Hilary Chappell

of object marking constructions in Sinitic languages

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

1.1

The issue

Although China has a long tradition in the compilation of rhyme dictionaries and lexica, it did not develop its own tradition for writing grammars until relatively late. 1 In fact, the majority of early grammars on Chinese dialects, which begin to appear in the 17 th century, were written by Europeans in collaboration with native speakers. For example, the Arte de la lengua Chiõ Chiu [Grammar of the Chiõ Chiu language] (1620) appears to be one of the earliest grammars of any Sinitic language, representing a koine of urban Southern Min dialects, as spoken at that time (Chappell 2000). 2 It was composed by Melchior de Mançano in Manila to assist the Dominicans' work of proselytizing to the community of Chinese Sangley traders from southern Fujian. Another major grammar, similarly written by a Dominican scholar, Francisco Varo, is the Arte de le lengua mandarina [Grammar of the Mandarin language], completed in 1682 while he was living in Funing, and later posthumously published in 1703 in Canton. 3 Spanish missionaries, particularly the Dominicans, played a significant role in Chinese linguistic history as the first to record the grammar and lexicon of vernaculars, create romanization systems and promote the use of the demotic or specially created dialect characters. This is discussed in more detail in [START_REF] Van Der Loon | The Manila incunabula and early Hokkien studies[END_REF][START_REF] Van Der Loon | The Manila incunabula and early Hokkien studies[END_REF]. The model they used was the (at that time) famous Latin grammar of Elio Antonio de Nebrija (1444Nebrija ( -1522)), Introductiones Latinae (1481), and possibly the earliest grammar of a Romance language, Grammatica de la Lengua Castellana (1492) by the same scholar, although according to [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF], the reprinted version was not available prior to the 18 th century. Not surprisingly, the Nebrija grammars were indirectly influenced by even earlier Greek models (for more detailed discussions, see Breitenbach 2001[START_REF] Mair | Ma Jianzhong and the invention of Chinese grammar. In Studies on the history of Chinese syntax[END_REF][START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF], 2001). 4 Since a Greco-Latin model is one that is evidently designed for highly inflectional languages, it is not surprising to find standard chapters in missionary grammars include the topics of verb conjugations with accompanying abundant description of tenses: the pluperfect preterite, the future, the infinitive and the subjunctive; also declination of nouns and pronouns, including features of case, gender and number. Consequently, information is not always presented economically or concisely. For example, in the 1620 Arte de la lengua Chiõ Chiu, complete verb conjugations are given for the verb lāy 'to come' in Southern Min for both the present and the perfect, even though the forms remain invariable. The 'paradigm' in (1) presents the typical case in the Sinitic taxon where the description of aspect and resultative phase markers would in fact be more appropriate for verb morphology than tense (see Chappell 1992a): The same situation obtains in Varo's grammar for conjugating the verb gái 愛 'to love' [contemporary Mandarin ài] in the Nanjing-based Mandarin koine of the late 17 th century (translated by Coblin and Levi 2001: 117). Note that Varo explicitly acknowledges Nebrija's grammatical framework in his prologue (page 1a, Coblin and Levi 2001: 5). While Varo does discuss the non-Indo-European category of the classifier in a chapter on numbers and numerals as the category of 'particles', de Mançano relegates these to an appendix at the end of his grammar of Southern Min. Similar phenomena and chapter layouts can be found in the grammars of Chinese languages written in Latin by Martino Martini, Grammatica Sinica, circa 1653, (see Bertolucci 1998: 349-481 for a reproduction) and Theophilus Bayer who presents an edited and revised version of the 1620 Arte translated into Latin, and a grammar of literary Chinese (1730). From this it should not be inferred that grammatical analyses from this period are completely inadequate, but rather that there is a distinct mismatch between the structure of the target language and the framework for analysing it. Hence, in this early phase of grammar-writing for Chinese languages, it is reasonable to claim there was little influence of language type on the design of grammars for Chinese languages. 5 The description of possible accusative marking for direct objects is a case in point. 6 The grammars by de Mançano and Varo both point out that there are no particles for the accusative case in Chiõ Chiu or Mandarin respectively, explaining that these cases can only be recognized by position in the sentence. This is certainly true for basic S-V-O clauses. Varo states that '[T]he accusative … has no particle which governs it. … However, common practice is to put it after the verb' (translation of p. 24 by Coblin and Levi 2001: 63).

Significantly, Varo goes on to make an astute observation regarding a certain usage in this Southern variety of Mandarin which would doubtlessly be labelled a 'serial verb construction' by contemporary linguistic theory. His remark concerns verbs of taking in two related structures containing a preposed object, which he does not however treat as being coded in the accusative case: 'In the verbs "to take" and "to bring" the accusative is anteposed to the verb, e.g., "bring water", xùi nà lâi 水拿來; … . If one wants to speak a bit better and more elegantly, one can start the sentence with the nà 拿, and then immediately after that put the name of the thing which is to be taken or brought, and finally the verb, e.g., nà xùi lâi 拿水來' (Coblin and Levi 2001: 65). Many examples of both kinds of construction, albeit in a more highly grammaticalized stage, will be treated in § §3-8. It is interesting to note that Varo does not mention the use of either bă or jiāng which were both in evidence in vernacular works during this period of Modern Mandarin. -As will be explained below, jiāng 將 is the main Medieval Chinese marker of the accusative or 'disposal' function, while bă 把 -which superseded jiāng by the time of Late Medieval Chinese -is the marker used contemporaneously in standard Mandarin and many Northern Mandarin dialects.

It is only much later, when the first indigenous Chinese grammar was published, that the promise of a potentially new tradition begins to emerge: this was the 1898 Mă Shì Wéntōng [Treatise on grammar by Ma] written by Ma Jianzhong near the end of the last Chinese dynasty, the Qing (1644Qing ( -1911)). It describes literary Chinese, however, and not any vernacular form. It, too, is based on a Greco-Latin model, as the author himself states at various points in the text, while it eclectically adheres to Chinese philological traditions at the same time (details are to be found in [START_REF] Mair | Ma Jianzhong and the invention of Chinese grammar. In Studies on the history of Chinese syntax[END_REF][START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF]. [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF] argues that Mă Shì Wéntōng uses the 17 th century Grammaire de Port-Royal as its model. 7 Since Classical Chinese is the object of description in his grammar, Ma treats only the use of instrumental yĭ, the Archaic Chinese precursor of the construction types discussed in this study. Nonetheless, many aspects of his terminology and framework are innovative, bearing discernible and lasting influence on the directions of contemporary linguistics in China [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF].

The 20 th century has since seen an exponential increase in the publication of grammars, particularly on spoken Mandarin Chinese. These are written in mainly structuralist and functionalist frameworks, with the best known of these in English, being undoubtedly Yuen-Ren Chao's A Grammar of Spoken Chinese (1968) and Charles Li and Sandra Thompson's Mandarin Chinese: A Functional Reference Grammar (1981), among many others. In the Chinese-literate world, Lü (1941), Wang [START_REF] Li | Modern Chinese Grammar[END_REF][START_REF] Li | Modern Chinese Grammar[END_REF]), Gao (1957) and [START_REF] Dexi | Yufa Jiangyi[END_REF] stand out as major opera inter alia. Notably, these works treat Mandarin Chinese on its own terms, with special chapters on categories and constructions that are not found in most European languages, such as classifier phrases and clause nominalizations, verb copying, complex stative constructions (verbal complements of extent and manner), double subject and topic prominence structures.

It is a curious paradox that standard Mandarin (pŭtōnghuà), in its turn, has become the model of grammar on which descriptions of other Sinitic languages are regularly based, both by Chinese and western scholars. 8 This templatic approach has a similar consequence that key typological features and patterns shared between Southern Sinitic languages such as Cantonese (Yue), Shanghainese (Wu), Hakka (Kejia) and Hokkien (Southern Min) are often overlooked, simply because Mandarin does not possess them. This problem is pointed out severally in Chappell (1992aChappell ( , 1994Chappell ( , 2000Chappell ( , 2001aChappell ( , 2001bChappell ( , 2001c, to appear and in prep.), to appear and in prep.), studies which examine the differences in the functions, types and range of usage for aspect markers, negative adverbs, dative, passive, causative constructions, evidentials, and say verbs inter alia. 9 This new Sinocentrism is pointed out in the relevant places in § §3-8. It also becomes clear that, from a linguistic point of view, Mandarin is not always in fact the ideal typological representative for Sinitic languages.

The disposal constructions in Standard Mandarin

In Sinitic languages, the canonical position for a direct object argument is to follow the transitive verb without any accusative case marking, as de Mançano and Varo rightly observed: Subject -Verb transitive -Object; similarly for intransitive verbs when not being used in a presentative function, the subject precedes the verb: Subject -Verb intransitive . When a direct object argument with the role of affected patient occurs in a non-canonical position preceding the main verb, this is signalled by a special marker preposed to it, for example, bă in standard Mandarin. Note, however, that preposed direct object arguments are not required by the grammar to take such accusative marking -morphologically unmarked OV constructions are common in Chinese languages, where the direct object noun has given information content (but is not necessarily an affected patient). In a similar fashion, disposal constructions may extend to coding affected patients of intransitive events, but not in all Sinitic languages. As a consequence of the affectedness feature, the predicate may be required to depict a telic event causing a change of state in the patient noun, as argued in Chappell (1992b) and Sun (1997) inter alia. This means that, for Mandarin, the predicate may not comprise a bare monosyllabic verb; and it is generally true that either complex resultative verbs, aspectually marked verbs or postverbal nominals (locatives, copular-like complements of equative and creation verbs and indirect objects of ditransitive verbs) are to be found in disposal constructions, for example in standard Mandarin and Hong Kong Cantonese. However, the precise constraints depend on the individual language, since Nanchang Gan, Meixian Hakka and Southern Min are not subject to this constraint in its strictest form.

