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Cooperative Coverage Extension in Vehicular Land

Mobile Satellite Networks

Giuseppe Cocco‡, Nader Alagha∗and Christian Ibars†

‡German Aerospace Center (DLR), Weßling, Germany

∗European Space Agency, Noordwijk, The Netherlands

†Intel Corporation, Santa Clara, CA, USA

giuseppe.cocco@dlr.de, nader.alagha@esa.int, christian.ibars.casas@intel.com

Abstract—We study the application of random linear network

coding (RLNC) forcooperative coverage extension in land mobile

satellite (LMS) vehicular networks. We perform an analytical

assessment of the limits of cooperation in the presence of both a

satellite and a terrestrial repeater (gap-ﬁller). Using the Max-ﬂow

Min-cut theorem we derive exact expressions as well as closed-

form lower bounds on the coverage in a setup of practical interest.

Furthermore, we propose a practical implementation of the

RLNC cooperative approach for the Digital Video Broadcasting

- Satellite services to Handheld (DVB-SH) standard. We evaluate

numerically the performance of the proposed protocol using

a simulator based on physical layer abstraction and widely

adopted propagation channel models for both the satellite and

the terrestrial segments. Our simulation results show that the

proposed scheme extends the coverage with respect to a system

in which simple cooperative relaying is used, making a more

efﬁcient use of the terrestrial channel resources. Additionally,

the proposed solution can help keeping a relatively low outage

probability while limiting the number of required gap-ﬁllers.

I. INTRODUCTION

In the last decade several proprietary solutions as well as

open standards have been developed to enable data broad-

casting via satellite to mobile users. An example of a recent

open standard is the Digital Video Broadcasting - Satellite

services to Handheld (DVB-SH) [1]. Satellite broadcast and

relaying capabilities give rise to the possibility of creating

mobile broadcast systems over wide geographical areas, which

opens large market opportunities for both handheld and ve-

hicular user terminals. Mobile broadcasting is of paramount

importance for services such as digital TV or Machine to Ma-

chine (M2M) communication, a new communication paradigm

which will bring about a tremendous increase in the number

of deployed wireless terminals [2].

The possibility for all nodes to correctly receive the data

transmitted by a central node (e.g., a satellite or a base

station), denoted here as system coverage, is a main issue for

networks with a large number of terminals. As an example,

such system could be used for navigation maps update in

vehicle-mounted positioning systems or for terminal software

and ﬁrmware update in M2M networks, where reliable broad-

cast transmission is of primary importance. Protocols such as

Copyright (c) 2015 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

Giuseppe Cocco was partially supported by the European Space Agency under

the Networking/Partnering Initiative.

Automatic Repeat reQuest (ARQ), although very effective in

point-to-point communication (see, e.g., [3, section 7.1.5]),

may not be applicable in multicast contexts; there may be

many retransmission requests by the terminals in case of

packets losses, which would saturate the return channel and

overwhelm the source [4]. A cooperative approach may be

applied in heterogeneous networks [2], in which terminals are

equipped with both a long range (i.e., satellite reception) and

a short range communication air interfaces.

A lot of work has been done on the use of cooperation [5]

in multicast and broadcast communications in both terrestrial

[6][7] and satellite networks [8][9][10]. Many of the proposed

solutions [4][11][12], particularly in terrestrial networks, are

based on network coding (NC) [13], that can achieve the Max-

ﬂow Min-cut capacity in ad-hoc networks. Cooperative content

dissemination from road side units to vehicular networks

based on rateless codes has also been studied in [14] and

[15]. Physical layer strategies for cooperative relaying in land

mobile satellite (LMS) networks have been studied in [16],

[17] and [18].

In the present paper we study the application of network

coding for cooperative satellite coverage extension in LMS

systems. Our solution does not require any modiﬁcation to

the the physical and the data link layers of existing standards

for LMS and vehicle-to-vehicle (V2V) communications. This

makes our approach different from those in [16], [17] and

[18]. In the solution we present, the LMS and the V2V

terminals, co-located in the vehicles, exchange information at

an intermediate level between the data link and the network

layer. We study the advantages of the propose approach at

system level.

The present work extends and consolidates the preliminary

results we presented in [19] and [20] by including the presence

of terrestrial repeaters, also called gap-ﬁllers, in both the

analytical and the numerical analyses. In particular, we extend

the results of [19] by building up an end-to-end system model

which is inspired by the Digital Video Broadcasting - Satellite

services to Handheld (DVB-SH) [1] standard. In this model

the same information is transmitted by the satellite and the

terrestrial repeaters, and combined at the physical layer by

the user terminal. The network of gap-ﬁllers constitutes the

complementary ground component (CGC) and is meant to

provide coverage to areas where the signal received from

the satellite suffers from shadowing caused, for example, by

tall buildings. It should be noted that the combination of the

2

signals from satellite and CGC is already foreseen in DVB-

SH [1]. We model the network as a directed graph. The joint

effect of the satellite and the gap-ﬁller are taken into account

through the statistics of the link between the source and each

terminal. By applying the Max-ﬂow Min-cut theorem [4] and

assuming Gaussian signalling under the hypothesis of block

fading channels, we derive an exact expression of the outage

probability as well as a closed-form lower bound expression

for the case in which either the link from the satellite or from

the gap-ﬁller suffers strong fading.

We support and complement our theoretical study with a

numerical analysis based on a simulator we developed. The

enhancements with respect to [20] are:

•the inclusion of a gap-ﬁller,

•the implementation of the physical layer of IEEE 802.11p

standard [21] 1,

•the use of widely adopted channel models to generate the

time series for the terrestrial channels [22] 2,

•the implementation of the physical layer combining of the

signals received from satellite and CGC at the terminal

nodes and the Raptor encoder/decoder as described in the

DVB-SH-B standard [23].

The simulator interface between the physical channel and

the protocol stack at higher layers leverages on physical

layer abstraction (PLA) [24] [25], which has been adopted

in the standardization process of the IEEE 802.16 standard

[26]. Several works [27] [28] showed that PLA allows to

evaluate the link level performance of a communication

system in a computationally affordable manner and with a

good accuracy. Our simulation results show that the proposed

scheme extends the coverage with respect to a system

where cooperation among vehicular terminals is implemented

through simple relaying. The results also suggest that the

cooperative approach can help to decrease the system outage

probability while limiting the number of required gap-ﬁllers

in areas with challenging propagation conditions such as

urban environments.

The rest of the paper is organized as follows. In Section

II the system model is described. In Section III we study the

non cooperative and the cooperative cases from a theoretical

perspective deriving analytical expressions for the coverage

in both setups. In Section IV we introduce the DVB-SH

standard. This is used as the reference baseline in Section V,

where a practical implementation of the cooperative approach

is described. The proposed scheme implements the cooperative

approach described in Section III-B within the limits of

existing standards. In Section VI we describe the adopted

simulation approach and the simulation setup, while in Section

VII we present the numerical results. Finally, Section VIII

contains the conclusions.

II. SYSTEM MODEL

A network is considered in which a source (S) has a set of

Ksource messages w1,...,wKof kbits each, to broadcast

1Modulation, channel code and a simpliﬁed version of the channel access

mechanism.

2Both vehicle-to-vehicle and gap-ﬁller-to-vehicle.

to a population of Mterminal nodes (or user terminals). The

set of Ksource messages is represents a generation. Each

user terminal is assumed to have both satellite reception (one-

way communication) as well as short range communication

(two-way, half duplex) capabilities. The source Sdelivers the

data to the terminals through two relay nodes S1and S2and

there is no direct link between Sand any of the terminals.

The links between Sand Si,i= 1,2, are assumed to be

lossless 3.S1and S2relay the data to the terminal nodes

through orthogonal lossy wireless channels. With reference to

DVB-SH-B, S1models a transparent satellite while S2models

a gap-ﬁller. The orthogonality is achieved in the frequency

domain by allocating two disjoint frequency bands for the

satellite and the gap-ﬁllers. No feedback from the terminals or

channel state information at the transmitter (CSIT) is assumed

at S,S1and S2, which implies a non-zero probability of

packet loss. S1and S2protect each message using the same

channel code (i.e., they transmit exactly the same signal) in

order to decrease the probability of packet loss on the channel.

A second level of protection is applied by Sat packet level

in order to compensate for packet losses. The encoding at

packet level takes place before the channel code is applied.

N≥Kcoded packets are created by Sapplying a random

linear network code (RLNC) to the Ksource messages. We

deﬁne R=K/N as the rate of the NC encoder at S. Network

coding operates in a ﬁnite ﬁeld of size q(GF (q)), so that each

message is treated as a vector of k/ log2(q)symbols. Source

messages are linearly combined to produce encoded packets.

