Cross-layer design for double-string cooperative communications in wireless ad-hoc networks

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONSEur. Trans. Telecomms. 2011; 22:471–486

Published online 1 September 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.1497

RESEARCH ARTICLE

Cross-layer design for double-string cooperativecommunications in wireless ad-hoc networksS. Sergi1*, F. Pancaldi2 and G. M. Vitetta1

1 Department of Information Engineering, University of Modena and Reggio Emilia, Via Vignolese 905/b, 41125 Modena, Italy2 Department of Science and Methods for Engineering, University of Modena and Reggio Emilia, Via Amendola 2, 42122,

Reggio Emilia, Italy

ABSTRACT

This paper proposes a novel architecture for cooperative communication in wireless ad-hoc networks capable of offeringreliable and low-latency services efficiently. The proposed solution is characterised by the following relevant features:(i) a wireless connection between each couple of network nodes is established via multiple relays; (ii) each source-to-destination link is characterised by a double-string topology, allowing the use of specific transmit diversity techniquesfor reliable communications; and (iii) a novel utility-based routing metric providing a fair exploitation of the availableenergy/bandwidth resources is employed. Simulation results evidence that our solution offers substantial energy savingswith respect to traditional ad-hoc architectures employing multihop routing and operating in the absence of cooperativestrategies. Copyright © 2011 John Wiley & Sons, Ltd.

*Correspondence

S. Sergi, Department of Information Engineering, University of Modena and Reggio Emilia, Via Vignolese 905/b, 41125 Modena, Italy.E-mail: [email protected]

Received 1 September 2009; Revised 28 February 2011; Accepted 4 June 2011

1. INTRODUCTION

In the last few years, research activities on distributed com-munication systems have received considerable attentionfrom both research and industrial communities. This inter-est is motivated by the need of both temporary and reliablebackup systems, able to be timely deployed to achieve afast and effective access to essential services if regularcommunication channels are down or overloaded, or ableto extend the coverage of traditional wireless communi-cation systems. Common requirements for such systemsinclude robustness against the impairments of the propaga-tion scenario, flexibility in the management of the availablespectrum to accommodate services with different needs interms of bit rate and latency, low power consumption inorder to keep the size of handheld communication devicessmall, and ease of setting up. These requirements can bemet resorting to the use of broadband wireless ad-hoc net-works [1], which can be deployed without relying on anypreviously existing infrastructure in emergency scenarios.

Most of recent research activities in the field of wirelessad-hoc networks mainly focus on the study of communi-cation techniques ensuring an efficient use of energy in

sensor networks [2–5] or a large capacity [6]. However, asfar as we know, few papers have addressed the problemof developing ad-hoc network architectures that are ableto handle both point-to-point high data-rate communica-tions and data-streaming services efficiently; such archi-tectures should operate in the presence of a large spatialdensity of high data-rate links in a reliable fashion, andwith limited latency [7] and energy/spectral resources, atthe price of acceptable cost/complexity. We believe thatthis target can be achieved adopting cooperative commu-nication strategies and a cross-layer approach in systemdesign. In fact, on the one hand, cooperative transmissiontechniques allow to exploit spatial diversity through thesharing of antennas belonging to distinct portable terminals[8, 9], hence improving system robustness against multi-path fading. On the other hand, a cross-layer approach tothe development of algorithms and protocols for the phys-ical, medium access control (MAC) and network layerscan lead to technical solutions ensuring an efficient useof the available resources in the network. In particular,we believe that, in a cross-layer perspective, substantialattention should be paid to the design of routing proto-cols, in order to improve the network performance with

Copyright © 2011 John Wiley & Sons, Ltd. 471

Double-string cooperative communications S. Sergi, F. Pancaldi and G. M. Vitetta

respect to a larger set of metrics. It is worth pointingout that recent research on routing algorithms for wire-less networks has focused on the problem of devising costmetrics different from the simple hop counting or theoverall energy consumption [10–12]. We also note thatmodern routing algorithms are often based on the defini-tion of a specific utility function, that is of a subjectivemetric expressing the degree of user’s satisfaction and,consequently, depending on user’s needs [13, 14]; suchalgorithms aim at the maximisation of the aforementionedmetric through an accurate selection of the communicationpath and of the pool of available radio resources.

Unlike scientific papers that usually cope with specificproblems in the area of cooperative networks, patent pub-lications typically deal with overall system design; this isdue to the requirement of ‘manufacturability’ for patent-ing new ideas. In particular, a number of patents concernsthe development of cooperative ad-hoc networks optimis-ing energy usage. For instance, a novel method based onthe availability of channel state information (CSI) at thetransmitter is proposed in [15] to improve the energy effi-ciency of two-hop relay links. The ideas of energy accumu-lation and mutual-information accumulation are introducedin [11] and [12], respectively. In these cases, all the nodesof the network can incrementally acquire information asthey receive different copies of a given data packet. Whena node (distinct from the source and the destination) gath-ers enough information to remove all the errors detected ina data packet, such a packet is forwarded. It can be shownthat if multiple copies of the same packet are transmittedusing a very limited radiated power, an appreciable energysaving can be achieved. Another interesting technical con-tribution is given in [16], where the idea of cooperativedistributed beamforming is investigated; in the proposedsolution, all the nodes that are able to properly decode apacket cooperate to set up a virtual antenna array focusingthe transmitted power towards the destination or towardsthe next relay stage.

In this paper, a cross-layer methodology is adopted todevise a new solution to the problem of designing the phys-ical, data-link and network layers of a flexible ad-hoc wire-less network. Note that, even if the proposed architecturepartly results from the combination of known communi-cation algorithms and protocols, as far as we know, similarsolutions to the aforementioned problem have not appearedyet neither in the technical literature nor as a practicalimplementation.

In the proposed solution, a wireless connection betweenan information source and a destination is achieved estab-lishing a multihop wireless link via a relay chain; each con-nection is based on a double-string topology [17], whosesimplicity and regularity allow to assess error performanceanalytically. Such topology is also useful to model ‘long’networks, like, for instance, ad-hoc networks formed byvehicles driving on a highway [17]. Multihop paths areselected by a utility-based distributed routing techniquethat endows the network with a self-configuration capabil-ity; the proposed technique is based on the classic Dijkstra

algorithm and employs a new cost (utility) function. Thisfunction aims at guaranteeing a balanced use of the avail-able radio resources (in terms of energy and bandwidth) ofnetwork nodes, jointly improving the network lifetime andits ability to satisfy the connectivity requests. In the MAClayer, the orthogonal frequency division multiple access(OFDMA) technique [18] is employed by network nodesto achieve a flexible management of the available spec-trum. In addition, a request-to-send (RTS)–clear-to-send(CTS) message chain [19] is adopted both to notify eachnode its cooperative counterpart and to allocate the radioresources assigned by the routing algorithm. In the physicallayer, two different transmit diversity schemes have beentaken into consideration in our work and have been usedwith orthogonal frequency division multiplexing (OFDM)modulation on a subcarrier-by-subcarrier basis. The firstscheme is based on the well-known Alamouti space–timeblock code (STBC) [20], the second one on the transmitselection diversity (TSD) technique [21, 22].

