probability. Assum-

ing link independence in a path, outage probability of path i

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with Mihops is given by

Pi

out= 1−

Mi

∏

m=1

(1−Pi

out,m) = 1−exp

(Mi

m=1

∑

ln(1 − Pi

out,m)

)

.

The path with optimal outage, iopt, can be computed as

{

{Mi

m=1

{Mi

m=1

Replacing link outage probability from Eq. (3) into Eq. (4),

we arrive at

iopt

= argmin

∀i

1 − exp

(Mi

m=1

∑

ln(1 − Pi

out,m)

)}

,

=argmax

∀i

∑

∑

ln(1 − Pi

out,m)

}

,

= argmin

∀i

−ln(1 − Pi

out,m)

}

(4)

iopt= argmin

∀i

{Mi

m=1

∑

γth

γi

m

}

.

(5)

Note γthis fixed for all links and can be eliminated from this

equation.

iopt= argmin

∀i

(

M

∑

m=1

1

γi

m

)

(6)

Eq. (6) suggests that the path metric is equivalent to the

summation of inverse SNR of all the links in the path. This

metric finds the outage optimum path and has two important

properties of a good routing metric. It is simple and compos-

able. By calculating the inverse SNR metric for all possible

paths from source to destination and finding the path with

minimum cost metric, we can find the most stable and reliable

path, i.e., the one with the minimum outage probability.

It is important to mention that the authors in [9] have used

outage probability model to find cost metric with the general

assumption that path outage only happens as a result of outage

in the weakest link of the path. This assumption has resulted

in a different routing metric which is not optimal and is not

composable. We call this metric MaxMinSNR in this paper.

We provide an example to better illustrate the difference be-

tween the Inverse SNR metric proposed in this paper, MinHop

metric used in [4]–[6] and MaxMinSNR metric proposed in

[9] and [13]. Figure 1 illustrates a simple network scenario.

There are six nodes: one source (S), one destination (D) and

four intermediate nodes. The SNR of each link is shown by

a number next to it. There are three different possible routes

from source to destination. Route 1 (S-N1-N2-D) and Route

3 (S-N4-N3-D) have three hops while Route 2 (S-N3-D) has

two hops. Therefore, MinHop routing will select Route 2 as the

best route without taking link SNR into account. MaxMinSNR

considers the minimum SNR of each path and will select the

route with the highest minimum SNR. Therefore MaxMinSNR

will select Route 3 as the best route.

In the case of Inverse SNR routing presented in this paper,

the metric for each route is the summation of inverse SNR of

all the links in that route. By simply adding link metrics, the

route metric for Routes 1, 2, and 3 are equal to 0.2667, 0.3175

and 0.4420 respectively. Therefore, Inverse SNR routing will

select Route 1 as the best route.

This simple example shows how each of the SNR-based

routing metrics may select a completely different route. In the

simulation section, we will provide the results and compare

the performance of these routing metrics.

Destination?

Source?

N1?

N2?

N3?

N4?

20?

20?

6?

7?

6.4?

6.2?

7?

Fig. 1. A simple example with three possible paths from source to destination

IV. A FRAMEWORK FOR ROUTING SEARCH

Calculating link and path metrics to find the best route

from source to destination among all possible routes can be a

very complex task in large networks. Therefore, simplicity of

routing protocols is very important. In this section, we propose

a general framework for mapping the Viterbi algorithm to

routing search protocols.

The first step is to model a multi-hop wireless network with

a Trellis diagram. A Trellis diagram is a finite state machine

which is constructed by states, branches and stages. In a Trellis

diagram, there are finite stages from the Trellis starting point

to its end point. Also, there are finite states at each stage. We

consider a Trellis diagram with M stages and N states at each

step (Fig. 2). Each branch which starts at state x in stage m

and ends at state y in stage m + 1, has a determined weight

(where x and y are less than N). There are several paths from

the Trellis start point to its end point and each path consists

of M states and branches. The path weight is composable of

its branch weights. As a result, each path has an associated

weight and the path with minimum weight will be selected as

the final solution.

The idea is to model a network as a Trellis diagram. A multi-

hop network has a finite number of hops and intermediate

nodes which we call relay. Assuming a network with a

maximum of M hops and N relays at each hop, each link

from node x at hop m to node y at hop m + 1 has a cost

metric (both x and y are less than N) which is an indicator of

the performance and quality of that link. Path metrics can be

calculated from link metrics.

With this general modeling, the Trellis start- and end- points

can be mapped to source and destination nodes in a network

and the number of stages in a Trellis diagram can be mapped

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Fig. 2.4-state Trellis Diagram

to the number of hops in a network. Each state in Trellis will

be similar to a node in the network and the number of states

will be equivalent to the maximum node degree in the network.

Branch weight in a Trellis is similar to link metric in network

routing and the goal in both Trellis and routing is to find the

path with minimum cost metric.