An encoded packet xis generated as follows:

x=

K

X

i=1

̺iwi,

where ̺i,i= 1,...,K are random coefﬁcients drawn ac-

cording to a uniform distribution in GF (q). The coefﬁcients

̺i,i= 1,...,K, are appended to each message xbefore its

transmission. The set of appended coefﬁcients represents the

coordinates of the encoded message xin GF (q)with respect

to the basis {wi},i= 1,...,K, and is called global encoding

vector.

The encoding at the physical layer is applied by S1and

S2to network-encoded packets, each consisting of of kbits.

S1and S2encode each packet using the same Gaussian

codebook of size 2nr, with r=k

nbits per channel use

(bpcu), associating a codeword cmof ni.i.d. symbols drawn

according to a Gaussian distribution to each xm,m= 1 ...,N

[3]. The time needed for S1and S2to transmit a packet is

called transmission slot (TS). Transmissions are synchronized

in time such that symbols from the two orthogonal channels

3In DVB-SH data is transmitted to the satellite through a high-throughput

and highly reliable feeder link, while the distribution to the CGC network

can take place either through a highly reliable satellite link or a terrestrial

distribution network. Due to their high reliability such links are assumed as

ideal, i.e., no packet loss occurs in the distribution network.

3

are aligned at the receiver 4.

S

1

N

2

N

1

N

2

N

S

Fig. 1. Example of the physical network under study (left) and the corre-

sponding graph representation (right).

The signals from S1and S2are combined by each terminal

at the physical layer using maximal-ratio combining (MRC).

In MRC received signals are weighted using coefﬁcients that

depend on the signal’s phase and amplitude and such that the

SNR of the combined signal is the sum of the SNRs of the

two received signals. Further details on the implementations

of the MRC in the DVB-SH standard can be found in [1].

Terminals cooperate in order to recover the packets that are

lost in the link from the transmitters. We assume terminals

with high mobility 5, so that nodes have little time to set

up connections with each other. For this, and in order to

exploit the broadcast nature of the wireless medium, nodes

act in promiscuous mode, broadcasting packets to all terminals

within reach. Similarly as in the broadcast mode of IEEE

802.11p standard, no request to send (RTS)/clear to send

(CTS) mechanism is assumed [29]. No CSIT is assumed at

the transmitting terminal in the terrestrial communication, so

that there is a non-zero probability of packet loss. Unlike in

802.11p, each terminal uses two levels of encoding, one at

the packet level and one at the physical level. The encoding

procedure is detailed in the following.

Let Lbe the number of packets correctly decoded at the

physical level by a terminal, received either through the satel-

lite or the short range communication interface. The terminal

selects the L′≤Lpackets which constitute the largest set

of linearly independent packets with respect to the basis wi,

i= 1,...,K. Without loss of generality we assume that

such set be x1,...,xL′. Linear independence can be veriﬁed

through the global encoding vectors of the packets. The L′

selected packets are re-encoded together using RLNC, and

then re-encoded at the physical layer. RLNC encoding at the

terminals works as follows. Given the set of received packets

x1,...,xL′, the message y=PL′

m=1 σmxmis generated, σm,

m= 1,...,L′, being coefﬁcients drawn at random according

to a uniform distribution in GF (q). Each time a new encoded

message is created, it is appended its global encoding vector.

4This is actually the case in DVB-SH-B, where synchronization is kept

between the satellite and the CGC such that symbol-level alignment can be

achieved at the user terminals in case the same code rates and puncturing

patterns are used in the two channels [1]. The different propagation delays

from the CGC to terminals at different distances are compensated by the guard

interval (GI) of the OFDM modulation used in the terrestrial segment.

5For instance, this is the case of vehicular networks.

The overhead this generates is negligible if messages are

sufﬁciently long [30]. The new global encoding vector ηcan

be easily calculated by the transmitting node as follows:

η=σenΨ,

where σen = [σ1··· σL′]is the local encoding vector, i.e.,

the vector of random coefﬁcients chosen by the transmitting

node, while Ψis an L′×Kmatrix that has the global encoding

vector of xm,m= 1,...,L′, as row m. We assume that the

transmission of a message by a terminal is completed within

one TS. The physical layer encoding at a mobile node takes

place in the same way as at the source, and using the same

average transmission rate r. The scenario just described is

depicted in Fig. 1.

A. Source-to-Node Channel Model

An urban environment is considered. We assume that chan-

nels from S1and S2to a given terminal Ni(SjNchannel,

j= 1,2) are affected by both Rayleigh fading and log-normal

shadowing. The two channels are assumed to be statistically

independent. The power of the signal received at the terminal

from Sj,j= 1,2, is modeled as the product of a unit-mean

exponential random variable (r.v.) γjand a log-normal r.v.

ΓSj. This model has been largely used to model propagation

in urban scenarios [31] and, with some modiﬁcations, in LMS

systems [32]. The fading coefﬁcient γjtakes into account

the fast channel variations due to the terminal motion. We

deﬁne a channel block as the time interval during which the

channel variation can be considered to be negligible. The

channel is assumed to remain constant within a channel block,

while changing in an i.i.d. fashion at the end of it. For

mathematical tractability we assume that the channel block

and the transmission slot have the same duration, i.e., the

time needed for Sto transmit a message coincides with the

coherence time of the terrestrial channel. Such simpliﬁcations

will be later removed when addressing the simulation part. The

shadowing coefﬁcient ΓSjincludes the transmitted power at Sj

and accounts for path loss and obstruction caused by buildings

in the line of sight and changes much slowly with respect to γj.

We assume that ΓSjremains constant for Ntransmission slots,

i.e., until all Npackets relative to a given generation have

been transmitted by S. We call the time needed to transmit N

messages a generation period (GP). The fading and shadowing

processes of two different nodes and between the two different

channels are assumed to be independent. We study the case of

groups of terminals close enough to each other so that short-

range communication can be used. We also assume that nodes

are relatively far away from the gap-ﬁller 6. The case of nodes

close to the gap-ﬁller is not explicitly considered, since such

nodes have good coverage with high probability and thus do

not constitute an issue. However, the mathematical results we

derive implicitly take this case into account.

Due to the lack of CSIT there is a non-zero probability that a

message is not correctly decoded at each of the terminal nodes.

This happens if the instantaneous channel capacity, assuming

6Under these assumptions the hypothesis of equal channel statistics across

nodes can be regarded as a good approximation.

4

maximal-ratio combining, is lower than the transmission rate

at the physical layer r. For ease of exposition we will refer to

such equivalent channel as the SN channel. Assuming the same

channel statistics for all nodes, the packet loss probability in

the SN channel for any given node is:

PSN =P r {log2(1 + γ1ΓS1+γ2ΓS2)< r},(1)

where γj∼exp(1) while ΓSj=eXj

10 , for j= 1,2, with Xj∼

N(µj, σ2

j).ΓSjis constant within a GP, while γjchanges

independently at the end of each channel block. Fixing the

values of ΓS1and ΓS2, the two random variables γ′

1=γ1ΓS1

and γ′

2=γ2ΓS2are exponentially distributed with parameters

1/ΓS1and 1/ΓS2, respectively. Using the fact that the sum

γ′

1+γ′

2in Eqn. (1) has a hypoexponential distribution with

parameters 1/ΓS1and 1/ΓS2, we ﬁnd the expression for the

packet loss probability PS N in the SN channel:

PSN = 1 −ΓS1

ΓS1−ΓS2

e−2r−1

ΓS1+ΓS2

ΓS1−ΓS2

e−2r−1

ΓS2.(2)

With reference to Fig. 1, the effect of the links from S1

and S2in the physical network is taken into account in the

SN link of the graph model by means of the packet loss

ratio given by Eqn. (2). In the rest of the paper we will use

the expressions “packet loss ratio” and “probability of packet

loss” interchangeably. Due to shadowing, ΓS1and ΓS2change

randomly and independently at each generation period and,

within a generation, from one node to the other. Thus the

packet loss ratio PSN is also a r.v. that remains constant within

a generation and changes in an i.i.d. fashion across generations

and terminals.

B. Node-to-Node Channel Model

We model the channels between the transmitting terminal

and each of the receiving terminals (NN channel) as indepen-

dent block fading channels, i.e., the fading coefﬁcient of each

channel changes in an i.i.d. fashion at the end of each channel

block. The probability of packet loss in the NN channel PN N

is:

PNN =P r {log2(1 + γΓN)< r}= 1 −e1−2r

ΓN,(3)

where ΓNaccounts for path loss and transmitted power, and is

assumed to remain constant for a whole generation period and

across terminals. In order not to saturate the terrestrial channel,

we assume that a node can transmit at most one packet within

one TS.

