Ludovic-Alexandre Vidal

Franck Marle

Jean-Claude Bocquet

BUILDING UP A PROJECT COMPLEXITY FRAMEWORK USING AN INTERNATIONAL DELPHI STUDY

Keywords: project management, complexity, systems analysis, Delphi methodology, position, gender, expert systems, Spearman Rank, measure, Analytic Hierarchy Process

Project management has spread around the world to become what it is today, that is to say a set of theories, principles, methodologies and practices. Past research works argue for a paradigm shift so that one could focus more on project complexity to manage projects more efficiently. However, there is a lack of consensus on what project complexity is, which makes it difficult to understand it good. As a consequence, this article reviews the literature in order to build a standardized project complexity framework. Then, it describes how a Delphi study was conducted over a panel of academic and industrial experts to refine it. Further on, it draws some conclusions regarding project complexity factors perception, functions of experts type (academic/industrial experts, gender study). Finally, after a correlation study based on the Spearman Rank, some perspectives are given to illustrate the applications of the project complexity framework which is built.

Introduction

A project is "is a temporary endeavor undertaken to create a unique product or service" (PMI 2004). Project management has grown up to become what it is today, that is to say a set of theories, principles, methodologies and practices, sometimes included in standard body of knowledge as PMI (PMI 2004) and IPMA (IPMA 2006). The traditional vision tends to rely upon the notions of planning and control to propose models and prescriptions as ways to increase the ability of humans to control complex worlds [START_REF] Stacey | Complex responsive process in organizations: learning and knowledge creation[END_REF][START_REF] Wood | Mind the gap ? A processual reconsideration of organizational knowledge[END_REF]. For all practical purposes, many studies have been done, based on statistical calculations or surveys. Their conclusion is that current methods have shown their limits, since they cannot face anymore the stakes of ever growing project complexity. Limits and lacks have been detected in research as well as in industry about the project predictability, since usual parameters (time, cost and quality) are clearly not sufficient to describe the complete situation at a given time [START_REF] Meijer | Reducing complexity through organisational structuring in manufacturing and engineering[END_REF].Jaafari thus argued that "a paradigm shift in project management is essential for it to be relevant and effective in the complex society of this century" [START_REF] Jaafari | Project management in the age of complexity and change[END_REF]. On his side, Williams underlined that "it is clear that classical project management techniques are unsuitable for dealing with [complex] projects" (WILLIAMS 1999): he gave the example of structural complexity since decomposition models (such as Work Breakdown Structure) cannot account for the compounding effects when individual phenomena, evolutions and perturbations accumulate within the project. He concluded that "what are needed, then, are new ways of looking at modern, complex projects, new models and techniques for analyzing them, new methods for managing them -in fact, new paradigms to underline our approach to them.".This article thus aims at building up a standardized project complexity framework in order to understandbetter the concept of project complexity, by understanding better its complex structure. This work thus addresses the issue of project structural complexity. This research issue is addressed regarding a project manager oriented view and mainly addresses engineering design and product or service development projects.

Problem setting and methodology

Whatever the vision, understanding project complexity to improve project management (and therefore project success rate) has thus become an even more strategic issue for organisations. Still, some work has to be done to clarify the notion of project complexity in order to cope with it more efficiently (VIDAL ET AL., 2007). This paper thus aims at addressing the notion of project complexity in terms of its characteristics and factors in order to build a standardized project complexity framework that could be a reference for any project. Our research methodology is based upon six successive steps.

 Reviewing the literature to build up a first version of the project complexity.

 Writing the Delphi survey using the first version of the project complexity framework.  Selecting the experts panel for the Delphi survey.  Conducting the Delphi survey according to the Delphi methodology.  Analyzing and discussing the results of the Delphi survey.

 Refining the project complexity framework using the results of the Delphi survey.

Elaborating the first version of a project complexity framework

Understanding projects as systems

Referring to the field of systems analysis [START_REF] Le Moigne | La théorie du système général. Théorie de la modélisation[END_REF][START_REF] Penalva | La modélisation par les systèmes en situations complexes[END_REF], a system is an object, which, in a given environment, aims at reaching some objectives (teleological aspect) by doing an activity (functional aspect) while its internal structure (ontological aspect) evolves through time (genetic aspect) without losing its own identity. According to this definition, a project can be considered as a system (VIDAL AND [START_REF] Vidal | Understanding project complexity: implications on project management[END_REF]. Indeed, it possesses the four aspects listed above. A project exists within a specific environment and aims at reaching objectives given this context (teleological aspect). A project has to accomplish a set of activities using some methods and methodologies (functional aspect). A project has an internal structure composed of resources, deliverables, tools, workers, etc… (ontological aspect). Finally, a project evolves through time, via resource consumption, product delivery, members' changes and gain of experience, without losing its own identity (genetic aspect).

Identifying project complexity factors : methodology

First, a literature review on project management and project complexity factors was carried out. The ambition of this literature review is to be relevant, and illustrative of what project structural complexity is in fieldwork (as the final framework is to encompass all the aspects of project complexity). However, it must be underlined that some factors may be absent from this version of the framework, and that this one is likely to be evolving. This literature review was performed, keeping in mind the definition of Edmonds which underlines complexity as the property which makes it difficult to formulate the behaviour of the project system (both in terms of diagnostic and prediction). We chose this initial definition and approach in order to draw the literature review by the consequences of project complexity, so that implications on project management processes are more direct. As a consequence, an important point we need to underline is that project ambiguities and uncertainties are to be considered as manifestations of the difficulty to formulate the project behaviour, given its complex structure. This means they are considered here as a consequence (and as crucial stakes) of project complexity. Therefore, uncertainty or ambiguity-related factors are not present in the framework, although sometimes cited as project complexity sources in the literature. In fact, in the literature, there are traditionally two kinds of ways to look at complexity, one including uncertainty factors into complexity factors (BACCARINI,1996) , and the other kind of approaches excluding them to consider them only as consequences or coexisting factors which lead to the existence of risks [START_REF] Aven | A unified framework for risk and vulnerability analysis covering both safety and security -Reliability engineering & systems safety[END_REF], (HELLSTRÖM, 2007). Our works belong to the second kind of approaches.

This issue being stated, the methodology which was followed to identify these factors was the following:  Step 1 -Constitution of a first list of factors usinga literature review based on: o Some project management academic standards (PMI, 2004), (IPMA, 2006) o Some project management industrial standards [START_REF] Iso | ISO:10006 Quality management systems". Guidelines for quality management in projects -ISO IVAN, I. and A[END_REF], [START_REF] Afnor | Modelling and managing project complexity[END_REF], [START_REF] Afnor | Modelling and managing project complexity[END_REF] o Some publications focusing on complexity and project complexity aspects (BACCARINI, 1996), (CALINESCU ET AL., 19998), [START_REF] Edmonds | Syntactic measures of complexity[END_REF], [START_REF] Williams | The need for new paradigms for complex projects[END_REF]

Steps 1 to 3 -Constituting a first list of factors using a systems thinking-based approach and common denominations

In order to identify factors, a literature review was conducted using the four aspects of systems thinking, which need to be encompassed in a project complexity framework.Some insights about the identification of factors and discussions about them are given at the end of the article in Appendix A.

Step 4 -Building up a first version of the framework using common denominations

The point is that speaking in terms of teleological, genetic, functional and ontological aspects of project complex is not the easiest manner to communicate about complexity in real projects and see what are the concrete phenomena behind these notions. We thus claim for a gathering of these factors into four more intuitive groups (see Figure 1), which were cited in several of the references which permitted to list factors. The first group gathers the factors that are relative to the size of the project system. The second one gathers those that are relative to the variety of the project system. These two first groups globally correspond to the ontological aspect of the project system. The third one gathers those that are relative to the interdependencies and interrelations within the project system, which corresponds to some extent to the functional pole of the project system. Finally, the fourth one deals with the context-dependence of project complexity, which mainly corresponds to the teleological and genetic poles of the project system.