The main contribution provided by this manuscript isrepresented by the analysis of the error performance pro-vided by multihop links employing relays characterisedby the aforementioned double-string topology. First, somemathematical tools are derived for assessing the achievableend-to-end symbol error rate (SER), even in the presenceof a carrier frequency offset (CFO) in the portable termi-nals. Our work in this area can be seen as an extension,to the TSD case, of some previous work, referring mul-tihop systems employing space–time (ST) block coding[23, 24]. Then, various numerical results are illustrated tocompare the performance offered by the proposed architec-ture employing the two selected transmission techniques;the effects of various transmission impairments, like aCFO and the presence of a delay in the update of routinginformation and CSI, are also assessed.

The remaining part of the paper is organised as fol-lows. Section 2 describes the proposed network architec-ture. Section 3 is devoted to the analysis of the end-to-enderror performance achievable in a multihop link. Numer-ical results are illustrated in Section 4. Finally, Section 5offers some conclusions.

2. SYSTEM MODEL

In this section, some specific features of the proposed net-work architecture are illustrated. In particular, we focus onthe following technical issues: (i) the adopted cooperativecommunication techniques at physical layer; (ii) OFDMAat MAC layer; (iii) distributed utility-based routing andresource management at network layer. In the following, itis always assumed that an information source S and a desti-nation terminal D are connected through a multihop path,consisting of the concatenation of NR relay stages. Eachstage operates according to a decode-and-forward strategyand is characterised by the double-string topology illus-trated in Figure 1 [17]. This means that each stage consistsof a couple of transmit nodes [17] (instead of a single one

472 Eur. Trans. Telecomms. 22:471–486 (2011) © 2011 John Wiley & Sons, Ltd.DOI: 10.1002/ett

S. Sergi, F. Pancaldi and G. M. Vitetta Double-string cooperative communications

Figure 1. Double-string link model.

[25]) and a couple of receive nodes; here, we assume thateach node is equipped with a single antenna.

In our system, the adopted cooperative transmissionschemes are based on well-known spatial diversity tech-niques [8, 9], suitable to the couple of 2 � 1 (i.e. multiple-input single-output, MISO) communication channels avail-able in each relay stage [26, 27]. More specifically, twotransmit diversity techniques have been taken into con-sideration: the well-known Alamouti STBC and the TSDscheme of [21]. Both techniques have been combined withOFDM, providing resiliency against multipath fading; inparticular, they have been employed on a subcarrier-by-subcarrier basis in the transmission from a couple of coop-erating nodes, as suggested, for instance, in [22]. It is worthnoting the following:

(1) The use of STBC, unlike TSD, does not require theavailability of a communication feedback channelto deliver periodically updated CSI to the transmitnodes.

(2) TSD outperforms STBC for slowly varying chan-nels, but the performance of both solutions becomessimilar when the CSI available for the TSD is notupdated frequently [28]. Moreover, the performancegap between TSD and STBC in a complicated mul-tihop cooperative link depends on various factorsso that a realistic optimal choice cannot be easilyidentified [23, 29].

(3) The use of both the proposed transmit techniques ispossible only if the same block of subcarriers is usedby the nodes belonging to the same relay stage. Forthis reason, in setting up a specific end-to-end link,a connection establishment phase (see Section 2.3)is needed to inform each node about the role that itwill play.

2.1. Orthogonal frequency divisionmultiple access

The use of OFDMA has been considered as a naturalchoice in MAC design because of the use of OFDM in thephysical layer and of the flexibility it offers in the spec-trum management in the presence of multiple links. Notethat the adoption of this strategy implies that, if a givennetwork node is involved in multiple distinct end-to-endlinks, it uses orthogonal subcarriers for each of them. In

principle, this does not exclude that in the network, differ-ent nodes, employed in distinct end-to-end links, can usethe same set of subcarriers. In fact, subcarrier selection isdone independently in each relay stage and aims at iden-tifying, in the pool of unused subcarriers, the ones associ-ated with the best subchannel gains, that is, those ensuringthe best connectivity. Moreover, this is accomplished afterthe distributed utility-based routing algorithm proposed inSection 2.2 has identified the multihop path offering thelargest availability of energy and bandwidth. In fact, pathselection is followed by an RTS–CTS message chain (seeSection 2.3), connecting the source node with the destina-tion node and avoiding collisions among nodes belongingto the same network.

Finally, it is worth pointing out the following: (i) inthe absence of frequency synchronisation inaccuracies, theoverall communication channel negotiated by each source–destination couple does not interfere at all with the chan-nel used by any other couple so that the network can behandled as a frequency division system; (ii) in principle,bit-loading and/or power-loading techniques [30] can beadopted in combination with the cooperative transmissiontechniques described in the previous section, but this is outof the scope of our work.

2.2. Utility-based routing

In the proposed routing strategy, the optimality criterion inpath search is represented by the minimisation of a specificcost (i.e. utility) function. The derivation of this functionhas been inspired by the pragmatic approach followed in[10] and by the guidelines illustrated in [31], where it isshown that network lifetime can be maximised using proto-cols that rely on the knowledge of CSI and residual energyinformation. To begin, we assign the cost �.i/

�.i/D cm.i/m.i/C cp.i/m.i/Pave.i/

Dm.i/.cm.i/C cp.i/Pave.i// (1)

to the i th node-to-node single-hop link, with i D 0;

1; : : : ; NSH, where NSH is the overall number of possiblelinks of this type in the network. Here, m.i/ is the num-ber of used subcarriers in the transmit node, Pave.i/ is theaverage radiated power per subcarrier (so that m.i/Pave.i/

denotes the overall power poured over the i th link), and

Eur. Trans. Telecomms. 22:471–486 (2011) © 2011 John Wiley & Sons, Ltd.DOI: 10.1002/ett

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cm.i/ (cp.i/) represents the marginal cost* assigned toa single subcarrier (to the power exploited for each sub-carrier) in the given hop. Note that the parameters cm.i/and cp.i/ are node dependent because their values are pro-portional to the shortage of bandwidth and energy, respec-tively, in the node transmitting over the i th link [32];further details about this specific issue are provided inSection 4.

