Fanny Magnoni
email: fanny.magnoni@iae-aix.com

Pierre Valette-Florence

Virginie De Barnier
email: virginie.de-barnier@iae-aix.com

Modeling the

Keywords: behavioral intentions, place brand, residents, serial mediations, comprehensive model

published or not. The documents may come

intentions toward a city: A mediation analysis

Introduction

For several years now, the branding of places and cities has been gaining popularity with city officials, as shown by the creation of city brand rankings such as the Anholt-GMI City Brands Index [START_REF] Anholt | The Anholt-GMI city brands index: How the world sees the world's cities[END_REF]. From a managerial perspective, place branding is of prime importance. Indeed, due to increasing competition issues, cities are trying to establish themselves as brands [START_REF] Braun | City Marketing: Towards an Integrated Approach[END_REF][START_REF] Zenker | Measuring success in place marketing and branding[END_REF], while city managers work on designing and managing those brands [START_REF] Merrilees | Multiple stakeholders and multiple city brand meanings[END_REF]. Places and cities hence use branding as a tool for achieving attractive positions and positive perceptions in the minds of key audiences [START_REF] Ashworth | Beyond the logo: Brand management for cities[END_REF]. The objectives are to generate wealth, enhance inward investment and tourism, and develop a sense of community by strengthening local identity [START_REF] Kavaratzis | City Marketing: The past, the present and some unresolved issues[END_REF].

City branding is a subfield of place branding that focuses on branding cities to (prospective) residents, tourists, and investors as a place in which to live and invest [START_REF] Merrilees | Antecedents of residents' city brand attitudes[END_REF]. Residents are often ignored in city branding practices, despite studies highlighting their importance [START_REF] Oguztimur | Synthesis of city branding literature (1988-2014) as a research domain[END_REF]. Losing residents means that cities and local authorities cannot request governmental resources (financial and urban services) or private investments, which in turn makes it difficult to obtain development funds [START_REF] Sadeque | An integrated model of city and neighborhood identities: A tale of two cities[END_REF]. Their actions are vital for sustainable tourism, especially in small and medium-sized cities strongly dependent on tourism for their economic viability [START_REF] Uchinaka | Classifying residents' roles as online place ambassadors[END_REF]. Residents' behaviors influence tourists' travel experiences, from information search to tourism product consumption [START_REF] Zenker | Branding the destination versus the place: The effects of brand complexity and identification for residents and visitors[END_REF]. Residents' involvement in tourism development is a determining factor in city branding because of increasing person-to-person interactions in tourism activity [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF].

For those reasons, understanding how cities can attract new residents, as well as retain and engage existing ones, is of major interest.

In this paper, we integrate product branding and place branding frameworks to build and test a comprehensive model that allows us to unravel the mechanism by which behavioral intentions toward a place brand are formed. We study that mechanism from the perspective of (prospective) residents.

A gap exists between the increasing importance of residents' place-related behaviors and the research effort. The relationship between place attachment and residents' behaviors is now well established in the literature on place branding (e.g., [START_REF] Braun | My citymy brand: the different roles of residents in place branding[END_REF][START_REF] Chen | Effect of dimensions of place attachment on residents' word-of-mouth behavior[END_REF][START_REF] Choo | The influence of the resident's identification with a tourism destination brand on their behavior[END_REF][START_REF] Daryanto | A meta-analysis of the relationship between place attachment and pro-environmental behaviour[END_REF]Styven et al., 2020;[START_REF] Taecharungroj | City ambassadorship and citizenship behaviors: Modelling resident behaviors that help cities grow[END_REF][START_REF] Zenker | An integrative theoretical model for improving resident city identification[END_REF][START_REF] Zenker | Is satisfaction the key? The role of citizen satisfaction, place attachment and place brand attitude on positive citizenship behavior[END_REF]. Place attachment has attracted increasing attention from researchers and practitioners due to its potential for interpreting and predicting behaviors.

Focusing on the phenomenon of "human-place bonding," place attachment has developed into a multidimensional concept that encompasses affect and emotions, knowledge and beliefs, and behaviors [START_REF] Kyle | Testing the dimensionality of place attachment in recreational settings[END_REF]. Nevertheless, little is known about how to create place attachment among residents. Indeed, there is a need for more detailed studies of the antecedents of residents' behaviors [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF]. Previous research has focused mostly on visitors, with very few studies investigating other place-related concepts, such as place brand experience or place brand equity, from the perspective of (prospective) residents linking them to place attachment and residents' behaviors. For example, a [START_REF] Beckman | The impact of brand experience on downtown success[END_REF] study empirically investigates place brand experiences that influence place attachment and positive outcomes (word of mouth and revisit intention) for residents and tourists. Research by [START_REF] Manyiwa | Influence of perceived city brand image on emotional attachment to the city[END_REF] shows that city brand image influences attachment to the city for both the residents and visitors. However, little is known about the interrelationships between those concepts and, more precisely, about the causal mechanisms that induce residents' favorable behavioral intentions toward a place of living.

Consequently, there is a strong need to develop and test integrated models encompassing residentfocused concepts.

In this study, we seek to close the above research gap and contribute to the existing literature. Our contribution is threefold. First, we draw on product branding and place branding concepts, and social identity theory [START_REF] Tajfel | The social identity theory of intergroup behavior[END_REF], to propose an integrated model that considers place brand heritage and place brand experience as independent variables, and place brand equity and place attachment as mediating variables able to generate residents' place-related behavioral intentions (i.e., brand-building behavioral intentions). With a sample of 571 (prospective) residents of a French city, we empirically test new relationships in place branding and confirm others previously observed in this research field.

Second, this research is one of the first to test a serial mediation model to explain the causal mechanisms that induce residents' favorable behavioral intentions toward a city. We examine through mediational relationships a three-stage process: place brand heritage and place brand experience increase place brand equity, which in turn enhances place attachment, which then influences brand-building behavioral intentions. In addition, we rely on recent methodological developments allowing competing models to be compared. We assess the uncertainty and plausibility of competing models to identify the best mediational model. We prove the usefulness of such an investigation for delineating a more parsimonious and sound research model. Finally, we reveal managerial implications for city brands management, propose communication actions for activating place brand heritage, and develop methods of enhancing place brand experience. Our results contribute to helping local governments and city brand managers to optimize the value of places of living, and to the understanding of how to develop strong place attachment so as to induce residents' favorable behavioral intentions toward their city.

This paper is structured as follows. The first section reviews the literature and introduces the conceptual model and research hypotheses. The second section explains the empirical study methodology. The third section presents the results, with the fourth discussing the implications, limits, and directions for future research.

Conceptual model and hypotheses

Section 2.1 presents two antecedents that should lead to behavioral intentions toward the city people want to live in, including the behavioral intentions toward the city selected for this research. Section 2.2. examines the mechanism by which behavioral intentions are formed by proposing mediation hypotheses. Figure 1 presents our conceptual model and hypotheses.

[Insert Figure 1 around here]

Antecedents of behavioral intentions toward a place of living

We rely on the literature on branding and place marketing to identify two independent variables particularly relevant in city branding for (prospective) residents: place brand heritage and experiences related to the place brand.

Place brand heritage

Brand heritage refers to a representation of the past related to the brand's identity. [START_REF] Urde | Corporate brands with a heritage[END_REF] define it from an internal perspective as a resource that can be activated and protected using identifiable characteristics that demonstrate the salience of brand heritage for companies (symbols, logos, etc.). From an external perspective, brand heritage is considered a set of brand associations based on historical references [START_REF] Balmer | Explicating corporate heritage, corporate heritage brands and organisational heritage[END_REF]. The literature on corporate and product branding identifies heritage as a temporal concept that presents specific characteristics such as omnitemporality (brands exist in the past, present, and future), consistency of institutional traits (invariance of corporate traits over time), or intergenerational continuity (brand longevity) [START_REF] Balmer | Corporate heritage, corporate heritage marketing, and total corporate heritage communications[END_REF][START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF].

Principles of heritage can be applied to the marketing of places. Most places and cities have a long historical and cultural legacy. Histories and symbols associated with places can be used as signals that a place is a great location to live [START_REF] Wilson | Transforming history into heritage: applying corporate heritage to the marketing of places[END_REF]. Logos and slogans can be used in a place heritage branding strategy to increase the effectiveness of territorial and cultural symbols that deliver familiarity, recognition, and affect [START_REF] Wilson | Transforming history into heritage: applying corporate heritage to the marketing of places[END_REF]. [START_REF] Hakala | Toponyms as carriers of heritage: Implications for place branding[END_REF] show the importance of a place's name as the carrier of identity and heritage from the residents' perspective. Places possess fundamental characteristics of corporate heritage: a place exists in the past, present, and future; a place has consistent and relevant traits, and has existed for at least fifty years; a place is infused with several identities (territorial, cultural, social, and ancestral); nurtures and maintains place traits through communications managed by private/public organizations; and a place guarantees that those traits meet the expectations of successive generations of stakeholders [START_REF] Wilson | Transforming history into heritage: applying corporate heritage to the marketing of places[END_REF].

Local residents are important co-creators of heritage [START_REF] Fredholm | Managing the image of the place and the past: contemporary views on place branding and heritage management[END_REF]. Places have a history of their own and heritage plays a fundamental role in constructing the identity both of the place and its people [START_REF] Fredholm | Managing the image of the place and the past: contemporary views on place branding and heritage management[END_REF][START_REF] Hakala | Toponyms as carriers of heritage: Implications for place branding[END_REF][START_REF] Wilson | Transforming history into heritage: applying corporate heritage to the marketing of places[END_REF]. We argue that places with a distinctive and strong heritage are perceived as more valuable and allow (prospective) residents to shape their own identity more easily.