Please insert Figure 1

The gathering of the identified project complexity factors into these four distinct groups makes more meaning both for direct industrial use (as these denominations make more sense for fieldwork) and for academic establishment (since these denominations have widely been used in research articles for instance). Indeed:

 Project size is to be defined as a whole as the sizes of elementary objects which exist within the project system. These sizes are likely to be assessed using appropriate quantitative measure (for instance time scale, cardinal scale, etc…).This aspect of project size (which is somewhat close to the ontological aspect of project complexity in terms of number of identified elements) then seems to be a necessary condition for project complexity which makes sense. Indeed, recent papers notably state that any organisational system should be over a minimum critical size to be considered as a complex system (CORBETT ET AL..,2002).  Project variety is to be defined as a whole as the diversity of elementary objects which exist within the project system.This aspect of project variety (which is somewhat close to the ontological aspect of project complexity in terms of diversity of identified elements) is indeed a group which makes sense. Indeed, as mentioned by Sherwood and Anderson (SHERWOOD JONES AND [START_REF] Sherwood Jones | Diversity as a determinant of system complexity[END_REF], "diversity relates closely to the number of emergent properties".Moreover, as underlined by [START_REF] Corbett | Tackling industrial complexity[END_REF], "the one thing that comes through loud and clear is that complexity is tied up with variety, be it in the world of biology, physics or manufacturing".  Project interdependence is to be defined as the existence of relationships between elementary objects within the project system.This aspect of project interdependence (which is somewhat close to the functional aspect of project complexity in terms of interactions between elements to execute the project) is indeed another category which makes sense. As underlined by several authors, interdependencies (and all the notions related with them such as interactions, interrelationships or interfaces) are even likely to be the greatest drivers of project complexity. Besides, [START_REF] Rodrigues | The role of system dynamics in project management[END_REF] explain that "experience suggests that the interrelationships between the project's components are more complex than is suggested by the traditional work breakdown structure of project network", suggesting that traditional project management tools cannot be sufficient to catch the reality of interdependence. This seems all the more problematic since "there is a complete interdependence between the components of the complexity: each element will depend and influence on the others" (CALINESCU ET AL., 1998).  Project context is defined here as what refers to the environment within which a project is undertaken.This aspect of project context-dependence (which is somewhat close to the teleological and genetic aspects of project complexity is indeed another relevant category. First, [START_REF] Chu | Theories of complexity -Common denominators of complex systems[END_REF] underline that contextuality is an essential feature of complexity, considering it as a common denominator of any complex system. The context-dependence of project complexity is also stressed by [START_REF] Koivu | Institutional complexity affecting the outcomes of global projects[END_REF] who notably insist on the fact that "the context and practices that apply to one project are not directly transferable to other projects with different institutional and cultural configurations, which have to be taken into account in the processes of project management and leadership". As a whole, this literature review and proposed classification permits to build a project complexity framework which aims at being a reference for any project manager to identify and characterize some aspects of its project complexity, so that he can understand more efficiently the stakes of its project complexity management. Once again, even though we had the ambition to be quite exhaustive, some others project complexity factors are likely to be added to this framework. Particular attention should be paid to the specificity of each project (and its context) when using this framework.

Please insert Table 1

Hereinbefore, inTable 1, the completed project complexity framework we have built using this research is exposed. It has to be noticed that approximately 70% of the identified complexity factors are related to organizational aspect, not technical. Principal sources of project complexity are thus likely to be organisational factors, as underlined by some former works on this issue [START_REF] Shenhar | Introduction[END_REF]. Moreover, even though the factors belonging to the family of interdependencies within the project system are hardly more numerous that the others, this group appears in the literature as the most important for project complexity and day-to-day project management [START_REF] Marle | Modèle d'informations et méthodes pour aider à la prise de décision en management de projets[END_REF]. Interactions management is likely to be both one of the causes of greatest value creation during the project and one of the riskiest parts of the project.

First applications of this framework

Defining project complexity

This literature review being made, this framework being elaborated and the concepts being discussed, we now propose a refined definition of project complexity. We state that: Definition :Project complexity is the property of a project which makes it difficult to understand, foresee and keep under control its overall behaviour, even when given reasonably complete information about the project system. Its drivers are factors related to project size, project variety, project interdependence and project context. This definition is an adaptation of Edmonds which was presented formerly [START_REF] Edmonds | Syntactic measures of complexity[END_REF]. The differences we introduce is first that there is no reference to any project model or language of modelling, and second, that its drivers are directly included in the definition to make the concept of "complexity" more easily comprehensible. Contrary to other definitions which were presented in our state of the art, this definition, through the inclusion of drivers, also permits to encompass every aspect of project systems, since those categories (and drivers) were identified using a systems thinking approach (the objective of which is to have an holistic approach to better understand project systems).Every aspect of systems thinking is thus part of the overall behaviour of the project system, which means that, according to this definition, project complexity is the property which makes it difficult to understand, foresee and keep under control any of these aspects. This definition we propose is finally different from other definitions of project complexity since it is:

 Oriented regarding the practical consequences of project complexity, which is to assist more easily complex project management,  Based on four aspects which permit to describe with simple words crucial aspects of project structural complexity, which is to improve communication about it. As a whole, as noticed by Ivan and Sandu (IVAN AND SANDU, 2008), there are three types of project complexity (as in the case of the majority of project characteristics): estimated, planned and actual. According to them, "Estimated complexity is based mostly on expertise gathered from of similar past projects. Planned complexity is a refinement of the estimated complexity, as some corrections are applied in order to adapt to the distinct project context. Actual complexity is finally measured after the project has been implemented." This classification permits us to insist on three direct possible uses of the project complexity framework which is proposed here:

 Predictive project complexity analysis. This application consists in the a priori project complexity evaluation. This finds direct implications in the management of the pre-project period and the project start processes. As underlined in [START_REF] Gareis | Critical infrastructure and systemic vulnerability :Towards a planning framework -Safety science[END_REF] "the project start is the most important project management subprocess, because in it the bases for the other project management subprocesses, such as the project plans, the project communication structures, the relationships to relevant environments, are established". As for them, (DVIR ET AL., 1998) also note that "pre-contract activities […] are highly influential in all types of projects".

Predictive project complexity analysis is thus a crucial issue to achieve properly the pre-contract and project start phases. Using the project complexity framework as a checklist is to ensure a better identification of possible complexity sources within the project. It may also influence decisions which are directly made during these phases. For instance, project team constitution should be addressed in terms of possible complexity sources by focusing on the factors "staff quantity", "diversity of staff (experience, social span,…)", etc… By paying attention to such phenomena when making decisions during the pre-contract and start phases, one is to avoid some unnecessary or undesired complexity sources.  Diagnostic project complexity analysis.

Diagnostic project complexity analysis is to be performed during the execution phase of the project. This analysis permits to assist project management processes during the execution phase, such as planning and re-planning, monitoring and control, decision-making, etc… The identification of existing project complexity sources during the project permits to stand back on some issues of the execution phase. We claim for the conjoint use of traditional project management tools as a basis and a more holistic approach which can permit to analyse more properly project complex situations. This approach is facilitated by the project complexity framework which is proposed here. Generally, people have a tendency to focus on some detail which appear to them as existing crucial problems in a project. But focusing on detail does not permit them to solve the problem, which causes some project failures (SHENHAR AND DVIR, 20007). Looking at these problems through the glass of complexity permits to have a holistic vision of the tackled issue and thus to make more influent decisions. Having a better vision of interdependencies for instance permits to understand better propagation phenomena and change implications on a whole project. In the case of design engineering for example, such understanding of change propagation is to avoid unnecessary and costly rework during the project (AUSTIN ET AL. 2002), (CLARKSON ET AL. 2004), [START_REF] Steffens | Change decisions in product development projects[END_REF]. Adaptive management practices should thus be employed when facing complex situations (SHENHAR, 2007), [START_REF] Lindkvist | Project management: exploring its adaptation properties[END_REF].  Retrospective project complexity analysis.

Retrospective project complexity analysis using the project complexity framework is to assist project closure and return on experience processes. Indeed, the a posteriori identification of complexity sources which existed during the project permits to assess what happened and thus draw some lessons for the future. The overall processes of lessons identification and lessons learned future use is to give some precious experience to the firm. As underlined by [START_REF] Williams | The contribution of mathematical modelling to the practice of project management[END_REF], "management's role in facilitating and encouraging learning from projects is vital", and particularly in the context of complex projects. Learning finally improves project maturity and future project complexity management within the firm. Indeed, building up databases on possible complexity sources of a firm's projects for instance is to facilitate future predictive and diagnostic project complexity analysis.