To serve as a starting point for the discussion, the configuration for the construction type identified in all the Sinitic languages in this survey can be stated in general terms as follows. Note however that a significant part of my description is to show variations on this theme which exist in particular dialect groups:

(NP CAUSE/SUBJECT ) -[MARKER + NP AFFECTED PATIENT ] -VP 10
The disposal constructions in Sinitic languages are in fact functional correlates to the well-researched bă construction in Mandarin, known as the chùzhìshì 處置式 in Chinese linguistics. In Mandarin, they serve to foreground a referential noun in preverbal position, specifically one which has the semantic role of affected patient, either the direct object argument of a transitive verb, the intransitive subject of an unaccusative verb, or even the subject of an unergative verb, provided this has a reflexive effect, thereby causing a change of state in the undergoer-subject. For this reason, the construction could be labelled 'absolutive', but just in the case of Mandarin. This is by virtue of the morphologically marked argument being a non-agent -it does not act upon any other entity -while the ergative argument is backgrounded. 12 Clause-initial agent NPs may in fact be ellipsed, as example (2) demonstrates from written Mandarin. 13 Hence, I begin the analysis with examples from the best-known and described of all the Sinitic languages, Standard Mandarin. The purpose is to provide the necessary background information on the state-of-the-art for research into this topic; and importantly to set the scene for highlighting the diversity which is evident in the following descriptions of other Chinese languages. Speakers of Mandarin dialects constitute the largest proportion of all Sinitic languages in China, totalling more than 70% of the Han Chinese population (Chappell 2001a, see also note 15 on standardization). 14 The first main subtype of the disposal construction in Mandarin is the most common one, where the use of bă serves to mark a direct object. It can be given the following representation: I.

( In this example, a specifiable result state can be interpreted as the change in location for Kugen, achieving his arrival at home. Note that the agent has been ellipsed but is recoverable from the surrounding context. Counterpart S-V-O forms of disposal constructions are not always possible, as in this case: *Wǒ sònghuiqu.Kŭgēn [1SG-escort-return-NAME]. 16 Nonetheless, let us consider the case for the next example of a bă construction, given in (3), which may be contrasted with a similar S-V-O example, in (4).

( Note, however, that when S-V-O correlates are possible, they are not equivalent from either a semantic or discourse point of view, for the features described. For instance, in (4), verb copying after the initial S-V-O portion is required to enable preservation of information concerning the manner of explanation (qīngchu 'clearly'), a feature more concisely coded in the bă construction.

As pointed out above, there is a second subtype of the disposal construction in Mandarin which permits an intransitive subject to occur in the same marked position as the direct object. It does not increase the valency of the verb, however, but has a distinctly causative meaning. In fact, the causing event can be coded in the slot for the erstwhile agent of a transitive clause: 17 The fact that some kind of specifiable result state must be coded particularly in the case of the intransitive variant is clear from the unacceptability of *bă tā lèi le 把 她累了[ABS-3SG-tired-CRS] which only expresses a general state of affairs.

Turning now to the non-Mandarin Sinitic languages, the trend in descriptive studies is to look for the cognates of either Mandarin bă < 'grasp, take' or its precursor jiāng < 'lead, guide, take', which serves the same function as bă but is found mainly in literary genres, for example, written Mandarin Chinese. This is particularly a problem in large dialect surveys which use questionnaires based on translating Mandarin sentences or eliciting equivalent morphemes in the target language, as, for example, in Zhan and Cheung (1988) on Yue dialects or Li and Zhang (1992) on Min dialects. It may also be noted that Southern Min, Cantonese and many Hakka dialects all make use of cognates of the literary marker jiāng and thus appear to preserve a more archaic feature of Chinese. Such descriptions usually concentrate on the fact that this construction tends to be more limited in use than in Mandarin.

While this may be true, what such a Mandarin-based Sinocentric approach inadvertently conceals are two other important sources for disposal markers in certain Sinitic languages. While many Sinitic languages use a verb of taking or grasping in this function, but not necessarily one that is cognate with either jiāng or bă, others such as Southern Min, and certain Wu and Hakka dialects, deploy accusative markers that have evolved out of a comitative. A third group of Chinese languages evinces a pathway from verbs of giving, in particular, Xiang and Wu dialects. Surprisingly, this kind of phenomenon, if mentioned, is treated as an oddity or aside in descriptive grammars, simply because it does not correspond to a model of grammar based on Standard Mandarin. Hence, there is a need for a tertium comparationis or truly typological approach in the study of Sinitic languages: empirical data from all major dialect groups within Sinitic must first be compared before setting up an eventual pan-Sinitic description of invariant syntactic and semantic features of accusative constructions. This study represents an initial step in this direction.

There are nonetheless important exceptions to this rule: While specific instances of this Sinocentric, specifically Mandarin-centred, tendency are pointed out in § §3-8 below, this analysis makes use of several recent and excellent studies of accusative constructions in Sinitic languages which do indeed examine the divergences from Mandarin. These include [START_REF] Cheung | The pretransitive in Cantonese[END_REF], [START_REF] Lin | Lun Keyu fangyan zhi 'pun' yu 'lau' (/ 'thung') [On pun and lau (/thung) in Hakka][END_REF], [START_REF] Teng | Disposal structures in Amoy[END_REF], [START_REF] Ying | Minnanyu 'ka' yongfa zhi jian de guanxi [The relationship between uses of ka in Southern Min[END_REF], Wu (1992), [START_REF] Xu | Wuyu de chuzhishi [Disposal constructions in the Wu dialects[END_REF][START_REF] Xu | Wuyu de chuzhishi [Disposal constructions in the Wu dialects[END_REF]Zhou (1991). The study of diversity is particularly well-developed in research on Southern Min languages -the difference in markers and structure is perhaps too striking to be overlooked, as §3 demonstrates.

In the main part of this study, I first outline the diachrony of bă and jiāng constructions, then present a description of a range of disposal constructions in a further six Sinitic languages, according to two main parameters: (i) the source of the case marker and (ii) the construction type in terms of its configuration; also (iii) semantic and syntactic constraints, where known. All three parameters are shown to differ across Sinitic languages. Not only do the markers have different etymological sources, but the construction types include those with postverbal resumptive pronouns, those which require a possessive NP in the accusative NP slot, and yet others which permit the accusative NP to occur in clause-initial position.

The six non-Mandarin languages are Southern Min, Hakka, Cantonese, Shanghainese, Xiang and Gan in that order. These constitute the linguistically best-established groups within the Sinitic branch of Sino-Tibetan; another three -Hui, Jin and Pinghua -are less well-studied at this point of time (see Chappell 2001a). This enables a final intra-Sinitic grouping of accusative constructions according to the first two typological parameters.

The terms 'subject', 'agent', 'direct object', 'indirect object', 'argument', 'case', 'ergative', 'accusative' and 'absolutive marker' are used as syntactic terms [START_REF] Dixon | Ergativity[END_REF][START_REF] Dixon | Ergativity[END_REF] whereas 'affected patient' refers to the semantic role of the accusatively marked NP. Whenever the label 'Mandarin' is used, it refers to Standard Mandarin or pŭtōnghuà, unless otherwise indicated. For the main discussion, including the next section on diachrony, I use the terms 'disposal construction' and 'accusative marker' given that the use of the construction with intransitive predicates is not well-researched at the present time with regard to most of the other Sinitic languages. Significantly, preliminary indications point to their use being restricted to transitive verbs in some languages, such as in Cantonese (see §5 below) and Hakka ( §4). Furthermore, the absolutive function in Mandarin itself did not develop prior to the Modern period, post-13 th century (Alain Peyraube, pers. comm.).

Diachrony of disposal constructions

It is well-known that jiāng 將 is the most frequent exponent of the disposal construction at the end of the Early Medieval period, specifically, during the Sui dynasty (6 th c. CE) but that it lost this position of pre-eminence to the bă 把 construction during the Tang dynasty (618-907 CE), most likely between the 7 th -8 th centuries [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF][START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF]. The marker jiāng itself had similarly developed by analogy with the instrumental yĭ construction dating back to the period of Late Archaic Chinese (5 th -2 nd centuries BCE) (see [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF], Sun 1996: ch. 3). 18 The disposal markers seen in vernacular texts of the Medieval Chinese period are typically deverbal prepositions (or 'coverbs') that evolve out of the V 1 position in serial verb constructions of the form:

(NP 0 [ SUBJECT ]) -V 1 [ take ] -NP 1 [ DO ] -V 2 -NP 2 [ DO ]
to first indicate instrumental then finally accusative functions. These include jiāng 將'to guide, lead', bă 把 'to grasp, hold', chí 持 'to grasp, hold', and zhuō 捉 'to clutch, hold, seize'. The degree of grammaticalization of these verbs into case markers can be tested with aspect marking: bă in Mandarin and jeung 1 in Cantonese do not take any aspect suffixes in their contemporary use. That is, they are no longer used as verbs, whereas disposal markers in other Sinitic languages can be, for example, lau 11 which can still be used as a verb meaning 'to mix together' in Hakka (see example (21) below). Construction types with similar sources and evolution pathways can be found in many Southeast Asian languages, as detailed in [START_REF] Bisang | Das Verb im Chinesischen, Hmong, Vietnamesischen, Thai und Khmer[END_REF].