Viterbi algorithm is a dynamic programming approach used

to run an optimal sequential Trellis search to minimize the

error by finding the most likely sequence of states. As it is

illustrated above, a Trellis diagram model can be implemented

for a network. Since both Viterbi algorithm and network

routing are dynamic programming approaches, the next step

will be to show how running Viterbi algorithm for a Trellis

diagram is similar to finding the best possible route from

source to destination in a network. A more comprehensive

modeling will be done in future works.

Viterbi algorithm will perform a full search while minimiz-

ing the complexity by dynamically eliminating sub-paths with

lower performance originating and ending at common nodes.

The Viterbi algorithm implementation will help reduce the

complexity of the full Trellis search while keeping the optimal

performance. This means that we can reduce the complexity

without any performance degradation. More significantly, this

mapping framework can be used as an initial step to implement

other (already existing) suboptimal Trellis search algorithms

with lower complexity into the network routing concept.

It is important to mention that the work presented in this

section is only the initial step of a general framework. More

details on this framework and other suboptimal schemes are

required for a more comprehensive modeling which is beyond

the scope of this paper and will be presented in future works.

V. SIMULATION

In this section, we will first explain details of the simulation

environment. Then, we will present simulation results for the

Inverse SNR metric introduced in this paper and compare them

to other techniques.

A. Simulation Environment

We use Qualnet [19] as the simulation environment for our

experiments. We randomly distribute 30 nodes in a 1000m ×

1000m square area with Rayleigh fading. For the stationary

scenario, nodes are fixed and for the mobility scenario each

node has a random speed of 1–10 m/s. This scenario mimics

an environment where people walk, run or ride bicycle.

Each node runs IEEE 802.11 as the MAC protocol and

802.11b as PHY model with a transmit power of 15 dBm.

For each measurement, two nodes are randomly selected as

source and destination. Constant-Bit-Rate (CBR) traffic is used

to simulate the performance of generic multimedia traffic.

This UDP-based, client-server application sends data at a

constant bit rate. The source node transmits 50000 packets

of size 2048 bits with 500 packets/sec CBR. The number

of received packets is measured to calculate delivery ratio.

Thirty measurements are done with different random pair of

source and destination nodes and averaged to represent the

performance of each technique.

B. Simulation Results

We modified the reactive DSR routing protocol [5] to

implement the Inverse SNR metric. When a source S is

interested in a destination D, the route is set up on-demand

by sending a Mesh Request (MR). The MR is replied by a

Mesh Acknowledgment (MA) from the destination D, which

is re-broadcasted by intermediate nodes toward the source. To

implement the Inverse SNR metric into DSR, a weight label

is defined for each route. Whenever a packet is received by

an intermediate node, the SNR of the packet is calculated.

Then the intermediate node adds the inverse of link SNR

to the weight label received from the upstream neighbor to

update the weight label. Therefore, the overall route weight

label is composable by adding link weight labels. This process

continues until we reach the source node S. The source node

receives weight labels from all routes and selects the route

with the lowest weight label (route metric).

Since link SNR can rapidly change in a mobile wireless

environment, exponential moving average is used for SNR

measurement smoothing as

SNRt= α × SNRt−1+ (1 − α) × SNRins.

SNRt and SNRt−1 are the new and old smoothed SNR

respectively and SNRinsis the current (instantaneous) SNR

value. Smaller α value gives more weight to the current

measured SNR, whereas larger values give more weight to the

previous average measurement. Having a small α may result

in rapid change in the average SNR and frequent switching of

the selected path, which is undesirable for the stability of the

system. On the other hand, a large α value may result in some

undesirable delay in route switching when the quality of the

route deteriorates. Therefore, optimization of α value can be

a determining factor in the performance. For our simulation,

α = 0.9 is used for different network scenarios.

Results are presented in terms of the number of delivered

packets and average end-to-end delay. Number of delivered

packets is a good metric for system stability performance.

Since the transmission data rate and the total number of

transmitted packets are fixed (CBR), the number of delivered

packets is also a representative of the throughput.

(7)

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End-to-end delay is the one-way delay between the time

that source sends the packet and the time that destination

receives it. It is averaged over all received packets. For

CBR transmission, delay can be due to the network layer

queue, MAC layer delay, transmission delay and propagation

delay [19]. The propagation delay depends on the distance

between nodes in a wireless network, and the transmission

delay depends on the link bandwidth. Therefore, analyzing

end-to-end delay will be more complicated than the number of

delivered packets since the former is dependent on the route’s

physical length, bandwidth and other network parameters.

We have conducted simulation results for two well-

established routing metrics, MinHop [5] and ETX [7] [16], as

well as two recently proposed metrics, MaxMinSNR [9] [13]

and Average SNR [14], all of which implemented for the DSR

routing protocol. The DSR implementation of ETX is done as

explained in [16] and the DSR implementation of MaxMinSNR

and Average SNR is done similar to the process explained

in [13]. The following text explains details of stationary and

mobile simulation scenarios.