Case study: Renault Multi-Purpose Vehicle (MPV) development projects

In order to illustrate this framework and show how it can be useful to identify possible complexity sources within a project, the case of several Renault Multi-Purpose Vehicle (MPV) development projects are explored. This case study corresponds to the third utilisation of the framework which was stated before, that is to say retrospective project complexity analysis. As an introduction, general description of MPVs is the following. The engine is mounted close to the front edge of the car, and its elements are generally grouped higher than in other cars, which minimizes front overhang length. Generally, seats are located higher than in lower cars, leaving more space for the legs. Larger minivans usually feature three seat rows, with two or three seats each. Smaller minivans tend to have two seat rows, with a traditional 2-3 configuration. Most current minivans are front-wheel drive. The main advantage is better traction than rear-wheel drive cars under slippery driving conditions. This configuration also permits to have more inner area along the floor, due to the absence of the driveshaft hump. Most modern MPVs feature unibody architecture (this is notably the case of the two projects which are to be studied), which offers better crashworthiness and a much more comfortable ride than a body-on-frame chassis.Two MPV development projects are the main basis of this study: the Renault Espace development project and the Renault Twingo development project. Some forewords about these two projects are given hereunder in order to appreciate the scope and context of these two projects. The framework was used in this case to perform a retrospective complexity analysis and learn lessons about these two projects regarding project complexity. Some factors were listed using the framework. For instance, we give three examples in this article:

 Example of SIZE-ORG factors : Number of stakeholders can affect project complexity. For instance, in the case of the Renault Espace development project, the coordination between the employees, cultures, processes, etc… of Renault and Matra due to the cooperation of these two firms implied greater managerial and organisational complexity.  Examples of INT-TECH factors Interdependence of the components of the product appeared to be a critical complexity factor in the Renault Espace development project. The technological innovation due to the MPV format implied changes in the windscreen inclination. Even though they had not been predicted, because of the component interdependence, this implied changes in the front windscreen wipers and also in the engine position. As for the Renault Twingo development project, resource and raw material interdependence made the project more complex regarding the same components. Indeed, a new kind of glass was used to elaborate the windscreen. But it had not been seen that this new material which was used was not compatible with the glue which was formerly used to fix the windscreen wipers. This implied some changes and rework in the end.  Example of CONT-ORG factors Local laws and regulations appeared to make these two projects more complex when trying to extend the commercialisation and production of these vehicles into different European countries. For instance, new local laws and norms appeared in the mid 1980s in Germany. These ones were not all compatible with the Renault Espace technical specifications and production processes, which implied major changes in order to keep the possibility for the Renault Espace to exist in Germany.

These were examples of project complexity factors which can be identified through the use of the project complexity framework. As a whole, a synthesis of identified project complexity factors in these two projects using this retrospective analysis is proposed in Table 2, where expert judgments attributed some importance (from negligible to 3) to possible project complexity factors. Still, if this list of factors permit to have a closer look on projects in terms of complexity, the factors are still very numerous and no a priori classification of these factors (in terms of the importance of their average contribution to project complexity) is proposed. That is why we carried out an international Delphi study to refine this framework.

Please insert Table 2

Conducting a Delphi study to refine the framework

The Delphi methodology

Refining our results by performing an international Delphi study is indeed to permit to have a more reliable definition and understanding of the project complexity framework we have built. The Delphi methodology (LINSTONE ET TUROFF., 2002), which was originally developed in the 1950's, is a systematic and interactive method which relies on a panel of independent experts. It is a very flexible tool which permits to reach a consensus, through the collection of experts' opinions on a given issue during successive stages of questionnaire and feedback. Direct confrontation of the experts, whose anonymity is kept at every stage of the study, is avoided (OKOLI AND PAWLOWSKI, 2004). As mentioned in (SKULMOSKI ET AL., 2007), " the Delphi method is well suited as a research instrument when there is incomplete knowledge about a problem or phenomenon". It has proven over the years to be a very popular tool for framework building, forecasting, issues prioritizing, decision-making, etc… It has been used for several studies in the field of industrial engineering and project management, which encouraged us in our research work. For instance, Schmidt and al. used the Delphi method in order to build up a list of common risk factors in software projects (SCHMIDT ET AL., 2001). Our research methodology is based on a two-round Delphi process (see Figure 2):

Please insert Figure 2 The Delphi survey was conducted using blind copy electronic mail sending to international academic and industrial experts in project management in order to save time and expenses for both the surveyor and the experts. The questions were formulated using a 5-level Likert scale, in order to express the importance of the contribution of a given factor to project complexity (from no contribution -1-to essential contribution -5-, leaving the possibility to answer "do not know" and "do not want to answer"). Furthermore, participants could leave commentaries and questions at any moment on any point of the Delphi questionnaire in order to generate some discussions about it or to suggest other potential project complexity factors. At each round, a little more than three weeks were left to the panelists to answer the survey.

Panel selection and survey scales definition

The Delphi survey group size can be very different in the literature. However, it is often recommended to have a group between 9 and 18 participants in order to draw some relevant conclusions and avoid at the same time difficulty to reach consensus among experts. We argue, such as in [START_REF] Okoli | The Delphi method as a research tool: an example, design considerations and application[END_REF], that an experts categorization should be made properly before undertaking the Delphi survey in order to build up the most representative panel. As for them, Skulmoski and al. require different aspects for the participants to be selected in the Delphi survey panel (SKULMOSKI ET AL., 2007):  Sufficient knowledge and experience about the survey issues,  Capacity, willingness and time to participate,  Good communication skills. Our prospective panel was constituted of 38 experts, 19 of them being industrial practitioners and 19 being academics, and at the same time 19 being men, 19 being women. Of those 38 solicited experts, 18 actually participated to the study from the beginning to the end, 10 of them being academics and 8 being industrials, and at the same time 10 of them being women, and 8 being men. Academics were notably identified with their publications regarding project complexity in the Web of Science and specialized conferences or revues (International Journal of Project Management, PMI Research Conference, etc…). Industrial practitioners were identified through the browsing of some professional social networks (Linkedln), the identification of some project managers of large firms websites, and the identification of project managers whose education was followed in some high standard schools, universities and institutions. We thus consider that the overall results are going to be relevant since the interrogation of 18 experts permits to trust them. In order to do comparisons and generate discussions during the next section, we also study separately men, women, academics and industrials. Even though the suggested minimum quota of 9 experts is not reached for men and industrials (8 for each category instead of 9), we will consider the results as relevant. We do insist here that the study was thus conducted with a project manager-oriented view.

Results and discussions

Global results and discussion

Our discussion starts with the overall analysis of the panelists' answers to our survey. The convergence of the experts was fast, even though they were of different origins and backgrounds. It must be noted that the factors which appear earlier in the Delphi questionnaire do not receive significantly higher or lower scores than the factors which appear at the end of it. This implies that there is no direct correlation between the order of the questions and the scores of the factors. This was notably observed when alternating the orders of the tabs in the Delphi questionnaire without observing a change in the average scores of each group of factors.A synthesis of their reached consensus can be seen after in Tables 3 and4.

Please insert Table 3

Average scores and mean deviations were calculated to perform the analysis of this questionnaire. Mean standard deviation of the answers, as shown in Table 3, is 0.682, which makes it a satisfying consensus for (also notice that all standard deviations are less than 1). Table 4 shows the statistical results of the survey. Average values lie between 2.278 and 4.889.

Please insert Table 4

When having a closer look at the answer of the panel, some points are to be noticed about project complexity:

 First, of the first 18 identified project complexity drivers after the panelists' evaluation (the mean value of which is over 4.500), only 2 of them are of a technological type (11.1%), as shown in Table 3. Organizational complexity thus seems to be the greatest source of complexity for projects and project management today. Project managers should thus focus on organizational issues when tackling and dealing with complexity. This is also legitimate when discussing with industrials facing their project day-to-day life.  Second, of these first 18 project complexity drivers, 11 of them belong to the family of project interdependencies (61.1%), making it the most contributive family of project complexity drivers, before context-dependence and variety (both 16,7%) and size (5.6%). Some bias might have been introduced because of the project manager view orientation of the study. Indeed, project managers traditionally have a transverse vision of projects, due to their responsibilities: this implies that they have a natural tendency to deal with organizational sources of complexity, notably at interfaces within and outside the project. Moreover, even technical issues, when addressed at a "project governance level", have organizational implications since they are often situated at interfaces between heterogeneous parameters (processes, technologies,…). In the end, this explains why our project complexity framework, which is to be used mostly by project managers or governance team members, has a majority of organizational factors (notably regarding interfaces and interdependencies). These results are consistent with former works of the academic literature (GENELOT, 2001) and with the industrials' feelings about complexity when discussing with us. This is also enlightened by the number of tools and works that have been developed to try to better catch project interactions and interdependencies, such as interactions model [START_REF] Marle | Modèle d'informations et méthodes pour aider à la prise de décision en management de projets[END_REF], or Design Structure Matrices [START_REF] Steward | The Design Structure Matrix: a method for managing the design of complex systems[END_REF]."

Position comparison

Results of the comparisons between academic and industrial experts can be seen hereinafter inTable 5. Two aspects are to be enlightened to compare those two populations:

Please insert Table 5  First, mean standard deviations appear to be different between populations since academics mean standard deviation on the survey is 0.615 and industrials' one is 0.738. This difference can express the fact that, even though there are very conscious of and interested in the concept of project complexity, they might not all understand it the same proper way. This observation is also enlightened by some commentaries during the Delphi survey, since some industrials wanted to have some details on some criteria, not understanding them, or not seeing them first as complexity sources.  Slight differences can be observed in the judgments of the two populations. First, SIZE-TECH complexity factors appear to be judged more important by academics than industrials (4.350 VS 3.938). To some extent, this lower maturity around the conceptual vision of project complexity is to explicit the lower assessments of these factors by industrials. However, some work should be carried out to clarify those relative divergence zones, which remain quite isolated, the whole survey showing a relative common vision of project complexity between academics and industrials.