Place brand experience

Brand experience is defined as "subjective, internal consumer responses (sensations, feelings, and cognitions), and behavioral responses evoked by brand-related stimuli that are part of a brand's design identity, packaging, communications, and environments" (Brakus et al., 2009, p. 53). Based on the five experiences identified by [START_REF] Schmitt | Experiential marketing[END_REF], namely sense, feel, think, act, and relate, [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty[END_REF] propose four dimensions of brand experience: affective, behavioral, sensory, and intellectual. Brand experiences generate lasting emotional impressions which can differ in terms of strength, intensity, and valence (positive and negative brand experiences). Strong and memorable brand experiences produce many benefits for companies, such as higher satisfaction, loyalty, brand relationships, and brand equity (e.g., [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty[END_REF][START_REF] Iglesias | The role of brand experience and affective commitment in determining brand loyalty[END_REF][START_REF] Iglesias | How does sensory brand experience influence brand equity? Considering the roles of customer satisfaction, customer affective commitment, and employee empathy[END_REF][START_REF] Lin | Innovative brand experience's influence on brand equity and brand satisfaction[END_REF].

Brand experiences also relate to place brands. Creating positive brand experiences is a major concern for place brand managers. People interact with place brands and can live pleasurable experiences that generate value for the place and place attachment [START_REF] Lindstedt | Place, identity and the socially responsible construction of place brands[END_REF]. [START_REF] Beckman | The impact of brand experience on downtown success[END_REF] consider residents and tourists in examining the effect of brand experiences on downtown success. They apply the [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty[END_REF] four dimensions of brand experience to a downtown brand. Their results show that brand experience dimensions influence place attachment (place dependence), which in turn influences positive outcomes (word of mouth and revisit intention) differently for residents and tourists.

Place brand experience may also play an important role in this research, since we focus on residents who are already familiar with the city due to prior real experiences of it. The residents live there and have detailed firsthand knowledge of the city [START_REF] Zenker | Branding the destination versus the place: The effects of brand complexity and identification for residents and visitors[END_REF], thus influencing their place brand experience. In addition, residents are a vital part of forming the place brand by constituting a part of the brand experience [START_REF] Braun | My citymy brand: the different roles of residents in place branding[END_REF], as place experience is co-created prior to, during, and after actual exchange(s) and use(s).

Behavioral intentions toward the city

Brand-building behavioral intentions in relation to the place are examined as the dependent variable in this research. The three dimensions we select as relevant for residents were also used by [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF]: word of mouth, leaving intention, and ambassador behaviors. Ambassador behaviors refer to residents' behaviors consistent with the image and values of the place, such as dress codes, manners, etc., as well as behaviors that satisfy tourists' needs in the tourism-specific context [START_REF] Choo | The influence of the resident's identification with a tourism destination brand on their behavior[END_REF]. Those behaviors are linked to social conformity.

Mediation hypotheses

2.2.1. Mediating variables: place brand equity and place attachment Place brand equity and place attachment are the two core mediating variables in our conceptual model (see Fig. 1), since those two constructs are probably the most important in both the branding and place branding literature, and well known for their strong potential for predicting behaviors. Those two constructs are defined in this section.

First, brand equity allows the capture of the complexity of place brands, as it encompasses multiple facets of place performance and value. Place brand equity is studied in a few papers through the concept of brand image [START_REF] Brandt | City branding: a brand concept map analysis of a university town[END_REF][START_REF] Zenker | Putting a price tag on cities[END_REF]. For instance, [START_REF] Zenker | Measuring place brand equity with the advanced Brand Concept Map (aBCM) method[END_REF] proposes a method of evaluating city brand image based on brand associations, as an important constituent of place brand equity. [START_REF] Zenker | Putting a price tag on cities[END_REF] examine the city image dimensions for talents and people's willingness to sacrifice, for example, annual salary for their preferred choice. From an investor perspective, Papadopoulos and Heslop (2012) also introduce the idea of country brand equity for investors (foreign direct investment), and [START_REF] Jacobsen | Investor-based place brand equity: A theoretical framework[END_REF] proposes drivers for investor-based place brand equity.

In addition, some research has proposed conceptualizations of place brand equity based mainly on the works of [START_REF] Aaker | Measuring brand equity across products and markets[END_REF] and [START_REF] Keller | Conceptualizing, measuring and managing customer-based brand equity[END_REF]. From the investment attractiveness perspective, [START_REF] Bose | Measuring customer-based place brand equity (CBPBE): an investment attractiveness perspective[END_REF] propose four dimensions for place brand equity: awareness, image, perceived quality, and loyalty. In the context of international relations (public diplomacy) between two places, [START_REF] Bose | Measuring customer based place brand equity (CBPBE) from a public diplomacy perspective: Evidence from West Bengal[END_REF] identify three dimensions for place brand equity: salience (awareness and image), perceived quality, and engagement (loyalty). That model closely resembles the [START_REF] Yoo | Developing and validating a multidimensional consumer-based brand equity scale[END_REF] model. Other studies evaluate place brand equity for a tourist destination [START_REF] Konecnik | Customer-based brand equity for a destination[END_REF][START_REF] Konecnik | Extending the tourism destination image concept into customer-based brand equity for a tourism destination[END_REF][START_REF] Yuwo | Customer-based brand equity for a tourism destination (CBBETD): the specific case of Bandung city, Indonesia[END_REF], but they all consider four dimensions: awareness, image, quality, and loyalty. Nonetheless, little is known about place brand equity from the residents' perspective [START_REF] Zenker | Measuring success in place marketing and branding[END_REF]. [START_REF] Kemp | A tale of a musical city: Fostering selfbrand connection among residents of Austin, Texas[END_REF] highlight that when city residents trust and are committed to a unique brand (city), they may form such strong connections with it that it is reflected in their self-concept. [START_REF] Shafranskaya | An empirical study of consumer-based city brand equity from signaling theory perspective[END_REF] show that city quality is a driver of city brand equity for residents, to the extent that the authors advance the idea that city branding is the signal that communicates city quality. The signal's credibility creates city brand equity. The literature on place branding highlights the need for place brand equity to be more thoroughly examined from the residents' perspective and integrated into a comprehensive model.

Second, the concept of attachment is widely used to analyze people-place relationships in the context of place branding. Several definitions of place attachment exist [START_REF] Lewicka | Place attachment: How far have we come in the last 40 years[END_REF].

Research into such attachment is increasing and draws on developmental theory [START_REF] Morgan | Towards a developmental theory of place attachment[END_REF], which refers to a developmental model of the process by which place attachment emerges from childhood place experience. For [START_REF] Morgan | Towards a developmental theory of place attachment[END_REF], place attachment is a developmental process whereby experiences in a place are internalized at an unconscious level and subjectively lead to place attachment, which comes from both social interactions and environmental evaluations, thus implying a bond between the brand and the self. Two dimensions of place attachment were initially proposed and widely accepted: place identity and place dependence. Recent research suggests two other dimensions to accommodate social, purely emotional, or symbolic components in the people-place relationship [START_REF] Kyle | Testing the dimensionality of place attachment in recreational settings[END_REF]: social bonding and affective attachment.

In line with the literature on place branding, including the classification proposed by Chen and Dwyer (2018), our research considers two dimensions of place attachment. The first is affective attachment, which reflects the purely affective aspects of place attachment and refers to an affective bond to a specific geographical area, and the meaning attributed to that bond. The second is place identity (or place identification) that encompasses the cognitive aspects of place attachment. Place identity is a subcategory of an individual's self-identity linked to the physical environment and "a self-categorization in terms of place" which reflects both sameness (continuity) and distinctiveness (uniqueness) [START_REF] Lewicka | Place attachment, place identity, and place memory: Restoring the forgotten city past[END_REF]. Place identity is an outcome of a cognitive justification process [START_REF] Rose | Place and identity: A sense of place[END_REF]. In that way, this research takes into consideration both affective and cognitive aspects of place attachment.

Serial mediation hypotheses

Our research suggests that place brand equity and place attachment are two mediators which induce a three-stage process: place brand heritage and place brand experience increase place brand equity, which in turn enhances place attachment, which then influences brandbuilding behavioral intentions. Two serial mediation hypotheses (H1 and H2) are hence advanced (Figure 1).

First, some empirical studies in branding show that brand heritage has a positive influence on brand equity [START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF][START_REF] Pecot | Cognitive outcomes of brand heritage: A signaling perspective[END_REF]. For example, [START_REF] Pecot | Cognitive outcomes of brand heritage: A signaling perspective[END_REF] integrate brand heritage into the model of brand equity. Their results indicate that brand heritage enhances brand credibility, perceived brand quality, and commands a price premium. To our knowledge, that effect has never been empirically tested in the context of place branding, but we predict that, for (prospective) residents, heritage also confers a meaningful and distinctive identity to the place that will generate added value and enhanced brand equity for that place. In other words, place brand heritage should improve place brand equity.

Place brand equity should enhance place attachment. Consistent with the place branding literature, place attachment is regarded in this research as a separate concept to place brand equity.

To our knowledge, place attachment, with its numerous dimensions, has never been conceptualized as a component of place brand equity (with awareness, image, quality, and loyalty as main components), only as a consequence of it. Indeed, associations stemming from the qualitative dimension of brand equity nourish attachment. Those associations draw on symbolic benefits and a sense of affiliation with the (place) brand that produce (place) attachment.