Each of these stages of grammaticalization for Medieval Chinese is exemplified with a lexical postverbal NP 2 [ DO ], a pronominal one, and finally a case where there is no NP 2 [ DO ] (all examples are taken from [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF][START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF]:

(6)
Medieval Chinese instrumental construction with jiāng:

(NP 0 [ SUBJECT ]) -V 1 [ jiāng 將] -NP 1 [ DO ] -V 2 -NP 2 [ DO ] 輕 將 玉版 橋 花片
(NP 0 [ SUBJECT ]) -V 1 [ jiāng 將] -NP 1 [ DO ] -V 2 -NP 2 [ DO ]
where According to Peyraube (1996: 169-170), after NP 2 [ DO ] is omitted under coreferentiality conditions with NP 1 [ DO ], V 1 grammaticalized into a preposition. Although it is very difficult to detect precisely when this syntactic reanalysis occurred, the following kind of example shows that semantically jiāng is being used more like an accusative marker than a verb of taking:

O 1 = O 2 [pronoun] 船者 乃 將 此 蟾 以 Chuán-
(8)
Medieval Chinese accusative construction with jiāng and no postverbal NP 2 [ DO ]:

(NP 0 [ SUBJECT ]) -Prep[ jiāng 將] -NP 1 [ DO ] -V 2 誰 將 此 義 陳 shéi jiāng cĭ yì chén who ACC this
idea expose 'Who could express this idea?' (Dufu: Ji Li Shi'er bai 杜甫﹕ 寄李十二白, 8 th century)

The use of both markers, jiāng and bă, continued throughout the Early Mandarin period. In contemporary Mandarin, however, jiāng is no longer a feature of the colloquial language but may still be found in literary genres. In the following sections, I will show that at least two of the Sinitic languages, Hakka and Cantonese, also permit postverbal pronominal objects, similar to the structure in ( 7). This appears to be clearly related to the structure found in these vernacular works of Late Medieval Chinese, and thus a retention which standard Mandarin no longer permits, as shown in the grammatically unacceptable use of a third person pronoun (* tā) in postverbal position: Yúshi chuánfū jiù bă zhè zhī chánchú yòng yóu jiān le (* tā) 於是船夫就把這隻蟾蜍用油煎了(*它) thereupon-boatman-then-ACC-this-CLF-toad-use-oil-fry-PFV-(*3SG).

Southern Min

The archaic Min dialect group has its heartland in China's southeastern province of Fujian and includes a large community of Southern Min speakers in neighbouring Taiwan, not to mention outliers in northeastern Guangdong (Chaozhou, Shantou), the Leizhou peninsula and Hainan island. Min dialect speakers comprise approximately 4.1% of Sinitic languages, with 2.8% belonging to Southern Min.

The morpheme kāng ~ kā in Taiwanese Southern Min has a function similar to the Mandarin bă construction where it marks a preverbal and typically referential direct object, though its usage appears to be broader than in Mandarin, in terms of co-occurring verb classes (see [START_REF] Teng | Disposal structures in Amoy[END_REF][START_REF] Tsao | On the mechanisms and constraints in syntactic change: Evidence from Chinese dialects[END_REF][START_REF] Ying | Minnanyu 'ka' yongfa zhi jian de guanxi [The relationship between uses of ka in Southern Min[END_REF]. Although most contemporary descriptions of Southern Min describe one use of kā or kāng as a marker of a preposed direct object, it occurs under different circumstances to the Mandarin correlate bă and is consequently not viewed as the true 'dialectal' counterpart. This role is rather taken on by a cognate of jiāng, as in Yuan (1960: 285). Two examples of kā follow from my transcription data on the Taiwanese variety of Southern Min.

(9)

Taiwanese Southern Min accusative construction with kā: (Chappell 2000). 19 Southern Min is a highly stratified language, with at least three historical layers involved in its formation, two colloquial and one literary, the latter being comprised of borrowings from the Tang dynasty (see [START_REF] Mei | Jĭge Mĭnyu& yu&fă chéngfe∃n de shíjiān céngcì [Stratification in the grammatical elements of several Min dialects][END_REF]. In many Southern Min dialects, a cognate of the Medieval Tang dynasty form of the disposal marker jiāng 將 is used [romanized as chiong in the Church romanization system] alongside kā, producing a hybrid form with colloquial kā, exemplified by ( 12). This construction type, exemplified for Taiwanese, differs markedly from the Mandarin type described in §1.2. 20 Note that the use of chiong belongs however to a somewhat more formal register, according to Tsao (1991: 383).

(NP SUBJECT ) -[KA ACC + NP DO ] -VERB PHRASE 所以 阮 攏 共 褲 褪 起來 só -í gún lóng kā k'ò t'n$ g -k'í-
(11) Taiwanese Southern Min hybrid form with two accusative markers:

(NP SUBJECT ) -[CHIONG ACC + NP DO(i) ] -[KĀ ACC + PRONOUN DO(i) ] -VP 將 門 共 伊 關 起來 chiong mnĝ kā yī kui n khì-lâi ACC 1
door ACC 2 3SG close INCH 'Close the door.' [more literally: take the door, take it and close] Fusion and contraction of kā with its following 3SG resumptive pronoun regularly occurs in Taiwanese: kā yī > kah [= ka/ 32 ], but not for any other pronominal form (Teng 1982: 337). Furthermore, both fused and unfused forms of kā can be used in a variation on this construction type in (12), where the patient noun is in clause-initial position. The example in (12) from a spoken narrative has been selected for its similarity to ( 11 Yuan (1960: 286) reports that this construction type with a clause-initial object is also found in the Xiamen, Chaozhou, Hainan and Southern Zhejiang dialects of Southern Min. Cheng and [START_REF] Ying | Minnanyu 'ka' yongfa zhi jian de guanxi [The relationship between uses of ka in Southern Min[END_REF] claim that the portmanteau form in (12) shows a further development in Taiwanese whereby kah is undergoing reanalysis as a passive prefix. This is aided by the fact that kah and kā are virtually indistinguishable in fluent speech, both being articulated without syllable closure and low falling tone in unstressed position: kà. This construction type also exists in certain Wu dialects (see §6).

Hakka

Hakka is concentrated in an area which straddles Northeastern Guangdong, Southern Jiangxi and Southwestern Fujian provinces. Nonetheless, communities are scattered throughout Guangdong province, inhabiting Yue or Cantonese territory, as well as being found in Sichuan province. The estimated number of speakers is circa 3.7% with Meixian or Sixian Hakka generally being considered the representative variety. This refers to a locality within Northeastern Guangdong province (see Chappell and Sagart in press). With regard to disposal markers, three main points of view are in evidence according to the main reference grammars of Hakka: (i) Hakka does not have a disposal construction in stricto sensu due to the fact a marker distinct from Mandarin bă is used (He 1993: 26 on Dabu Hakka tet); (ii) only the cognates of jiāng are identified (Yuan 1960: 176;Luo 1985: 300;Rey 1926: III) with the non-colloquial nature and lack of 'linguistic development' of this construction, compared to Mandarin, being alluded to, as in Xiang (1997: 421); or (iii) the accusative case is claimed to be never marked (translation of (1909) Basel grammar of Sin-on Hakka, in Part 3, Chappell and Lamarre 2005: 59).

In contradistinction to these studies, I first illustrate some disposal constructions with the exponent tsiong 44 in Hakka (cognate with Mandarin jiāng), and second, a variant form with a resumptive pronoun. Finally, I examine two spectacular cases of disposal markers in Hakka which show quite distinct sources from Mandarin and most other Sinitic languages, excepting Wu. In Hakka dialects, the use of cognates of Medieval Chinese jiāng 'guide, lead' is widespread, according to published descriptions. However, two construction subtypes can be identified: one is similar in form to Mandarin, while the other is distinct due to the presence of a postverbal resumptive pronoun.

Subtype (i):

Two examples follow, the first one from a story told in a southern variety of Guangdong Hakka from Sung Him Tong near Hong Kong. Both are of the same construction type as in Mandarin. Hence, it is only the use of the marker jiāng which differs.

(15) Sung Him Tong Hakka disposal construction with tsjiong 1 : Subtype (ii): However, in Hakka dialects, a trace of the earlier serial verb construction of Medieval Chinese can be found, as exemplified by (7) above: Rey (1926: III) gives an example of a resumptive third person singular pronoun being used with the disposal marker in the Jiayingzhou variety of Northeastern Hakka, the dialect represented in his dictionary. Note that 'Jiayingzhou' is in fact an older obsolete name for Meixian Hakka. Apart from the use of the marker tsiong 44 , several Hakka dialects make use of disposal markers which are distinct from either Mandarin bă or jiāng. The use of a different exponent for this function in the Dabu dialect of Hakka makes an interesting case, particularly given that it lies in geographic proximity to the prestige dialect of Meixian. Instead of using the widespread marker tsiong 44 , Dabu employs tet 得 < 'to gain, to give'. Another distinction is the requirement of a possessive NP as the patient following the marker tet, as described by He (1993: 73-74), exemplified in ( 18 One of the comitative prepositions in Hakka dialects is t'ung 11 'with, and' (< 'to accompany'). 23 It also has a benefactive use but, strikingly, can be employed in Meixian Hakka in the same way as tsiong 44 in accusative function. Similarly to the case in Dabu Hakka, Lin (1997: 103) observes that the disposal noun phrase governed by t'ung 11 must be possessive. This is not the case, however, for the benefactive use in ( 19 [START_REF] Lin | Lun Keyu fangyan zhi 'pun' yu 'lau' (/ 'thung') [On pun and lau (/thung) in Hakka][END_REF] provides further data on Hakka dialects, showing that not only may t'ung 11 be used as an disposal marker, but also another comitative, lau 11 'and, with' (< 'to mix together'), found in most varieties of Hakka (e.g. see the Basel mission grammar of Sin-on or southern Guangdong Hakka, translated in Part 3, Chappell and Lamarre 2005: 60). Note that the construction with lau 11 is structurally isomorphic to the Mandarin; it is merely the etymology of the markers which differs.

(NP SUBJECT ) -[TSJIONG 1 ACC + NP DIRECT OBJECT ] -VERB PHRASE 卒 之 就 將 囗 隻 鷦 崽 tsut 5 -
SUBJECT -V 1 [take] -O 1 -V 2 -O 2 .
(21) Meixian Hakka -Comitative use of lau 11 NP -[LAU ' Lin (1990: 79) Unlike the disposal use of comitative t'ung 11 , the construction with lau 11 is not subject to the constraint requiring a possessive NP to follow the disposal marker. This is evident in the previous two examples with inanimate NPs 'ants' and 'house'. In particular, 'house' is not to be understood as owned by the agent until the purchase is completed. This furnishes another tantalizing difference from Standard Mandarin which does not permit 'inward' verbs of receiving in the bă construction. This could be due to the trace semantic features of bă, originally a verb that denotes coming into possession of an entity by grasping hold of it (see Ziegeler 2000 for a discussion of possession schemata and Mandarin bă) . This has grammaticalized at the discourse level into the requirement for the givenness or 'pre-existence' of the object.

