Abstract —Simultaneous data transmission over multiple

paths can improve the performance of wireless ad-hoc

network. To avoid data rate degradation because of inter-

path interference, smart path selection should be done. It

requires very clear understanding of network and path

characteristics influencing path capacity.

An analytical method is adapted for multi-path conditions

and implemented in MATLAB tool. A statistical analysis of

many randomly chosen scenarios was performed to

determine the inter-path distance effect on path capacity.

Simulation results show that there is no significant increase

in capacity if paths are more distant.

Keywords — wireless ad-hoc network, multi-path routing,

MATLAB

I. INTRODUCTION

imultanious data transmission over several paths is

believed to increase capacity of wireless ad-hoc

network [1],[2]. However, as it has also been shown in [2],

there is no significant capacity improvement, if paths are

chosen without taking into account mutual interference

between them.

Data rate degradation in IEEE802.11 ad-hoc networks is

caused by imperfection of CSMA/CA channel access

protocol. Two main reasons are channel contention by

nodes and interference caused by simultaneous

transmissions of several nodes in the same channel.

Additional degradation of data rate is caused by hidden

and exposed nodes.

One should consider that for video transmission in

multi-path conditions these negative effects can be even

more intense. There are more nodes involved in data

transmission, shared end-points (source and destination)

limit possibility to create disjoint paths, attempts to

separate paths (increase distance between them) leads to

even more nodes involved (additional hops), and intense

parallel data streams congest the network.

There could be two approaches to cope with

interference: eliminate the causes already during path

selection phase or try to soften consequences after. The

interference could be minimized by smart path selection

algorithm – finding the optimal number of paths, selecting

such paths in which less interference is created. For that

This research is supported by the Latvian National Research program

“Development of Innovative Multifunctional Materials, Signal

Processing and Information Technologies for Competitive Science Intensive Products”, project No.2 „ Innovative Signal Processing

Technologies for Development of Efficient Cognitive Electronic

Systems”. Lauris Cikovskis is a doctoral student at the Faculty of Electronics and

Telecommunications, Riga Technical University, Azenes str. 12, Riga,

Latvia (phone: +371 67089236; e-mail: lauris.cikovskis@rtu.lv).

one should have a very clear understanding of network and

path characteristics influencing its capacity. In [3] it is

shown that path capacity is affected by different

interconnected network parameters in combination with

path selection algorithm thus making the optimization task

very complex.

There have been lot of attempts to elaborate analytical

models and methods to estimate wireless ad-hoc network

capacity [2], [4]-[6]. A common assumption for these

methods, which makes them idealistic, is existence of

central coordination unit which regulates channel access

and also traffic during assigned time slot. Despite this fact,

results can be used as a best case scenario to aim.

One of authoritative papers in the field [4] seeks to find

theoretical limits for capacity of wireless ad-hoc networks.

They prove that data rate at which two nodes may

communicate in random network scenario decreases

asymptotically as

√ , where W is data rate and n is

number of nodes. In contrast to [4] where random network

structure, routing and traffic is assumed, this work, as well

as others mentioned below [2], [5]-[6], focuses on specific

network topologies and routing strategies having capacity

well under theoretical limit. These works tend to offer

methodology for capacity estimation for different protocol

and routing strategies.

Authors of [5] offer general methodology based on

conflict graph framework to maximize data flow between

single source and destination pair over one or several

paths. As stated by the authors themselves, their physical

and protocol models underlying conflict graphs differ from

IEEE802.11. In protocol model, interference is evaluated

only at receiver. In real network both physical carrier

sensing at transmitter and SNIR threshold at receiver

determine whether links may be active at the same time.

Ignoring this doesn’t allow to evaluate Career Sense

Threshold (CST) effect on network capacity. In [5] also

cases when links are not heavily loaded and mean load is

below maximum (e.g. bursty traffic) are analysed. An

important observation is that connection between capacity

and number of nodes found in [4] doesn’t hold anymore.

The method [5] are later used and adapted for studies of

multi-path transmission in [2]. Author analyses capacity

dependence on path disjointness. In contrast to [5]

specific, previously determined path sets are chosen.

Additionally also background traffic is taken into account.

Independent sets delivered from conflict graphs don’t

include those pairs which simultaneous transmission is not

allowed by physical carrier sense. Partially it solves

shortcoming of the original method [5], however still

Method for Analyses of Data Transmission over

Multiple Paths in Wireless Ad-hoc Networks

Lauris Cikovskis, Graduate Student Member, IEEE

S

21st Telecommunications forum TELFOR 2013 Serbia, Belgrade, November 26-28, 2013.