Note that expression (2) has been derived assuming that the

same information is transmitted over both the satellite (S1)

and the gap-ﬁller (S2) links and the two signals are combined

by the terminal nodes at the physical level. Since (3) grasps

the effect of both links it allows to simplify the equivalent

network topology by removing the intermediate nodes S1and

S2as shown in the example of Fig. 1.

III. COVERAGE ANALYSIS

A. Non-Cooperative Coverage

Let us consider a network with a source Sand Mter-

minals. We deﬁne the coverage (Ω) as the probability that

all Mterminals correctly decode the whole set of Ksource

messages. Assuming that Kis large enough, and using the

results in [4], the probability that a given node Nican decode

all the Ksource messages of a given generation in case of no

cooperation is:

P r {PS Ni<1−R},(4)

R=K/N being the rate of the NC encoder at S. We

recall that, due to shadowing, the packet loss ratio PSNiis

a r.v. which changes in an i.i.d. fashion across generations

and terminals. The coverage is the probability that each of the

nodes decodes all source messages, that is:

Ω = P r {PS N1<1−R,...,PSNM<1−R},(5)

where PSNiis the packet loss ratio in the SN link of node

Ni,i= 1,...,M. Under the assumption of i.i.d. channels we

have FPSNi=FPSN ,∀i∈ {1,...,M}. Thus, using Eqn. (2),

we can rewrite Eqn. (5) as:

Ω = (P r {PS N <1−R})M

=

P r

1−ΓS1e−2r−1

ΓS1

ΓS1−ΓS2

+ΓS2e−2r−1

ΓS2

ΓS1−ΓS2

<1−R

M

=

P r

ΓS1

ΓS1−ΓS2

e−2r−1

ΓS1−ΓS2e−2r−1

ΓS2

ΓS1−ΓS2

> R

M

.

(6)

Finding a closed form expression for Eqn. (6) for the general

case is a challenging task since ΓS1and ΓS2are lognormal

random variables with parameters (µ1, σ1)and (µ2, σ2),

respectively. However, in Theorem 1 we derive a closed form

expression in case either µ1→ ∞ or µ2→ ∞. Note that

these are cases of practical interest since they correspond to

a situation in which either the signal from the satellite or

that from the gap-ﬁller are faintly weak, which is the case of

dense urban areas and rural areas, respectively.

Theorem 1: Theorem 1: For any non-zero ǫµ,ǫσiand ǫσj

if 0< ǫµ< µi<∞,0< ǫσi< σi<∞,0< ǫσj< σj<∞,

i6=j, then

lim

µj→−∞ P r ΓS1

ΓS1−ΓS2

e−2r−1

ΓS1−ΓS2

ΓS1−ΓS2

e−2r−1

ΓS2> R

=1

2−1

2erf

10 ln h1−2r

ln(R)i−µi

2σ2

i

(7)

Proof See the Appendix.

Note that, ﬁxing Rand M, the expression in Eqn. (7)

goes to 0as the rate at physical level rgoes to inﬁnity.

This conﬁrms the intuition according to which in the non-

cooperative case the coverage decreases as the transmission

rate increases. As said previously, this result holds for any

value of qas long as Kis large enough. Thus, Eqn. (7) can

also be interpreted as the coverage in a network of Mnodes

5

in presence of fading and shadowing that can be achieved for

a rate couple (r, R)by a fountain code such as, e.g., a Raptor

code.

B. Cooperative Coverage

The wireless network is modeled as a directed hypergraph

H= (N,A),Nbeing a set of nodes and Aa set of hyperarcs.

A hyperarc is a pair (i, J ), where iis the head node of the

hyperarc while Jis the subset of Nconnected to the head

through the hyperarc. Jis also called tail. A hyperarc (i, J )

can be used to model a broadcast transmission from node i

to nodes in J. We want to study the relationship between the

coverage and the rate at which the information is transferred to

mobile terminals, which depends on both the rate at physical

level rand the rate at which new messages are injected in the

network, which is the rate at packet level R. In [4] (Theorem

2) it is shown that, if Kis large, random linear network

coding achieves the network capacity in wireless multicast

connections, even in case of lossy links, if the number of

innovative packets transmitted by the source per unit of time

is lower than or equal to the ﬂow across the minimum ﬂow

cut between the source and each of the sink nodes, i.e.:

R≤min

Q∈Q(S,t)

X

(i,J)∈Γ+(Q)X

T*Q

ziJT

,(8)

where ziJT is the average injection rate of packets in the arcs

departing from ito the tail subset T⊂J,Q(S, t)is the set

of all cuts between Sand t, and Γ+(Q)denotes the set of

forward hyperarcs of the cut Q, i.e.:

Γ+(Q) = {(i, J )∈ A|i∈Q, J \Q6= 0}.(9)

In other words, Γ+(Q)denotes the set of arcs of Qfor which

the head node is on the same side as the source, while at least

one of the tail nodes of the relative hyperarc belongs to the

other side of the cut. The rate ziJT is deﬁned as:

ziJT = lim

τ→∞

AiJT (τ)

τ,(10)

where AiJT (τ)is the counting process of the packets sent by

ithat arrive in T⊂Jin the temporal interval [0, τ ). The

existence of an average rate is a necessary condition for the

applicability of the results in [4]. In the following we derive

ziJT for the considered network setup as a function of both

physical layer and MAC layer parameters such as transmission

rate, transmission power and medium access probability.

C. Medium Access in the Terrestrial Channel

Let us consider a network with Mterminal nodes. We

assume that all nodes have independent SN and NN channels.

We further assume that channel statistics are the same for all

terminals, which is the case if the distances from node Nito

node Njchange little ∀i, j ∈ {1, . . . , M },i6=jand with

respect to each node’s distance to the source.

In our setup the terminals are set in promiscuous mode so

that each node can receive the broadcast transmissions of any

other node within communication range [29]. The terminals

share the wireless medium, i.e., they transmit in the same

frequency band. We assume that an ideal CSMA/CA protocol

is adopted by the nodes and that all nodes hear each other,

so that the medium is shared among the terminals willing

to transmit but no collision happens. The communication

rate ziJT has been derived in [19] and has the following

expression:

ziJT =1−(1 −pa)M

Mh1−(PNN )|T|i,(11)

where |T|is the cardinality of T, and the term 1−(PN N )|T|

is the probability that at least one of the |T|nodes whose S-

link belongs to the cut receives correctly a transmission from

a node that is in the other side of the cut. We do not report

here the derivation for a matter of space. Note that expression

(11) represents the rate at which packet are received by the

subset of terminals Tconsidered as a single node, that is, the

counting process AiJ T (τ)increases of one unit when at least

one of the terminals in Treceives one packet, independently

from how many terminals receive it.

D. Coverage Derivation

In the following we derive an expression for the maximum

coverage as a function of relevant network parameters by

applying the Max-ﬂow Min-cut theorem. We recall that such

maximum coverage can be attained by using the random

coding scheme described in Section II.

Let us consider Eqn. (8). For each of the Mnodes we must

consider all the possible cuts of the network such that the

considered node and the source are on different sides of the

cut. We recall that a cut is a set of edges that, if removed

from a graph, separates the source from the destination. Fig. 2

gives an example of a network with four nodes where the cut

QSN4(i.e., the cut such that N4and Sare on the same side)

is put into evidence. In the example we consider Nt=N1

as the destination node. The dashed black lines represent the

edges which are to be removed to get the cut. Note that the

set of nodes that receive from S(only node N4in the ﬁgure)

are isolated by the cut from the nodes with satellite cut (nodes

N1,N2and N3in Fig. 2). We deﬁne an S-edge as an edge

of the kind (S, Nj), j 6=t. We further deﬁne a T-edge as one

of the kind: (Nj, Nt), j 6=t. Unlike in [19], here each S-edge

incorporates the effect of the availability of two different paths

for the signal transmitted by Sthrough S1and S2and the fact

that the signals are combined at the physical level. This is

reﬂected by the lower packet loss ratio within each generation

which is given by Eqn. (2). As mentioned in Section II this

does not change the equivalent graph representation of the

network. Hence the derivation of the coverage carried out in

[19] is still formally valid. Thus the expression of the coverage

is given by Eqn. (12) [19], where Yj=PSN j is a r.v.

representing the packet loss ratio within a generation for node

Nj,Qnsis one of the cuts with nssatellite links relative to

the node Nt,

α(ns) = 1 −R+ (M−ns)1−(1 −pa)M

M[1 −(PNN )ns],

(13)

6

S

1

N4

N

2

N3

N

4

SN

Q

Fig. 2. Graph model for a network with four terminals. There are 2M−1= 8

possible cuts for each of the Mnodes. The set of nodes that receive from

S(only node N4in the ﬁgure) are isolated by the cut from the nodes with

satellite cut.

while S(ns,Nt)is the set of subsets of N \ Ntwith ns

elements, N \Ntbeing a set including all nodes except Nt.