Moreover, affective attachment and place identity are both outcomes of the cognitive justification process based on comparisons and evaluations. [START_REF] Proshansky | Place-identity: Physical world socialization of the self[END_REF] note that place identity results from a complex cognitive process influenced by attitudes, values, thoughts, beliefs, meanings, and behaviors. In addition, several studies have identified and tested drivers of place attachment, such as place image [START_REF] Chen | A closer look at destination: Image, personality, relationship and loyalty[END_REF][START_REF] Fan | Examining the effects of tourist resort image on place attachment: a case of Zhejiang, China[END_REF][START_REF] Manyiwa | Influence of perceived city brand image on emotional attachment to the city[END_REF][START_REF] Strandberg | Places in good graces: The role of emotional connections to a place on word-of-mouth[END_REF], service quality [START_REF] Su | Empirical study of destination loyalty and its antecedent: The perspective of place attachment[END_REF], and place attractiveness [START_REF] Cheng | The influence of place attachment on the relationship between destination attractiveness and environmentally responsible behavior for Island tourism in Penghu, Taiwan[END_REF][START_REF] Hou | Antecedents of attachment to a cultural tourism destination: The case of hakka and non-hakka taiwanese visitors to Pei-Pu, Taiwan[END_REF]; all those antecedents can be viewed as dimensions of, or proxies for, place brand equity. Consequently, we expect that place brand equity will enhance place attachment.

Finally, we predict that place attachment influences behavioral intentions toward the place. That relationship is well established in the place branding literature. Based on the study by [START_REF] Morhart | Brand-specific leadership: Turning employees into brand champions[END_REF], [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF] analyze the influence of place attachment and place satisfaction on brand-building behaviors (ambassador behaviors, intention to stay or leave, and word of mouth). Their results show that place satisfaction strongly influences residents' intentions to stay or leave, whereas place attachment more strongly affects residents' word of mouth and ambassador behaviors. Other studies also report that word of mouth about a place is positively influenced by place attachment and residents identifying with their place of living [START_REF] Chen | Effect of dimensions of place attachment on residents' word-of-mouth behavior[END_REF][START_REF] Choo | The influence of the resident's identification with a tourism destination brand on their behavior[END_REF]. Such residents are more likely to participate in activities and decision-making processes about their place of living, and become ambassadors for it [START_REF] Braun | My citymy brand: the different roles of residents in place branding[END_REF]. Resident identification has a positive relationship with city citizenship behavior [START_REF] Taecharungroj | City ambassadorship and citizenship behaviors: Modelling resident behaviors that help cities grow[END_REF] that encompasses word of mouth about the place and intention to stay there [START_REF] Zenker | An integrative theoretical model for improving resident city identification[END_REF][START_REF] Zenker | Is satisfaction the key? The role of citizen satisfaction, place attachment and place brand attitude on positive citizenship behavior[END_REF].

We draw on social identity theory [START_REF] Tajfel | The social identity theory of intergroup behavior[END_REF] to explain the psychological mechanism by which brand-building behaviors arise in the context of place branding. According to that theory, individuals define their self-concepts by their connections with social groups or organizations. That logic extends to brands: consumers identify with brands that can be considered as self-relevant social categories [START_REF] Fournier | Consumers and their brands: Developing relationship theory in consumer research[END_REF][START_REF] Lam | Resistance to brand switching when a radically new brand is introduced: A social identity theory perspective[END_REF][START_REF] Stokburger-Sauer | Drivers of consumer-brand identification[END_REF]. As for brands, we argue that place brands with meaningful social identities can fulfill residents' key self-definitional needs and constitute valid targets for identification. Social identity theory posits that individuals adopt behaviors that are consistent with salient aspects of their identities within their self-concepts and help institutions embodying those identities (the place brand in our research) [START_REF] Ashforth | Social identity theory and the organization[END_REF]. Individuals confirm their self-concept with identity-consistent behaviors that meet their needs for self-consistency and self-expression [START_REF] Shamir | The motivational effects of charismatic leadership: A self-concept based theory[END_REF]. Therefore, we assume that (prospective) residents with a strong place attachment (affective attachment and place identification) should adopt identity-congruent behavioral intentions in the form of positive word of mouth, negative leaving intention (retention), and ambassador behaviors. As a result, we expect that: H1: Place brand equity and place attachment will mediate the effect of place brand heritage on behavioral intentions such that a more positive place brand heritage leads to a stronger place brand equity, which in turn leads to a stronger place attachment. Place attachment has an effect on behavioral intentions. Formally: Place Brand Heritage  Place Brand Equity  Place Attachment  Behavioral Intentions.

Second, the link between brand experience and brand equity has also been well investigated. In the service sector, empirical studies indicate that experience has a positive effect on brand equity dimensions [START_REF] Biedenbach | The impact of customer experience on brand equity in a business-to-business services setting[END_REF][START_REF] Chen | What drives cyber shop brand equity? An empirical evaluation of online shopping system benefit with brand experience[END_REF] or on overall brand equity [START_REF] Xu | A conceptual framework of hotel experience and customer based brand equity: Some research questions and implications[END_REF]. The study by [START_REF] Zarantonello | The impact of event marketing on brand equity: The mediating roles of brand experience and brand attitude[END_REF] also demonstrates that the above-mentioned four dimensions of brand experience identified by [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty[END_REF] positively influence brand equity. In line with those findings, we posit that for (prospective) residents, place brand experience should favorably affect place brand equity. Then, following the same logic as for hypothesis H1, we expect that place brand equity will increase place attachment, which in turn influences brand-building behavioral intentions. As a result, we propose that: H2: Place brand equity and place attachment will mediate the effect of place brand experience on behavioral intentions such that a more positive place brand experience leads to a stronger place brand equity, which in turn leads to a stronger place attachment. Place attachment then has an effect on behavioral intentions. Formally: Place Brand Experience  Place Brand Equity Place Attachment  Behavioral Intentions.

Research method

Sample

An online survey was carried out between April and June 2019 with an alumni sample 1 from Aix-en-Provence university business school and other universities located in the city to test empirically the research model. In total, 859 responses were recorded on SurveyMonkey, of which 571 were completed (66.47%). The sample comprised males (49%) and females (51%), with an average age of 33. Aix-en-Provence was chosen as the place brand for this research due to its residential attractiveness, and the research was conducted in collaboration with the city hall.

Aix-en-Provence university alumni were chosen since the city is well known for its excellent university environment. Alumni constitute an interesting sample with various origins (from Aix-en-Provence, other French cities, and other countries) who decided whether to reside in Aix-en-Provence after their studies. Those respondents are well adapted for our study, because they can be either residents or potential residents if they plan to return to live in the city.

Moreover, since our research model focuses on a people-place brand relationship construct (e.g., place attachment), respondents need to have prior real experiences of the place brand (objective familiarity with the place). Alumni samples allow us to target respondents with experience of the city as residents (or frequent visitors if they lived in the surroundings areas) during their period of study. Respondents were asked to consider Aix-en-Provence as a brand.

1 Alumni were contacted via alumni databases provided by universities and alumni associations.

We chose various five-point Likert scales (strongly disagree to strongly agree) with established reliability and validity (see Appendix A). To evaluate place brand heritage, we adapted [START_REF] Pecot | Consumers' responses to brand heritage: Cognitive and affective paths[END_REF] six-item version of the brand heritage scale encompassing three dimensions: stability, longevity, and adaptability (two items per dimension). Place brand experiences were measured by the [START_REF] Beckman | The impact of brand experience on downtown success[END_REF] twelve-item, four-dimensional scale, including sensory experience, affective experience, behavioral experience, and intellectual experience (three items per dimension). To measure place brand equity, we used a fifteen-item, five-dimensional scale adapted from existing measuring instruments that have passed confirmatory factor analyses. Items were modified to suit the resident context. Consistent with place branding studies (e.g., [START_REF] Bose | Measuring customer-based place brand equity (CBPBE): an investment attractiveness perspective[END_REF][START_REF] Bose | Measuring customer based place brand equity (CBPBE) from a public diplomacy perspective: Evidence from West Bengal[END_REF][START_REF] Konecnik | Customer-based brand equity for a destination[END_REF][START_REF] Konecnik | Extending the tourism destination image concept into customer-based brand equity for a tourism destination[END_REF][START_REF] Yuwo | Customer-based brand equity for a tourism destination (CBBETD): the specific case of Bandung city, Indonesia[END_REF], we selected awareness, image (or uniqueness), quality (or value), and loyalty as dimensions. Place brand awareness was measured by items from [START_REF] Yuwo | Customer-based brand equity for a tourism destination (CBBETD): the specific case of Bandung city, Indonesia[END_REF], place brand uniqueness by items from [START_REF] Kemp | A tale of a musical city: Fostering selfbrand connection among residents of Austin, Texas[END_REF], place brand perceived value by items from [START_REF] Netemeyer | Developing and validating measures of facets of customer-based brand equity[END_REF] and [START_REF] Yoo | Developing and validating a multidimensional consumer-based brand equity scale[END_REF], and place brand loyalty by items from [START_REF] Yuwo | Customer-based brand equity for a tourism destination (CBBETD): the specific case of Bandung city, Indonesia[END_REF] and [START_REF] Yoo | Developing and validating a multidimensional consumer-based brand equity scale[END_REF]. Place brand social value was added as a fifth dimension and measured by items from [START_REF] Guizani | Proposition d'une mesure psychométrique du capital client de la marque[END_REF]. Social value reflects the notion of identification with a group, with people living in the city (other residents), sharing similar values, and social recognition. [START_REF] Lassar | Measuring customer-based brand equity[END_REF] were first to identify that dimension, which fits well with the relational approach to brands adopted in this research and may be relevant for (prospective) residents.