978-1-4799-1420-3/13/$31.00 ©2013 IEEE

cumulative interference is not taken into account at carrier

sensing. Authors show analytically and using simulations

that the best results can be achieved with fully radio

disjoint paths. However, in real life scenario creation of

radio-disjoint paths may require more hops. As it is

showed below, “longer” paths may not give expected

improvement, especially if links are highly loaded.

In [6] network capacity regions are introduced which

describe the set of achievable rate combinations between

all source-destination pairs under various transmission

strategies. These can be multi-hop routing, CSMA/CA etc.

Similarly to independent link sets in [2], [5] data rate

matrices are sought which include information about

network activity. In contrast to previous works where

maximum flow problem was solved to find sustainable

data rate, capacity regions include information about vast

number of data rate combinations depending on

transmission schedule.

The aim of this work is to improve analytical method

[6] for evaluating different aspects of data transmission

using multiple paths and test it for determining the inter-

path distance effect on path capacity. The method is

adapted for multi-path conditions under CSMA/CA

protocol and implemented in MATLAB tool. This tool is

used for statistical evaluation of network capacity for

randomly chosen scenarios.

In the second chapter the analytical method for multi-

path analyses is described. Application on the method and

some preliminary results are presented in the third chapter.

II. ANALYTICAL METHOD

In this chapter analytical method to evaluate

IEEE802.11 ad-hoc network capacity if data is transmitted

over several paths simultaneously is described. Single

source and destination pair is considered.

A. Theoretical background

Capacity of a path is determined by capacities of

individual links between nodes which mutually compete

for wireless channel. Bitrate at which two nodes

communicate is determined by channel conditions and

wireless technology used. Reception conditions can be

characterized by signal-to-noise-interference ratio (SNIR).

It is calculated as useful power against power sum of

Gaussian noise and interfering signals (1). Interference in

multi-user systems can be also treated as Gaussian [7].

∑ (1)

where PRx is received signal power, N – background noise

at receiver, B – bandwidth and PI received interference.

Analytical calculation of SNIR is based on assumption that

power levels of useful signal and interfering signals are

known. Power is obtained from radio propagation models.

In this work free space model is used.

Nodes will communicate at a speed which will satisfy

bit-error rate requirements at given SNIR. Usually for

different SNIR thresholds there are known possible

modulation schemas and accordingly bitrates. In this work

simplified approach is used where bitrate (link capacity) is

calculated according to Shannon theorem. Shannon limit

for a link capacity C (as bits per second):

( ) (2)

If we assume that interference has Gaussian statistics we

may replace SNR to SNIR from equation (1).

B. The Method for network capacity estimation

The analytical method used in this work is based on

capacity regions introduced in [6]. Network activity at a

certain moment can be characterized by transmission

scheme. It illustrates all simultaneous data transmission

which are possible physically or acceptable by network

protocol, e.g. CSMA/CA. In another moment activity is

described by different scheme where other nodes are

active. It is possible to find different transmission schemes

containing different combination of node pairs which

characterizes different network states. Sequentially

switching form one scheme to another it is possible to

perform full data transmission in a time interval.

A scenario with four nodes is given in Fig. 1 where

node n1 transmits to n4 but n4 to n1. Since there is an

obstacle transmission is done in two hops.

Fig.1 A network scenario with an obstacle in middle

One possible scheme (S1) which will characterize the first

hop for each transmission:

[

]

If assumed that node cannot transmit and receive at the

same time there cannot be other active pairs in this

scheme. At the next time moment after data is received at

n2 and n3, there are active other two pairs in scheme (S2)

[

]

Applying weights τi ( ∑ =1) to schemes

and summing the schemes will give full transmission.

Weight characterizes a fraction of time the scheme is

active. Time fractions can be considered as time-division

schedule. For the above scenario one possible schedule is

(3)

In [6] authors perform transition from transmission

schemes to data rate matrices which more precisely

characterizes data flows in network. It is not presented

here in detail, but just for illustration link data rates has

been added to topology in Fig.1. These can be calculated

using (1) and (2).