This cursory look at Hakka dialects has identified (i) a construction using the cognate of Medieval jiāng which has a subtype with a resumptive pronoun; (ii) constructions with tet 'obtain, get' in Dabu and comitative t'ung 11 in Meixian which both require a possessive object NP and (iii) a construction with comitative lau 11 , also found in Meixian, which is less constrained in application than Mandarin bă in permitting a wider range of verb classes. This description of Hakka disposal constructions has shown that reference grammars particularly overlook the comitative source as an important native strategy for building disposal constructions.

Cantonese Yue

The Yue dialects, of which Cantonese is the best known, are distributed throughout Guangdong province and parts of adjacent Guangxi. Speakers of these dialects comprise approximately 5% of the Han Chinese population. Hong Kong Cantonese, like many Hakka and Min dialects, makes use of jeung 1 , cognate with jiāng, to code accusative case. This construction type is nonetheless generally overlooked in the major grammars of Cantonese, or treated as a gap in the grammar when compared with Mandarin (Li 2001: 33 on fehlende bă-Konstruktion). 24 The explanation for this may lie in the fact that its use is much more restricted than Mandarin bă, according to [START_REF] Cheung | The pretransitive in Cantonese[END_REF], who provides a detailed study of jeung 1 .

In a survey of the lexicon, including grammatical function words in 25 Pearl River Cantonese dialects (Zhan and Cheung 1988: 441), the findings reveal that 23 use a cognate of jiāng. The issue at stake here is the problem of posing the question in terms of how the speaker would translate a Mandarin bă sentence, which tends to elicit the closest correlate in the given Cantonese dialect to written or formal Mandarin jiāng, rather than to any local forms.

Treating the construction with jeung 1 first, Cantonese does not have the extended intransitive use exemplified by ( 5) above with an unaccusative verb lèi 'be tired', nor with unergative verbs as in (1) above with xĭ 'wash' or (25) below. Compare the Cantonese example with its Mandarin counterpart in ( 24) and ( 25) respectively (data taken from Cheung 1992, his romanization and translations). This corresponds to where the absolutive NP is both the intransitive subject and agent of xiào 'laugh', yet ends up being the affected patient whose belly aches due to the reflexivity of the event (briefly described in §1.2, but presented in detail in Chappell 1992b). ( 24 Second, the jeung 1 construction is obligatory with certain kinds of verbs, namely, many ditransitives and verbs which take the bound complement sihng 'become' in equative or copular-like clauses (Cheung 1992: 254-260). In other words, these are predicates which could result in the dispreferred situation of two object nouns postverbally: V 1 -O 1 -O 2 , as in a regular S-V-O type clause. Hence, the preference is to express them with accusative jeung 1 as jeung 1 Once again, the observation can be made that this resembles the construction type with two coreferential objects found in Medieval Chinese (see example (7) above), suggesting that Cantonese, like Hakka, preserves structural features of earlier forms of the disposal construction whereas Mandarin has innovated, namely, by suppressing coreferential postverbal pronouns.

In my own data, I found that although jeung 1 predominated, other take verbs such as ling 1 and loh 2 could be used in this function, albeit arguably retaining their more literal meaning of 'take'. The marker jeung 1 , for example, may occur with predicates such as 'to fool someone' whereas there is no evidence that these two other take verbs can. They form a serial verb construction rather than a conflated grammaticalized form as with jeung jeung 1 . Matthews and Yip (1994: 142-145) discuss similar constructions, comparing them with the use of jeung 1 . The following examples are thus of ling 1 and loh 2 in serial verb constructions (see also §8 on Gan dialects for similar phenomena):

(28) Cantonese serial verb construction with ling 1 'take': Finally, according to [START_REF] Cheung | The pretransitive in Cantonese[END_REF], jeung 1 is more likely to appear in formal contexts for Cantonese. This is similar to the situations in both Hakka and Min dialects for the relevant cognate.

(NP SUBJECT ) -LING 1 -NP DO -VERB 1 -X-VERB 2 -NP IO 16. … 噉 有 個 書生 呢 就 拎 一個 琴 …

Shanghainese Wu

The Wu dialects, comprising approximately 8% of Chinese speakers, are spread over most of Zhejiang province on the eastern seaboard of China as well as in southern Jiangsu, the neighbouring province to the north. Shanghainese is nowadays the prestige and probably best-known dialect of this group. While Shanghainese reveals no surprises as to the source of its disposal marker, other dialects such as Shaoxing make use of a comitative, while still others use verbs of helping and giving. Yuan (1960: 101) similarly describes the use of a verb of taking as a disposal marker in the former prestige dialect of Suzhou.

In Shanghainese, the marker for the disposal construction is derived from a verb of taking nç 53 拿, that is, from the same semantic domain as for Mandarin bă 把.

( [START_REF] Xu | Wuyu de chuzhishi [Disposal constructions in the Wu dialects[END_REF] Qian (1997: 287) claims, however, that topicalized preverbal objects are more frequent than the use of the disposal construction with nE 53 ~ nç 53 拿. The use of other syntactic means for highlighting an object-NP is a common claim found in studies on Chinese dialects, as noted in grammars for Gan, Cantonese, and Hakka. This generally results, however, in the disposal construction not being analysed in depth, since it is viewed as less frequent than, if not dispreferred to structures with unmarked preposed objects. Consequently, the possibility of other kinds of 'local' strategies, such as the deployment of a comitative in accusative function, are similarly overlooked.

In many other Wu dialects including Shaoxing, Zeguo and Wenzhou another kind of disposal construction can be found: this is the type in which a resumptive pronoun is used after the disposal marker when the direct object occurs in clause-initial slot. This particular configuration is isomorphic with that of Southern Min, discussed in §3.

(31) Wenzhou dialect accusative dei 11 construction with a clause-initial object: Xu and Tao (1999) also note that the source for disposal markers in Wu dialects is not restricted to verbs of taking. Apart from Shanghai, Suzhou and areas to the north of the Qiantang River, which use a variety of 'take' verbs, two other main semantic domains are in evidence: comitatives in the Taihu subgroup, and verbs of giving and helping elsewhere, for example, Wenzhou dei 11 (see example (32) above). The latter domain is in fact the most widespread source in Wu dialects (Xu and Tao (1999: 137) while it is an equally typical source in the Xiang dialects, as described in §7 below. The following examples show the syncretism of the comitative and the disposal marker in the Shaoxing dialect: tse/ 45 (Xu and Tao 1997: 139) Note that if an inanimate object NP is preposed into clause-initial position, a resumptive pronoun in possessive form appears after the disposal marker, as in (33). Additional evidence for the comitative source comes from Huang et al (1996: 525-529, no transcriptions provided) who report that the Huaiyin and Shuyang dialects in Jiangsu province, both Jiang-Huai Mandarin dialects, make use of another comitative marker 跟 GEN 'to follow' in the function of accusative. 25

Xiang dialects

The Xiang dialects, comprising 4.8% of Sinitic languages, are distributed over most of Hunan, except in the north and the northwest and some southern parts of this province where Southwestern Mandarin is spoken. Little has been written on their grammar apart from [START_REF] Wu | An etymological study of disposal and passive markers in Hunan dialects[END_REF] who presents a large scale study of passive and disposal constructions in Hunan involving 107 localities, where dialects of several different Sinitic languages are spoken (mainly Xiang, Gan, Hakka and Mandarin). In the case of Xiang dialects, she claims that the predominant pattern is for both passive and disposal markers to derive from verbs of giving, but, importantly, verbs with distinct etymologies. Note that in Sinitic languages, the passive marker introduces the agent NP which means that these dialects have markers from the same lexical source with semantically contrastive functions: agent versus undergoer.

This contrasts with Southwestern Mandarin, also spoken in Hunan, which opposes a disposal marker whose source is a verb of giving to a passive marker whose source is a verb 'to suffer'. In Standard Mandarin, the passive markers also have their sources in verbs meaning 'to suffer', if not in causative verbs, but the disposal marker is not related to a verb of giving (rather , as we have seen, it comes from a verb of grasping, bă). Two such fossilized verbs used as passive markers in Mandarin are bèi 被 < 'put on the body'-> 'cover'-> 'suffer'-> PASSIVE MARKER and ái 挨 'be next to' -> 'endure' -> 'suffer'-> PASSIVE MARKER. The historical development of the bèi passive is the subject of Peyraube (1989a) and Sun (1996), while synchronic constructional semantics are treated in Chappell (1986, in prep.).

It may thus appear at first contradictory to find that the disposal marker in more than half of the localities that Wu investigated is derived historically from verbs cognate with Mandarin bă. The striking difference is that in Hunan this verb has extended its meaning from 'to hold, grasp, take' to that of 'to give', as in the Changsha dialect of New Xiang, where the form of the disposal construction is otherwise deceptively the same as for Standard Mandarin (data from Wu 1999: 95):

(34) Changsha dialect of Xiang -Verbal use of pa 41 meaning 'to give': (NP SUBJECT ) -PA 41 A grammar of the Changsha dialect of New Xiang by Y. Li (1991: 532-534) also discusses and abundantly exemplifies the verbal use of pa 41 . However, he preempts any description of the syntax and semantics of the accusative marker in the disposal construction, claiming that its use is exactly the same as in Mandarin, and consequently finds there is no need to introduce it. Of comparative interest for the present analysis is the use of cognates of gĕi 給 'to give' as disposal markers in the Shuangpai and Chenzhou dialects (both Southwestern Mandarin) (Wu 1999: 92).