As a precaution, the five-dimensional factorial structure was first verified through a preliminary study conducted on a sample of Aix-en-Provence university business school alumni (N = 134). That sample comprises male (47%) and female (53%) Aix-en-Provence alumni with an average age of 29. Data were collected online between November and December 2017. Of the 157 responses recorded, 134 were completed (85.35%). A series of exploratory factor analyses were run using promax rotation (SPSS Software). Item purification2 based on loadings greater than 0.5 resulted in a final place brand equity scale comprising fifteen items and five factors: awareness, uniqueness, social value, loyalty, and perceived value (see Appendix B). That model accounts for 77% of the total variance and the items show strong loadings with their representative factors (between 0.634 and 0.948). Place attachment was measured through two dimensions: place identity and affective attachment.

To measure place identity, in line with social identity theory, we adapted two items3 developed by [START_REF] Bergami | Self-categorization, affective commitment, and group selfesteem as distinct aspects of social identity in the organization[END_REF] and used by [START_REF] Lam | Resistance to brand switching when a radically new brand is introduced: A social identity theory perspective[END_REF] to capture the extent to which a resident identifies with the place brand to measure place identity (cognitive aspects of place attachment). We selected Chen and Dwyer's (2018) one-dimensional scale to measure affective attachment (affective aspects of place attachment). Finally, the three brand-building behavioral intentions-positive word of mouth, leaving intention (retention), and ambassador behaviors-were measured by the three one-dimensional scales proposed by [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF], thus capturing place-related behaviors based on [START_REF] Morhart | Brand-specific leadership: Turning employees into brand champions[END_REF].

Analysis

A structural equation modeling (SEM) approach4 was chosen for testing the causal research model. Structural equation models have been shown to be more effective [START_REF] Bagozzi | On the use of structural equation models in experimental designs[END_REF][START_REF] Russell | Analyzing data from experimental studies: a latent variable structural equation modeling approach[END_REF] when the analysis seeks to accommodate measurement errors in relation to the concepts examined. A covariance structure analysis (CSA) was chosen for the estimation method of our research model. Moreover, due to the lack of multivariate normality5 of the measurement variables, we relied on [START_REF] Browne | Asymptotically distribution-free methods for the analysis of covariance structures[END_REF] asymptotically distribution-free (ADF) method and a systematic bootstrap procedure with 5,000 replications.

In this research, all relationships between latent variables were tested at the second-order level in a reflective manner. The reflective measurement mode was chosen over the formative for two main reasons. First, the logic underlying reflective measurement modes clearly fits the prior conceptualizations of concepts relied on in this research at the first-order level (e.g., stability, longevity, and adaptability for place brand heritage). The same holds true concerning the secondorder constructs (e.g., place brand equity). Indeed, awareness, uniqueness, social value, loyalty, and perceived value are more appropriately considered to be manifestations of the latent construct of place brand equity. The same reasoning applies for other constructs such as place brand experience or place attachment. The latter is hence conceptualized as a second-order latent concept, which reflects the two first-order latent dimensions of place identity and affective attachment. Second, from a theoretical perspective, the second-order dimensions encompassed in this research clearly correspond to constructs that reflect in their respective facets, rather than formative measures that could define them. Moreover, according to [START_REF] Bagozzi | Measurement and meaning in information systems and organizational research: Methodological and philosophical foundations[END_REF] and [START_REF] Edwards | The fallacy of formative measurement[END_REF], the coefficients in formative models tend to vary according to the number of measures and factors used, thus making them less reliable and appropriate for assessing the validity of a network of plausible mediational relationships such as that investigated in this research. Overall, our research model consists of five second-order factors, with seventeen first-order factors measured by forty-seven observed variables.

We also tested for common method bias using model 2 proposed by [START_REF] Podsakoff | Common method biases in behavioral research: a critical review of the literature and recommended remedies[END_REF]table 4) for testing a causal model with a general method factor linked to all the measurement variables and orthogonal to all the other latent variables. In our case, the method variance effect, calculated as the average of the square loadings of the method factor, equals 4.8%, which indicates that the method bias is rather low, below the reported values in the literature [START_REF] Schaller | Alternative techniques for assessing common method variance: an analysis of the theory of planned behavior research[END_REF], and hence does not seem problematic in our research.

In total, all the goodness of fit indices of the model [START_REF] Cheung | Evaluating goodness-of-fit indexes for testing measurement invariance[END_REF] suggest an acceptable fit model with a χ² (2771, df = 1057; p < .001); root mean square error of approximation (RMSEA) = .057; non-normed fit index (NNFI) = .905; comparative fit index (CFI) = .952; standardized root mean residual (SRMR) = .061.

Once the overall quality of the proposed model had been established, we then assessed reliability, as well as convergent and discriminant validity. First, concerning the measurement variables, the factor loadings were high and all statistically significant (see Appendix A). Second, indicators of convergent validity and reliability were also satisfactory: all but two (which were close to 0.7) of the reliabilities were greater than 0.76, and the convergent validities were equal to or greater than 0.5 (see Table 1), either at the first-or second-order level. Indeed, the betas from the second-order factors to their respective first-order factors are all statistically significant and in absolute value ranging from 0.677 6 to 0.976. Those results statistically validate our second-order conceptualization of place brand equity, which is in line with previous theoretical and empirical considerations [START_REF] Bose | Measuring customer-based place brand equity (CBPBE): an investment attractiveness perspective[END_REF][START_REF] Bose | Measuring customer based place brand equity (CBPBE) from a public diplomacy perspective: Evidence from West Bengal[END_REF] 7 . Finally, we also tested discriminant validity by estimating the disattenuated latent correlations (Psi) between multiple pairs of variables to test whether their 95% confidence intervals fell significantly below 1.0 [START_REF] Bagozzi | Specification, evaluation, and interpretation of structural equation models[END_REF]. The results confirmed very good discriminant validity between all our encompassed latent variables, thus bring additional credence to the proposed model. Hence, we can examine the main results stemming from the structural path coefficients estimates. [Insert Table 1 around here] 6 Not surprisingly, the only negative second-order path coefficient (-0.677) is related to leaving intention. That means that the latent variable "Behavioral Intentions" refers as outcome to a favorable and positive orientation. 7 Indeed, a second-order conception seems preferable for at least five reasons: (1) it accounts for the pattern of relationships between the first-order factors, with high factor loadings between the second-order factor and the first-order ones, as mentioned in the text; (2) it puts a structure on the pattern of covariance between the firstorder factors which explains the covariance in a more parsimonious way, with fewer parameters; (3) it provides more parsimonious and theoretically error-free estimates of both the general factor and each specific factor; (4) focusing on the relationships at higher-order level results in a more parsimonious model, which is easier to analyze. Moreover, as pointed out by [START_REF] Liu | A new approach to testing nomological validity and its application to a second-order measurement model of trust[END_REF], such parsimony is not detrimental to the overall predictive power, provided that the R² with the second-order construct alone and those obtained only with lowerorder facets, are comparable 7 (5) it enables getting a more impactful incidence on the explained variables, since it corresponds to the common variance of all lower-order factors [START_REF] Liu | A new approach to testing nomological validity and its application to a second-order measurement model of trust[END_REF][START_REF] Valette-Florence | Effects of emotions and brand personality on consumer commitment, via the mediating effects of brand trust and attachment[END_REF].

Results

Our main research focus is on testing and validating two positive serial mediation paths (Figure 1). However, before we go for a formal statistical test, we have to ensure that other plausible alternative models could not bring a better fit to our empirical data. To do that, we rely on recent developments enabling competing models to be compared. Hence, the assessment of uncertainty and plausibility of these models is presented first, then the subsequent section addresses more specifically the testing of the two serial mediation hypotheses.

Uncertainty and plausibility assessment

In this section, we systematically compare our baseline model with models in which new additional direct links are introduced one by one. Chi² differences hence allow validation of the improvement in fit provided by each newly introduced relationship. Three main models are worth looking at: 1) a fully saturated model (A2) (Figure 5), in which all the relationships between the different concepts are estimated; 2) a simpler model (A1) (Figure 4), in which direct links are solely specified on a full mediation basis, and 3) an "in-between" model, as provided by our research model (RM) (Figure 3). A significant Chi² difference (Δ χ² = 21, p < 0.001) shows that model RM provides a better fit than model A1. Globally, that result validates the additional direct links of both place brand heritage and place brand experience with place attachment. Likewise, a significant Chi² difference (Δ χ² = 48, p < 0.001) shows that model A2 provides a better fit than model RM, hence supporting the direct links of both place brand heritage and place brand experience on behavioral intentions.