A fraction of time in which each scheme is active will

influence capacity of individual links. Different

combinations of time fractions applied to schemes will

form capacity region of network which includes all

achievable link data rates. A region of possible data rates

between links n1→n3 and n2→n1 is given Fig. 2.

n3

n4 n2

n1

1.7 Mbps 1.7 Mbps

0.47 Mbps

0.47 Mbps

Fig.2. Capacity region slice for links n1→n3 and n2→n1

To be able to characterize path set capacity it is not

required finding all possible data rates and schedules but

only those which provide maximal throughput in paths. To

characterize network performance with a single value

authors of [6] offer uniform capacity which is achieved at

optimal schedule when all nodes communicate with

maximally possible common rate. Indeed, uniform

capacity is a point on the capacity region (Fig.2). Uniform

rate can be obtained also using max flow method (applied

in [2] and [5]) by adding constrain that all flows (data rates

between nodes) are equal.

For larger network topologies more schemes are

possible which consist of different combinations of links

under the rules of given transmission protocol. A

transmission scheme and a collection of schemes have

analogy with independent set and conflict graph in [2], [5].

For more detailed explanation of the method and

mathematical representation of capacity region refer to [6].

C. Adaption of the method for multi-path transmission

If set of paths has been already found and there is no

other transmission outside the paths, all active links are

also known. Unlike original study [6], here transmission

schemes are formed from links belonging to the paths

rather than combinations of all nodes.

Our assumption for further studies is that it is enough to

find time schedule that ensures uniform capacity for all

links between nodes (belonging to any of paths) to be able

to characterize path set capacity. This assumption can be

justified by two points:

uniform flow in a single path ensures that a node in

multi-hop conditions doesn’t transmit more data than

receives from neighbour;

equal and uniform flow in all paths is frequent scenario

in multi path transmission (e.g. MDC video streams)

Such approach allows us to calculate aggregated path

capacity as .

D. CSMA/CA implementation

Transmission schemes are formed considering only

protocol model. It means that the only restriction for links

to be in same scheme is based on physical carrier sensing

(PCS) at transmitter. There is no SNIR threshold at

physical level which restrict simultaneous transmissions.

RTS/CTS is considered to be switched off.

PCS threshold is used to evaluate whether transmissions

may happen simultaneously. Additional restriction is that

nodes may not receive and transmit at the same time.

Transmission scheme contain all possible link

combinations formed in such way that interference level PI

which is sensed in any of transmitters belonging to scheme

is less than PCS threshold (PPCST). Also ambient noise Pn

is considered. Condition is expressed as (PI+Pn)< PPCST.

E. Restrictions of the method

Uniform capacity is possible only theoretically at

optimal time schedule. Such can be provided by centrally

coordinated MAC protocol. In IEEE802.11 ad-hoc

network nodes access channel in random manner which

also means non-optimal scheduling. Despite this fact,

results obtained by the method can be used as a best case

scenario to aim. It is expected that comparing different

path sets, one with better theoretical performance should

perform better also in real network.

When forming transmission schemes, all allowable links

must be included, although real life scenario may allow

partial scheme. One should take into account worst case

scenario which is very likely to happen because of

continuous video stream. There won’t be idle nodes in the

paths.

Also it is assumed that nodes in their time slot transmit

continuously. It means that nodes should always have data

in buffer which without hesitation are forwarded. It

doesn’t conflict with multi-path video transmission where

full path capacity usually is used.

F. MATLAB tool for capacity evaluation

Improved method for evaluation of network capacity

has been implemented in MATLAB tool using source code

published by authors of [6]. MATLAB tool includes

wireless ad-hoc network, multi-path routing, CSMA/CA

and data transmission models and allows to evaluate path

capacity for many random scenarios. Current

implementation allows only static scenarios. Different

input parameters can be changed: physical carrier sense

threshold, background noise, transmission distance, field

size, number of nodes, directivity of antennas etc. In such

way different features of multi-path transmission can be

verified. Additional information about the tool in [8].

III. EVALUATING MULTI-PATH TRANSMISSION

This chapter presents an application of the method to

evaluate inter-path distance effect on aggregated path

capacity. First, the inter-path distance itself must be

defined. It is not simple task since distance could be

measured between any two nodes belonging to different

paths but not all pair’s gives reasonable result. I propose to

characterize the distance by the area occupied by whole

path set (Fig.3).

Fig.3. Inter-path distance expressed as convex hull

Mathematically it is expressed as convex hull of node

coordinates in 2D plain. Unfortunately such approach

doesn’t allow distance evaluation of internal paths (such

that reside between outer). Therefore initial studies are

done only with two-path sets.