Gender study

One of the ambitions of this research work was also to compare two other populations, men and women, in order to see if their perception of project complexity, whether they are industrial practitioners or academics, was the same or not. Others works had indeed shown that no difference was observed between men and women when dealing with managerial tasks. The results synthesized in Table 6 give us a part of answer, since the results obtained for those two populations are impressively similar. Mean standard deviation is 0.699 for men and 0.734 for women. Mean evaluations of organizational and technological complexity appear to be the same (3.963 VS 3.990 and 4.045 VS 4.028). Gender does not thus seem to be a source of different project complexity perception.

Please insert Table 6

Deeper analysis of the results using a correlation study

In order to understand better the relationships between the identified project complexity factors, a correlation analysis has been performed with the realization of Spearman Rank correlation analysis (see Figure 3). This analysis is well-established in statistics and permits to identify some correlations. Our aim here is to underline the possible existing correlations between factors in the set of answers of the panelists.

Please insert Figure 3

We highlighted the correlations which were superior to the critical values of the Spearman Rank for the value of 19 pairs (for p <0.05 in orange and p <0.01 in red). The conclusion is that the project complexity factors tend to be positively correlated. It must be noticed that less than 7% of the values in the correlation matrix are negative. Moreover, this positive correlation is somewhat limited since the average value of r S 2 is equal to 0.16. Finally, less than 5% of the values are above the critical value for p < 0.05 and less than 2% of them are above the critical value for p < 0.01, which means that strong correlations are very rare in this case. However, organizational factors seem to be more correlated than technical factors, with a mean square Spearman Rank reaching the value of 0.22 and a level of values over the critical value for p < 0.01 reaching 5%. Furthermore, some strong correlations are to be highlighted and discussed. For instance, the highest value in the matrix (r S =0.92) indicates that "numbers of team/structures/groups to be coordinated" and "number of departments involved" are strongly positively correlated factors regarding project complexity. So are "variety of organizational interdependencies" and "processes interdependence" (r S =0.91) as well as "variety of organizational skills needed" and "variety of the interests of stakeholders" (r S =0.90). Less intuitive correlations but very strong ones are for instance "combined transportation" and "organizational environment complexity" (r S = 0.88) or "stakeholders interrelations" and "dependencies with the environment" (r S =0.83). Finally, in all these cases, Kruskall-Wallis tests were conducted (both over the gender and position of panelists). No distinction (with a sensitivity of p < 0.05) according to the panelists' profile was observed for all of these correlations, underlining that the strong positive correlations are not due to similar responses within males/females or academics/industrials. This highlights that these strong correlations tend to be commonly shared by the panelists.

Refinement of the project complexity framework

In the end, after this deeper study of factors' correlation, using the Delphi survey, we propose a refined project complexity framework with the 18 most important complexity drivers according to the panellists. Our choice was to keep only the factors which would appear as essential (a score of 5 in our questionnaire). To do so, the mean scores of each factor were rounded up/down to the nearest integer, and that is why factors with a mean score which was at least 4.5 were considered as essential (since their scores were rounded up to 5). This was all the more interesting that they represented 26% of the initial factors, which was fairly consistent with the traditional 20% cut of Pareto.The users should in the end consider this refined framework and feel free to incorporate factors which are not in the refined version but which were present in the first framework, or even other factors, depending on the context of their projects. Table 7 draws as a synthesis the refined project complexity framework.

Please insert Table 7

As seen before, the majority of complexity factors are organisational and interdependence-related.

Final applications

This Delphi study is one part of a global research work about project complexity, its stakes, influences, and its measure. Indeed, one of the general objectives of our research works is to assess project complexity, notably in multi-project environments. The main potential use of this refined project complexity framework is to assess project complexity according to the selected criteria through the use of a multi-criteria evaluation method. We are using the Analytic Hierarchic Process [START_REF] Dyer | Remarks on the Analytic Hierarchy Process[END_REF][START_REF] Saaty | Response to holder's comments on the Analytic Hierarchy Process[END_REF][START_REF] Saaty | Decision-making for leaders: the Analytic Hierarchy Process for decisions in a complex world[END_REF] to assess project complexity on different project alternatives, given our project complexity framework. With the refined project complexity framework, an AHP hierarchical structure is to be built according to Figure 9.

Please insert Figure 4

We hope that this structure is going to be the basis for an effective industrial tool to assess and visualise project complexity. Moreover, given the ranking obtained with the AHP calculations on the set of alternatives, we do propose a relative measure of project complexity. Alternatives can be projects in a multi-project environment, or possible future scenarios in a mono-project environment, etc… Let α i be the priority value of alternative A i obtained with the AHP calculations (0 ≤ α i ≤ 1). We propose that the relative complexity of alternative A i , given the specific context of the set of alternatives, can be expressed as:

1 0 ) max(     i i i i C C  
A relative project complexity scale between 0 and 1 can thus be built using this method. It permits to give a relative indicator of project complexity given the multi or mono-project environment context. Indeed, this complexity measure can be used as an indicator to assist project selection in a portfolio, as an indicator to analyze the complexity of existing projects in a given portfolio, or an indicator to compare future possible project scenarios in the mono-project case. Another advantage of a multi-criteria methodology like the AHP is to permit an application in different industries, since it permits to change the weights of the criteria (complexity factors here), depending on the context of the industries. The generic computing of it is notably still to be done, with the ambition to give to the user default values and this default hierarchical structure (the structure being the one of the framework, the values being initially calculated through the use of a Saaty scale and the results of the Delphi study). However, we will leave the user the opportunity to add the complexity criteria which were eliminated between the original and the refined version of the framework. We will also leave the possibility to add new criteria or new values which could better cling to the project context the user is working in. This tool is finally to be tested on case studies, notably one in the stage musicals production industry. More details about this global research project are given in (VIDAL ET AL.., 2010). In the future, we also aim at refining this approach with the use of the Analytic Network Process which would consider the criteria (complexity factors) as non-independent. This would permit to introduce correlation coefficients which could be obtained using the Spearman Rank correlation analysis. All of these points make the point of ongoing works and/or publications.

Conclusion

This paper reports on the use of the Delphi methodology to address some issues about project complexity and its drivers. One of the ambitions of the study was to build up a project complexity framework. A large literature review permitted us to build a first theoretical version of the framework. The Delphi study which was conducted enabled us to refine this framework, falling from 68 drivers to 18. The main conclusions of the study are the following. First, organizational complexity, compared to technological complexity, is the major source of project complexity (88.9% of the selected criteria). Second, project interdependencies, compared to variety, size and context-dependence, seem to generate the most project complexity drivers (61.1%). Comparisons between experts permitted us to highlight that industrials seem to show less consensus on their perception of project complexity than academic experts. They also give lower estimates than academics. It also appeared that gender had fairly no influence on complexity perception. At this stage, no comparison between oriental and occidental population was possible, but this is to be another perspective of work around this notion. Finally, a first correlation analysis of the project complexity factors is proposed. As well as the results of this study, it should be extended through the interview of other experts. As a whole, the refined project complexity framework is to be the basis of an AHP hierarchical structure or an ANP complex structure, which enables us to define a relative project complexity measure. This measure is notably to assist project selection in the case of multi-project management or project scenario assessment in the case of mono-project management. Some work and case studies are still to be achieved to carry out this specific work.

any resources due to sharing

  , (LAURIKKALA ET AL,2001), (SINHA ET AL., 2001), (BELLUT, 2002), (CORBETT ET AL.., 2002), (JAAFARI, 2003), (KOIVU ET AL.., 2004), (SHERWOOD JONES AND ANDERSON, 2005)  Step 2 -Gathering of some complexity factors under a same common denomination and obtaining as a consequence a refined list of factors.  Step 3 -Gathering of factors into several groups through the analysis of the factors list and the identification done during Step 1.  Step 4 -Final construction of the first version framework

  The questionnaire was introduced by a page explaining, such as in (BRYANT AND[START_REF] Bryant | Estimation of terrestrial chemical spill risks factors using a modified Delphi approach[END_REF], the overall purpose and structure of the survey as well as the experts anonymity conditions at each stage of the study. The questionnaire was divided into eight sections, following the structure of the first version of the project complexity framework: SIZE-ORG, SIZE-TECH, VAR-ORG, VAR-TECH, INT-ORG, INT-TECH, CONT-ORG, CONT-TECH. An excerpt of the questionnaire is given in Appendix B in a Table format (the excerpt consists of the answers and commentaries of a respondent for the INT-ORG tab of the questionnaire).

Figure 1 .

 1 FIGURES TO BE INSERTED

Figure 4 .

 4 Figure 4. AHP-based assessment of project complexity

Table 1 .

 1 Project complexity framework : classification of project complexity factors

Table 2 .