Even if the results tend to favor a saturated model, it remains worth investigating the plausibility of the usefulness of the various uncovered mediation effects. Recent advances proposed by [START_REF] Wu | Simple use of BIC to Assess Model Selection Uncertainty: An Illustration using Mediation and Moderation Models[END_REF] in the context of mediation models show that switching from a frequentist approach to a Bayesian investigation helps to assess the uncertainty and hence the believability linked to each mediation model. Relying on the most recent advances in the field, we then calculated posterior probability distribution, called BIC posterior (BICP), to assess the model selection uncertainty of the various mediation models. Whereas the frequentist method seeks the model with the best fit, the posterior probability distribution can be used to form a credibility set of models and hence allows the usefulness of the diverse significant mediation links to be compared. In their founding article, [START_REF] Wu | Simple use of BIC to Assess Model Selection Uncertainty: An Illustration using Mediation and Moderation Models[END_REF] point out that, from a Bayesian perspective, predicting how well a model predicts the data can be assessed by BIC posterior, hence allowing any number of plausible models to be compared. In practice, the BIC is calculated for each model, and then all probabilities are normalized to one. Such normalized values are called BIC posteriors, which give a full representation of how the sum of probability is distributed across all models and form a posterior probability distribution. That approach is very useful, especially when testing different mediation models, as [START_REF] Wu | Simple use of BIC to Assess Model Selection Uncertainty: An Illustration using Mediation and Moderation Models[END_REF] illustrate. In our case, besides the fact that all mediating models are statistically significant, that approach helps us to decide which is the most plausible and therefore should be preferred. We then compare the posterior BIC for the three mediation models tested in this research, relying on the Wu et al. ( 2020) formula (p 5) 8 .

The results presented in Table 2 show that our research model could be retained, since it has the highest BIC posterior (0.405). Model A1 has to be discarded, as it has the lowest probability (0.274). Model A2 could be a plausible choice, but it has a lower BIC posterior (0.322) than our research model (0.405). In other words, that means that our research model is the most plausible, with a more parsimonious relationships network. Clearly the search for parsimony favors our research model, thus reinforcing the mediating role of both place brand equity and place attachment. The following section discusses the results generated based on the proposed research model.

[Insert Table 2 around here].

[Insert Figure 3, Figure 4 and Figure 5 around here]. 8 Formally, for a given model M i with equal prior:

Test of the two serial mediation hypotheses

All tests are performed within a structural equation modeling (SEM) 9 framework and a systematic bootstrap procedure with 5,000 replications. Table 3 provides details of the direct and indirect path coefficients with their corresponding confidence intervals 10 . Although the uncertainty and plausibility assessment shows the superiority of the RM model over models A1 and A2, it is still instructive to compare those models in order to assess the nature of the mediations as either partial or full.

Between model A1 and model RM, the inclusion of a direct path from place brand heritage to place attachment (β = 0.630) is not detrimental to the corresponding indirect path estimate, which remains significant (β = 0.351 vs. β = 0.398). A similar pattern arises for the incorporation of a direct path between place brand experience and place attachment (β = 0.281) which is again not detrimental to the indirect path coefficient, which also remains significant (β = 0.205 vs. β = 0.233).

The same scheme applies between model A2 and model RM, where the inclusion of a direct path from both place brand experience (β = 0.128) and place brand heritage (β = 0.135) to behavioral intentions still leads to statistically significant indirect paths (β = 0.214 and β = 0.438 vs. β = 0.318 and β = 0.642, respectively). Only the estimated path coefficient from place brand equity to behavioral intentions proves to be non-significant (β = 0.051).

In summary, Figure 2 presents all the estimated direct path coefficients, whereas Table 4 synthetizes the nature and role of the mediating variables, along with their respective direct, indirect, and total path coefficients. These results provide support for the two research hypotheses 9 Even though SEM and the popular PROCESS software usually give perfectly comparable results for observed variables [START_REF] Hayes | The analysis of mechanisms and their contingencies: PROCESS versus structural equation modeling[END_REF], SEM has been preferred because (see also [START_REF] Sarstedt | Beyond a tandem analysis of SEM and PROCESS: Use of PLS-SEM for mediation analyses![END_REF]: (1) contrary to PROCESS, it gives formal tests for validating improvements in fit between concurrent models; (2) it allows testing of more complex mediational network not available with PROCESS; and (3) it explicitly takes into account measurement errors, not available with PROCESS, which is an important point as our research focuses on the relationships between latent variables. 10 Only one of the confidence intervals includes zero, hence validating the statistical significance of the path coefficient estimates.

H1 and H2 and hence provide an incremental contribution to the literature on place branding. It is worth noting the full mediation 11 role played by brand attachment (β = 0.440) between place brand equity and behavioral intentions. To the best of our knowledge, that role has never been put forward before. Moreover, a comparison of the indirect effects shows that place attachment plays a greater role 12 than place brand equity as regards the impact of place brand heritage and place brand experience on behavioral intentions. Those results hence illustrate the core role played by place attachment.

From a more managerial perspective, we also note that leaving intention is negatively influenced by place attachment (β = -0.443). As for product brands, place brands are social identities with which residents can identify. As the overlap between how a resident perceives their self-identity and the place brand identity increases, the leaving intention decreases. In other words, place attachment encourages resident retention in the city. In addition, place attachment positively influences ambassador behavior (β = 0.463) and word of mouth (β = 0.570). These findings confirm those of [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF]. Due to the positive serial mediation, through place attachment, between place brand equity and behavioral intentions, the same happens for place brand equity, but to a lesser extent (see Appendix C for details).

Globally, place brand equity and place attachment demonstrate a partial positive mediator role which induces a three-stage process: place brand heritage and place brand experience increase place brand equity, which in turn enhances place attachment, which then influences residents' behavioral intentions toward the city. From a theoretical perspective and according to the seminal work of [START_REF] Zhao | Reconsidering Baron and Kenny: Myths and truths about mediation analysis[END_REF], 13 our results show that omitted mediators are likely to exist and hence should be added in future extensions of this research. More precisely, place brand heritage and place brand experience both entail cognitive and affective dimensions which are not fully mediated by place brand equity. A more complete spectrum of brand relationships is perhaps 11 Direct β = 0.051; p = 0.619. 12 The incremental indirect effect of place brand equity compared to that of place attachment is only 0.134 vs. 0.184 and 0.229 vs. 0.412 for place brand experience and place brand heritage, respectively. 13 We are indebted to the reviewers for pointing that out.

missing. In that spirit, the effect of introducing the two hot and cold components of the Brand Relationship Quality (BRQ; [START_REF] Nyffenegger | Service Brand Relationship Quality: Hot or Cold?[END_REF] introduced by Fournier (1998) could be worth investigating.

Overall, the two mediation hypotheses comprise two main sections. The upstream part is focused on the mediating role of place brand equity. Our results confirm the partial mediations of place brand equity as regards the impact of place brand heritage and place brand experience on place attachment. More precisely, place brand equity positively (and partially) mediates the relationship between place brand heritage and place attachment (direct β = 0.630 and indirect β= 0.351). Place brand equity also positively (and partially) mediates the relationship between place brand experience and place attachment (direct β = 0.281 and indirect β = 0.205).

The downstream part relates to the partial mediations involved in place attachment. Our results also confirm its mediations regarding the indirect influence of place brand equity, place brand heritage, and place brand experience (serial mediations) on behavioral intentions. Indeed, the impact of place brand heritage on behavioral intentions is positively and serially mediated by place brand equity and place attachment (direct β = 0.135 and indirect β = 0.438). Moreover, the impact of place brand experience on behavioral intentions is positively and serially mediated by place brand equity and place attachment (direct β = 0.128 and indirect β = 0.214). Nonetheless, we also note that the direct paths of either place brand heritage or place brand experience on behavioral intentions are significant but rather low. In addition, the difference between the R² for a model with those direct paths (67.83%) and the R² without those paths (65.83%) is rather small. Such operational and predictive considerations question the usefulness of the saturated model A2, which indeed has been shown to be less plausible than our proposed and validated research model.

[Insert Table 3, Table 4, and Figure 2 around here]

Discussion and conclusion

Theoretical and methodological contributions

This study unravels the mechanism that leads to behavioral intentions of (prospective) residents toward a city by testing a comprehensive model based on branding and place branding frameworks. We empirically test among (prospective) residents serial mediation hypotheses that allow identification of a three-stage process: place brand heritage and place brand experience increase place brand equity, which in turn enhances place attachment, which then influences brand-building behavioral intentions. Our findings refine and extend existing knowledge of the antecedents of residents' behaviors [START_REF] Braun | My citymy brand: the different roles of residents in place branding[END_REF][START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF][START_REF] Chen | Effect of dimensions of place attachment on residents' word-of-mouth behavior[END_REF][START_REF] Choo | The influence of the resident's identification with a tourism destination brand on their behavior[END_REF][START_REF] Daryanto | A meta-analysis of the relationship between place attachment and pro-environmental behaviour[END_REF][START_REF] Taecharungroj | City ambassadorship and citizenship behaviors: Modelling resident behaviors that help cities grow[END_REF][START_REF] Zenker | An integrative theoretical model for improving resident city identification[END_REF][START_REF] Zenker | Is satisfaction the key? The role of citizen satisfaction, place attachment and place brand attitude on positive citizenship behavior[END_REF]. This research is theoretically relevant in several ways.

We integrate brand heritage and brand experience as antecedents in our research model to shed new light on residents' place-related behavioral intentions (i.e., brand-building behavioral intentions). Those concepts come from the branding literature. In this way, we add to the body of research on place branding by proposing and empirically testing relationships among underexplored constructs in this field. Heritage is a dimension of brand identity, and we demonstrate that its principles are relevant to our research. Places of living associated with a high degree of stability, longevity, and adaptability generate place value and attractiveness. In the branding literature, little research examines it from the consumer perspective (external perspective) including brand heritage in integrative models [START_REF] Pecot | Cognitive outcomes of brand heritage: A signaling perspective[END_REF][START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF]. Our results show that place brand equity and place attachment mediate the effect of place brand heritage on behavioral intentions. Thus, our findings bring new insights to this body of literature by demonstrating that place brand heritage is a critical driver of residents' behavioral intentions toward a city.