The MATLAB tool described in the previous chapter is

used to analyze random two-path scenarios. Square field

size was gradually increased and it was tried to find two-

paths sets between randomly chosen source-destination

pair. Only node disjoint and not crossing paths were

chosen. Table 1 summarizes the main simulation

parameters. TABLE 1: SIMULATION PARAMETERS

Parameter Value

Field size 1000x1000m-2500x2500m

Number of scenarios 30563

Number of nodes 45 – 282

Ptx 0.1 W (20 dBm)

PPCST 3.8e-011 W (~500 m)

Pnoise 8∙10-14

W (-101 dBm)

Radio propagation model Free space

Transmission distance 250 m

Carrier frequency 2.45 Ghz

In Fig.4 path set capacity dependence on inter-path

distance (expressed as convex hull area) is presented.

Convex hull area depends not only on inter-paths distance

but also on direct distance between end-points (arrow in

Fig.3). Therefore average capacity for different ranges of

distance between source and destination nodes is given.

Least square linear regression was applied to fit scattered

results (dots). Each dot represents capacity for a scenario.

Additionally confidence interval for each regression line is

given.

Fig.4. Capacity dependence on inter-path distance for different

source-destination distances

The main conclusion from this simulation is that there is

no significant impact to aggregated capacity if inter-path

distance increases. These results contradict to assumption,

that disjoining paths improves performance because of

more effective spatial reuse. One of hypotheses for a slight

increase is a fact that greater inter-path distance requires

more nodes to be involved. As it was proven in [4],

capacity falls asymptotically as

√ .

The same results has been examined to find out if inter-

path distance is relevant if node number in paths set

doesn’t change a lot. In Fig. 5 capacity dependence on

inter-path distance for similar node quantity is given.

Fig. 5. Capacity dependence on inter-path distance for similar

number of nodes

Much higher correlation between capacity and inter-

path distance can be observed. These results are consistent

with the research done in [5] where node disjointness was

achieved by separating paths while keeping node number

in path constant.

CONCLUSIONS

Improved method for evaluation of multi-path

transmission capacity in wireless ad-hoc network under

CSMA/CA protocol has been presented. Although it has

several idealizations and limitations, still it is applicable to

gain basic guidelines for optimal path selection. In future a

use of more complex radio propagation models is planned.

MATLAB tool has been developed for implementation

of the method. First results using MATLAB tool reveal

that there is no significant increase in path capacity if

paths are more distant since it requires more nodes to be

involved. Aggregated capacity is influenced by

combination of both factors.

REFERENCES

[1] J. G. Apostolopoulos and M. D. Trott, “Path diversity for enhanced media streaming," IEEE Communications Magazine, vol. 42, no. 8,

pp. 80-87, 2004.

[2] K. Kuladinithi, C. An, A. Timm-Giel, and C. Görg, “Performance evaluation of radio disjoint multipath routing,” European

Transactions on Telecommunications, 20 (7), pp. 668-678, 2009.

[3] L. Cikovskis, and I. Slaidins, "Analysis of wireless ad-hoc network

parameters for efficient multipath video transmission," Second

International Conference on Digital Information Processing and

Communications (ICDIPC), pp.16-21, 10-12 July 2012 [4] P. Gupta, and P.R. Kumar, “The capacity of wireless networks,”

IEEE Transactions on Information Theory, 46 (2), pp. 388-404,

2000. [5] K. Jain, J. Padhye, V.N. Padmanabhan, and L. Qiu, “Impact Of

Interference On Multi-hop Wireless Network Performance,”

Proceedings of the Annual International Conference on Mobile Computing and Networking, MOBICOM, pp. 66-80, 2003.

[6] S. Toumpis, and A. Goldsmith, “Capacity regions for wireless ad

hoc networks,” IEEE Transactions on Wireless Communications, 2 (4), pp. 736-748, 2003.

[7] A. Goldsmith, Wireless Communications, New York: Cambridge

University Press, 2005 [8] L.Cikovskis, “Research notes,” September 2013. [Online].

Available: https://sites.google.com/site/researchwirelessnetworks/

[Accessed: Sep. 2013].

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 106

0.5

0.6

0.7

0.8

0.9

1

1.1

Convex hull area, m2

Agre

gate

d c

apacity, M

bps

Nr.1; paths=2; CS=500;

999<s-d distance<=1776

1776<s-d distance<=2553

2553<s-d distance<=3330

0.5 1 1.5 2 2.5 3 3.5 4

x 106

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Convex hull area, m2

Agre

gate

d c

apacity, M

bps

Nr. 1; Paths=2, 999<distance<=3330; Cs=500

10<nodes<=19

19<nodes<=27

27<nodes<=36

36<nodes<=44