In the cost metric (1) m.i/ can be related to Pave.i/, tothe minimum bit rate needed to provide a certain qualityof service (QoS) and to the CSI. To derive an explicit rela-tionship between these parameters, let us focus now on anarbitrary node-to-node single-hop link, using m of the Nsubcarriers available in a multicarrier transmission on anoverall bandwidth B . Then, the available capacity C in thepresence of additive white Gaussian noise (AWGN) andfrequency flat fading on each subcarrier is given by [33]

C DXn2S

B

Nlog2

1CN

Pn jhnj2

N0B

!(2)

where S denotes the set of used subcarriers, hn is thecomplex channel gain affecting the nth subcarrier, Pn isthe power poured on the nth subcarrier, and N0=2 is theAWGN two-sided power spectral density. Note that theevaluation of C via Equation (2) requires an appreciablecomputational effort because the knowledge of the opti-mal subcarrier selection and power allocation is needed.In addition, in any application, the channel gains fhngare time varying so that capacity needs to be periodicallyrecomputed. For these reasons, following [33], in our work,Equation (2) is replaced by the approximate expression

QC DmB

Nlog2

�1CN

Pave˛ave

N0B

�(3)

where Pave is the average transmit power assigned to eachsubcarrier,m is the number of used subcarriers, and ˛ave isthe average power gain of the communication channel. It isworth pointing out the following: (i) Equation (3) requiresonly an average knowledge of the communication channel;(ii) it provides a rough estimate of the available capacity inthe presence of a uniform power distribution; and (iii) thechannel parameter ˛ave, representing a power channel gainaveraged with respect to subcarriers and time, can be com-puted in a number of ways.† If the given single-hop link isrequired to support the minimum bit rate Cr , the availablebandwidth and power resources should be used in a waythat

QC � Cr (4)

*The marginal cost is the change in total cost, which arises when the

amount of the considered resource changes by one unit; similarly, the

marginal cost function is the derivative of the total cost function with

respect to the amount of used resource.†A specific procedure for the computation of ˛ave is proposed in

Section 4.

Then, substituting Equation (3) into Equation (4) leads tothe result

NPave DN0B

N˛ave

�2NCr

mB � 1

�(5)

expressing the minimum transmit power needed to achievethe capacity Cr when m subcarriers with a uniform powerdistribution are used in the presence of an average powergain ˛ave. Taking advantage of Equation (5), Equation (1)can be replaced by the new cost metric

Q�.i/D cm.i/m.i/

C cp.i/m.i/N0B

N˛ave.i/

�2NCr

m.i/B � 1

�(6)

that explicitly depends on the target capacity Cr , the aver-age CSI ˛ave.i/ and the number of employed subcarrierm.i/. For each link, if the selected metric is expressed byEquation (6), cost minimisation can be accomplished withrespect to the number of subcarriers m.i/. In fact, tak-ing the first partial derivative of Q�.i/, Equation (6), withrespect to m.i/ and setting it to zero yields

@ Q�.i/

@m.i/D cm.i/C cp.i/

N0B

N˛ave.i/

�2NCr

m.i/B � 1

�

C cp.i/N0Cr ln.2/

m.i/˛ave.i/2NCrm.i/B D 0 (7)

From this equality, it is easily inferred that the numberof subcarriers that minimise the i th link cost ensuring therequired capacity Cr is

m.i/D

2666

ln.2/N Cr

B W�cm.i/N˛ave.i/� cp.i/N0B

cp.i/N0BeC 1

�3777 (8)

where d�e and W .�/ denotes the ceiling function and theLambert W function‡ [34], respectively.

The proposed routing algorithm initialises and updatesthe routing table stored in each node of the wireless net-work. In particular, the entry of each table provides, fora specific destination node, the next-hop node to whichdata should be forwarded and the overall price of thewhole link towards the destination. The routing strategyalternates between two distinct phases. In the first one,the well-known Dijkstra’s algorithm [35] is exploited toperiodically update the routing tables. Given some QoSconstraints (namely, the minimum capacity Cr and theacceptable latency expressed in terms of the maximumnumber of hops), each node retrieves the costs of allthe node-to-node (i.e. single-hop) connections in the net-work using a simple message-passing mechanism (likethat described, for instance, in [36]). Indeed, each node A

‡The function lambertw .x/ generates the solution w of the equation

xDw � exp.w/.



reached by message passing computes all the cost metrics˚Q�.A! B/, with B 2 V .A/

�associated with the single-

hop communication from A to any node B within its cov-erage area (here, V .A/ denotes the set of nodes withinthe coverage area of A). This computation is accomplishedresorting to the following procedure, which also fairlysummarises the layer interaction:

(1) Given the number of available subcarriers (or,equivalently, the busy ones) and the residual power(hence, the battery level) of node A, the marginalcost cm.A ! B/ and cp.A ! B/ are computed§

for every node B 2 V .A/.(2) Assuming that the average power gain ˛ave (see

Equation (3)) is known for any B 2 V .A/, thenumber of subcarriers (ensuring the required bitrate with minimum cost) and the transmit powerare evaluated using Equations (8) and (5), respec-tively, so that the link cost can be evaluated viaEquation (1).

When a node S needs to set up a new connection, it sortsits list of end-to-end links on the basis of the related pricescontained in its routing table. The path having the lowestcost is adopted as the ‘main string’ of the double-stringlink; afterwards, a collaborative path characterised by thesame number of hops needs to be identified. It is worthpointing out that the problem of identifying a ‘cooperativestring’ is far from being trivial because the nodes belongingto the same relay stage need to exchange CSI, and hence,for each relay stage, the nodes of the collaborative stringneed to be located within the coverage area of the nodes ofthe main string. Some solutions has been proposed in tech-nical literature to find a cooperative cluster for a node (e.g.,see [6, 37]). However, because of the need of a specifictopology, a simpler strategy (suboptimal but able to guar-antee, in principle, the presence of all the required links)is proposed. Our procedure eases the following source-to-destination link analysis, which is one of the main goal ofthis work and can be summarised as follows:

(1) Dijkstra’s algorithm [35] (already used to identifythe main string) is applied again in a reactive fash-ion.¶ including one more constraint: the collabora-tive node at the r th relay stage must be directlyreachable, at the same time, by the nodes of the mainstring at the stages r�1, r and rC1. In practice, eachnode sets its cost metric to 1 if it cannot commu-nicate with such nodes of the main string, otherwisecomputes its price using Equations (6) and (8).

(2) The node S sorts the list of the retrieved end-to-endpaths and selects the cheapest one.