 2 Synthesis of the retrospective project complexity analysis

Acknowledgements

We would like to thank the 18 anonymous experts for their time and effort in participating to our Delphi survey and providing their comments during the study.Special acknowledgements are addressed to Jean-Louis Giordano, who worked as a project manager at Renault for several years.

Availability of people, material and of

AppendixA Project complexity teleological and genetic aspects

The genetic aspect of a project system describes its evolution (i.e. the phases it evolves in). As for it, the teleological aspect of a project system addresses the issue of project values creation by identifying the expected target values (objectives) of a project (by identifying the project stakeholders and environment). Project complexity teleological and genetic aspects are to be mainly related to these aspects of the project system. As explained, several project complexity factors regarding project teleological and genetic aspects were identified and gathered under a common denomination. These factors are notably:

 Competition A competitive context is a more demanding and complex one since the targeted business is to choose the best products, processes, etc… in terms of expected values. Competition can be either technological or organisational.

 Environment complexity (networked environment)

Environment complexity in terms of network (networked environment) is to increase project complexity and make its management harder. Indeed, the management of the relationships with the project environment is one of the core activities of project management. Performing this activity in a networked environment is more complex since the impact of any relationship or decision is to propagate through this network.

 New laws and regulations

New laws and regulations (in both organisational and technological aspects) can increase project complexity since they may result in the need for changes in the processes/outcomes, given the requirements of new laws and regulations (such as security norms for instance).

Project complexity functional aspects

The functional aspect of a project system focuses on what the project system executes in terms of tasks and processes. This functional aspect is the principal cause of interactions and interrelationships within the project system since resources, actors, information systems, etc… interact when project tasks are executed. Project complexity functional aspects are thus to be mainly related to these aspects of the project system. After gathering factors under a common denomination, we obtain a list of functional factors. Here are some examples :  Availability of people, material and of any resources due to sharing Projects may share their people, material and all their resources within the firm. Moreover, within a given project some resources may be shared between people, tasks, etc… Such a non-availability of resources during a project make it in essence more complex.

 Dependencies between schedules

Dependencies between schedules make it all the more complex to manage people within a project. Indeed, for instance, if a change happens in a project team member schedule, then other project team members schedules may change. But, these schedules are constrained (notably by permanent organizations). As a consequence, the needed changes may not be possible, which make project management processes even more complex.

 Relations with permanent organizations

In most cases, within a firm, several projects have to coexist with several permanent organisations. Any project team member is to be involved in one or several projects and in one or several permanent organisations. Relations with permanent organizations make it more complex to manage a given project since these permanent structures may exert constraints on the project. For instance, the dependencies between the corresponding schedules generate complexity when trying to accommodate them and meet the requirements of each of them.

Project complexity ontological aspects

Finally, the ontological aspect of a project system focuses on what the project system is in terms of its constituting elements which permit the execution of tasks and processes (resources, actors, information systems, etc…). Project complexity ontological aspects are thus to be mainly related to these aspects of the project system. These factors, gathered using common denominations, are for instance:  Diversity of staff (experience, social span …).

When the staff is varied, notably in terms of work experience, social span or culture, then the project coordination and control appear to be more complex.

 Geographic location of the stakeholders (and their mutual disaffection) When stakeholders of the project are far from one another in terms of geographic location, then the project analysis, coordination and prediction are harder because of numerous effects (loss of information during information exchange, lack of information sharing due to their mutual disaffection, variety of local contexts of the stakeholders, etc…).

 Variety of the stakeholders' status

When the stakeholders' statuses are diverse, then it is more complex to coordinate the project since the control of the relationships with the stakeholders may imply varied procedures or behaviours for instance.

AppendixB

Here can be found a short excerpt of the questionnaire in a simple Table Format. This excerpt includes the answers and commentaries of one of the respondent. It corresponds to the "Organizational -Interdepencies" tab of the questionnaire file, which is composed of 8 different tabs (the 8 categories of our framework).

Complexity Driver


Adrien Baldit

Dominique Ambard

Fabien Cherblanc

Pascale Royer

Annulus fibrosus microstructure: an explanation to local heterogeneities

Keywords: Annulus Fibrosus, Intervertebral Disc, Hydro-Chemo-Mechanical Model, Finite Element, Digital Image Correlation

come

Introduction

Annulus fibrosus (AF) is the outer tissue of intervertebral discs (IVD). Its peculiar microstructure and biphasic composition define by an oriented fibre network embedded in a highly hydrated matrix (60-70%) is usually assimilated to porous composite material. It confers to AF a nonlinear, viscous and anisotropic behaviour. Many experimental and numerical studies underlined the anisotropic and non-linear mechanical behaviours on averaged values [START_REF] Ambard | Mechanical behavior of annulus fibrosus : a microstructural model of fibers reorientation[END_REF][START_REF] Malandrino | The effect of sustained compression on oxygen metabolic transport in the intervertebral disc decreases with degenerative changes[END_REF] but fail to represent the experimental strain heterogeneities [Baldit et al, 2013a;[START_REF] Michalek | The effects of needle puncture injury on microscale shear strain in the intervertebral disc annulus fibrosus[END_REF], that would be related to the microstructure and the biphasic constitution. On the other hand, characterization rarely relies on volumic behavior but it's relevant when models deal with soft porous media [Baldit et al, 2013b]. This work aims to couple a poro-hyper-elastic model identification with homogenized and discretized geometries highlighting model sensitivity and limits regarding experimental transverse strains measurements.

Methods

19 pig and 10 human specimens have been carved out from respectively 5 and 3 lumbar IVD to provide samples with dimensions of L rr xL θθ xL zz = 4 x 10 x 4 mm 3 . An experimental process has been developed to measure simultaneously stress and transverse strains fields (E rr , E zz ) during cyclic tensile tests and relaxation tests with in vivo conditions [Baldit et al, 2013a;2013b]. Strain fields were computed from a digital image correlation (DIC) technique (Kelkins, University of Montpellier 2) performed on both transverse planes. Then, AF tissue was modelled (LMGC90, University of Montpellier 2) with a hyper-elastic and quasi-incompressible porous material [START_REF] Malandrino | The effect of sustained compression on oxygen metabolic transport in the intervertebral disc decreases with degenerative changes[END_REF]Baldit et al 2013b] to represent the underlying fibres network embedded in an isotropic, porous matrix. First of all, the parameters characterization has been performed on a simplified geometry for computational cost reasons [Baldit et al, 2013b]. This geometry was focused on central part (L θθ = 1 mm) assuming that sample ends were rejected to infinity in circumferential direction. Furthermore, considering a homogeneous material, radial and vertical symmetries have been used to work with a 169 elements mesh. Then, the real complete sample geometry allowed comparing numerical and experimental strain fields using experimental boundary conditions plus the right number of lamellae. Therefore, the vertical symmetry cannot be used anymore and the element number reached 5280 or 10560 depending on impair (radial symmetry used) or pair lamellae number.

Results and Discussion

Experimental results exhibit the classical non-linear stiffening behaviour with hysteresis under loading cycles on Fig.1a [START_REF] Ambard | Mechanical behavior of annulus fibrosus : a microstructural model of fibers reorientation[END_REF]. Furthermore, the anisotropic behaviour clearly appears on averaged transverse strain fields illustrated on Fig. 1b. Compared to the fibre plane where a strong shrinkage is systematically observed, three main behaviours have been captured in lamellae plane with a shrinkage, a progression from shrinkage to swelling (Fig. 1b) or a swelling [Baldit et al, 2013a]. It's noteworthy that when swelling appeared, we systematically obtained a shrinkage/swelling/shrinkage pattern as illustrated on Fig. 2b. The identification on simplified geometry provided parameters values for each sample leading to represent their behaviours in circumferential stress and in averaged transverse strains Fig. 1 with averaged correlation coefficient (R) values of 0.99 on stress and respectively 0.11 and 0.78 on radial and vertical averaged strains. Therefore, something was missing in our model to correlate experimental and numerical results in radial direction. Simulations at sample scale, Fig. 2a and2c, showed that real boundary conditions don't play a major role on central part and comfort our first assumption. Although, we can notice that the whole sample swells with a homogeneous geometry while the discretized one allows to obtain the experimental pattern. Moreover, interesting local values appear on swelling part, while in vertical boundaries we cannot reach the strong experimental shrinkage.

Conclusions

Uniaxial tensile test enriched by DIC transverse strain measurements improves the hydromechanical behaviour characterization of soft biological tissues. To work at AF tissue level, it appears that the homogeneity assumption doesn't allow to fairly describe the heterogeneous strain pattern observed experimentally. Nowadays, research is focused on interaction between tissue and cell scales to model tissue development and renewal [START_REF] Malandrino | The effect of sustained compression on oxygen metabolic transport in the intervertebral disc decreases with degenerative changes[END_REF]]. These results highlight the limit of main literature simulations unable to reach the local mechanical cell environment. This work will be used within an inverse method taking into account full strain fields to obtain an accurate tissue description useful for multiscale predictive models.