The effects of brand experiences have been investigated in a few studies in the place branding literature for downtown brands [START_REF] Beckman | The impact of brand experience on downtown success[END_REF] and destination brands [START_REF] Barnes | Destination brand experience and visitor behavior: Testing a scale in the tourism context[END_REF][START_REF] Yang | How customer experience affects the customer-based brand equity for tourism destinations[END_REF]. Our research completes existing studies by examining place brand experience as a critical driver of behavioral intentions toward a city. Place brand equity and place attachment mediate the effect of place brand experience on behavioral intentions. Brand experiences are relevant from the perspective of (prospective) residents. Thus, we confirm that residents should be considered as the first customers of a place. Brand experience theory is often used for product and service brands (e.g., [START_REF] Iglesias | The role of brand experience and affective commitment in determining brand loyalty[END_REF][START_REF] Iglesias | How does sensory brand experience influence brand equity? Considering the roles of customer satisfaction, customer affective commitment, and employee empathy[END_REF][START_REF] Lin | Innovative brand experience's influence on brand equity and brand satisfaction[END_REF]; our paper contributes to that theory by extending it to city branding research. Moreover, our findings validate the two serial mediation hypotheses and, consequently, the mediating role of both place brand equity and place attachment. The effect of both place brand heritage and place brand experience on behavioral intentions is serially mediated by place brand equity and place attachment. Place brand equity contributes to explaining the causal mechanisms at work to make the relationship between place brand heritage, place brand experience, and place attachment more efficient. To our knowledge, this research is the first to demonstrate those interrelationships. We also contribute to enriching existing studies on brand equity in place branding by demonstrating that place attachment generates positive word of mouth, lower leaving intentions, and ambassador behaviors for places. Word of mouth and ambassador behaviors are positively influenced by place attachment, whereas leaving intention is negatively influenced by place attachment. That result is in line with [START_REF] Chen | Residents' place satisfaction and place attachment on destination brand-building behaviors: conceptual and empirical differentiation[END_REF]. Thus, this research extends their work, in which they request that future research test their structural model in other contexts.

Mediation analysis also highlights the critical role of place attachment, as the effect of place brand equity on behavioral intentions is fully mediated by place attachment. Consequently, we confirm the relevancy of considering both affective and cognitive aspects of place attachment (place identity and affective attachment) in terms of their impacts on behavioral intentions. That highlights more globally the central role of attachment in predicting behaviors consistent with previous studies [START_REF] Hosany | Mediating effects of place attachment and satisfaction on the relationship between tourists' emotions and intention to recommend[END_REF][START_REF] Park | Brand attachment and brand attitude strength: Conceptual and empirical differentiation of two critical brand equity drivers[END_REF]. These findings enrich the literature on place attachment and its dimensionality in understanding residents' behaviors. In line with social identity theory, the more (prospective) residents identify with a city and are emotionally attached to it, the more they will: (1) spread positive word of mouth, (2) intend to reside there, and (3) act as ambassadors. Consequently, we contribute to marketing uses of social identity theory by showing its relevance to city branding. The relevancy of identification processes is also confirmed through place brand social value, which is one of the five dimensions we identified in the measurement of place brand equity. Social value reflects the notion of identification with people living in the city (other residents), meaning that, to be a valued place of living, residents need to feel that they share similar values. In other words, to be attractive, generate attachment, and lead to city-supporting behaviors, a place of living and its people must be consistent with a resident's identity and self-image.

Finally, from a methodological perspective, we have assessed the uncertainty and plausibility of the mediation models based on the calculation of BIC posterior (BICP). To our knowledge, this methodological approach has never been used before to investigate mediation models in the field of place branding. The Bayesian approach allows any number of plausible models [START_REF] Wu | Simple use of BIC to Assess Model Selection Uncertainty: An Illustration using Mediation and Moderation Models[END_REF] to be compared and the most plausible one identified. Our findings indicate that, when compared with two other models, our research model has the highest plausibility and a more parsimonious relationships network, which reinforces the mediating role of both place brand equity and place attachment. Consequently, our paper contributes to this very recent methodological approach by applying it to city branding research.

Managerial implications

Our results have important implications for city brand management; they may help managers to define effective place branding actions.

First, marketing communication is one of the primary ways in which heritage is activated and communicated to stakeholders [START_REF] Urde | Corporate brands with a heritage[END_REF]. As branding elements, symbols, historical references, logos, slogans, images, photographs, and texts can be used to reinforce corporate heritage and competitive positioning. In a place branding setting, using those branding elements enhances the effectiveness of territorial and cultural symbols, thereby providing strong evidence of a place heritage branding strategy [START_REF] Kotler | Country as a brand, product, and beyond: A place marketing and brand management perspective[END_REF]. For the messages to be persuasive, historical references and symbols need to be relevant and meaningful to the intended targets [START_REF] Wilson | Transforming history into heritage: applying corporate heritage to the marketing of places[END_REF]. We also recommend selecting heritage traits based on their degree of perceived stability, longevity, and adaptability, as well as their distinctiveness. Since heritage plays a major role in the construction of both place and resident identities [START_REF] Hakala | Toponyms as carriers of heritage: Implications for place branding[END_REF], cities with a distinctive heritage may help residents to shape their own identity more easily.

The city of Porto (second largest city in Portugal) illustrates how heritage traits can contribute to the identity of a place of living. The city's visual identity was redesigned in 2014 to enhance citizen engagement14 . To represent what Porto means for each citizen, more than seventy geometric icons (traditional Portuguese blue earthenware tiles) illustrating the city and its people were used to show its history. More than simple logos, the icons became a visual code to express the identity and soul of the city, uniting history and modernity in a surprising way, with all facets of the city represented (past, future, sea, food, culture, innovation, etc.). Porto provides an example of how, from a competitive positioning perspective, selected heritage traits should be distinctive and constitute actionable points of differentiation. With those aims in mind, city brand managers could benchmark their city against others.

Second, residents' experiences related to the place of living are also crucial. The stronger and more positive residents' experiences related to the place brand are, the stronger their attachment to the place of living will be. Thus, to attract new and retain existing residents, city managers should create and optimize place brand experience (sensory, affective, behavioral, and intellectual), inspired by practices in service and tourism contexts in which hedonic or experiential consumption is central. [START_REF] Beckman | The impact of brand experience on downtown success[END_REF] recommend implementing marketing actions specifically aimed at enhancing sensory and behavioral experiences when considering local residents (vs. tourists). Sensory brand experience refers to sensory experiences had when people are exposed to a city. Such experiences can be improved by integrating unique elements into the city that may appeal to all the senses (sight, sound, touch, smell, and taste), making the city memorable and inducing a more positive experience (e.g., architecture, landscapes, lights, food and drink, music, traffic, and mountain breezes).

Behavioral brand experience encompasses physical actions and behaviors stimulated by the city. For residents, those experiences can be improved by various initiatives that engage them, such as offering a weekly farmers' market, discounted tickets to museums and events, or actions to attract a local workforce [START_REF] Beckman | The impact of brand experience on downtown success[END_REF]. Paris Plages, an event created in 2002 by the city of Paris, is an example of how to generate sensory and behavioral experiences. Every summer, the banks of the Seine and the Bassin de la Villette turn into a seaside resort. The event offers free relaxation and leisure spaces to Parisians during the heat of summer: fresh lawns, parasols, deckchairs, palm trees, cultural and sporting activities, and swimming, enabling people to cool off and enjoy the beautiful weather.

Third, we demonstrate the importance of identification and attachment processes to place of living in inducing residents' behavioral intentions. Thus, city managers could investigate how to generate a strong identification with the place, a sense of belonging, and how to make the city a valuable target for identification. With globalization, it is increasingly rare for countries, nationalities, and cities to inspire a sense of belonging, so cities could aim to trigger it. A good example is the city of Amsterdam, which implemented that very idea with the "I Amsterdam" slogan to create a strong emotional bond between the city and the residents through identification with the place. Based on social identity theory, [START_REF] Elbedweihy | Customer relationship building: The role of brand attractiveness and consumer-brand identification[END_REF] highlight that value congruence increases identification with a brand. Applied to our research, congruence between the values of the target market (current and potential residents) and the brand (the place of living) could also be nurtured by marketing actions aimed at positioning the city as a salient category in residents' minds [START_REF] Elbedweihy | Customer relationship building: The role of brand attractiveness and consumer-brand identification[END_REF], for example by communicating that the city's values match those of the residents, thus making the city more appealing to target people by satisfying their self-verification needs, and drawing favorable comparisons with other cities to emphasize the values perceived as important for the city's actual and potential residents.

Finally, this research provides a reliable and valid scale of place brand equity. This tool should help city brand managers to estimate the extent to which residents perceive the value of a place of living. Our results show that place brand equity is a mediating variable. Consequently, by managing place brand equity efficiently, city brand managers could also better manage place attachment and behavioral intentions toward their city. More generally, our results contribute to helping local governments and city brand managers to diagnose and better manage performance of places of living, to understanding how to create and develop strong place attachment so as to engage residents, and to encouraging managers to initiate actions that not only increase residentplace connections but also internalize the place of living and induce place-supportive behaviors.

Limitations and future research

Several limitations of this study present opportunities for further research. First, it was conducted on a single city, so it is impossible to make generalizations relevant to all places.