§A detailed procedure for the computation of cm and cp from the

residual resource level is illustrated in Section 4.¶In a generic reactive routing protocol, a route is computed only

when required; in other words, the protocol does not track the routing

information of every node periodically.

The combination of the main string with the cooperativestring forms the double-string link. Note that the previousprocedure may not result in a fully cooperative path; how-ever, simulation results have evidenced that this situationis very unlikely in scenarios characterised by a density ofnodes large enough.

Finally, it is worth pointing out the following:

(1) Various parameters characterising the physical layer(transmit power, number of subcarriers, etc.) areexploited by the routing algorithms to identify the‘best’ multihop path so that the technique describedearlier can be interpreted as a form of cross-layeroptimisation [10, 25].

(2) The cost function (1) assigns a cost proportionalto the power/bandwidth resources allocated to aspecific link. This allows to exploit the availableradio resources (in terms of energy and bandwidth)in a balanced fashion, jointly improving the net-work lifetime and its ability to satisfy the connec-tivity requests. In particular, the proposed routingstrategy privileges the network operativeness overthe efficiency of the multihop links. Following thisrationale, nodes endowed with plenty of availableenergy and bandwidth are encouraged to work asrelays, whereas nodes short of radio resources tendto preserve their connectivity.

(3) The function (1) is unable to account for the energygain derived from multiuser diversity; in fact, themetric takes into account the radio resources spentby a single node, neglecting the gain originatingfrom its cooperation with other nodes. Moreover,the proposed strategy neglects the capability ofeach node to overhear the transmission of the otherpaths when the overall double-string link is consid-ered. From this perspective, the proposed solutionappears suboptimal; despite this, it is able to set upa mesh link using a simple routing strategy. Anyreader interested in optimal routing the can refer to[6] or [37].

(4) On the one hand, the use of the approximate expres-sion (3) enables a pragmatic approach to the prob-lem of radio resource allocation; however, on theother hand, this may appreciably affect the outagecapacity of the system because the effect of thefading distribution is neglected (e.g. see [38]). Inpractice, this problem can be circumvented, allo-cating resources for target capacity larger than thatstrictly required by the specific application, that is,substituting Equation (4) with the inequality

QC � Cr CCo (9)

where the correction term Co depends on thegiven propagation scenario (i.e. on the fadingdistribution).

(5) Table updating for each node can be forced bothby some types of time information and by the


475


connection establishment phase of other nodes inthe network.

(6) Even if a specific node is not involved in a commu-nication link, it needs to be periodically connectedto the network in order to exchange routing infor-mation. The overhead required for handling this taskis similar to that of more traditional protocols usedin multihop communications and based on proactiverouting.

(7) The overhead originating from the need of link setupcannot be deemed negligible; however, it is notexpected to be substantially larger than that requiredby traditional multihop communication strategies.

(8) For the specific use of cross-layer techniques and,in particular, for the exploitation of physical layerparameters in handling the routing process, the net-work topology and the aim of a fair exploitation ofthe network resources for a given QoS request, ourdesign approach to routing cannot be compared withthe resource-aware routing algorithms available inthe technical literature (e.g. see [4–6, 37, 39].

2.3. Resource management

As already stated in the Introduction, the strategies pro-posed in this manuscript aim at providing efficient but reli-able communications. The severe requirements in terms ofreliability have lead us to consider a connection-orientedapproach to data communications because this can pro-vide efficient multimedia services and, above all, can easethe radio resource management (RRM). In fact, in ourarchitecture, the RRM problem can be solved resortingto well-known techniques, as explained in the following.To begin, note that the routing strategy described in theprevious Section identifies a complete double-string pathconnecting a source node S to a destination node D, thenumber of subcarriers and a rough estimate of the transmis-sion power to be employed over each point-to-point link||;then, the radio resources in terms of power and subcarrier(bandwidth) should be assigned to the transmit nodes oper-ating in each relay stage. To this end, a protocol similar tothe carrier sense multiple access with collision avoidance[19] is exploited. This means that, once S has identified thedouble-string path, an RTS message chain is sent over thenetwork to notify which nodes are involved in the coop-erative transmission and to allocate the radio resourcesrequired in each node. When the RTS reaches D, a CTSmessage chain goes through the reverse path to confirm thatthe communication can take place. This procedure allowseach node to become aware of its collaborative counter-part so that each relay stage is able to jointly identify the

||Note that, once the couple of nodes forming the relay cluster is set

up, a more sophisticated power control algorithm (e.g. see [36]) can be

locally exploited, taking advantage of a punctual channel knowledge.

This discussion, however, is beyond the aim of this paper.

set of available subcarriers characterised by the best chan-nel gains via a simple CSI exchange. Finally, it is worthpointing out the following:

(1) Because a decode-and-forward strategy has beenadopted, distinct relay stages can employ differentset of subcarriers. Then, the radio resource allo-cation can be accomplished on a relay stage basisrather than taking into account the overall end-to-end link [40]; in other words, the resource manage-ment is distributed along each multihop path.

(2) Minor changes to this protocol may be required tohandle deadlocks, as suggested in [41].

(3) At the end of the communication process, the allo-cated resources can be released using a messagechain similar to that mentioned for the connectionestablishment.

3. ERROR PERFORMANCE

In this Section, some analytical tools for the evaluationof the SER for the adopted cooperative communicationtechniques are derived; both single-hop and multihop sce-narios are considered. Our approach relies, in part, on someresults derived in [24], which deals with the performanceachievable both in single-input single-output (SISO) and2 � 1 MISO OFDM systems employing the AlamoutiSTBC in a single-hop link. In this Section, we first applythe methodology proposed in [24] to the evaluation of theSER of a 2 � 1 MISO OFDM system employing TSD.Then, we show how the single-hop results can be exploitedin the multihop case.

It is important to point out the following:

(1) the main target of our analysis is not assessingthe performance comparison between TSD and theadopted STBC scheme. In fact, our efforts are moti-vated by the need of assessing the robustness ofa multihop cooperative link based on the OFDMAtechnique and operating in the presence of a CFO**

in a frequency-selective Rayleigh fading channel.(2) The subcarrier allocation procedure carried out in

the connection establishment phase eases error per-formance analysis. In fact, the co-channel interfer-ence due to nodes belonging to distinct end-to-endlinks and employing the same subcarriers can bedeemed negligible, thanks to the RTS–CTS reserva-tion procedure described in Section 2.3. This claimis motivated by the fact that the reservation pro-cedure is carried out without exploiting any coop-erative transmission technique; this is unavoidablebecause the double-string structure, at that time, isunknown to the nodes excluding the source. Once

**This represents an important impairment in our scenario because

distinct subcarriers can be assigned to different wireless nodes.



the cooperative topology has been set up, coop-erative transmission scheme can be adopted; thisresults in a general reduction of the power radi-ated by each node (as a consequence of the lowersignal-to noise ratio (SNR) requirements to achievea target SER) and, consequently, of the interferenceslevel affecting the neighbour nodes. It is also worthnothing that, for this reason, neglecting the pres-ence of co-channel interference is more optimistic,in terms of error performance, for a noncooperativelink than for any cooperative counterpart employinga transmission power control.