Gan dialects

Gan dialects are concentrated in Jiangxi province in central China and make up approximately 2.4% of speakers of Chinese languages. According to [START_REF] Liu | Comparative research on Kejia and Gan dialects[END_REF], verbs of taking prevail as the source of accusative markers in the Gan dialect area. These include bă 把 'to hold', ná 拿 'to take', tí 提 'to carry' and băi 擺 'to put'. Liu (1999: 743-744) attributes the use of the disposal form to Mandarin influence, in his claim that for many Gan dialects, a non-disposal form, either S-V-O or a topicalization is preferred and is somehow more native than a disposal construction. No evidence for this claim is provided, nor statistics for the disposal versus topicalization or S-V-O strategies. Moreover, he is implicitly using Standard Mandarin as the benchmark for his comparative analysis, while a comprehensive description of Chinese dialects by [START_REF] Yuan | Hànyu& Fāngyán Gàiyào[END_REF] does not discuss this construction type at all. This section makes use of a sketch grammar of the representative dialect for this group, Nanchang (the capital of Jiangxi province) by Laurent [START_REF] Sagart | Notes on the Nanchang dialect (Sketch grammar and transcriptions[END_REF], as well as the data and transcriptions therein. An example of the Nanchang disposal construction using bă 把 'hold' follows:

(36) Nanchang dialect of Gan -Accusative use of pa 3

(NP SUBJECT ) -[PA 3 ACC + NP DIRECT OBJECT ] -VERB PHRASE 隔 又 把 水 都 完全 kaq 7
yiu 6 pa 3 suїi 3 tu 1 won 5 chüon 2 KAQ NEW again ACC water all completely

濾 乾 了 li 6
kon 1 lieu filter dry PFV 'Once again, strain off all the water.' (Text 5 : 119 Noodles) Speakers of Nanchang Gan also make use of two other verbs of holding: na 2 拿 'to hold, take' and laq 7 搦 'to hold', particularly with ditransitive verbs of giving in the latter case.

(37) Nanchang dialect of Gan -Accusative use of laq 7 (NP SUBJECT ) -LAQ 7 ACC -NP DIRECT OBJECT -VERB PHRASE 人家 就 搦 糖 把 你人 喫 nyin 5 ka 1 chiu 6 laq 7 Dong 2 pa 3 n 3 len c[h]iaq 7 people then ACC sweets give 2SG eat 'People would give you sweets.' (Text 3: 65 New Year)

(38) Nanchang dialect of Gan -Verbal use of na 2 (NP SUBJECT ) -NA 2 -NP DIRECT OBJECT -X 拿 細伢子 到 我 na 2
xi 5 nga-tsї tao 5 ngo 3 take child reach/to 1SG 'Give me the children.'

According to Sagart's informants, the use of pa 3 is not permitted in (38) in particular. However, these markers appear to be losing ground to the Mandarinized disposal form with pa 3 把 (Sagart 1999: 76). Nonetheless, their mere use gives the lie to any inference that the native strategy involves avoidance of the disposal form, as Liu (1999: 744) supposes and, in fact, claims to be particularly the case for Nanchang Gan. Note that pa 3 把 can also be used as a verb of giving, as in the Xiang dialects, as exemplified by the main verb in (37).

Although there is no evidence to hand of other types of disposal construction, such as those with resumptive postverbal pronouns, the use of the construction with pa 3 is not subject to exactly the same constraints as in Mandarin. For example, it is possible for unmodified monosyllabic verbs to occur in the predicate, unlike the case in Standard Mandarin.

(39) Nanchang dialect of Gan -Imperative with pa 3

[PA 3 ACC + NP DIRECT OBJECT ] -VERB 把 佢 煮 pa 3 cie 3 tsu 3 ACC 3SG boil 'Boil it.'
(Text 5 : 85 Noodles)

Standard Mandarin would require at least a resultative verb or phase complement such as shóu 'cooked, ripe, mature', as a minimum verb form in the imperative: bă miàntiáo zhŭ-shóu 把麵條煮熟 [ACC-noodles-boil-cooked] 'Boil the noodles (till done)'. The lack of a semantic constraint on telicity of the predicate is also reported for Hakka [START_REF] Lin | Lun Keyu fangyan zhi 'pun' yu 'lau' (/ 'thung') [On pun and lau (/thung) in Hakka][END_REF]) and Southern Min dialects [START_REF] Teng | Disposal structures in Amoy[END_REF] as well.

Conclusion

Sources for disposal markers

These data from Sinitic show there are three main sources for disposal markers in Sinitic languages, broadly defined as follows:

Verbs of taking and holding > Disposal markers, e.g. cognates and synonyms of bă 把 'to take' as in Standard Mandarin; jiāng 將 'to take, lead' as evidenced in more formal registers of Hakka, Southern Min and Cantonese; ná 拿 'take, hold' = nç 53 in Shanghainese (Wu); na 2 拿 and laq 7 搦 in Gan dialects, also the borrowed disposal form pa 3 把 in Gan (which otherwise serves as a verb of giving). Verbs of giving and helping > Disposal markers, e.g. cognates and synonyms of gĕi 給 'to give' as in Southwestern Mandarin; bă 把 which means 'to give' in the Hunan Xiang dialects; bāng 幫 'to help' in Wu and Xiang dialects, tet 得 'to gain, to give' in Dabu Hakka; dei 11 代 'to help' in Wenzhou (Wu). Comitatives > Disposal markers, e.g. cognates and synonyms of kā 共 in Min dialects, t'ung 11 同 and lau 11 㧯in Hakka dialects, tse/ 45 則 in Shaoxing (Wu); GĒN 跟 in Jiang-Huai Mandarin dialects, all with the comitative meanings 'and, with' which can be traced still further back to verbs meaning 'to share, to gather', 'to mix' or 'to accompany'.

The detailed stages of the grammaticalization pathways have been well-described for verbs of taking and holding in Chinese (for example in [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF], 1989b, 1994and Sun 1996) but are still to be worked out for the two additional sources of give/help verbs and comitatives. I propose that this in fact proceeds via dative and oblique usages respectively for the semantic domains of give/help verbs and comitatives in Chappell (in prep.). Typologically, the accusative use of comitatives such as kāng~kā in Southern Min and t'ung 11 and lau 11 in Meixian Hakka would otherwise represent an unusual conceptual shift, if direct and 'one-step', both in the case of Sinitic languages and crosslinguistically. While Heine and Kuteva (2002: 84-86) list the semantic shift from COMITATIVE > INSTRUMENTAL, they have no category for COMITATIVE > PATIENT. It is significant that the stage COMITATIVE > INSTRUMENTAL is not attested for comitatives in Sinitic but rather only in the case of grammaticalization of take verbs (see §2 above) pace Lakoff and Johnson (1980: 135) who state with respect to the comitative 'With few exceptions, the following principle holds in all languages of the world: The word or grammatical device that indicates ACCOMPANIMENT also indicates INSTRUMENTALITY.'

Similarly to schemata proposed for verbs of taking [START_REF] Heine | Possession. Cognitive sources, forces, and grammaticalization[END_REF][START_REF] Ziegeler | A possession-based analysis of the ba-construction in Mandarin Chinese[END_REF], a type of possession is clearly involved for comitatives (and self-evidently for proprietives); this is one based on accompaniment or co-presence.

The conceptual shift for give/help verbs into object markers has been very little researched, if at all. While crosslinguistically, the shifts to benefactive, purposive and causative markers for give verbs are well-documented, as in [START_REF] Newman | Give: a cognitive linguistic study[END_REF] and [START_REF] Song | Causatives and causation. A universal-typological perspective[END_REF], the further step into an accusative marker is not attested.

I propose that for both domains of give/help verbs and the comitative, the semantic change occurs in the following manner, noting that this is just one of the attested pathways of grammaticalization for each class of morpheme, which possesses several:

(3) The main difference between the two domains is that the comitative develops into an oblique marker 'with respect to' and not specifically into a dative marker (see Chappell 2000 on Southern Min comitatives). 26 In fact, the semantic change for give verbs echoes similar developments for Old English pronouns him DAT > him DAT/ACC and hire DAT > her DAT/ACC , not to mention Spanish accusative case-marking of animates by means of the erstwhile dative (Heine and Kuteva 2002: 103, 37).

Finally, note that in other parts of the world, as in many West African Benue-Kwa languages, accusative markers typically have their source in verbs of taking and holding, and may have an instrumental function in addition, similar to the use of bă and jiāng in the Medieval Chinese period (see Lord 1993: 453-457;Heine and Kuteva 2002: 286-289).

Construction type

At least four types of disposal construction have been identified in this study. These can be defined in terms of syntactic configuration:

(i) (NP SUBJECT ) -[MARKER ACC + NP DIRECT OBJECT ] -VERB PHRASE (ii) (NP SUBJECT )-[MARKER ACC + NP DIRECT OBJECT(i) ] VERB 1 -(VERB 2 )-PRONOUN (i) (iii) NP DIRECT OBJECT(i) -[MARKER ACC + PRONOUN (i) ]-VERB PHRASE (iv) (NP SUBJECT ) -[CHIONG ACC -NP DIRECT OBJECT(i) ] -KĀ ACC -PRONOUN (i) -VERB PHRASE
All the Sinitic languages examined in this brief survey have been shown to possess at least one type of disposal construction:

(NP SUBJECT ) -[MARKER ACC + NP DIRECT OBJECT ] -VERB PHRASE While the basic structure is isomorphic in form with the Standard Mandarin bă construction, it may make use of an etymologically distinct marker, according to the classification in §9.1. In addition to this, certain Sinitic languages permit resumptive or anaphoric pronouns in the postverbal slot (Hakka, Cantonese):

(NP SUBJECT ) -[MARKER ACC + NP DIRECT OBJECT(i) ] VERB 1 -[VERB 2 ]-PRONOUN (i)
In a third construction type, the direct object is placed in clause-initial position and a resumptive pronoun follows the disposal marker (certain Min and Wu dialects):

NP DIRECT OBJECT(i) -[MARKER ACC + PRONOUN (i) ]-VERB PHRASE
In both construction types, the pronoun must be coreferential with the direct object preposed to it, not to mention, invariably in third person singular form. This contrasts strikingly with the case for standard Mandarin which does not possess either structural subtype for its bă construction. A fourth structure found only in Southern Min involves hybridization and the use of a resumptive pronoun, whereby both the native and Medieval markers of the disposal construction co-occur:

(NP SUBJECT ) -[CHIONG -NP DIRECT OBJECT(i) ] -KĀ -PRONOUN (i) -VERB PHRASE TELIC An interesting semantic constraint has also been observed for certain Hakka and Wu dialects: the direct object governed by the disposal marker is required to be coded as a possessive NP.