Although formally equivalent, Eqn. (12) differs from that in

[19] in the Yvariables, that in this case take the form given

in Eqn. (2).

E. Lower Bound on Achievable Coverage

Finding a simple closed form expression for Eqn. (12) is

a challenging task. Thus in the following we derive a lower

bound ΩLB on Ω.Ωcan be lower bounded as follows:

Ω = P r

\

Nt∈N \

ns∈{1,...,M}

\

Qns∈S(ns,Nt)

Y

j∈Qns

Yj< α(ns)

≥P r

\

Nt∈N \

ns∈{1,...,M}

ns

Y

j=1

Y(j)< α(ns)

(14)

≥P r

\

Nt∈N \

ns∈{1,...,M}hYns

(1) < α(ns)i

(15)

=P r

\

Nt∈N \

ns∈{1,...,M}hY(1) <ns

pα(ns)i

=P r Y(1) <min

ns∈{1,...,M}

ns

pα(ns)

=

P r

ΓS1e−2r−1

ΓS1

ΓS1−ΓS2

−ΓS2e−2r−1

ΓS2

ΓS1−ΓS2

> β

M

,(16)

where Y(i)is the i-th largest packet loss ratio across all S-

edges of the network, i.e., Y(i)≥Y(j)if i < j, ∀i, j ∈ N , and

we deﬁned

β= min

ns∈{1,...,M}

ns

pα(ns).(17)

Inequality (14) derives from the fact that:

Y

j∈S

Yj≤

ns

Y

j=1

Y(j),for S∈ S(ns,t),∀ns, t, (18)

i.e., we substitute the product of nsrandom variables, chosen

within a set of Mvariables, with the product of the nslargest

variables of the same set. Inequality (15) follows from the fact

that

ns

Y

j=1

Y(j)≤Yns

(1) ,∀ns, t. (19)

Expression (14) can be further simpliﬁed in case one between

the satellite link and the terrestrial link is strongly degraded.

Using the result of Theorem 1 we ﬁnd:

lim

µj→−∞ ΩLB =1

2M

1−erf

10 ln h1−2r

ln(1−β)i−µi

2σ2

i

M

,

(20)

where j= 1 or j= 2 if the degraded link is the one from the

satellite or from the gap-ﬁller, respectively.

Ω = P r

\

Nt∈N \

ns∈{1,...,M−1}\

Qns∈S(ns,Nt)

Y

j∈Qns

Yj<1−R+ (M−ns)1−(1 −pa)M

M[1 −(PNN )ns]

.(12)

7

IV. COOPERATIVE COVERAGE EXTENSION IN DVB-SH

In the following we propose a practical scheme that im-

plements the cooperative approach described in the previous

section in heterogeneous satellite vehicular networks.

A. Space Segment

1) Satellite Channel: The considered setup is an LMS

system with a GEO satellite broadcasting a DVB-SH-B (time-

division multiplexing (TDM) waveform from satellite and

OFDM from the gap-ﬁllers) signal to a population of mobile

terminals. Propagation conditions change due mainly to the

shadowing effect of building and trees and are classiﬁed in

urban, suburban and rural. The main cause of channel impair-

ment in urban and suburban environments is the long-lasting

shadowing of the buildings that causes an intermittent satellite

connectivity, while in the rural propagation scenarios the main

source of impairment is tree shadowing. Signal reception in

LMS systems is limited by three phenomena, namely path loss

at large scale, shadowing at mid-scale and multipath fading at

small scale. We adopt the Perez-Fontan (LMS) channel model

[33], based on a three-state Markov chain in which the possible

states represent line of sight reception, moderate shadowing

reception and deep shadowing reception.

2) Channel Impairment Countermeasures in DVB-SH: In

the following we recall the channel impairment countermea-

sures foreseen in the DVB-SH standard.

a) Physical Layer: The physical layer error protection

scheme of the DVB-SH standard consists of a turbo code with

different rates/word lengths, a bit interleaver, which works

at bit level within a turbo codeword and a time interleaver,

the depth of which spans more than one codeword and uses

interleaving blocks of 126 bits each. This last element is partic-

ularly important to counteract long blockage periods, as it can

span time intervals of up to about 10 seconds. The drawbacks

in using a long time interleaver are the large decoding delay

and the memory requirements at mobile terminals, which can

be met only by high class user terminals.

b) MPE-IFEC in DVB-SH: The MPE-IFEC is a process

section between the IP and the transport layers introduced in

DVB-SH in order to counteract long lasting shadowing which

is typical of LMS channels. The encoding is made over several

datagram bursts, i.e., groups of datagrams. Two different kinds

of code are envisaged in the standard, namely Raptor codes

and Reed-Solomon codes [34]. The Raptor code adopted for

the DVB-SH is the same as in the 3GPP standard, which has

also been adopted in the DVB-Handheld (DVB-H) standard

[1]. In this paper we only consider the solution based on the

Raptor code, as described in the following. We remind the

interested reader to reference [34] for details related to the

Reed-Solomon encoding process.

Let us consider a datagram burst entering the MPE-IFEC

process. The burst is reshaped in a matrix of Tby Kbytes

called Application Data Table (ADT). The Raptor code, always

systematic, is applied on the ADT producing a Tby Nrparity

matrix, called IFEC Data Table (iFDT). In Fig. 3 the ADT

matrix is shown (on the left) together with the iFDT (parity)

matrix (on the right). The reshaped datagrams composing the

ADT are also shown for sake of clarity. After the iFDT is

calculated, an IFEC burst is generated by taking groups of

columns from the iFDT. Each columns of the parity matrix is

a parity symbol called repair symbol. With reference to the

notation introduced in Section III, the rate of the Raptor code

is R=K

K+Nr(i.e., N=K+Nr).

Systematic and repair symbols are jointly referred to as

encoding symbols. Each symbol is identiﬁed by an Encoding

Symbol Identiﬁer (ESI). The encoding procedure consists in

the sequential application of a high rate low-density parity

check (LDPC) encoder, a binary reﬂected Gray encoder and a

Luby Transform (LT) encoder. Each of the encoding symbols

is transmitted together with its ESI and a triple (d, a, b)where

dis the symbol degree and aand bare integer numbers

related to the encoding procedure. The encoding symbol triple

together with the ESI and the value Kallows the decoder

to determine which source symbols were (linearly) combined

together to form a given encoding symbols. Further details on

the encoding procedure can be found in [35] 7. An IFEC burst

is made up of several IFEC sections. Each section is comprised

of a header, a payload containing gcolumns from the same

iFDT and a cyclic redundancy check (CRC). The k-th IFEC

burst is merged with the (k−E P )-th datagram burst (and

eventual MPE-FEC redundancy) to form a time-slice burst.

The time slice burst is then multiplexed on Moving Picture

Expert Group - Transport Stream 2(MPEG2-TS) frames and

passed down to lower layers.

Datagram 1

Datagram 1 (cont.) Datagram 2

Datagram 2 (cont.)

Datagram 2 (cont.) Datagram 3

Last datagram

Last datagram (cont.) Padding bytes

Padding bytes

K systematic symbols (columns)

T bytes

Repair symbol 1

Repair symbol 2

Repair symbol

repair symbols

Fig. 3. Reshaping of datagram bursts in an ADT (left) and parity matrix

(right) in case a Raptor code is used.

B. Ground Segment

1) Terminal Types: We consider high class terminals as

deﬁned in [23]. High class terminals are not energy constrained

and have relatively good computation capabilities and memory

[23]. This is the case of vehicular terminals, which are powered

by rechargeable batteries and can host computation units of

high speed, thanks to the relatively low impact in terms of

cost, space and weight. We assume that each terminal has both

satellite and short-range communication capabilities, which

7Note that a source block in [35] corresponds to an ADT and a source

symbol is a column of the ADT.

8

give rise to the possibility of implementing a vehicular ad-

hoc network.

2) Terrestrial Channel: In [36] a measurements campaign

made on the 5.9 GHz frequency is presented. The measure-

ments presented in [36] have been made using a Dedicated

Short Range Communication (DSRC)/IEEE 802.11p prototype

radio. In the paper a dual slope model for the path loss in

urban V2V scenarios is derived based on real measurements.