(3) CFOs in wireless nodes produce inter-carrier inter-ference (ICI), which can lead to an apprecia-ble performance degradation [42, 43]. Note thataccounting for the ICI effects can be useful toassess the degradation originating from differentproblems, for example, the mismatch of local oscil-lators employed by wireless nodes belonging to thesame relay stage (and which, in principle, use thesame subcarrier frequency) and by wireless nodesusing adjacent subcarriers in distinct links.

3.1. Error probability for a multiple-inputsingle-output 2�1 orthogonal frequencydivision multiplexing using transmitselection diversity

The methodology proposed in [24] for the evaluation ofthe average symbol probability Pe on a given subcarrier inSISO and MISO OFDM systems is based on the formula

Pe D

1Z0

Pe .�/ pH .�/ d� (10)

where Pe .�/ is the aforementioned probability condi-tioned on an ‘instantaneous’ post-equalised signal-to-interference plus noise ratio†† (SINR) �, and pH .�/

represents the probability density function of SINR. In our2 � 1 MISO OFDM system employing TSD, the post-equalised SINR on the nth subcarrier can be expressed as

�TSD.n/D�.�; �/maxnjhn.k1/j

2 ; jhn.k2/j2o

(11)

where hn.k1/ (hn.k2/) is the subchannel gain between thefirst (second) transmit antenna and the receive antenna and

�.�; �/Djs0j

2

1� js0j2 C ��1

(12)

Here, � is the mean SNR [44], and

s0 Dsin "

N sin . "=N/exp

�j "

�1�

1

N

��, (13)

††A Gaussian interference is assumed in the evaluation of Pe .�/.

where � is the CFO normalised to the subcarrier frequencyspacing [42].

The cumulative distribution function for the randomvariable Y Dmaxfjhn.k1/j

2 ; jhn.k2/j2g is given by

FY .y/D PrfY < yg

D Prfjh0.k/j2 < y; jh1.k/j

2 < yg (14)

We assume that the subchannel gains hn.k1/ and hn.k2/are statistically independent complex Gaussian randomvariables, so that

FY .y/D Prfjh0.k/j2 < yg � Prfjh1.k/j

2 < yg

D FVn;1.y/ � FVn;2.y/ (15)

where Vn;i , jhn.ki /j2, i D 1, 2, are independent chi-square distributed random variables, each having degree 2.Because [45]

FVn;i .y/D 1� exp��y

2�2

�(16)

with �2 D 1=2 (if we assume that the mean statisticalpower associated with each subcarrier gain is unitary),Equation (15) can be expressed as

FY .y/D .1� exp .�y//2

D 1C exp .�2y/� 2 exp .�y/ (17)

and the corresponding probability density function is

fY .y/DdFY .y/

dyD 2 exp .�y/� 2 exp .�2y/ (18)

Then, the probability density function of the SINR (seeEquation (11)) is given by

pH .�/D1

j�.�; �/jfY

��

�.�; �/

�

D2

�.�; �/�

�

�exp

��

�

�.�; �/

�� exp

��

2�

�.�; �/

��(19)

The SER for an M -PSK modulation conditioned on theSINR � can be expressed as [46]

Pe;PSK.�/D1

Zo

exp

��

�a

sin2

�d (20)

with a D sin2. =M/ and ˇ D � =M . SubstitutingEquations (19) and (20) in Equation (10) leads to theexpression for the average SER in Equation (21) (someanalytical details are provided in the Appendix).


477


P TSDe;PSK.�; �/D

ˇ

�

2�.�; �/a

p�.�; �/a.�.�; �/aC 1/

arctan

s�.�; �/aC 1

�.�; �/atanˇ

!

C�.�; �/a

p�.�; �/a.�.�; �/aC 2/

arctan

s�.�; �/aC 2

�.�; �/atanˇ

!(21)

Similarly, in the case of a M -quadrature amplitudemodulation (QAM), it is found that

Pe;QAM.�/D4q

=2Z0

exp

��

�g

sin2

�d

�4q2

=4Z0

exp

��

�g

sin2

�d (22)

with g D 3=2.M � 1/ and q D 1 � 1=pM , and the

corresponding average SER is given by Equation (23)(analytical details are given in Appendix).

P TSDe;QAM .�; �/D 4q

1

2�

�.�; �/gp�.�; �/g.�.�; �/gC 1/

C12�.�; �/gp

�.�; �/g.�.�; �/gC 2/

!

�8q2

8�

�.�; �/gp�.�; �/g.�.�; �/gC 1/

arctan

s�.�; �/gC 1

�.�; �/g

!

C12�.�; �/gp

�.�; �/g.�.�; �/gC 2/arctan

s�.�; �/gC 2

�.�; �/g

!!(23)

3.2. Single-hop relay link

In this section, we focus on the case of space–time cod-ing in a MISO scenario; similar considerations still hold,however, for the TSD case. Moreover, we focus on thescenario illustrated in Figure 2, where S , D, R1 and R2denote the source, the destination, the first and the secondrelay nodes, respectively. Here, the end-to-end link can bedecomposed into a couple of SISO transmissions from S

Figure 2. Cooperative link with a single-relay stage.

to R1 and R2 (first stage), followed by a MISO transmis-sion (fromR1 andR2) towardsD (second stage). First, weconsider an asymmetric scenario, that is a case in which theSISO links S ! R1 and S ! R2 are not characterised bythe same error performance. In this case, we can identifythe following three distinct error events (all referring to thetransmission of a single symbol), which are relevant in theevaluation of the overall error probability in the end-to-endlink.

(1) Event #1—In the first stage, both SISO links S !R1 and S !R2 are affected by transmission errors;this occurs with a probability P SISO

eS!R1� P SISOeS!R2

,

where P SISOeS!Ri

represents the average error proba-

bility of the SISO link S ! Ri , with i D 1, 2; thisyields a unitary error probability in the second stage.