Intra-typological classification

A highly preliminary intra-typological classification of the seven major Sinitic languages with respect to disposal constructions can be proposed with the caveat that detailed research into the syntactic and semantic constraints needs to be made before a full typology is possible.

Standard Mandarin stands out as a singleton: it possesses just the one main type of disposal construction which has semantically generalized to mark absolutive NPs, and not just accusative ones. The Southern Sinitic languages of Cantonese, Hakka and Min all evince a Medieval stratum, represented in their use of cognates of jiāng; with Hakka and Cantonese further related by their use of a subtype with the postverbal resumptive pronoun. Hakka and Min also possess distinct markers which belong to the native stratum. Min and Wu dialects are naturally associated by their use of the construction type with a clause-initial patient noun coreferenced by the following accusatively-marked pronoun. These two dialect groups are reputed to be two of the oldest branches of Sinitic, with Min dialects having possibly split off from an ancestral proto-Wu-Min language (see Chappell 2001a). Furthermore, Hakka, Min and Wu are conspicuous for their use of comitatives in the function of disposal markers.

In contrast to these Southern Sinitic languages, the central zone Sinitic languages of Gan and Xiang which have remained in prolonged linguistic contact with Mandarin dialects can be grouped together for their use of 'give' and 'take' verbs in the function of disposal markers. 'Give' is also the commonest source for Wu whose northern dialect areas are also in close proximity with Mandarin, possibly forming an areal feature for this central transitional zone.

Finally, from examination of the data in these six Sinitic languages for disposal constructions, it should be clear that many important phenomena are overlooked if only direct correlates of the Mandarin bă or jiāng constructions are searched for. By 'direct correlates', I mean those which 'translate' the constituents and word order for standard Chinese bă or jiāng constructions slot-by-slot, and use cognate markers. This results in two main linguistic 'crimes': Either constructional subtypes are considered as somehow 'deviant' when they do not conform to the structural framework for bă or jiāng constructions (for example, resumptive pronouns) or important kinds of disposal constructions are completely overlooked because the markers are non-cognate with bă or jiāng, as in the case of comitatives and give/help verbs.

Clearly, we have a case of standard Mandarin taking the place of European languages such as Greek and Latin as the new model for descriptive grammarwriting in Chinese linguistics. In other words, a Eurocentric model has been replaced by a Sinocentric one, specifically one that is based on the standard language, Mandarin. Paradoxically, Mandarin in its turn has not proven to be the best departure point for typological comparison within Sinitic: it possesses just the one type of disposal construction, and the one accusative marker, whose use has further evolved into an absolutive, placing it somewhat out in 'left field', at variance with its sister languages, many of which possess two or more construction types not to mention several markers. At the same time, its constraint on telicity of the predicate appears to be stronger than for other Sinitic languages, although certain dialect groups permit the use of intransitive predicates too, such as Southern Min. The possibilities are more restricted than Mandarin, however, including only certain kinds of undergoer subjects (see [START_REF] Teng | Disposal structures in Amoy[END_REF].

The extensive range of structural possibilities and semantic constraints which shape these different disposal constructions shows that it is an erroneous exercise to simply assume a broad syntactic isomorphism between Mandarin and other Sinitic languages. It is therefore crucial to explore the diversity of the Sinitic languages in a more detailed and thorough way for the purposes of working out intra-Sinitic typological parameters and for finding conceptual links with structures that have similar functions in other languages of the world.

uncovered this precious manuscript in the University of Barcelona Library some years ago. However, a grammar by Juan Cobo (d. 1592) entitled Arte de la Lengua China [Grammar of the Chinese language] may be the earliest grammar of any Chinese language. The manuscript is mentioned in Coblin and Levi (2000: ix) but has not been sighted, presuming a copy still exists.

3 Information regarding Funing 福寧 in Fujian province as Varos's main place of work comes from W. South Coblin (pers. comm.), and not Fuzhou 福州, as previously believed (e.g. [START_REF] Gonzales | Grootaers, Willem 1954 Initial 'pe' in a Shansi dialect[END_REF]). 4 A list of works by the Dominicans who were the most active sect among missionaries in the production of grammars and descriptions of Chinese languages and dialects can be found in [START_REF] Gonzales | Grootaers, Willem 1954 Initial 'pe' in a Shansi dialect[END_REF]. [START_REF] Van Der Loon | The Manila incunabula and early Hokkien studies[END_REF][START_REF] Van Der Loon | The Manila incunabula and early Hokkien studies[END_REF]) also provides a brief historiography of the study of Chinese languages by western scholars, discussing major works from 16 th century onwards. An early important bibliography on works published in China by Europeans is that of [START_REF] Cordier | L'Imprimerie sino-européenne en Chine: Bibliographie des ouvrages publiés en Chine par les Européens au XVIIe et au XVIIIe siècle[END_REF]. 5 Abel-Rémusat's grammar (1822) of vernacular Chinese is an exception to this rule, for the reason that it sets out to explain Chinese grammar on its own terms (see [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF]. Thus, Abel-Rémusat provides brief descriptions of both bă and jiāng . 6 I use the term 'accusative marking' for nouns preceded by a preposition whose grammatical function is to indicate that the dependent noun is in the argument role of direct object. This is mainly to avoid ambiguity, given the large number of senses 'object' has. 'Accusative marker' is also used interchangeably with 'disposal' marker, a term adopted from the domain of Chinese linguistics.

Even though Sinitic languages are clearly not inflectional and do not possess morphological case marking per se, the disposal construction is the kind of structure from which eventual inflections emerge when the grammaticalization process has taken its full course. Furthermore, in terms of typology, there are benefits to be gained from unifying the use of terminology across languages. 7 This is the more common name for Grammaire générale et raisonnée (1660) by A. Arnauld and C. Lancelot. Reprint, 1997. Paris: Editions Allia. 8 One of the anonymous reviewers observes that the same situation applies in the study of unrelated minority languages in China. 9 Yue-Hashimoto (1993) also provides a description of dialectal differences for many different construction types, and includes a comprehensive reference list on dialectal studies of Sinitic languages. 10 Abbreviations used in the glossing of examples are as follows: ABS=absolutive marker preceding affected object noun, ACC= accusative marker preceding affected object noun, ACH=achievement aspect marker, ADV=marker of adverb formation, AGT=agentive marker, ASST=assertive modality particle, CLF=classifier, COMP=completive aspect marker, COMPR=comparative marker, CONT =continuative aspect marker, COP=copula, CRS=sentence-final marker of a currently relevant state of affairs, DEM=demonstrative, DIMN=diminutive suffix, DIR=directional aspect marker encliticized to verbs, EXT=extent, marker of a postverbal complement indicating the extent of an action or its result state: 'so X that', GEN = genitive marker, INCH= inchoative aspect marker, INTS=intensifier, LIG=marker of ligature and dependency for attributive phrases, also for relative clauses, LOC=locative, NAME = proper name, NEG=negative adverb, NEG:IMP=negative imperative modal verb, NOM=nominalizer, PFV=perfective aspect marker, PL= plural, PRT=modal or discourse particle, Q=quantifier, SG=singular. 11 In fact, many semantically reflexive unergative predicates such as chī-kĕ le eat-thirsty 'to eat so that one becomes thirsty' or zǒu-fá walk:exhausted 'cause oneself to become exhausted through walking' are possible (see Chappell 1992b). Furthermore, in older forms of Mandarin and in certain non-standard Mandarin dialects, the use of motion verbs with bă constructions is permitted (see [START_REF] Frei | The ergative construction in Chinese: Theory of Pekinese pa[END_REF], Grootaers 1954). For example, Bă ge zhū păole. [ABS-CLF-pig-run-CRS] 'A pig is running away.' In the latter case, the definition for the constructional semantics would need to be broadened. 12 Given information in most Chinese languages is typically coded into a preverbal position; new is postverbal (see Li and Thompson 1981 on Mandarin). 13 This may appear to be at variance with Frei's extremely perceptive analysis (1956) of the baconstruction as an ergative construction; however, this is in nomenclature only: I choose 'absolutive' in preference to 'ergative' for the reason that the ergative NP is not morphologically marked at all (see Chappell 1992b however for a contrasting position). 14 Percentages of the population are quoted throughout this chapter as a rough approximation of speaker numbers, given that the most recent censuses in China have not surveyed maternal language or knowledge of other dialects. In other words, these are estimates, absolute figures not being possible. 15 I use the pīnyīn romanization system for the Mandarin examples, a system adopted in 1958 for transcription and language pedagogy purposes by the Chinese government. Note that Standard Mandarin, or pŭtōnghuà, 'the common language' refers to a formal, educated variety of the Beijing dialect from the Northern group of Mandarin. Consensus for the definition of 'standard Mandarin', or pŭtōnghuà, was achieved at the Symposium on the Standardization of Modern Chinese held in China in 1956. It is specifically based on the pronunciation of the Beijing dialect, the lexicon of the northern dialects and the grammar of modern vernacular works (Chappell 1980). Chinese characters in tradtional fántĭzì form are provided, and where feasible, also for the six other Sinitic languages treated in this study. Where a demotic character is not known or attested, the use of an empty box, thus 囗, is conventional practice in Chinese linguistics.