We adopt the model of [36] for the path loss together with

the TU6 multi-tap channel model [37]. An OFDM signal with

52 carriers (48 information carriers) and a rate 1/2convolu-

tional encoder are assumed. All physical layer parameters are

taken from the 802.11p standard. As usual practice in V2V

simulations, we assume a ﬁnite communication range which

is ﬁxed for all vehicles. Collisions are taken into account, as

they constitute an important throughput-limiting and delay-

increasing factors in ad-hoc wireless networks [38].

V. NETWORK-CODED COOPERATION FOR DVB-SH

The analysis carried out in Section III-B gives hints about

the advantages and the limits of cooperation in providing

missing coverage in mobile satellite networks. Although useful

to understand the effect of relevant system parameters such as

the number of nodes, the probability of accessing the terres-

trial channel and the physical layer channel statistics, many

other interacting factors are present in a real system. These

can not be accurately taken into account in a mathematical

way without incurring in a model which is overwhelmingly

complex. Among these factors are the speciﬁc communication

standards considered, that may lead to a gap with respect to

the theoretical performance derived in subsections III-A and

III-B. In particular, the interaction between the physical layer

of the considered standards and the propagation channel can

be quite complex. Such interaction gives rise to speciﬁc packet

loss patterns at the higher layers, where the throughput of the

system is measured. Apart from this, the changing terrestrial

network topology and connectivity, together with the imper-

fections in the medium access mechanism, further complicate

the picture. A possible implementation of the cooperative

approach described in the previous sections has been presented

in [20]. Such scheme, called Network-Coded Cooperative

Coverage Extension (NCCCE), has been designed such that

existing PHY layer communication standards do not need to

be modiﬁed. The main novelty with respect to [20] is the

enhancement in the simulator used to evaluate the performance

of the NCCCE protocol. Speciﬁcally, we included a gap-ﬁller,

implemented the physical layer of 802.11p standard 8, we used

widely adopted channel models to generate the time series

in the terrestrial channels (both vehicle-to-vehicle and gap-

ﬁller-to-vehicle) and included the physical layer combining of

the signals received from the satellite and the CGC at the

terminal nodes and the Raptor encoder according to DVB-

SH standard. All these features were not taken into account

in the preliminary simulation results presented in [20]. In the

following we describe the NCCCE protocol.

8Modulation, channel code and a simpliﬁed version of the channel access

mechanism.

Let us consider a satellite broadcasting a DVB-SH-B sig-

nal with MPE-IFEC protection to a population of vehicular

terminals with both DVB-SH-B and IEEE 802.11p radio

interfaces. During a time window (0, t)the satellite transmits

N=K+NrIFEC symbols generated starting from an

ADT. Terrestrial and satellite communications take place in

orthogonal frequency bands. Due to long-lasting shadowing

caused by urban propagation conditions, it can happen that a

user decodes less than Klinearly independent symbols during

the interval (0, t). In this case the user cannot decode the entire

source data block. In order to enhance satellite coverage each

node re-encodes the received packets (either received directly

from the satellite or from other terminals) and broadcasts

them to nodes within its transmission range. In Fig. 4 a block

diagram of the proposed cooperative method is shown. In the

MPE-IFEC

MPEG TS

DVB-SH

Transparent payload

MPE-IFEC

MPEG TS

DVB-SH

Network Coding

802.11p

MPE-IFEC

MPEG TS

DVB-SH

Network Coding

802.11p

Terminal #1 Terminal #2

Gateway

Satellite

Fig. 4. Block diagram of the proposed cooperative scheme for two cooperating

nodes. Red lines represent IFEC blocks ﬂowing from the satellite to the

terminal nodes while blue lines represent network coded packets exchanged

between nodes on the short range communication channel.

following sections we give further details on the proposed

NCCCE.

A. Encoding at Land Mobile Nodes

Let us assume that a node is able to decode some of the

encoding symbols directly from the satellite. Each symbol

carries an ESI and a triple (d, a, b). As described in subsection

IV-A2b the node can use this information to ﬁnd out which of

the source symbols were combined together to form a received

encoding symbol. We propose to apply a network encoding

scheme at land mobile nodes using the source symbols of

iFEC as source symbols of the network code. In other words,

nodes exchange linear combinations of encoding symbols in

some ﬁnite ﬁeld, with the aim of recovering all the source

symbols.

Each received encoding symbol is interpreted by a node as

a linear combination of source symbols with coefﬁcients 0or

1in GF (q). The node, then, applies the network encoding

procedure described in Section II. The encoding vector of the

received encoding symbol can be derived from symbol’s ESI

and triple (d, a, b).

9

The probability to access the channel in each slot is deter-

mined by the parameter cooperation level, ﬁxed for all nodes,

which we indicate with ζ,0≤ζ≤2. If ζ≤1, in each slot,

if a node stored a number of linearly independent packets

which is larger than the number of transmitted packets in the

current generation, it creates a linear combination of all the

stored packets as described in Section III-B and tries to access

the channel with probability ζ. If ζ > 1two cases must be

considered. In case the number of transmissions made by the

node is lower than the number of linearly independent packets

received, the node tries to access the channel with probability

pa= 1. If the node has a number of stored packets which is

lower than or equal to the number of those transmitted, instead,

it tries to access the channel with probability pa=ζ−1.

When a node receives a packet from another node, it checks

whether such packet and those previously stored are linearly

independent and, if this is the case, the new packet is stored.

Otherwise, it is discarded.

Another possible relaying choice is to have the nodes simply

forwarding the received symbols without combining them.

We call this scheme simple relaying (SR) and use it as a

benchmark. SR is described more in detail in Section VI.

B. Implementation Aspects

According to the DVB-SH standard we consider a source

symbol size of 1024 bytes each. Each source symbol is divided

into nss subsymbols of 1024

nss bytes. Each of these subsymbols

is multiplied by a randomly chosen coefﬁcient in a ﬁeld with

q= 2 1024

nss ×8elements. The coefﬁcient is the same for all

subsymbols within a symbol. In this way the complexity of

the network encoder/decoder can be kept at a reasonable level

[12]. A ﬁeld size of 28(one byte) may constitute a valid

choice. The NC is applied as in [12], appending the encoding

vector at the end of each packet. Thus, for a Ksymbols

generation, a ﬁeld with K×qbits is appended to each symbol.

The loss in spectral efﬁciency is then (Kq)/8192. Assuming

coefﬁcients of 1byte are used, the loss becomes K/1024.

In order to keep the loss at a reasonable value we should

limit the size of the generation. For instance, if generations

of K= 100 symbols are used, the loss is below 10%. The

adoption of small generation sizes has the drawback that the

code efﬁciency is reduced. For example, it is known that the

efﬁciency of the Raptor code increases with the source block.

There is, however, an advantage in terms of delay in using

small blocks. In Section VII we show the gap between the

asymptotic results obtained in Section III-B and the simulation

results obtained in the same setup but with the 3GPP Raptor

code, having ﬁnite block-length.

An important aspect in the implementation of the proposed

cooperative scheme is the complexity,mostly due to the decod-

ing at LMS nodes. The complexity of a Raptor based on belief

propagation is O(K). However, in practical implementation

of the code, decoding blockage can occur due to the lack of

degree-1 nodes. Thus more complex methods are used such

as inactivation decoding [39]. Inactivation decoding can be

described roughly as an efﬁcient way of carrying out Gaussian

elimination. In the system we propose, RLNC is plugged to

a Raptor code at LMS terminals. The use of RLNC modiﬁes

the degree distribution (and the ﬁeld size) originally used in

the Raptor code. This leads to a higher probability of early

blockage in the iterative decoding process, which implies that

the decoder has to turn more often to Gaussian elimination,

which has a complexity that grows with K3. Depending on

the speciﬁc packet loss pattern in the satellite segment, the

ﬁnal coefﬁcient matrix may be still partially decodable using

belief propagation, which would lower the size of the matrix

on which the Gaussian elimination is applied, thus reducing

complexity. Although we consider vehicular terminals, which

can potentially host decoders with high computational power,

keeping complexity low may still be required. In order to limit

complexity, the block size Kcan be kept at relatively low

values. In general, it would be interesting to study the impact

of reducing the block size Kon the system performance in

terms of coverage. The vastness of the subject and the space

limitations do not allow for an in depth analysis within the

present paper and open up possibilities for future studies.

VI. SIMULATION SETUP

A. Interaction of Physical Layer and Upper Layers

In order to evaluate numerically the performance of the

proposed methods at the system level, the simulator must be

capable of taking into account the channel impairments of the

physical layer. Physical layer simulations should be run for

each of the nodes, taking into account the channel characteris-

tics and the error correction capabilities of the considered PHY

layer standard as done in [40]. Such approach is, however,

extremely time consuming, which makes it unﬁt for a system

level simulation. A valid alternative is given by the PLA [24]

[25]. The use of PLA allows to take into account the effects

of physical layer elements such as coding, modulation and the

presence of an interleaver in a computationally affordable way.