(2) Event #2—In the first stage, an error occurs in thefirst (second) SISO channel, whereas in the second(first) channel, the transmitted symbol is correctlydetected; this occurs with a probability P SISO

eS!R1��

1�P SISOeS!R2

� ��1�P SISO

eS!R1

��P SISOeS!R2

�; in

the second stage (R1, R2 ! D), only a SISO linkcan be exploited for the transmission of correct datawhereas the remaining one, even if no data transmis-sion occurs, is characterised by an error probabilityP SISOeR1!D

(P SISOeR2!D

).(3) Event #3 - In the first stage, no detection

error is made (this occurs with a probability�1�P SISO

eS!R1

��1�P SISO

eS!R2

�, but the collabora-

tive transmission technique employed in the secondstage can still introduce errors (with a probabilityP STBCe or P TSD

e , depending on the use of STBC orTSD, respectively).



Then, the overall average SER of the system with asingle stage of relay and asymmetric channels is

P.R/e .1/D

�P SISOeS!R1

P SISOeS!R2

�

C��1�P SISO

eS!R1

�P SISOeS!R2

��P SISOeR1!D

C��1�P SISO

eS!R2

�P SISOeS!R1

��P SISOeR2!D

C�1�P SISO

eS!R1

� �1�P SISO

eS!R2

��P STBCe

(24)

In a symmetric scenario, we have that P SISOeS!R1

D

P SISOeS!R2

D P SISOe so that Equation (24) turns into

P.R/e .1/D

�P SISOe

�2

C

�P SISOe � 2

�P SISOe

�2��P SISOe

C

��1�P SISO

e

�2��P STBCe (25)

when STBC is adopted.

3.3. Multihop relay link

In this Paragraph we analyse the achievable error perfor-mance for a relay link with multiple hops. We first focuson a double-hop relay link, and then we extend the derivedresults to the case of multiple hops. More specifically, inthe double-hop case we consider the logical communi-cation architecture illustrated in Figure 3. Note that thedata transfer towards the relay nodes R3 and R4 followsthe procedure outlined in Paragraph 3.2 (and sketched inFigure 2), so that the SER perceived by the relay nodes R3and R4 can be computed using (25) and (24) for the sym-metric and asymmetric case, respectively. Moreover, thecooperative transmission fromR3 andR4 towards the des-tination transceiver D can be analysed following exactly

Figure 3. Cooperative link with a double-relay stage.

the same line of reasoning as Paragraph 3.2. Therefore,the overall SER associated with the multihop path charac-terised by two relay stages is given by (see Equation (25))

P.R/e .2/D

�P.R/e .1/

�2

C

�P.R/e .1/� 2

�P.R/e .1/

�2��P SISOe

C

��1�P

.R/e .1/

�2��P STBCe (26)

if the links R3 ! D and R4 ! D are characterised thesame error performance, or, in the most general conditions,by (see Equation (24))

P.R/e .2/D

�P.R/eA .1/ P

.R/eB .1/

�

C�P.R/eB .1/

�1�P

.R/eA .1/

��P SISOeA!D

C�P.R/eA .1/

�1�P

.R/eB .1/

��P SISOeB!D

C�1�P

.R/eA .1/

� �1�P

.R/eB .1/

��P STBCeD

(27)

Here, P .R/eA .1/ and P.R/eB .1/ denote the symbol error

probabilities characterising the first and the second nodes,respectively, within the last (i.e. the second) relay stage.Note that, in this case, the last two parameters correspondto the SER of a system with a single-relay stage. Moreover,P SISOeA!D

, P SISOeB!D

and P STBCeD

represent the SER of the twoSISO links and the SER of the cooperative MISO chan-nel established from the last relay stage to the destination,respectively.

Equations (26) and (27) highlight the relationshipsbetween the single-hop and the double-hop case. It is notdifficult to understand that these equations can be gener-alised to express the SER for a cooperative link exploitingn relay stages in terms of the same quantities for the previ-ous .n�1/ relay stages, provided that each ‘string’ consistsof the same number of nodes. Then, in the symmetric andasymmetric cases, we have the recursive expressions

P.R/e .n/D

�P.R/e .n� 1/

�2C�P.R/e .n� 1/

�2�P.R/e .n� 1/

�2��P SISOe C

C

��1�P

.R/e .n� 1/

�2��P STBCe (28)


479


and

P.R/e .n/D

�P.R/eA .n� 1/P

.R/eB .n� 1/

�CP

.R/eB .n� 1/ �

�1�P

.R/eA .n� 1/

��P SISOeA!D

CP.R/eA .n� 1/ �

�1�P

.R/eB .n� 1/

��P SISOeB!D

C�1�P

.R/eA .n� 1/

� �1�P

.R/eB .n� 1/

��

�P STBCeD

(29)

respectively. Note that the error probability P .R/e .0/ refersto the case of direct transmission; that is, it corresponds toP SISOe .

4. NUMERICAL RESULTS

Numerical simulations have been carried out with atwofold goal: (i) assessing the SER of the proposed com-munication architectures, taking into account utility-basedrouting, radio resource allocation and cooperative ST tech-niques and (ii) validating the analytical models derived inSection 3. Note that the performance of the proposed solu-tion at the MAC and network layers has not been assessedbecause the routing technique exploiting the same topol-ogy and having the same properties as the strategy that wepropose is not available in the technical literature.

The ad-hoc network considered in our simulations hasthe following relevant characteristics.

� Cost function—As far as we know, a study aboutmarginal cost functions suitable to our scenario isunavailable in the technical literature. For this reason,in our work, a heuristic approach has been adoptedto set the price cm.i/ assigned to each subcarrier andthe price cp.i/ of the power exploited for each subcar-rier in Equation (1). More specifically, the followinghas been agreed: (i) cm.i/ is equal to the third powerof the number of busy subcarriers at the considerednode at the instant corresponding to last update of therouting table in the involved node; (ii) cp.i/ dependslinearly on the energy spent by the node transceiveruntil the same epoch. In addition, equal importancehas been assigned to frequency and power resources,so that the proportionality constant in the linear lawrelating cp.i/ to the power is such that, when all thesubcarrier are busy and no energy is left, the marginalcosts cm.i/ and cp.i/ are equal.

� Average power gain—The average power gain ˛ave.i/

in the metric (6) for the i th link has been evaluated,in a time varying scenario, as the time average (com-puted over the last 10 OFDM symbol intervals) of thetime-dependent geometric mean

˛ave.i ; k/D

2640@ NYnD1

jhn .i ; k/j2

1A1=N

375 (30)

where hn .i ; k/ denotes the channel gain associatedwith the nth subcarrier in the kth OFDM symbolinterval.‡‡ Note that, as shown in [33], the perfor-mance gap, in terms of spectral efficiency, betweena system relying on the instantaneous knowledgeof the channel gains and one relying on an aver-age knowledge of the same quantities is expected tobe negligible for slow fading scenarios; in the citedwork, however, the sensitivity of the proposed solu-tion to the procedure employed in the computation ofaverage channel gains has not been investigated.