Replicating this study for other cities and countries should allow us to test the model in other contexts. Second, data were collected from an alumni sample, so a multi-sample study, based on potential residents who are not specifically alumni, would be beneficial. Such a study would allow validation of both the model and the managerial recommendations regarding the contributory factors to a city's attractiveness. As our model is partly based on prior experiences related to the place brand, other drivers would need to be investigated to understand how to attract residents who have no previous experience of the city. Moreover, other relatively new dimensions of place attachment, such as social bonding, should be added to the study for a better understanding of the social phenomena arising from place branding issues. As discussed above, the partial mediations clearly indicate that omitted mediators are likely to exist, so future research should add other mediators to the model. Relying on a more complete spectrum of brand relationships, the hot and cold dimensions of the BRQ [START_REF] Fournier | Consumers and their brands: Developing relationship theory in consumer research[END_REF], could be useful from that perspective. Finally, brand equity has only recently been conceptualized as a process [START_REF] Chatzipanagiotou | Decoding the complexity of the consumer-based brand equity process[END_REF][START_REF] Stocchi | A comparison of brand equity strength across consumer segments and markets[END_REF]. Future studies could extend our findings by analyzing how the dimensions of place brand experience and place brand heritage are relevant to understanding the place brand equity creation process using fuzzy-set Qualitative Comparative Analysis.

TABLES AND FIGURES

Figure*

  Figure 1. Research Model and Hypotheses

Figure 4 .

 4 Figure 4. Alternative Model 1 (A1): Simple mediation model

Table 1 . Reliability and convergent validity Latent variable (order 2)

 1

			Convergent	Reliability	Latent variable (order 1) Number	Reliability	Convergent
			validity	(Rhô)		of items	(Rhô)	validity
	Place	brand	0.546	0.783	Stability	2	0.795	0.662
	heritage				Longevity	2	0.668	0.502
					Adaptability	2	0.831	0.711
	Place	brand	0.811	0.945	Sensory	3	0.856	0.665
	experiences			Affective	3	0.828	0.616
					Behavioral	3	0.763	0.518
					Intellectual	3	0.784	0.548
	Place	brand	0.542	0.854	Awareness	2	0.672	0.506
	equity				Uniqueness	3	0.861	0.674
					Social value	2	0.856	0.748
					Loyalty	3	0.914	0.726
					Perceived value	4	0.904	0.702
	Place attachment	0.863	0.927 Place identity	2	0.792	0.547
					Affective attachment	4	0.929	0.767
	Brand building	0.573	0.799	Positive WOM	3	0.907	0.765
	behavioral			Leaving intention	3	0.794	0.563
	intentions				Ambassador behavior	3	0.858	0.668

Table 2 . Model uncertainty assessments Model Uncertainty Assessments: SEM Fit indices, BIC & BIC Posteriors

 2

	Fit Indices & BIC Posteriors	Research Model	Alternative Model A2	Alternative Model A1
		χ²/df	2.62	2.28	2.64
		CFI	0.952	0.953	0.948
		NFI	0.905	0.907	0.883
	SEM Fit indices	TLI	0.950	0.951	0.946
		RMSEA	0.057	0.057	0.058
		SRMR	0.061	0.059	0.062
		AIC	5.206	5.656	5.884
		BIC	6.137	6.597	6.921
	BIC & BIC Posteriors	Δ (BIC -BIC min )	0.000	0.795	0.676
		BIC Posterior	0.405	0.322	0.274

Grey shading represents best value, from lighter (worst) to darker

(best)

Table 4 . Synthezis of Mediation analyses for Research Model (RM) Investigated Relationships: Source --->Target Mediating Variables Direct Effects Indirect Effects Nature of Mediation Omitted Mediators

 4 : PM = Partial Mediation; b : FM = Full Mediation; c : SPM = Serial Partial Mediation; *Estimates in italics are not statistically significant

	Place Brand Experience Place brand heritage	--->Place Attachment	Place Brand Equity	0.281 0.630	0.205 0.351	P M a	Likely
	Place Brand Experience Place brand heritage	--->Place Behavioral response	Place Attachment	0.128 0.135	0.184 0.412	P M	Likely
	Place Brand Experience Place brand heritage	--->Place Behavioral response	Place Brand Equity & Place Attachment	0.128 0.135	0.318 0.642	SPM c	Likely
	Place Brand Equity	--->Place Behavioral response	Place Attachment	0.051*	0.440	F M b	Unlikely

a

The initial pool of items is available from the authors upon request.

The visual item includes a series of Venn diagrams indicating the extent of overlap between oneself and the place brand identity; respondents choose the level of overlap that best reflects their relationship with the place brand. The verbal item is a seven-point scale, where 1 = "completely different,"

= "neither similar nor different," and 7 = "completely similar." 4 We relied on both SEPATH and AMOS for the SEM estimation.

Mardia's normalized multivariate coefficient =

61.193, far above the recommended threshold (below 5).

Source: https://www.behance.net/gallery/20315389/New-identity-for-the-city-of-Porto (accessed on February 17, 2020).


Ali Mokh

Julien De Rosny

George C Alexandropoulos

Mohamed Kamoun

Abdelwaheb Ourir

Ramin Khayatzadeh

Arnaud Tourin

Mathias Fink

Experimental Validation of Time Reversal Multiple Access for UWB Wireless Communications at the SubTHz Frequency Band

Keywords: Time Reversal, low-complexity reception, pulse position modulation, THz communications, UWB

Increase data rate while having low power consumption and low computational complexity at the receiver are the key elements for the research in wireless communication for low complexity devices. Sub Terahertz (SubTHz) radio-frequency domain can support ultra-wideband (UWB) communications, and thus the unprecedented increase in the wireless network capacity, that could be the next breakthrough for the next 6G standards. However, the technology of subTHz transceivers is not yet completely mature to apply the same advanced processes as the ones that are currently implemented for microwaves communications. We propose to test the effectiveness of Time Reversal (TR) precoding which is simple and robust processing to focus on time and space UWB waveforms in exploiting the channel diversity. In this paper, we first investigate experimentally the performance of subTHz TR focusing on multiple access transmission scenarios at a high data rate, while keeping the receiver simple and with low computational complexity.

I. INTRODUCTION

Internet of Things (IoT) technologies offer advanced services in different domains such as medicine, power, connectedsmart cities, smart homes, agriculture, etc. Some of the main requirements of the IoT are the support of massive deployment, scalability, high efficiency, low power consumption, and intermittent connectivity. An important part of the IoT network is the wireless network which needs to support low-power devices equipped with very low complexity transceivers [START_REF] Georgiou | The IoT energy challenge: A software perspective[END_REF], [START_REF] Luo | Analysis and optimization of embedded software energy consumption on the source code and algorithm level[END_REF], [START_REF] Gray | Power consumption of IoT access network technologies[END_REF]. Various communication strategies have been proposed to limit the energy consumption of the communication modem of IoT devices both from software and hardware perspectives [START_REF] Gray | Power consumption of IoT access network technologies[END_REF], [START_REF] Henkel | Ultra-low power and dependability for IoT devices[END_REF]. In particular UWB waveforms have ushered in a new era in short-range wireless communications for wireless sensor networks, by enabling both robust communications and accurate ranging capabilities [START_REF] Zhang | UWB systems for wireless sensor networks[END_REF]. To support large bandwidth for multiple devices, the initial discussion indicates that frequencies in the range of subTHz and above will be considered for 6G as there are plenty of available bands suitable to satisfy these requirements [START_REF] Saad | A vision of 6G wireless systems: Applications, trends, technologies, and open research problems[END_REF], [START_REF] Tariq | A speculative study on 6G[END_REF]. It appears that 6G will utilize a spectrum beyond 140GHz with particular applications in very short-range communication or 'whisper radio' [START_REF] Xing | Propagation measurement system and approach at 140 GHz-Moving to 6G and above 100 GHz[END_REF]. One central issue facing UWB waveforms for low complexity devices is to effectively collect energy that is dispersed in rich multi-path channels. TR appears to be a paradigm shift in exploiting this rich multi-path to focus in time and space UWB pulses [START_REF] Lerosey | Time reversal of electromagnetic waves[END_REF] while shifting the complexity to the transmitter side. In [START_REF] Qiu | Detection of physics-based ultrawideband signals using generalized RAKE with multiuser detection (MUD) and time-reversal mirror[END_REF], TR was considered in UWB communications. The increasing of SNR thanks to temporal focusing have been experimentally verified with a multi-antenna transmitter [START_REF] Qiu | Time reversal with MISO for ultrawideband communications: Experimental results[END_REF], [START_REF] Mokh | Indoor experimental evaluation of ultra-wideband MU-MISO TRDMA[END_REF], [START_REF] Mokh | Time reversal for multiple access and mobility: Algorithmic design and experimental result[END_REF]. The concept of TR division multiple access was introduced in [START_REF] Han | Timereversal division multiple access over multi-path channels[END_REF] for multiuser communication. Very recently, we evaluated the performance of TR in the subTHz domain in [START_REF] Mokh | Time reversal precoding at subTHz frequencies: Experimental results on spatiotemporal focusing[END_REF] for spatiotemporal focusing, and we used the experimentally measured signals in a simulation chain to simulate data transmission using spatial modulation.

In this paper, we propose to experimentally evaluate the capability of TR in the sub-THz domain for multiple access transmission, for low complexity devices, and at a high data rate. An experimental setup is used to perform the channel estimation and time-reversal transmission at 273.6 GHz carrier frequency and with a bandwidth up to 2 GHz, where the link between the transmitter and the receiver is a waveguide with a tilted incident angle. We selected two different positions for the receiver as 2 different receivers, and we transmitted binary data using a modulation technique that depends on the position of the peak of the received signal. The detection was performed via two incoherent receivers with a simple power detector.

The rest of the paper is organized as follows. In section II, the principle of TRDMA is described. In section III, we present the subTHz experimental setup to estimate the channels and to measure the TR signals in multiple access. In section IV, we present the experimental results for data transmission for different data rates. Finally, section V is devoted to the conclusion.