This is particularly useful in case of time-selective channels,

in which the channel gain changes within the duration of a

codeword. The PLA has been widely studied in the last decade

achieving a growing accuracy for a wide range of transmission

setups.

In recently proposed types of PLA the instantaneous sym-

bol signal to interference plus noise ratio (SINR) vector

transformed in a single SINR value, the effective SINR

(SI N Ref f ). Such approach is called effective SINR mapping

(ESM). Several ESM PHY abstraction methods have been pro-

posed in the literature based on mean instantaneous capacity,

exponential-effective SINR mapping and Mutual Information

Effective SINR Mapping (MIESM). A more detailed descrip-

tion as well as more references on the topic can be found

in [26]. The SIN Ref f in the ESM methods is obtained as

follows:

SI N Ref f = Φ−1 1

n

n

X

i=1

Φ(SI N Ri)!,(21)

where Φ(x)is an invertible function that depends on the

speciﬁc ESM method and nis the codeword length. In MIESM

such function can be related to the mutual information per

received coded bit. This approach is referred to as Received

10

Bit Information Rate (RBIR). The function Φ(x)is a function

obtained by normalizing the modulation-constrained symbol

mutual information (SI) vs SNR function. Once S I N Reff is

obtained, it is used to determine the FER using curves for the

considered channel code in AWGN. Note that SIN Ref f is

referred to the coded symbol, which means that modulation

order and coding rate must be taken into account before using

it in the FER curves. In our simulator we implemented the

RBIR approach and validated it by comparing the obtained

FER curve with that resulting from the simulation of the whole

transmission chain. The results of the RBIR validation are not

reported here for a matter of space but can be found in [20].

B. Simulated Scenario

We evaluated the performance of the proposed scheme

through a simulator that models a satellite to land mobile

broadcast transmission over DVB-SH-B. 150 nodes were

randomly placed on a Manhattan grid of one square kilometer

with 10 intersecting roads. The distance between two parallel

roads is 110 m. Each node moves at a speed of 50 km/h along

one of the roads 9, keeping a constant direction of motion

during the whole simulation. The verse of motion is chosen

at random for each node. When a node reaches the border

of the map it enters back into the map from the opposite

side, as is common practice in this kind of simulations. Nodes

can communicate with each other and have network coding

capabilities. Communication can take place between two nodes

only if they are within a radius of 300 m. A combination of

the path loss model derived in [36] and the TU6 multi-tap

propagation model [37] is used. The coding and modulation

considered are the ones of 802.11p, namely OFDM modulation

and rate 1/2convolutional code at 5.9GHz. The correctness

of the reception is evaluated through PLA. One IFEC block

of K= 150 IFEC symbols, corresponding to a generation,

is transmitted at each trial. Each block contains Ksource

symbols of 1024 bytes each. The total number of coded

symbols transmitted for a single generation is ⌈K/R⌉, where

Ris the rate of the Raptor encoder and ⌈x⌉is the smallest

integer larger than or equal to x. The 3GPP Raptor encoder

described in [35] has been implemented. Each IFEC symbol

is encapsulated within an MPEG2-TS packet and sent to the

channel encoder. The channel encoder is the turbo encoder

speciﬁed in [41]. Each source message of the channel encoder

has a ﬁxed length of 12288 bits (about one and a half IFEC

symbols per Turbo codeword). Once encoded at PHY layer

with a rate r, the IFEC symbols are ﬁrst interleaved with

the bit interleaver and successively with the time interleaver,

which provides time diversity to the signal. In the simulator

we implemented two of the time interleavers described in [23],

namely the short uniform interleaver and the long uniform

9Note that in a real scenario vehicles can move at different speeds. Although

the different speeds impact the correlation in both LMS and terrestrial

channels, we veriﬁed through simulations that the effect in terms of coverage

is negligible if lower speeds (in the range 10 −50 kmph) are used. This is

mainly due to the fact that the differences in terms of packet loss ratio in both

channels (satellite and terrestrial) appear to be negligible. Furthermore, since

the time needed for the transmission of a generation (using the parameters

described in the following) is around 1.5 seconds, the difference in the distance

traveled by different vehicles during a generation period is also negligible.

interleaver. The former has a depth on the order of 200

milliseconds while the latter has a depth on the order of 10

seconds. After time interleaving, the bits are QPSK modulated

and transmitted with roll-off factor 0.35. For each of the

mobile nodes we generate a channel time series according the

three state Perez-Fontan LMS channel model. The correctness

of the reception of each turbo codeword is evaluated using

PLA as described in Section VI-A, taking into account data

rate, channel interleaver, channel code rate, and other relevant

parameters. In the setup in which the gap-ﬁller is present, an

OFDM modulation with 6048 carriers and a guard interval GI

of 224 microseconds is used by the gap-ﬁller. All parameters

conform to the DVB-SH-B standard. The propagation model

from the gap-ﬁller to each of the nodes is a combination of the

modiﬁed COST 231 Hata path loss model with the classical

TU6 channel model, as suggested in [1]. The signals from

the satellite and the gap-ﬁller are combined (after the time

de-interleaver has been applied) at the physical level by each

terminal using maximal-ratio combining. As recommended in

[1], a weighted sum of the two received signals (at the physical

level) is generated and sent to the demodulator/decoder. The

successful or unsuccessful decoding of a given codeword is

evaluated using PHY abstraction and considering the same

channel code as in DVB-SH standard. The same channel code

and interleaver are used at both the satellite and the gap-ﬁller.

The gap-ﬁller is located at a distance dgap f ill < GI ·cfrom

the center of the map, where c= 3 ·108m/sec is the speed

of light. The link budget adopted for the satellite network

is the one in [1], Table 11.28. Table I below summarizes

the main simulation parameters. The sequence of decoded

TABLE I

SIMUL ATION PA RAME TERS .

Environment Urban

Satellite carrier frequency 2.2 GHz

Satellite SNR (LOS) 12 dB

Time interleaver depth 200 ms - 10 s

Modulation QPSK

Roll-off factor 0.35

Bandwidth 5MHz

LL-FEC symbol size 1024 bytes

Size of LL-FEC blok (K) 150 (∼150 kB)

Rate Turbo Code (r) 1/2

Rate Raptor Code (R) 1/4

Gap-ﬁller distance (dgap fill )3 km

Gap-ﬁller carrier frequency 2.12 GHz

EIRP gap-ﬁller 25 dBW

Number of gap-ﬁller OFDM carriers 6048

Subcarrier spacing gap-ﬁller 0.69754 kHz

Scenario surface 1sq. km

Number of terminals 150

Terminal type Vehicular

Terminal speed 50 km/h

V2V carrier frequency 5.9 GHz

V2V transmission power 20 dBm

Number of IEEE 802.11p OFDM carriers 52

Subcarrier spacing IEEE 802.11p 0.15625 MHz

Conv. code rate IEEE 802.11p 1/2

IFEC symbols are determined based on on the codewords that

are correctly decoded at the physical layer. Nodes exchange

IFEC messages using DSRC/IEEE 802.11p interfaces. The

11

transmission rate in the ground segment is set high enough

so that an IFEC symbol can be transmitted before the next

one is received on the satellite channel. The MAC mechanism

in the terrestrial segment is a simpliﬁed version of the CSMA

used in 802.11p. Nodes are set in promiscuous mode so that

each node can receive the transmissions of any other node.

We compare two different relay methods. One is the NC-

CCE scheme described in Section V, which is based on

network coding. The other relay scheme is the simple relaying

(SR) scheme, also introduced in Section V. Unlike in the

NCCCE scheme, in the SR scheme nodes do not combine

IFEC symbols, they just transmit the oldest non transmitted

packet. In SR, if all the received packets have already been

transmitted, then, if ζ > 1, a node tries to access the channel

(with probability 1−ζ) and transmit a randomly chosen packet.

The amount of received data is measured at the interface

between the IFEC and the upper layers, as indicated in Fig.

5, considering the IFEC block as a fundamental data unit.

The reason for this choice is that data coming from the upper

layers are reshaped in the ADST’s. Thus, receiving one or

more IFEC symbols, even if systematic, may not be useful,

as they are part of a larger bunch of data, or may be parts

of incomplete IP datagrams. Thus when we refer to decoded

data we mean decoded IFEC blocks. Linear independence of

packets is evaluated through their global encoding vectors.