� Radio resource use—The following model for theexploitation of radio resources in the overall ad-hocnetwork has been adopted. For each node, the percent-age of busy subcarriers and that of consumed energyhave been assumed to be Gaussian distributed. In par-ticular, the number of busy subcarriers (the amountof spent energy) has mean value N=5.E=2/ and stan-dard deviationN=8 (E=6), whereE denotes the nodeinitial energy.

� Channel modelling—Statistical independence hasbeen assumed between the channels associated withdistinct links and, for a given link, between thecomplex gains associated with different subcarriers(which are also affected by the effects of CFO). Thechannel gain affecting each subcarrier is modelledas a complex Gaussian random variable having zeromean and unitary variance (i.e. Rayleigh fading isassumed).

In our work, the error performance offered by adirect link between the source S and the destinationDhas been also assessed in order to estimate the energysaving provided by a multihop communication archi-tecture operating over the same distance. To achieve afair comparison, the large-scale model [47]

PL.d/D PL.d0/

�d

d0

�n(31)

for the path loss PL.d/ at a distance d has beenadopted (shadowing is neglected), where n is the pathloss exponent, d0 denotes the reference distance andPL.d0/D 1. In addition, we have assumed that in ourrelay system the distance between two consecutiverelay nodes is equal to d0 so that the large-scale pathloss is unitary. In other words, the distances betweenthe nodes of adjacent relay stages are the same (andare unitary). As far as the direct link is concerned,the received power reduces with distance accordingto Equation (31), with nD 5 to account for an indoorpropagation scenario with rich scattering. Note that,however, different models for both shadowing andpath loss can be easily acoounted in the term ˛ave.i/.

‡‡Channel variations are deemed negligible over each OFDM symbol

interval.



In addition, in all the following performance results, wealways assume the following: (i) the SNR is defined asEb=N0, where Eb , defined as the average received energyper information bit, is equal to the energy spent over thewhole source-to-destination link per information bit; (ii) allthe communications channels are static, unless explicitlystated, and, in the presence of time variations, the subchan-nel gains can be deemed static over each OFDM symbolinterval and are characterised by a Jakes’ Doppler spec-trum with Doppler bandwidth, normalised to the symbolrate 1=Ts , BDTs ; (iii) the power poured on each subcar-rier is inversely proportional to the channel gain ˛ave.i/

(see Equation (5)); (iv) the number of OFDM subcarriersin each node is N D 256, with 192 subcarriers employedfor information data transmission and the remaining onesfor both guard and synchronisation purposes; and (v) chan-nel coding schemes have not been used. As far as the lastpoint is concerned, we note that the main scope of thiswork is to assess the spatial diversity gain provided bycooperative architectures, whereas channel coding allowsto compensate for the frequency diversity loss related toOFDM signalling [48–50].

Figure 4 refers to a single-hop link employing binaryphase-shift keying (BPSK) and shows some SER results

10-7

10-6

10-5

10-4

10-3

10-2

10-1

SER

2520151050

SASH (simulated) STBC (simulated) TSD (simulated) SASH (analytical) STBC (analytical) TSD (analytical)

Eb/N0, dB

Figure 4. symbol error rate (SER) comparison between analyti-cal results and their simulated counterparts. Transmit selectiondiversity (TSD) and Alamouti’s space–time block code (STBC) ina 2�1 multiple-input single-output system and a single-antenna

single-hop (SASH) system are considered.

generated by means of the error rate formulas derived inthe following: (i) Section 3.1 for a MISO 2 � 1 systememploying TSD and (ii) [24] for both a MISO 2 � 1

ST block-coded system and for a system exploiting asingle-antenna single-hop transmission from S to D.Such results are compared with those resulting from ournumerical simulations. These results evidence an excellentagreement between simulation results and their analyticalcounterparts.

Some SER results concerning multihop relay links areshown in Figures 5 and 6 referring to BPSK and 16-QAMformats, respectively. Here, the case of single-antennatransmission and that of cooperative signalling (based onST block coding or TSD) are considered and the presenceof NR D 1 or 3 relay stages is assumed. The perfor-mance offered by a single-antenna multihop transmissionis also shown for comparison. These results evidence thefollowing: (i) the energy gain offered by multihop archi-tectures over single-hop systems is large because of theappreciable path loss predicted by the model (31); (ii)cooperative schemes can benefit from a substantial spatialdiversity gain; (iii) the TSD-based cooperative scheme out-performs the one based on Alamouti’s coding by 2–4 dB;

10-7

10-6

10-5

10-4

10-3

10-2

10-1

SER

302520151050

SASH, NR = 1 SASH, NR = 3 SAMH, NR = 1 SAMH, NR = 3 STBC, NR = 1 STBC, NR = 3 TSD, NR = 1 TSD, NR = 3

Eb/N0, dB

Figure 5. Symbol error rate (SER) performance offered bysingle-hop and multihop transmissions employing binary phase-shift keying signalling. The cases of single-antenna and cooper-ative signalling are considered in the presence of NR D 1 and3 relay stages. SASH, single-antenna single-hop; SAMH, single-antenna multihop; STBC, space–time block code; TSD, transmit

selection diversity.


481


10-4

10-3

10-2

10-1

100

SER

302520151050

SASH, NR = 1 SASH, NR = 3 SAMH, NR = 1 SAMH, NR = 3 STBC, NR = 1 STBC, NR = 3 TSD, NR = 1 TSD, NR = 3

Eb/N0, dB

Figure 6. Symbol error rate (SER) performance offered bysingle-hop and multihop transmissions employing 16-quadratureamplitude modulation signalling. The cases of single-antennaand cooperative signalling are considered in the presence ofNR D 1 and 3 relay stages. SASH, single-antenna single-hop;SAMH, single-antenna multihop; STBC, space–time block code;

TSD, transmit selection diversity.

and (iv) the spatial diversity gain increases slightly withthe number of relay stages. The last point can be relatedto the fact that the availability of multiple parallel con-nections enables to recover from errors appearing in somerelay stages.

The robustness of the proposed cooperative architec-tures against frequency synchronisation inaccuracies isevidenced by Figure 7, referring to the case of NR D 3

relay stages, each using BPSK and operating in the pres-ence of normalised CFOs � D 0:01 and 0:02. Note thatonly a negligible error performance degradation is visibleat large SNRs and error floors are well below 10�6.