1) Stationary network: In this section, we evaluate a sta-

tionary network scenario where all 30 nodes are fixed during

the simulation. For each metric, the simulation is done for 50

random node pairs and results are averaged and displayed. We

provide and compare the average number of delivered packets

and average end-to-end delay as performance indicators for all

five above mentioned metrics.

As it is shown in Fig. 3, Inverse SNR has the highest

and MinHop has the lowest average packet delivery ratio.

Average-SNR technique shows improvement compared to Min-

Hop, which is consistent with the results in [14], but the

improvement is only less than 5 percent. The reason for this

minor improvement is that Average SNR modifies the route

only when there are multiple routes with the same number

of hops which is not applicable to all scenarios. MaxMinSNR

shows better performance compared to MinHop which is also

consistent with [13] but still has a lower delivery performance

compared to ETX and Inverse SNR. As it is shown here and

previously in [12], ETX performs well in stationary networks,

however Inverse SNR continues to be superior. This is in

line with our analytical work where it is demonstrated that

Inverse SNR minimizes the outage path probability resulting

in maximized delivery performance.

The average end-to-end delay comparison is shown in Fig.

4. As explained before end-to-end delay can occur as a result

of network layer queue, MAC layer delay, transmission delay

and propagation delay. Therefore, analyzing details of end-

to-end delay for all five techniques is complicated, but our

simulation results shows the superiority of the Inverse SNR

metric. Also as it is shown, MinHop demonstrates fairly good

delay performance compared to other techniques which could

be attributed to a lower propagation delay compared to other

techniques.

2) Mobile Network: We have also conducted simulations

for the mobile scenario where nodes are moving with random

mobility of 1–10 m/s. This case can be a representative of

Fig. 3.

metrics

Inverse SNR delivers more packets on average than all the other

Fig. 4.Inverse SNR has smaller average delay than all the other metrics

the scenario when people are roaming while holding wireless

transceiver enabled devices in an office environment.

The average delivery performance for all five metrics is

presented in Fig. 5. Similar to the stationary cases, Inverse

SNR provides better stability (delivery ratio) and throughput

performance. ETX has the worst performance compared to

others because it allocates an initial probing time before the

actual data transmission for link metric calculation. By the

time of actual data transmission, the metrics calculated during

probing may change resulting in an inaccurate evaluation of

the link performance. Therefore, ETX only provides perfor-

mance improvement for stationary cases which is consistent

to findings in [12].

Average end-to-end delay comparison for mobile cases is

shown in Fig. 6. For this scenario, MinHop and Average SNR

provide slightly better performance of 6 and 4 percent respec-

tively compared to Inverse SNR while ETX and MaxMinSNR

have the highest average end-to-end delay. Similar to the

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Fig. 5. Inverse SNR has the highest throughput in a mobile scenario

stationary case, analysis of end-to-end delay for all five tech-

niques is complicated because it depends on many different

network parameters.

Fig. 6. End-to-End Delay Comparison of all metrics mobile environment

Given the superior performance of this technique for station-

ary networks and better packet delivery for mobile scenarios,

this approach is particularly suitable for applications that are

sensitive to packet losses. Note that the delay of this technique

is very close to the best techniques in our simulations.

VI. CONCLUSION

This paper introduces a new routing metric based on the

inverse SNR criterion for wireless networks. This metric

is derived by theoretical calculations to minimize the path

outage probability in a wireless network and maximize the

network delivery performance in fading environments. Sim-

ulation results show that this Inverse SNR metric has better

delivery performance compared to MaxMinSNR, Minhop, Av-

erage SNR and ETX routing in both mobile and stationary

wireless networks. Further, the Inverse SNR scheme is a

composable metric which is desirable for path selection. We

also demonstrated how to take advantage of Viterbi algorithm

to implement Inverse SNR approach.

ACKNOWLEDGMENT

This research was partially sponsored by the U.S. Army

Research Laboratory under the Network Science Collabora-

tive Technology Alliance, Agreement Number W911NF-09-

0053, by the Army Research Office under agreement number

W911NF-05-1-0246, by the National Science Foundation un-

der grant CCF-0729230, and by the Baskin Chair of Computer

Engineering. The views and conclusions contained in this

document are those of the author(s) and should not be inter-

preted as representing the official policies, either expressed

or implied, of the U.S. Army Research Laboratory or the

U.S. Government. The U.S. Government is authorized to

reproduce and distribute reprints for Government purposes

notwithstanding any copyright notation hereon.

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New York, 2005, pp. 69–72.

[19] TheQualnet simulator,Scalable

networks.com/products/qualnet

Networks,http://www.scalable-