SRTP/UDP

IP

MPE IFEC

MPEG2 TS

DVB-SH physical layer

Fig. 5. The amount of received data is measured at the interface between the

IFEC and the upper layers.

VII. NUMERICAL RESULTS

Before moving to the simulation results relative to the

scenario described in Section VI-B, we evaluate the theoretical

bounds obtained in Section III. Although simpliﬁed assump-

tions are taken, such results give an indication of the extent

of the gains that can be obtained with a cooperative approach

and the way relevant system parameters impact such gains,

independently of the speciﬁc types of channel code or packet

level code considered.

Fig. 6 shows the coverage Ω, obtained by evaluating nu-

merically Eqn. (12), plotted against the rate at physical level

rfor a ﬁxed message rate Rand different network sizes. The

relative lower bounds and the coverage curve in case of no

cooperation are also shown. In the simulation we assumed that

one between the satellite and the gap-ﬁller links is affected by

severe fading and set R= 2/3,pa= 0.2,ΓN= 10 dB in

the NN channel, µ= 3 and σ= 1 in the SN channel for the

available link. We recall that pais the probability of channel

access, assumed to be the same for all nodes. It is interesting

to note how increasing the number of nodes also increases the

achievable rate rfor a given Ω. This is because the higher

is the number of nodes, the higher is the probability that all

the information broadcasted by Sreaches at least one node of

the network, i.e., it has not been lost. Once the information

has reached the network, it is efﬁciently distributed among the

terminals using RLNC. An important gain in the transmission

rate can be observed, with an increase of about 0.4bpcu

when passing from no cooperation to cooperation in a network

with 2nodes, and about 1bpcu in case of a network with

4nodes. The lower bound is fairly tight for M= 2 and

M= 4. We point out that this result is achieved without any

feedback to the source or any packet request among nodes,

as the decision on whether to encode and transmit or not

is taken autonomously by each terminal depending on the

probability of medium contention pa. As mentioned in the

previous sections, such performance curves are achievable,

which implies asymptotically long code lengths should be

used. In order to evaluate the loss in performance due to

ﬁnite code lengths and real coding schemes implementation,

we also show in Fig. 6 the curves obtained for the same setup

but with a ﬁnite block-length Raptor code (NC Raptor). The

Raptor encoder is the one used in DVB-SH and introduced in

Section VI 10. A block length of K= 150 source symbols was

chosen. Although an important gain in terms of physical layer

rate is achieved thanks to cooperation and such gain increases

with the number of terminals as in the asymptotic case, a gap

between theoretical and numerical results is present. This is

due to the ﬁnite and relatively small block length. Such gap can

be reduced by applying NC directly in the space segment [42].

However, such approach has the drawback that the decoder

complexity is higher also in case no cooperation is used, which

is not the case when a Raptor code is adopted. Moreover, it

would imply a modiﬁcation in the satellite segment, which, in

our proposed scheme, remains unaltered. In Fig. 7 the coverage

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

0

0.2

0.4

0.6

0.8

1

Ω

r (bpcu)

NC theory M= 2

NC theory M= 4

NC theory M= 6

NC Raptor M= 2

NC Raptor M= 4

NC Raptor M= 6

NC LB M= 2

NC LB M= 4

NC LB M= 6

No coop. M= 2

No coop. M= 4

No coop. M= 6

No coop. Raptor M= 2

No coop. Raptor M= 4

No coop. Raptor M= 6

Fig. 6. Coverage Ωplotted against rate at physical layer rin the cooperative

case for different values of M. The lower bound and the non cooperative case

are also shown. In the simulation we set R= 2/3messages/slot, pa= 0.2,

ΓN= 10 dB in the NN channels, µ= 3 and σ= 1 in the SN channel.

is plotted against the per-node probability of transmission

attempt pafor M= 4,ΓN= 10 dB,r= 1 bpcu and R= 2/3.

10Decoding has been implemented taking inactivation decoding into ac-

count.

12

It is interesting to note that relatively small values of pa(lower

than 0.15 for the asymptotic case) are sufﬁcient to achieve full

coverage for values of rand Rwhich are of practical interest.

We further observe that the lower bound tightly approximates

the simulated theoretical curve. In the ﬁgure we also plotted

the curve for the case of a practical cooperative scheme using

the 3GPP Raptor code with source block length K= 150 (NC

Raptor). As in Fig. 6, the loss with respect to the theoretical

curve is due to the ﬁnite block length. The coverage for the

non cooperative case in the setup considered in Fig. 7 is 0,

coherently with Fig. 6.

0.06 0.08 0.1 0.12 0.14 0.16 0.18

0

0.2

0.4

0.6

0.8

1

Ω

pa

NC theory

NC lower bound

NC Raptor

Fig. 7. Coverage Ωplotted against the probability of medium contention

pain the cooperative case for a network with M= 4 and ΓN= 10 dB.

The lower bound ΩLB curve and the curve of a practical scheme with ﬁnite

block length Raptor code are also shown. In the simulation we set R= 2/3

messages/slot, r= 1 bpcu, µ= 3 and σ= 1 in the SN channel.

In the rest of the section we compare the performance of the

three practical schemes described in previous sections, namely

the proposed NCCCE scheme described in Section V, the SR

system described in Section VI and a non cooperative system

in which the nodes can receive only from the satellite (or

from the satellite + gap-ﬁller, when present). We consider

as performance metric the average percentage of nodes that

receive all the transmitted data. The metric is evaluated for

different values of the cooperation level ζin the range [0,2].

Note that the system with satellite-only reception corresponds

to a cooperative system with ζ= 0. Considering different

values of ζwe can evaluate the performance gain of the

cooperative methods with respect to the non cooperative

system as a function of the terrestrial channel utilization. Fig.

8 shows the average percentage of nodes that receive all data

plotted against ζ. In the simulations we set the rate at physical

level to 1/2while the rate of the Raptor encoder has been set

to R= 1/4. The short interleaver has been used. We also

evaluated the case of long interleaver with and without gap-

ﬁller and with no IFEC protection (which corresponds to a

Raptor rate of R= 1). We did not consider the case of long

interleaver with forward error correction because, according

in the DVB-SH-B standard, the IFEC protection is meant to

be applied only in combination with the short interleaver. In

case the long interleaver is used together with a gap-ﬁller

(not shown in the ﬁgure) 100% of the nodes are covered.

The NCCCE scheme achieves the best performance among

all others setups, with a gain of about 25% with respect to the

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

10

20

30

40

50

60

70

80

90

100

ζ

covered nodes (%)

NCCCE w.o. gf, R=1/4

SR w.o. gf, R=1/4

No cooperation w.o. gf, short int., R=1/4

No cooperation w.o. gf, long int., R=1

NCCCE w. gf, R=1/4

SR w. gf, R=1/4

No cooperation w. gf, short int., R=1/4

No cooperation w.o. gf, short int., R=1

Fig. 8. Average percentage of nodes that decode all data plotted against the

cooperation level ζfor NCCCE, SR and the non cooperative scheme. The rate

couple (r, R) = (1/2,1/4) has been set in the simulation and the DVB-SH

short interleaver has been considered. The non cooperative case with long

interleaver and R= 1 is also shown for comparison.

non cooperative scheme and a gain of about 29% with respect

to the SR scheme in case no gap-ﬁllers are user (w.o. gf). It

is worth noting that full coverage is achieved by the NCCCE

scheme for ζ= 0.05, i.e., with little use of the terrestrial

channel, either in case a gap-ﬁller is used or not. We further

notice that this is similar to what shown in Fig. 7, in that

the maximum advantage of the network-coded cooperative

scheme is achieved for small values (smaller than 0.15) of

the channel access probability pa. The performance of the

scheme worsens as ζapproaches 2. This is due to the fact that

the terrestrial channel load increases with ζ, determining an

increase in the number of collisions due to hidden nodes and

thus decreasing the spectral efﬁciency of the vehicular ad-hoc

network. From Fig. 8 we also notice that the NCCCE scheme

with short interleaver achieves a higher percentage of covered

nodes with respect to the non cooperative conﬁguration with

long interleaver. On the one hand this result suggests that a

short interleaver can be used instead of a long one, with a

huge memory saving in the physical layer architecture of the

receiver. Of course this comes at the expense of larger memory

resources at higher levels (IFEC), which are likely to have,

however, an overall cost which is lower than the memory at

lower levels. On the other hand, for a fair comparison we

must take into account that the long interleaver scheme does

not use IFEC protection, which implies a gain in terms of

spectral efﬁciency of 1/R = 4, i.e., there is a tradeoff between

complexity and transmission rate.