Finally, the results shown in Figure 8 refer to the caseof NR D 3 relay stages using BPSK in a time-varying sce-nario with BDTs D 10�1, 10�2 and 10�3. They aim atshowing the impact of a delayed update in the CSI avail-able in the network nodes on the routing algorithm and onTSD if used. In fact, in this case, both SISO detection andST decoding rely on the availability of ideal CSI in eachnetwork node. Our results evidence the robustness of theproposed solutions against delayed CSI so that the needof a limited overhead should be expected in the proposedrouting approach.

10-7

10-6

10-5

10-4

10-3

10-2

10-1

SER

302520151050

SAMH SAMH, CFO 1% SAMH, CFO 2% STBC STBC, CFO 1% STBC, CFO 2% TSD TSD, CFO 1% TSD, CFO 2%

Eb/N0, dB

Figure 7. Symbol error rate (SER) performance offered bymultihop transmissions employing binary phase-shift keying sig-nalling in the presence of a normalised carrier frequency offset(CFO) � D 0:01 and 0:02. The cases of single-antenna andcooperative signalling in the presence of 3 relay stages are con-sidered. STBC, space–time block code; SAMH, single-antenna

multihop; TSD, transmit selection diversity.

5. CONCLUSIONS

A technical solution to the problem of the design of anad-hoc wireless network based on OFDMA and capableof offering reliable, scalable and low latency serviceshas been proposed. Our design methodology is basedon a cross-layer optimisation of the network, data-linkand physical layers. Both the devised routing algorithmand RRM techniques are distributed and aim at maximis-ing the lifetime of the network; in particular, routing isbased on cost metric depending on the residual powerand bandwidth available at each node. In addition, the useof specific cooperative communication techniques allowsto exploit spatial diversity, thus further improving theoverall energy efficiency of the network. The connection-oriented nature of multihop double-string paths makesthe proposed ad-hoc network suitable to real-time com-munications; the achievable energy efficiency, however,may decrease in the presence of a large burstiness of thedata traffic.

Numerical results have shown that cooperative trans-mission techniques can provide a large energy saving(or, equivalently, more reliable links) with respect to



10-6

10-5

10-4

10-3

10-2

10-1

SER

20151050

SAMH STBC TSD

BD Ts = 0

BD Ts = 10-3

BD Ts = 10-2

BD Ts = 10-1

Eb/N0, dB

Figure 8. Symbol error rate (SER) performance offered bymultihop transmissions employing binary phase-shift keying sig-nalling in the presence of a delay in the channel state infor-mation available at the network nodes for routing and antennaselection (when transmit selection diversity (TSD) is used). Thecases of single-antenna and cooperative signalling in the pres-ence of NR D 3 relay stages are considered. The communica-tion scenario is time varying with various Doppler bandwiths(BDTs D 10�1, 10�2 and 10�3). SAMH, single-antenna multihop;

STBC, space–time block code.

traditional solutions, even in the presence of a reducednumber of hops and of a severe frequency selectivity of theradio channel.

APPENDIX: DERIVATION OF THEPROBABILITY PTSD

e

Substituting Equations (19) and (20) in Equation (10) gives


Z 10

Pe.�/p Oy.�/d�

D2

�.�; �/

Z ˇ

0

Z 10

exp .��

�

�a

sin2 C

1

�.�; �/

�d�

�

Z 10

e��

�a

sin2 �C 2�.�;�/

�d�

d (32)

from which it can be inferred that


2

�.�; �/

Z ˇ

0�.�; �/d

�

Z ˇ

0

1

2�.�; �/d

�

Z ˇ

0

�2.�; �/a

�.�; �/aC sin2 d

C

Z ˇ

0

12�

2.�; �/a

�.�; �/aC 2 sin2 d (33)

Then, Equation (21) can be easily derived fromEquation (33) taking into account that [51]

Zdx

aC b sin2.x/D

sign.a/pa.aC b/

�

� arctan

raC b

atan.x/

!(34)

with .b=a/ > �1 (where sign.a/ denotes the sign of thereal quantity a). Similarly, substituting Equations (19) and(22) in Equation (10) produces, after some manipulation,

P TSDe;QAM.�; �/D

8q

0B@ =2Z0

�1�

�.�; �/g

�.�; �/gC sin2

�d

�1

2

=2Z0

�1�

�.�; �/g

�.�; �/gC 2 sin2

�d

1CA

�8q2

0B@ =4Z0

�1�

�.�; �/g

�.�; �/gC sin2

�d

�1

2

=4Z0

�1�

�.�; �/g

�.�; �/gC 2 sin2

�d

1CA

(35)

Finally, solving the two integrals in the right hand side ofEquation (35) by means of Equation (34) leads easily toEquation (23).

ACKNOWLEDGEMENT

The authors wish to acknowledge the activity of theNetwork of Excellence in Wireless COMmunicationsNEWCOM++ of the European Commission (contract no.216715) that motivated this work.


483


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AUTHORS’ BIOGRAPHIES

Simone Sergi was born in Modena, Italy, in April 1982.He received the Dr. Ing. Degree in TelecommunicationEngineering in 2006 and the PhD Degree in 2010, bothfrom the University of Modena and Reggio Emilia, Italy.His main research interests lie in the areas of cooperativecommunication techniques for wireless ad-hoc and sensor

networks, with particular emphasis on the development ofdistributed protocol for the organisation and exploitation ofvirtual antenna array, resource management and distributedsignal processing.

Fabrizio Pancaldi was born in Modena, Italy, in July1978. He received the Dr. Eng. Degree in Electronic Engi-neering (cum laude) and the PhD degree in 2006, bothfrom the University of Modena and Reggio Emilia, Italy.Since March 2006, he is holding the position of Assis-tant Professor at the same university and he gives thecourses of Telecommunication Networks and ICT Sys-tems. He works in the field of digital communications, bothradio and powerline. His particular interests lie in the widearea of numeric transmissions, with emphasis on chan-nel equalisation, statistical channel modelling, space–timecoding, radio localisation, channel estimation and clocksynchronisation.

Giorgio Matteo Vitetta received the Dr. Ing. Degree inElectronic Engineering (cum laude) in 1990, and the PhDDegree in 1994, both from the University of Pisa, Pisa,Italy. From 1995 to 1998, he was a Research Fellow withthe Department of Information Engineering, University ofPisa. From 1998 to 2001, he was an Associate Profes-sor with the University of Modena and Reggio Emilia,Modena, Italy, where he is currently a full Professor. Hismain research interests lie in the broad area of communica-tion theory, with particular emphasis on coded modulation,synchronisation and channel equalisation.


Cross-layer design for double-string cooperative communications in wireless ad-hoc networks

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