II. TIME REVERSAL DIVISION MULTIPLE ACCESS

We consider a multi-access wireless communication system comprising one transmitter that is equipped with a single antenna element and communicates in the downlink direction toward N single-antenna. We represent by h i [k] the baseband channel impulse response (CIR) at discrete time k between the transmitter and the i-th (i = 1, 2, . . . , N ) receiving antennas. TR preprocessing consists of using the time reversed CIR, i.e., h * i [L -k] to focus the electromagnetic field on the i-th antenna. As a consequence, the signal sent by the transmit antenna to focus individually the baseband message x i [l] on each receiving antenna is given by

s[k] = N i l x i [l]h * i [L + l -k] l |h i [l]| 2 , ( 1
)
where it is assumed that the CIR is composed of L significant taps. The normalisation ensures that the power emitted toward each user is the same.

Typically, the symbol rate can be lower than the system CIR rate. Considering T p be the pulse duration used to estimate the channel and to perform the TR precoding. T p is related to the system bandwidth B, where T p = 1/B. And let D be the rate backoff factor that is introduced to match the symbol rate with the pulse duration, then the symbol duration is T s = DT p . Then, the signal received by each antenna is sampled every T s = DT p seconds at t = kDT p , in order to detect the symbol x[k]:

y j [k] = y[t = kDT p ] = L l N i x i [l]R j,i [L + l -kD] + n j [k].
(2) where the expression of the correlation function between the CIRs of users j and i is given by

R j,i [k] = m,k ′ h * i,m [k -k ′ ]h j,m [k ′ ] m ′ ,l |h i,m ′ [l]| 2 , (3)
and n j [•] is the zero-mean additive white Gaussian noise with standard deviation σ at user j. TR precoding aims to focus the received signal in time and space at the targeted receive antenna by applying its time reversed CIR [START_REF] Fink | Chaos and time-reversed acoustics[END_REF], and we can see from equation 3 that the autocorrelation function has a real-value peak at R i,i [0]. This is referred to the fact that all the M ×L signals add up coherently at this time and location (R

i,i [0] = m ′ ,l |h i,m ′ [l]| 2
). However, the imperfect space-time focusing of the TR precoding produce 2 kinds of interference:

• ISI from the signals that add incoherently at the same antenna i = j in the time that is different than 0, i.e. R i,i [k] for k <> 0.

• IUI from all the signals in the auto-correlation function for i ̸ = j.

III. SUBTHZ EXPERIMENTAL MEASUREMENTS

In this section, the TR focusing and TRDMA transmission in the sub-THz domain are tested experimentally. In such frequencies, the attenuation of the channel becomes very high, and it is difficult to have a multi-path channel even for indoor application. So we prepared a specific setup for the experiment to be able to create a multi-path channel.

B. Channel Estimation and Time Reversal Focusing

The estimation of the CIR and TR precoding was performed as follows. First, a chirp signal spanning the range [f c -B/2 f c + B/2] is transmitted by the Tx. Synchronously, the signal is probed by the Rx antenna. The computer performs the CIR estimation by correlating the recorded signal with the chirp signal. Even if TR generates high amplitude pulses, the gain is not sufficient to directly probe the pulse with an Rx antenna. For this reason before emission, the CIR flipped in time is also convoluted with the same chirp signal. Similar to the CIR estimation, the TR-focused signal is reconstructed in the computer by cross-correlation. The results of the channel estimation and the TR received signals for 2 GHz bandwidth are shown in Figure 2.

Thanks to the waveguide, the rays coming from the transmitter that is inclined of angle α from the direction of the

C. Multiple Access Measurements

We measured the CIR for different positions of the Rx antenna spaced by 1 mm between x =-3mm to 3 mm, where x = 0 is the position facing the center of the tube output, using a bandwidth B= 2 GHz. We then select two positions where the CIRs are less correlated, namely z 1 = -3 mm and z 2 = 0, to apply the TR precoding for multiple access transmission. Fig. 3 shows the baseband received signals at the two spatial positions z 1 and z when applying TR to focus towards z 1 or z 2 , i.e. the focusing signal and the IUI when targetting one of the two positions. A peak signal localized in time appears at the targeted position (for the two positions). The figure shows the capability of the TR to focus the signal in time and space at the targeted position.

To investigate the capability of transmitting data in multiple access scenarios, we use the same scenario to modulate binary data with the focusing signal using a modulation technique that is explained in the next section.

IV. PULSE POSITION MODULATION IN TRDMA

In this section, we perform experimental measurements that apply the TR precoding for data transmission. The binary data is transmitted using the Pulse Position Modulation (PPM).

A. System Model

The idea is to use the TR precoding to target two spatial positions, to transmit two data streams at the same time and frequency, by exploiting the channel spatial diversity. As explained in the previous section, we convoluted the reversed signal (for TR precoding) by a chirp to increase its energy, since we are limited by the maximum power of the transmitter, and so the duration of each symbol is related to the chirp duration. For this purpose, we propose to use PPM modulation to code the binary information, where the position of the maximum amplitude of the received signal (or the maximum of R i,j [k] in equation 3) will code the information.

Let τ c be the chirp length in taps (i.e. the time duration of the chirp is τ c /B seconds), D be the rate backoff, and n is the order of the PPM modulation or the number of bits per chirp. So the modulation with TR multiple access to transmit data two positions z 1 and z 2 is performed as follow:

• The baseband CIR of each corresponding z i are flipped in time and convoluted with a chirp each. • The corresponding n i bits to be transmitted for each receiver is converted to an integer m i that represents the corresponding position, and then the previously precoded signals are rotated by circular rotation with m i taps and transmitted after normalization. • At the receiver side, the receiver has to estimate the position of the peak to decode the information. A simple power detector for each receiver can detect the position. The motivation is to show the capability of TR in the sub-THz domain to spatial multiplexing, with a very simple receiver that does not need phase detection and synchronization between antennas.

In our experiment, we evaluated the transmission for different data rates that correspond to a different order of modulation and chirp length. The data rate to 2 users can be calculated as follow:

Bit Rate = 2 × Bn τ c . (4)
Table I shows the different configurations of chirp length and the order of modulations that have been used in the experiment, as well as their corresponding bit rate. Figure 4 shows the received signals at two positions z 1 = -3 mm and z 2 = 0 mm, when using a chirp of τ c = 40000 at 2 GHz bandwidth (i.e. the duration of the chirp is 20 µs). The order of modulation is n = 10 and D = 39 for each receiver. We can see that for each spatial position, the received signal has a maximum value at the temporal position that corresponds to the transmitted PPM symbol, and the second peak is the interference from the signal of the other position (inter-user interference).

B. Simulation Results

We used the signals from the measurement section, and we calculate the signal and the interference at the two positions z 1 = -2.7 mm and z 2 = -1.8 mm, and for different D.

Fig. 5 shows the SINR of the received signal at each position in terms of the bit rate that is calculated in Table I. It is shown that the SINR of the signal degrades with a higher bit rate, and this is referred to the combination of two factors: the first one is the length of the chirp that decreases with a higher bit rate, and so the energy transmitted per symbol is reduced. The second factor is the rate backoff that is reduced in case of saturation of the order of modulation for a certain chirp length (if the chirp is 1100 taps and the order of modulation is 10 bits per symbol, then we have one position per tap). In addition, even for a high data rate, the SINR remains greater than 0 dB, and this shows the capability for the multiple access transmission of the TR in the subTHz domain. These experiments are done in offline (non-real time measurements), and the CIR estimation is maintained through the computer that connects the transmitter and the receiver. The goal is to show the capability of transmission in high data rate while keeping the receiver simple. In future work, a real channel estimation with disconnected transmitter and receiver should be considered. For this reason, and to keep the receiver simple, the channel estimation protocol should take into account that the receiver is incoherent (no complex data is generated).

V. CONCLUSION

In this paper, we investigated the capability of TR-based precoding for multiple access transmission in the subTHz frequency band. An experimental setup with a waveguide at the carrier frequency 273.6 GHz with 2 GHz transmission bandwidth has been designed and realized to first estimate the channel, and then for performing TRDMA. In particular, the channel estimation at two different positions separated by 3 mm has been used for multiple access transmission. The presented results validated the capability of TR for multiuser communications in subTHz frequencies, and showcased data communication with simple PPM detection exceeding 340 Mbps. In the future, we intend to consider reconfigurable intelligent surfaces [START_REF] Alexandropoulos | Reconfigurable intelligent surfaces for rich scattering wireless communications: Recent experiments, challenges, and opportunities[END_REF] for reprogrammable rich scattering conditions, enabling TR-based THz wireless communications.

Figure 1 .

 1 Figure 1. SubTHz Experiment Setup

Figure 2 .

 2 Figure 2. Channel Impulse response and Time reversed signal at B=2GHz

Figure 3 .

 3 Figure 3. Baseband received signals at the two spatial positions z 1 = -3mm and z 2 = 0 when applying TR to focus towards z 1 or z 2 .

Figure 4 .

 4 Figure 4. Received signals at positions z 1 = -3mm and z 2 = 0 when applying TRDMA with PPM.

Figure 5 .

 5 Figure 5. SINR at the 1st and 2nd position for different data rate.

Table I CORRESPONDING

 I DATA RATE FOR MODULATION CONFIGURATION

	Chirp length [taps]	bit per chirp	Bit Rate [Mbps]
	70	6	343
	300	8	107
	1100	10	36.4
	2200	10	18
	4000	10	10
	40000	10	1