Figure 1 Figure 2

 12 Figure 1 Experimental and numerical results on a) stress (Piola-Kirchhoff 1) and b) averaged transverse strains as function of imposed circumferential strain.


Yasser Fadlallah
email: yfadlallah@gmail.comjean-marie.gorce

Leonardo S Cardoso
email: leonardo.cardoso@insa-lyon.fr

Jean-Marie Gorce

Demo: Non-classic Interference Alignment for Downlink Cellular Networks

Our demo aims at proving the concept of a recent proposed interference management scheme that reduces the inter-cell interference in downlink without complex coordination, known as non -classic interference alignment (IA) scheme. We assume a case where one main Base Station (BS) needs to serve three users equipments (UE) while another BS is causing interference. The primary goal is to construct the alignment scheme ; i.e. each UE estimates the main and interfered channel coefficients, calculates the optimal interference free directions dropped by the interfering BS and feeds them back to the main BS which in turn applies a scheduling to select the best free inter-cell interference directions. Once the scheme is build, we are able to measure the total capacity of the downlink interference channel. We run the scheme in CorteXlab ; a controlled hardware facility located in Lyon, France with remotely programmable radios and multi-node processing capabilities, and we illustrate the achievable capacity gain for different channel realizations.

I. INTRODUCTION

Current networks aim to support high data rates to end users by increasing the spectral efficiency in bits-per-Hertz of the network, at the expense of the energy efficiency of the network. Indeed, an important part of the energy consumption of mobile networks is proportional to the radiated energy, which relies on the frequency bandwidth and the transmission power. Any energy efficient transmission scheme should exploits the whole system bandwidth by allocating the entire available spectrum to each base station. Such an approach, however, leads to significant interference increase and performance degradation for mobiles located at the cell edges. The key challenge is to balance interference avoidance and spectrum use to reach an optimal spectral efficiencyenergy efficiency (EE-SE) trade-off [START_REF] Tsilimantos | Spectral and energy efficiency trade-offs in cellular networks, Wireless Communications[END_REF]. This challenge has been addressed in the past, for instance using frequency/code planning in 2G/3G networks or with cooperative multiple point antennas in 4G [START_REF]Technical Specification Group Radio Access Network[END_REF]. The aim of our work is to demonstrate the concept of a recently driven interference management scheme that not only leverage the current technology but also achieves greater overall energy efficiency [START_REF] Ferrand | Interference Alignment for Downlink Cellular Network[END_REF]. It exploits Interference Alignment (IA) concept for downlink to reduce inter-cell interference without complex coordination. The theoretical achievements of IA has been largely discussed e.g. [START_REF] Maddah-Ali | Communication over MIMO X channels: Interference alignment, decomposition, and performance analysis[END_REF], [START_REF] Cadambe | Interference alignment and degrees of freedom of the-user interference channel, Information Theory[END_REF], [START_REF] Gshasemi | Interference alignment for the K user MIMO interference channel[END_REF], [START_REF] Gou | Degrees of freedom of the user MIMO interference channel[END_REF]. It has been concluded that one of the key results is that, under specific conditions, dense and high-power wireless networks are not fundamentally interference limited. As an example, under idealized assumptions, using IA in the setting of an interference channel formed by K transmitter-receiver pairs interfering between one another allows an achievable data rate per pair equal to half of his interference-free channel, regardless of K [START_REF] Cadambe | Interference alignment and degrees of freedom of the-user interference channel, Information Theory[END_REF]. Strong efforts in the research community have been done to extend IA far beyond the initial K -user interference channel. The recent review [START_REF] Ayach | The feasibility of interference alignment over measured MIMO-OFDM channels[END_REF] highlights the different technical challenges to be solved before envisioning a practical application among which implementing accurate feedback loops is probably the most important challenge. But even beyond the practical implementation of IA solutions in a network, the actual model of the network tends to be complex and involve a large number of hypothesis. These assumptions, or lack thereof, are needed and will play a significant role in the design of IA schemes. These IA schemes are in return heavily tuned to the specific hypotheses made and may not adapt to all cellular configurations, thereby justifying the need to develop an experimental evaluation of these techniques. A downlink cellular network is basically an interfering broadcast channel, where Base Stations (BS) transmit towards a number of users and interfere with each other. However, several tries to extend this approach in the context of cellular networks revealed some limiting improvement [START_REF] Aziz | System-level performance study of interference alignment in cellular systems with base-station coordination[END_REF] for the following reasons: i) The direct extension of the IC model to cellular networks relies on defining first the association of each mobile to a given subset of resources. Thus in each cell, the BS decides without coordination which set of resources is given to each mobile. To have a significant gain, IA should be performed for users mutually suffering from interference. ii) Many works rely on a clustering approach [START_REF] Tresch | On the achievability of interference alignment in the K-user constant MIMO interference channel[END_REF], however, users located at cluster edges cannot benefit from any improvement and are still subject to strong interference. iii) Signaling requirements reduce the theoretical gain of the system.

In [START_REF] Suh | Downlink interference alignment[END_REF], Suh et al. proposed an IA scheme for downlink channels by considering a scenario where each BS uses a reduced space for its own transmission, preserving a given free subspace for other cells. Their solution extended in [START_REF] Ferrand | Interference Alignment for Downlink Cellular Network[END_REF], allows users in a cell to cancel their dominant interferer as well as the intra-cell interference for users in the same sub-band, achieving one degree of freedom (DoF), without any communication between the BSs. In other words, each BS create an interference-free hole in which the other BSs can serve their mobile users. Each mobile measures and feeds back its own free subspace to its main BS. After receiving this information from all associated UE the BS jointly computes a set of precoders and schedules the UE to maximize the overall capacity, under some fairness/priority constraints. Basically, a certain cooperation between cells is not explicit but exists through the feedback channels. The performance of such scheme relies on many parameters such as synchronization, feedback capabilities, precoders choice... In this paper, we review the aforementioned non-classic IA scheme for downlink proposed in [START_REF] Suh | Downlink interference alignment[END_REF] and [START_REF] Ferrand | Interference Alignment for Downlink Cellular Network[END_REF]. Then, we show the implementation scenario in the experimentation shielded room CorteXlab located in Lyon, France, and we discuss some experimental issues. Finally, we present the results of our demo and highlight the capacity gain of the implemented IA scheme over the classical OFDMA scheme.

Notations: boldface upper case letters and boldface lower case letters denote matrices and vectors, respectively. The superscripts (.) T and (.) H stand for the transpose and transpose conjugate matrices, respectively. The following notation

V = V left (SVD(A)) N -d+1:N , (1)
denotes the last d vectors of an N -dimension space matrix V defined as the left-singular matrix of a matrix A, where SVD(A) stands for the Singular Value Decomposition (SVD).

II. NON-CLASSIC INTERFERENCE ALIGNMENT

A. System model

For our demo, we consider a cellular network with two BS and three user equipment (UE), all equipped with a single antenna. The transmission scheme is based on OFDM with K available sub-carriers. The transmit signal of the interfering BS is written as

x i = M H x i , (2)
where x i is the data vector of length K -N f before Hadamard precoding. In the implemented scheme, each BS preserves N f DoF for the other BSs, thereby creating a hole free of interference at all cell-edges. The maximum number of transmitted streams is then N s = K -N f . M H is a unitary trunk Hadamard matrix of dimension K × N s that allows the use of the N s reduced space.

We denote H mb the fading channel matrix between the b th BS and the m th UE. Let the reduced channel denotes G mb = H mb M H , where b = d and b = i refer to the desired and interfering channel, respectively. The received signal at the m th UE is written as

y m = G md x d + G mi x i + w m , (3)
where w m is the noise vector. In addition to the Hadamard trunking matrix, each original stream s b,i with i ∈ {1, • • • , N s } is carried over the precoding vector c i ; the i th vector of a precoding matrix C b . The precoded stream vector at the b th BS is defined as

x b = C b s b , (4)
and includes all streams associated to the b th BS. In order to accomplish a reliable interference management scheme, we review the non-classic IA technique extended in [START_REF] Ferrand | Interference Alignment for Downlink Cellular Network[END_REF] that calculates an optimal precoding set lying over the free-interference subspace and then selects the best subset that maximizes the total capacity of the downlink interference channel.