Tone marks are indicated on all syllables, apart from unstressed ones, and without indicating tone sandhi. For the Southern Min examples, I use the Church Romanization system, as exemplified in the Carstairs Douglas dictionary (1990). McIver (1991), unless examples from Rey (1990) are being quoted which uses a francophone system. The Cantonese examples from Cheung (1992) use the Yale system while my own data employs the Sidney Lau system. The Shanghainese, Xiang and Gan examples are rendered in the International Phonetic Alphabet. 16 This S-V-O counterpart is dispreferred for the reason that the postverbal noun is fully lexical and thus, creates a 'heavy VP' following the polysyllabic verb with its directional complement. 17 I do not agree with one of the anonymous reviewers that the intransitive bă constructions increase the valency since the causing event is generally not an argument of the verb. The absolutive NP may also represent the grammatical subject of a reflexive predicate in Mandarin, see Chappell (1992b). Intransitive predicates such as lèi 'be tired' are causativized by the constructional semantics of the disposal form, which indeed has several subtypes, as argued in Chappell (1992b). 18 [START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF][START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF][START_REF] Peyraube | Zaoqi 'ba' ziju de jige wenti (Some problems concerning the early 'ba' forms[END_REF] has argued convincingly that bă did not directly supersede the Archaic Chinese construction with yĭ, but was rather in competition with the earlier jiāng construction. 19 The bridging stage may be the use of kāng as a general marker of the oblique, if not via a benefactive/dative interpretation. This point of view is taken in Chappell (in prep,chapter 4). Note also that in contemporary Min dialects, kā ~ kāng is a polysemous morpheme, coding several functions, as described in Chappell (2000). 20 Chappell (2001c) devotes a section to the topic of hybridization of syntactic constructions in Sinitic languages. 21 Apparently, this construction can be used by younger generation speakers of Taiwanese Mandarin (thanks to Dylan Tsai, National Tsing Hua University, for this observation). In this case, it can be viewed as a calque from Taiwanese Southern Min (see also Chappell 2001c and to appear for the same phenomenon with say verbs). 22 In the original documents, examples ( 17) and ( 18) are given in character only. I have transcribed them in one of the most widely used transcription systems which was devised by missionaries in the 19 th century, as represented in the Hakka dictionary of McIver (1991). Translations are similarly my own. 23 The reader will note various romanizations for the comitative marker in Hakka: t'ung 11 , t'oûng and thûng. This authentically reflects the original works from which the examples were taken. 24 For example, this construction type is not treated in any depth in Matthews and Yip's reference grammar of Cantonese (1994), nor mentioned in [START_REF] Yuan | Hànyu& Fāngyán Gàiyào[END_REF]. 25 I use Mandarin pīnyīn romanization in small capitals for the comitative marker 跟 GEN, as no transcription has been provided in the original source for this character, in either of the dialects listed. 26 This standpoint contradicts and supersedes my earlier view (Chappell 2000) that the accusative meaning developed from an ablative or Source use of kā, the comitative marker, in Southern Min. I am now of the view that the comitative 'and, with' did not develop into a polysemous preposition meaning 'to', 'for', 'from' but rather grammaticalized into a preposition with the vague semantics of 'with respect to'. I owe this enlightenment and solution to William McGregor. One of the anonymous reviewers also observed that the BENEFACTIVE > ACCUSATIVE link might explain the comitative source, if not the give/help source as in the semantic re-interpretation 'He helped the child get dressed' > 'He dressed the child.'

( 17 )

 17 Northeastern Hakka: Jiayingzhou or Meixian Hakka (NP SUBJECT ) -[TSIONG ACC + NP DIRECT OBJECT(i) ] VERB 1 -(VERB 2 )-PRONOUN (i) 3SGDe cette poule, n'en laissez rien.['Eat up all this chicken.']

  ): (18) Dabu Hakka construction with tet and a possessive object: (NP SUBJECT ) -[TET ACC + POSSESSIVE NP DO ] -VERB 1 -(VERB 2 ) 3SG ACC 1GEN bowl break:into:pieces 'S/he broke my bowl.'

  TONE DIACRITICS: v (no marking) = high level 55; v¤ = high falling 53; v$ = low falling 21; vfl = mid rising 24; vì = low level 22, vh = low checked 32 (glottalized ending), v ' C = high checked 4 where C = plosive. Meixian Hakka examples follow the romanization devised by

Table 1 :

 1 Arte de la lengua Chiõ Chiu [Grammar of the Chiõ Chiu language] (1620: 11)

	Spanish romanization	Chiõ Chiu	17 th century Spanish translation and
		characters	English
	guà lāy	我來	--'I come'
	lu lāy	汝來	tu bienes 'you (sg) come'
	ý lāy	伊來	aquel biene 'that one comes'
	guàn lāy	阮來	nosotros benemos
			'we come'
	lǔn lāy	恁來	vosotro benis
			'you (pl) come'
	ín lāy	因來	aquellos bienen 'those ones come'

  ).

	gnî	t'oûng ngaî sià	ŷt	tchōng tān
	2SG BEN 1SG write one	CLF	list
	'écris-moi une liste' ['Write a list for me.'] (Rey 1926: 1131)
	(20) Meixian Hakka -Accusative use of t'ung 11
	(NP SUBJECT ) -[T'UNG 11 +POSSESSIVE NP OBJECT ] -VERB 1 -(VERB 2 )
	thìn-chho ' k	òi	thûng a-shuk kài	vuk
	定著		愛	同	阿叔 個	屋
	certainly	want ACC uncle GEN house
	tsò-háu-lôi
	做好來
	make-COMP-come
	'You certainly have to finish building uncle's house.'
	Y.
	(19) Meixian Hakka -Benefactive use of t'ung 11
	(NP SUBJECT ) -[T'UNG 11 +BENEFACTIVE NP] -VERB 1 -(VERB 2 )
	你	同	我	寫	一	張	單

  ) Hong Kong Cantonese accusative construction with jēung:

	(NP SUBJECT ) -[JEUNG ACC + NP DIRECT OBJECT ] -VERB 1 -(VERB 2 )
	*哩個		故事 將	我	笑	到	肚
	*Nīgo		gujái jēung ngóh siu	dou tóuh
	this-CLF	story ABS 1SG laugh EXT belly
	都	痛	咧
	dōu	tung le.
	all	hurt PRT
	(25) Mandarin disposal construction with bă:
	(NP CAUSING EVENT ) -[bă+ NP S ] -VERB PHRASE TELIC
	這	故事 把	我	笑	得	肚子 都
	Zhè gùshi bă	wŏ	xiào de	dùzi dōu
	this	story ABS 1SG laugh EXT belly all
	疼	了
	téng le
	hurt PFV
	'This story made me laugh so much that my belly ached.'

  Cantonese, like certain Hakka dialects, allows a postverbal resumptive pronoun, always 3 rd person singular in form: kéuih. This is particularly a feature of colloquial speech, according toLi (2001: 33).

						-O 1 -V 2 -O 2 .
	(26) Hong Kong Cantonese accusative construction with jēung and a postverbal
	complement noun:
	(NP SUBJECT ) -[JEUNG ACC + NP DIRECT OBJECT(i) ] VERB 1 -(VERB 2 ) -NOUN (ii)
	將	你	打扮 成	一個	伯爺婆
	Jēung néih	dábaahn-sihng yāt-go	baakyepó
	ACC	2SG	dress:up-become one-CLF old:lady
	'Dress you up like an old lady.'
	Third, (27) Hong Kong Cantonese accusative construction with jēung and a
	postverbal pronoun:
	(NP SUBJECT ) -[JEUNG ACC + NP DIRECT OBJECT(i) ] VERB 1 -(VERB 2 )-PRONOUN (i)
	千祈		唔 好	將	D	頭髮
	Chìnkèih	m$ h.hóu	jēung dī	tàuhfaat
	be:sure		NEG:IMP	ACC	CLF PL hair
	染黑		佢
	yíhm-hāk	kéuih
	dye-black	3SG
	'Be sure not to dye your hair black.'

  gam 2 yau 5 goh 3 sue 1 sang 1 le 1 jau 6 ling 1 yat 1 goh 3 kam 4 ,

	721. ... 哩個	幕 --
		... lei 5°g oh 3 mo 6 --
		this:CL grave
		'(He) was about to take his axe and split open the doors of the tomb.'
		[Balcony Rendezvous]
		so have CL scholar	P TOP then take one:CL	lute
	17.	… 出來	嘅
		… chut 1-lei 4 ge 3	.
		out-come GE ASST
	18.	就 係 還返 jau 6 hai 6 waan 4 -faan 1	俾 bei 2	哩個 li 1 / lei 5 0 /goh 3	then be
		give:back-return			give	this:CL
		女仔	嘅。
		lui 5 jai 2 ge 3	.
		girl	GE ASST
		'Then a scholar came with a lute to return it to this girl.' (Tale of the
		Reborn Lady of the Red Flowering Plum)
	(29) Cantonese serial verb construction with loh 2 'take':
		(NP SUBJECT ) -LOH 2 -NP DO -VERB 1 -X-VERB 2 -NP DO
	720. ... 就 要	羅 個 斧頭	來=,
		... jau 6 yiu 3	loh 2 goh 3 foo 2 tau 4* lei 4
		then about:to take CL axe	COME PURP
		劈 開	哩個		=,
		pek 3 -hoi 1	lei 5°g oh 3		=,
		split-open	this:CL

  You give back the money to him.' (N.B. All data in this section are taken from

	30	Shanghainese accusative construction with nç 53 :
		(NP SUBJECT ) -[nç 53	+ NP DIRECT OBJECT ] -VERB 1 -(VERB 2 )
		儂	拿	鈔票	還	拔	伊
		noN 42 nç 53 ts h ç 34 p h iç 34 ˙uE 23 p´? 5 ˙i 23
		2SG ACC money	return give 3SG
		'

  Eat up the apple!' [more literally: apple, take it and eat it]

	NP OBJECT(i) -[DEI 11 +PRONOUN OBJECT(i) ] -VP
	蘋果	代	渠	吃	交
	beN 31 ku 35	dei 11 gei 31 ts h ˆ313 ˙uç o
	apple	ACC	3SG eat