The gain of the cooperative schemes with respect to the non

cooperative case derives from the use of the terrestrial channel

bandwidth. In order to evaluate which between the NCCCE

scheme and SR scheme uses such resources more efﬁciently,

we plot the average number of decoded messages (per node

and per channel access) against the average number of channel

accesses (per node and per generation) for the NCCCE and

the SR schemes. Although the efﬁciency in the use of the

terrestrial channel decreases with the number of transmissions,

the NCCCE scheme makes a much more efﬁcient use of ter-

restrial channel resources with respect to the SR scheme. The

13

30 40 50 60 70 80 90 100 110

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Number of channel accesses p er node per generation

Number of decoded messa ges per channel access

NCCCE w.o. gf

SR w.o. gf

NCCCE w. gf

SR w. gf

Fig. 9. Average number of decoded source symbols per node normalized to

the average number of channel accesses plotted against the average number

of times the channel is accessed per node within a generation for the NCCCE

and the SR schemes. For each of the schemes both the curve for the case with

and without gap-ﬁllers are shown. Although the efﬁciency in the use of the

terrestrial channel decreases with the number of transmissions, the NCCCE

scheme makes a much more efﬁcient use of terrestrial channel resources with

respect to the SR scheme.

ﬁgure indicates how, ﬁxing the number of channel accesses per

node within a generation period (horizontal axis) the NCCCE

decodes on average more messages (IFEC source symbols)

compared to the SR scheme. Fig. 8 and Fig. 9 show that the

NCCCE scheme achieves a larger gain in terms of percentage

of covered nodes with respect to the SR scheme by using the

terrestrial channel resources in a more efﬁcient way.

Note that, although latency in GEO satellite communica-

tions is large with respect to delays typically found in wireless

terrestrial networks, the system we propose is completely

transparent to the satellite transmission. The Raptor code ap-

plied at the satellite is already foreseen by the ETSI DVB-SH

standard and no feedback channel is assumed from terrestrial

nodes to the satellite, which means that no further delay is

added on the satellite segment. Moreover, each LMS terminal

can begin to exchange messages relative to a given generation

before the whole generation is received from the satellite (i.e.,

the correspondent signals reach the ground). The additional

delay that may be introduced by the NCCCE is the delay

due to the V2V communication, which is much smaller than

the GEO round trip time. If on the one hand the absence of

feedback suits well networks with large delays, on the other

hand it implies a non-zero probability that a node can not

decode some of the messages. In practical applications such

probability can be usually kept reasonably low by tuning some

of the system parameters such as, but not limited to, r,Rand

N.

VIII. CONCLUSIONS

We investigated the performance of a cooperative approach

to provide missing coverage in heterogeneous LMS networks

in the presence of both a direct satellite link and a link

from a gap-ﬁller. We carried out an analytical study consider-

ing a mathematically tractable and yet practically interesting

network model assuming a combination of the signals from

the two links if performed by the receivers at the physical

level. Fading and shadowing effects in both links, as well

as the medium access mechanism in the V2V network, have

been taken into account. By applying the Max-ﬂow Min-cut

theorem we derived an exact expression for the coverage as a

function of both the information rate at physical layer and the

rate of innovative packets injected in the network per unit-time

as well as a closed form expression of a lower bound in case

one of the two physical links is severely degraded. Our results

show a tradeoff between the coverage and the rate at which

the information can be injected in the network and at the same

time quantify the gain derived from node cooperation through

the short range interface. We showed that the diversity gain

grows with the number of terminals, opening up the possibility

of increasing the transmission rate at the source while still

guaranteeing a good coverage.

Based on the considered theoretical model we proposed

a practical cooperative scheme which leverages on network

coding for enhancing coverage in heterogeneous satellite ve-

hicular LMS systems over DVB-SH. The proposed scheme

does not require any modiﬁcation at the lower layers. Our

numerical results, based on physical layer abstraction, show

that a cooperative relaying system based on random linear

network coding can bring important beneﬁts in terms of

both coverage and terminal complexity (since shorter time

interleaver could be used) with respect to a system in which

nodes receive from satellite only, as well as with respect to

a relaying scheme in which network coding is not used. As

a ﬁnal remark we point out that the delay induced by the

NC decoding as well as the relative memory requirements are

essentially the same in the proposed scheme an in DVB-SH

LL-FEC, since the NC encoding is done only within an LL-

FEC block. This is thanks to the fact that the terminals need

to buffer only network coded packets relative to the same LL-

FEC block, as is also the case in LL-FEC without NC.

ACKNOWLEDGEMENTS

The authors would like to thank Roberto Prieto-Cerdeira of

the European Space Agency for providing the LMS channel

time series simulator.

The view expressed herein can in no way be taken to reﬂect

the ofﬁcial opinion of the European Space Agency.

APPENDIX

Proof of Theorem 1

P r

ΓSje−2r−1

ΓSj

ΓSj−ΓSi

−ΓSie−2r−1

ΓSi

ΓSj−ΓSi

> R

=P r Ξ + e−2r−1

ΓSi> R

=P r Ξ + e−2r−1

ΓSi> R |e−2r−1

ΓSi> RP r e−2r−1

ΓSi> R

+P r Ξ + e−2r−1

ΓSi> R |e−2r−1

ΓSi≤RP r e−2r−1

ΓSi≤R

(22)

where we deﬁned

Ξ,

ΓSje−2r−1

ΓSj−e−2r−1

ΓSi

ΓSj−ΓSi

.

14

The ﬁrst term of the sum in Eqn. (22) can be written as:

P r Ξ> R −e−2r−1

ΓSi|R−e−2r−1

ΓSi<0P r e−2r−1

ΓSi> R

=P r e−2r−1

ΓSi> R,

(23)

where the equality follows from the fact that ΓSi>0and

ΓSj>0, hence the left side term of the inequality in the

expression within brackets is always non negative. Let us now

consider the second term of the sum in Eqn. (22). We show

that it goes to zero in the limit of µjgoing to inﬁnity. Let us

rewrite Eqn. (22) as follows:

P r Ξ> R −e−2r−1

ΓSi|R−e−2r−1

ΓSi≥0P r R−e−2r−1

ΓSi≥0

=P r {Ξ> δi|δi≥0}P r {δi≥0}

=P r Ξ> δi|δi≥0,ΓSj>ΓSiP r δi≥0|ΓSj>ΓSi

·P r ΓSj>ΓSi

+P r Ξ> δi|δi≥0,ΓSj<ΓSiP r δi≥0|ΓSj<ΓSi

·P r ΓSj<ΓSi,

(24)

where we deﬁned the r.v. δi=R−e−2r−1

ΓSi. The ﬁrst term

of the sum in Eqn. (24) is the product of three probabilities.

Recalling that γj∼exp(1) while ΓSj=eXj

10 , for j= 1,2,

with Xj∼ N (µj, σ2

j), we have:

P r ΓSj>ΓSi=P r ne

Xj

10 > e Xi

10 o=P r {Xj> Xi}

=Z+∞

−∞

1

p2σ2

i

e−(xi−µi)2

2σ2

iZ+∞

xi

1

q2σ2

j

e−(xj−µj)2

2σ2

jdxjdxi

=Z+∞

−∞

1

p2σ2

i

e−(xi−µi)2

2σ2

i

1

2−1

2erf

xi−µj

q2σ2

j

dxi,

(25)

where erf(x)is the error function, deﬁned as 2

√πRx

0e−t2dt.

Eqn. (25), under the hypotheses in the theorem statement, goes

to 0as µj→ −∞. Let us now consider the second term of

the sum in Eqn. (24). It can be easily shown that the ﬁrst of

the three probabilities that multiplied together compose such

term goes to zero as µj→ −∞. Let us call such term P1.

Then we have:

P1=P r Ξ> δi|δi≥0,ΓSj<ΓSi

=P r

ΓSje−2r−1

ΓSj−e−2r−1

ΓSi

ΓSj−ΓSi

> δi|δi≥0,ΓSj<ΓSi

≤P r ΓSj

ΓSi−ΓSj

·R > δi|δi≥0,ΓSj<ΓSi

=P r ΓSj>ΓSi

δi

R(1 + δi)|δi≥0,ΓSj<ΓSi.(26)

It can be shown in a similar way as in Eqn. (25) that (26) goes

to zero asymptotically as µjgoes to −∞. Using equations

(23)-(26) in Eqn. (7) we ﬁnally have:

lim

µj→−∞ P r ΓS1

ΓS1−ΓS2

e−2r−1

ΓS1−ΓS2

ΓS1−ΓS2

e−2r−1

ΓS2> R

=P r e−2r−1

ΓSi> R

=1

2−1

2erf

10 ln h1−2r

ln(R)i−µi

2σ2

i

.

(27)

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