B. Non-classic IA technique

The fading channels connecting the UEs to their main BS and to the strongest interferer BS are firstly estimated at the all UEs. This is possible through training sequences provided by both BSs. Then, each UE determines the interference null space thanks to the SVD of the reduced channel G mi . It is calculated as

V ⊥ = V left [(SVD (G mi )) Ns+1:Ns+N f . (5)
By applying a linear projection on the interference null space V ⊥ , the received signal is rewritten as

V ⊥ y m = V ⊥ G md x d + V ⊥ w m , (6)
In other words, the signal y m is being received in the inter-cell interference-free hole created by the strongest interferer. This means that the best for a UE is to have its desired streams aligned with the equivalent channel G ⊥ mb = V ⊥ G mb which guarantees a maximum received power of the desired signal. It is worth noting that in practice, the UEs at cell edges can be interfered from more than one BS. Dealing with such as a case requires either considering the interference as noise or estimating all interfering channels while the transmission is focused in the joint hole created by the union of the interference. For the sake of simplicity, we only assume one interfering BS for our demo.

Each UE calculates its optimal N f precoding vectors and feeds them back to the main BS, which in turn collects N u N f precoding vector where N u is the total number of user fixed to three in our demo. However, the maximum number of streams allowed for a BS is N s . When N s > N u N f , all vectors are used for transmission. Otherwise, i.e. N s < N u N f , an N s precoding vectors must be selected among the total set. That is, we have to run a scheduling to select which users and streams are best to serve. Among the different existing criteria, we choose to maximize the total channel capacity given by

R d = Ns l=1 log 2 (1 + sinr l ) , (7)
where the term sinr l stands for the signal to interference and noise ratio at the l th selected stream after scheduling.

When a scheduling is required, the precoding vectors set can be presented as an underdetermined matrix of dimension N s × N u N f . The problem is seen as selecting the best determined matrix that maximizes the total rate. The optimal solution is through exhaustive search. For this to happen, we need to build all possible subset combination and to calculate the achievable rate of each candidate. The data symbols are carried over the vectors yielding a maximum achievable rate. The precoding vector of the l th stream of the m th user is calculated as

c l = G ⊥,H md,l , (8)
where G md,l is the l th row of the reduced interference-free channel. In other words, the precoding vector aims at maximizing the power of the desired part of the received signal.

Hence, each user relies on the fact that its interference-free directions are independent from the interference-free directions of the other UEs associated to the same BS, which means that channel diversity between UEs has a major impact for achieving a desired performance of the described interference management scheme. That is, when the channels are almost orthogonal there is no intra-cell interference and the achievable rate is maximum. In contrast, when the channels between UEs are completely correlated, the interference reaches its maximum and the rate is highly degraded.

Going back to the scheduling problem, it can be expressed as

arg max R d (p 1 , • • • , p Ns ) s.t. {p 1 , • • • , p Ns } ∈ C (9)
where C = {c 1 , • • • , c t } and t = N u N f . Such a problem is known as a discrete optimization that requires in most cases an exhaustive search to find out the global optimum. However, this becomes so costly and expensive with the dimension increases.

Other sub-optimal algorithms based on heuristic methods or local minima search can be applied with no guarantee of any improved performance. Since we do not assume high dimensions systems and we apply non-classic IA technique over only four sub-carriers, the optimal exhaustive search is feasible with low computational cost. Once the best subset is selected, we proceed to calculate the precoding matrix of all streams that cancels the intra-cell interference. It is given by

V IA P = I Ns , (10)
where the selected precoding vectors are the columns of the matrix P and I Ns is the identity matrix. The achievable rate can be then written as

R d = Ns l=1 log 2 (1 + α l sinr l ) , (11)
where α l = 1 v l and v l is the l th column of V IA . It can be noticed that α l ≤ 1 and is equal to one when the selected vectors are all orthogonal.

The performance of the addressed non-classic IA approach has been evaluated through exhaustive simulations in different networks and load scenarios. It has been found that in comparison to a reference scenario without IA, the cell capacity can on average be increased by a factor 2 and that the spectral efficiency of cell edge users can be increased up to a factor 4 [START_REF] Ferrand | Interference Alignment for Downlink Cellular Network[END_REF]. Our work herein gives a proof of concept and focuses on the main challenges related to the non-classic IA approach for downlink, namely the knowledge of the interference footprint and the scheduling algorithms to make use of the interference information to maximize the spectral efficiency. We implement an experimental scenario with two transmitting BSs, i.e. the main BS and an interfering one and three UEs associated to the main BS. We show that the IA is feasible, in the sense that UEs are able to measure a channel, feed it back to the BS which in turn applies a scheduling to select the best set and calculates the theoretical Spectral Efficiency (SE) gain over a classical dumb OFDMA allocation.

III. SCENARIO AND EXPERIMENTATION

A wireless network is emulated on CorteXlab (http://www.cortexlab.fr) [START_REF] Cardoso | CorteXlab: A Cognitive Radio Testbed for Reproducible Experiments[END_REF], [START_REF]Cortexlab: Cognitive radio testbed[END_REF], [START_REF] Massouri | Cortexlab: An open fpga-based facility for testing sdr and cognitive radio networks in a reproducible environment[END_REF], a controlled hardware facility located in Lyon, France with remotely programmable radios and multi-node processing capabilities. During the live demo, a control laptop is remotely connected to the facility, deploying software on the radios and launching an IA scenario and collecting real-time performance feedback. The efficiency gain of IA is then shown for various experimental conditions that can be tuned from the control laptop.

A. Radio Platforms

Represented by the National Instruments USRP 2932, the general-purpose Software Defined Radio (SDR) nodes use the GNU Radio toolkit for rapid prototyping of transmission techniques mostly reliant on the general purpose processor (GPP) of the host PC. The USRP 2932 is a high end radio platform, counting with a 400 MHz -4.4 GHz RF board, data rates of up to 40 MHz (with reduced dynamic range, nominal band of 20 MHz), a precise OCXO clock source and a 1 gigabit ethernet (GigE) connection to the host PC. The host PC is based on a Linux environment and allow users to test PHY and MAC layer techniques. It is preferable to first use both Linux and GNU Radio for the development and test at the user's own computer and then to bring the experiment over to CorteXlab.

B. Implemented scenario

Among the forty available SDR nodes in CorteXlab, five are selected where two serve as main and interfering BS and the remainders serve as mobile UEs. All transmitters (TX) and receivers (RX) are equipped with single antenna. Therefore, the IA scheme lies on the frequency dimensions provided by the OFDM transmission scheme implemented at all TXs and RXs. In the first transmission phase, the UEs need to estimate the main and interfering channels. This can be done by assigning two orthogonal time slots to the BSs through which they transmit the training sequences. However, the synchronization of the two BS nodes remains a challenge since they are distantly separated. Herein, we propose an over-air synchronization as follows. Holding a unique ID, the interfering BS starts the transmission to let the user nodes measure the interference channel coefficients while the main BS tries to decode the ID of the transmitter. If the decoded ID corresponds to the interferer, the main BS node transmit OFDM symbols (one or more) for channel estimation. By collecting both estimated channels, each receiver is able to calculate the d optimal precoding vectors in the free dimensions such that the desired signal power is maximized. In order to avoid imperfections in the IA scheme, we use a wire connection provided in the experimentation room between all nodes to perform a perfect feedback to the TX (main BS). This latter gathers the precoding vectors from all UEs and run the scheduling algorithm to seek the best (N -N ) precoding vectors that minimizes the intra-cell interference, and hence maximizes the achievable data rate of the cell. The maximized rate is then compared to the classical OFDMA and the theoretical gain is calculated. The OFDMA scheduler select at each users the L u streams that maximizes the Signal-to-Interference and Noise Ratio (SINR) given by

ρ u,l = |h u,l | 2 |h i,l | 2 + σ 2 n , (12)
where ρ stands for the SINR, h u,l is the channel coefficient between the main BS and the u th user at the l th stream, h i,l

C. Experimentation and results

In the live demo, we show a spectral efficiency gain that can largely vary between 1 and 3. This variation is due to the influence of many factors summarized by the following parameters: the noise power, the interference power, the channel diversity, the distance between the different nodes, the TX gain... For instance, in perfect conditions the ratio gain R d /R ref given in ( 11) and ( 13), tends to its maximum when the inter-cell interference power is of the same order or higher than the desired signal power ; i.e. SINR is low, this is the case of cell edge mobile users. However, as long as the users get closer to the main BS, this ratio decreases. Another critical parameter that highly impacts the performance gain is the channel diversity and correlation, the less the channel is correlated the higher the efficiency gain is. This is because the applied IA scheme requires a completely decorrelated channel coefficients for the scheduling, otherwise the intracell interference dominates the desired signal. In order to get a better decorrelation in the shielded room, we emulate a virtual channel on all TXs and RXs, however, this still induces some correlation at the different mobile UEs. A better way is to use a multi-antennas node at the TX to generate multi-paths through the different antennas. Each path is randomly attenuated, phase shifted and delayed. Such a multi-paths generation creates a perfect decorrelation since the paths generated by the different nodes are totally independent. An illustration of our demo is given in Figure 2. In our demo, we assume two BSs and N u = 3 users. The IA is applied over four sub-carriers which gives a total dimension of 4, one is free of interference and three other used by each BS. We focus on the average theoretical capacity gain offered by the non-classical IA over the classical OFDMA scheme with respect to the number of transmission as shown in Figure 3. We also plot the channel spectrum at the all sub-carriers and for the different transmission to show how decorrelated the channel coefficients are. For each channel realization, we display the SNR of the interference-free streams and the SINR of all streams when the classical OFDMA is applied to see their impact over the efficiency gain.

IV. CONCLUSION AND WORK UNDER-DEVELOPMENT

In this demo, we have implemented the first phase of a non-classic IA approach for interference management. It consists in measuring the channel coefficients, calculating the interference-free sub-spaces, feeding them back to the main BS, and applying a scheduling to decide which stream to transmit. We have shown in experiment that a significant theoretical capacity gain over the classical OFDMA scheme can be achieved depending on the channel conditions and the interference dominance. The remaining work is to start the IA transmission and to apply linear decoding criteria at the receiver such as Zero-Forcing (ZF) or Minimum Mean Squared Error (MMSE) to recover the original data. However, the challenge here is to synchronize the transmission between both TXs for the IA transmission and to compare the theoretical gain to the practical one. It is also worth trying to face more practical issues related to de-synchronization, which means to study the impact of the delay and phase shift between the different TXs on the IA scheme.

Figure 1 .Figure 2 . 2 nlog 2 ( 1 +

 12221 Figure 1. The proposed scenario

Figure 3 .

 3 Figure 3. Experimentation results


Nawal Ould-Amer
email: nawal.ould-amer@imag.fr

Mathias Géry
email: mathias.gery@univ-st-etienne.fr

LaHC at CLEF 2015 SBS Lab

Keywords: Field-based Information Retrieval, Re-ranking, Relevance Feedback

This paper describes the work of the LaHC lab of Saint-Étienne for the Social Book Search lab at CLEF 2015. Our goals were i) to study a field-based retrieval model (BM25F), exploiting various topics and documents fields, in order to build a strong baseline for further experiments, ii) to compare it with a Log logistic (LGD) retrieval model, and iii) to exploit some documents related to each topic (i.e. the documents given as negative or positive examples for a topic). The official results show that LGD outperforms BM25F, and that our approaches exploiting documents related to the topic requesters are based on a different interpretation of this additional information than the interpretation of the Social Book Search organizers.

Introduction

This paper describes the work of the LaHC lab of Saint-Étienne for the Suggestion track of the Social Book Search lab at CLEF 2015. The goal is to investigate techniques to support users in searching and navigating the full texts of digitised books and complementary social media as well as providing a forum for the exchange of research ideas and contributions [START_REF] Koolen | Overview of the INEX 2014 Social Book Search Track[END_REF]. Participants to this track have to suggest books based on rich search requests combining several topical and contextual relevance signals, as well as user profiles and real-world relevance judgments. The dataset is based on 1.5 million books descriptions and metadata, some of them user-generated, crawled from Amazon and LibraryThing.

Our participation to the Social Book Search lab at CLEF 2014 [START_REF] Hafsi | LaHC at INEX 2014: Social Book Search Track[END_REF] has shown us that the SBS dataset contains many various kind of data, and that before experimenting our Social Information Retrieval models, we need a better understanding of how to represent and how to exploit non-social (but nevertheless complex) data using classic models.

Especially, our work for the Social Book Search lab at CLEF 2015 focuses on:

study a field-based retrieval model (BM25F [START_REF] Robertson | Simple BM25 extension to multiple weighted fields[END_REF]), exploiting various topics and documents fields, in order to build a strong baseline for further experiments; compare BM25F with some other Information Retrieval models, especially the Log logistic (LGD [START_REF] Clinchant | A Log-Logistic Model for Information Retrieval[END_REF]) retrieval model; exploit some non-social data (but nevertheless related to the users), especially the documents given as negative or positive examples for a topic.

Our experiments were conducted using the Terrier Information Retrieval System3 [START_REF] Ounis | Terrier: A High Performance and Scalable Information Retrieval Platform[END_REF], that implements various IR models and especially LGD and also some field-based models as BM25F.

The paper is organized as follows: Section 2 presents briefly the Information Retrieval models used. Then, Section 3 details our approaches aiming at exploiting the positive or negative documents related to each topic. Finally, Section 4 presents the official results obtained, before concluding in section 5.

BM25F vs LGD (runs UJM 1 and UJM 2)

The Social Book Search 2015 dataset contains many various data describing or related to the documents, the topics and the users. Among all these information, we have used the Terrier Information Retrieval System implementation of the field-based models BM25F [START_REF] Robertson | Simple BM25 extension to multiple weighted fields[END_REF], in order to exploit the following fields from documents and topics:

the fields title, summary, content and tags from the documents; the fields title, mediated query and narrative from the topics; BM25F was used with the parameters values presented in Table 1, taken from our participation to Social Book Search lab 2014 [START_REF] Hafsi | LaHC at INEX 2014: Social Book Search Track[END_REF], generating our run named UJM 1. LGD is the Terrier implementation of the Log logistic model [START_REF] Clinchant | A Log-Logistic Model for Information Retrieval[END_REF]. Grid optimization of parameter c on SBS 2014 data led to fix it at 0.2, generating our run named UJM 2.

3 Documents given as "examples" (runs UJM 3, UJM 4, UJM 5, UJM 6)

Our last goal was to exploit some non-social data (but nevertheless related to the users): the list of documents given as negative or positive examples for each topic.

Our idea was that a user might be interested (respectively unsatisfied) if he finds as answers documents that he has read and that he appreciated (respectively disliked) and thus defined as positive (respectively negative) example for the topic.

We implemented this hypothesis in two ways:

Re-ranking (RR): Achieve a re-ranking where the document a user likes are boosted, and the documents he dislikes are removed for the result. After the score normalization between 0 and 1, we add 1 to the normalized score of document that the user likes and to set the score to 0 for the document that he dislikes. This process is then a post-processing of an existing run. It is worth noting that, if several retrieved documents are liked by the user, their relative initial ranking is preserved; It has been applied on our BM25F run UJM 1 (generating our run UJM 4) and also on our Log logistic run LGD run UJM 2 (generating our run UJM 6);

Relevance Feedback (RF): Define a relevance feedback, positive for the documents that the topic user likes, and negative for the documents he does not like. We achieved such relevance feedback on our BM25F UJM 1 run (generating our run UJM 5), and also on our Log logistic LGD run UJM 2 (generating our run UJM 3). The relevance feedback uses all the positive documents and selects the top 10 terms according to the default selection of Terrier [START_REF] Ounis | Terrier: A High Performance and Scalable Information Retrieval Platform[END_REF].

Results

The Table 2 presents the official results obtained by our 6 runs. Log logistic (LGD) outperforms BM25F, regarding the official nDCG@10 measure as well as regarding the 3 other measures, despite the fact that BM25F is designed to take into account and to weight the different fields describing the documents. Our approaches "Re-ranking (RR)" and "Relevance Feedback (RF)", both exploiting the list of documents given as negative or positive examples for each topic, lower the quality of the results. These approaches are based on a different interpretation of this list of documents than the interpretation of the Social Book Search organizers. Actually, these "examples" documents (the negative ones as well as the positive ones) are not considered as relevant by the organizers. Thus, re-ranking positively the positive examples (or using them as relevant documents in a relevance feedback process) can only lower the results. On the other hand, removing the negative examples from our runs (or using them as irrelevant documents in a relevance feedback process) may sometimes improve the results. All in all, the quality of our results is lowered. Our 2015 participation allows us to build a strong basis in order to experiment in the future some more advanced some Personalized Information Retrieval approaches.

Table 1 .

 1 BM25F parameters

			Fields
		title summary content tags
	Parameter c 1.0	0.10	0.45 0.00
	Weight w	1	2	1	6

Table 2 .

 2 Official results for the 6 UJM runs This paper describes the work of the LaHC lab of Saint-Étienne for the Social Book Search lab at CLEF 2015. Our quite basic experiments show that Log logistic (LGD) outperforms BM25F. Four of our six runs were based on a misinterpretation of the documents given as negative or positive examples for a topic.

	Rank	Run	nDCG@10 MRR	MAP R@1000 Profiles
	17	UJM 2 (LGD)	0.088	0.174	0.065	0.483	no
	20	UJM 6 (LGD + RR)	0.084	0.160	0.060	0.483	no
	24	UJM 1 (BM25F)	0.081	0.167	0.056	0.471	no
	29	UJM 3 (LGD + RF)	0.079	0.155	0.059	0.485	no
	30	UJM 4 (BM25F + RR)	0.079	0.158	0.055	0.471	no
	33	UJM 5 (BM25F + RF)	0.074	0.150	0.054	0.471	no
	5 Conclusion

Terrier: http://www.terrier.org

Acknowledgment

This work is supported by Région Rhône-Alpes through the ReSPIr project.