PRT '

  則.

	thing	3SG	ACC	1SG:GEN do	broken-PRT
	'S/he broke my things.'
	(32) Shaoxing dialect -Comitative use of tse/ 45 則
	NP SUBJECT -[TSE/ 45 +COMITATIVE NP] -VERB 1 -(VERB 2 )
	我	則	偌	一堆 生	去
	No 13 tse/ 45 no/ 12 ie/ 5 te 5 saN 53 t˛Hi 33
	1SG COM 2SG together	go
	'I'll go with you.' (Xu and Tao 1997: 139)
	(33) Shaoxing dialect -Accusative use of tse/ 45 則
	NP DO -NP SUBJECT -[TSE/ 45	ACC + NP POSSESSIVE ] -VERB 1 -(VERB 2 )
	東西	渠	則		我	捻	破	哉
	toN 53 ˛i53 ˙i13	tse/ 45 No 13	˜ie< 13 pHa 33 dze *

  -NOUN PHRASE INDIRECT OBJECT -NOUN PHRASE DIRECT OBJECT

	媽媽 誒	把		我	兩塊	錢	咯
	ma 33 ma ei,	pa 41 ŋo 41 lian 41 k h uai 41 t˛iE) 13 lo	mother
	PRT	give 1SG two :CLF	money PRT
	'Mum, give me two dollars please.'
	(35) Changsha dialect of Xiang -Accusative use of pa 41 :
	(NP SUBJECT ) -[PA 41	ACC + NP DIRECT OBJECT ] -VERB PHRASE
	把	窗戶			打開
	pa 41 t˛hyan 41 fu	ta 41 k h ai 33
	ACC	window		strike-open
	'Open the window!'

I thank the editors, William McGregor, Alain Peyraube, Laurent Sagart and the anonymous reviewers for their comments and critique of this study, also for their many excellent suggestions. I am indebted to Wen Huiping, CRLAO, for checking the Mandarin data. A note on terminology: I use the term 'Sinocentrism' in preference to the more unwieldy 'Mandarincentrism' or 'Mandarocentrism', and, moreover, use it with a negative connotation. This neologism refers to the bias in choosing the official and standard language, Mandarin, as representative of all Chinese languages, and in fact, reflects the common use of 'Chinese' to mean 'Mandarin'.

This has the handwritten title of Gramatica China and annotation on the first page that it was written by Father Melchior de Mançano for the use of Father Rajmundo Feijoo. It is part of a corpus of early Southern Min materials being used by this author in a joint project with Alain Peyraube on the diachronic syntax of Southern Min (16 th -20 th centuries). Prof. Peyraube


Simon Bicaïs
email: simon.bicais@cea.fr

Jean-Baptiste Doré

José Luis Gonzalez Jimenez

Adaptive PSK Modulation Scheme in the Presence of Phase Noise

Keywords: Millimeter wave, Phase noise, Phase shift keying, Adaptive Systems, Performance analysis, Channel estimation

Phase noise is one of the major impairments affecting severely performance of millimeter-wave systems. This paper addresses the problem of link adaption for coherent and non-coherent phase modulated signals subject to Gaussian and Wiener phase noise. We first derive closed-form approximations of the bit error rate. Then, in contrast to usual link adaptation techniques, we propose a simple scheme exploiting estimations of not only the signal-to-noise ratio but also of the phase noise variance, which is essential to achieve reliable communications.

I. INTRODUCTION

Future 5G millimeter-wave (mmWave) bands should lead to user throughputs above 1 Gbit/s. However, additional breakthrough technologies are necessary to reach this requirement. Therefore, for the first time in the telecommunication history, bands above 90 GHz are studied for future communications [START_REF] Fettweis | Entering the path towards terabit/s wireless links[END_REF]. In particular, mmWave systems are critically impacted by phase noise (PN) due to the poor performance of high frequency oscillators [START_REF] Voicu | Performance and trends in millimetrewave cmos oscillators for emerging wireless applications[END_REF]. This has motivated extensive work on PN estimation and compensation [START_REF] Yi | Phase estimation for coherent optical ofdm transmission[END_REF], [START_REF] Munier | Estimation of phase noise for qpsk modulation over awgn channels[END_REF]. Further, achieving high-rate communications over wireless links in the mmWave domain demands tremendous amount of power, and so, highefficiency and wide-bandwidth power amplifiers [START_REF] Song | Present and future of terahertz communications[END_REF]. Therefore, coherent Phase Shift Keying (PSK) modulations are highly valuable since they demonstrate a constant envelope property, and thus, offer an efficient use of power amplifiers. Yet, PSK modulations are highly sensitive to phase related impairments: Carrier Frequency Offset (CFO), PN. Differential PSK (DPSK) has been introduced as a more robust scheme. At the expense of a noise enhancement, DPSK enables noncoherent communications [START_REF] Proakis | Digital Communications, ser. McGraw-Hill series in electrical and computer engineering : communications and signal processing[END_REF]. Prior work in [START_REF] Burr | Comparison of coherent and noncoherent modulation in the presence of phase noise[END_REF] has confronted the robustness of PSK and DPSK when affected by a Tikohonov PN. Setting the modulation scheme to maximize spectral efficiency while maintaining robustness is correspondingly the motivation behind link adaption. Such adaptive systems are now implemented in most of practical systems [START_REF] Technologies | LTE and the Evolution to 4G Wireless: Design and Measurement Challenges[END_REF] and rely on a channel quality estimation to set the modulation.

Contributions: In this paper, we seek to improve the design of inherently robust communication systems impacted by PN. First, we assume a high Signal-to-Noise Ratio (SNR) and a Gaussian PN to derive a closed-form approximation of the Bit Error Rate (BER) for any M -ary PSK. Considering that the superposition of a Gaussian and a Wiener process is a more realistic PN model [START_REF] Demir | Computing timing jitter from phase noise spectra for oscillators and phase-locked loops with white and1/f noise[END_REF], [START_REF] Khanzadi | Calculation of the performance of communication systems from measured oscillator phase noise[END_REF], we derive and confront the BER performance of PSK and DPSK for such PN. Furthermore, in contrast to usual link adaptation techniques, we propose a simple scheme exploiting estimations of not only the SNR but also of the PN variance, which proves to be truly essential to achieve reliable communications. We hence derive the appropriate Maximum Likelihood (ML) estimators of the thermal and phase noise variances. Eventually, we propose a statistical test to determine whether the coherent or noncoherent modulation is the most robust one and should be employed.

Organization: The remainder of this paper is structured as follows. Section II introduces a brief description of the channel and PN models. Section III is devoted to the performance analysis of PSK and DPSK impacted by Gaussian and Wiener PN. Finally, Section IV derives the appropriate channel estimation to implement the link adaptation scheme.

II. SYSTEM MODEL A. Channel model

Considering a single carrier communication system with a perfectly mitigated channel, the received symbol at time instant k is defined by

r k = s k • e jφ k + n k , (1)
where s is the modulated symbol from constellation C with average symbol energy E s , φ is the oscillator PN and n represents independent identically distributed samples of a zero-mean complex Additive White Gaussian Noise (AWGN) with variance 2σ 2 n . A PSK constellation with modulation order M is defined by

C = { √ E s exp j 2π M •i |i = 1, ..., M }.
In the case of a DPSK, information is encoded in the phase difference from one symbol to another denoted δθ k = s ks k-1 . We denote by s and |s| the phase and amplitude of a symbol s.

B. Phase noise model

Oscillators PN is generated from the transformation of amplitude fluctuations into phase fluctuations [START_REF] Chorti | A Spectral Model for RF Oscillators With Power-Law Phase Noise[END_REF], such that it describes a cumulative random process [START_REF] Demir | Computing timing jitter from phase noise spectra for oscillators and phase-locked loops with white and1/f noise[END_REF], [START_REF] Hajimiri | A general theory of phase noise in electrical oscillators[END_REF]. If only white noise sources are considered 1 , the oscillator PN φ may thus be modeled by the superposition of a Wiener (Gaussian random-walk) process φ w and a Gaussian one φ g [START_REF] Demir | Computing timing jitter from phase noise spectra for oscillators and phase-locked loops with white and1/f noise[END_REF]. This may be expressed by

φ k = φ w,k + φ g,k , φ g,k ∼ N (0, σ 2 g ), φ w,k = φ w,k-1 + δφ w,k , δφ w,k ∼ N (0, σ 2 w ), (2)
where σ 2 w and σ 2 g denote respectively the variances of the Wiener PN increment δφ w and the Gaussian PN. Besides mathematical convenience [START_REF] Khanzadi | On models, bounds, and estimation algorithms for time-varying phase noise[END_REF], [START_REF] Krishnan | Constellation optimization in the presence of strong phase noise[END_REF], the Gaussian distribution is also a relevant PN model. When considering wide bandwidth systems 2 , the oscillator noise floor represents the greatest contribution to the overall PN [START_REF] Khanzadi | Calculation of the performance of communication systems from measured oscillator phase noise[END_REF], such that the Wiener PN becomes negligible compared to the Gaussian one, i.e. σ 2 g >> σ 2 w . Thereby, Section III-A and IV-A use the Gaussian PN model to pursue a simple analytical analysis while Section III-B and IV-B extend it to the sum of Wiener and Gaussian PN.

III. PERFORMANCE ANALYSIS A. PSK over Gaussian phase noise

To begin with, let us assume that the channel is dominated by Gaussian PN. Regarding symbol-by-symbol detection, it is known that the ML criterion minimizes the Symbol Error Probability (SEP) [START_REF] Proakis | Digital Communications, ser. McGraw-Hill series in electrical and computer engineering : communications and signal processing[END_REF], [START_REF] Moon | Mathematical Methods and Algorithms for Signal Processing[END_REF]. In order to design such optimum receiver, let us derive the likelihood function, which may be rewritten as

p(r k |s k ) = p |r k | , r k |s k | , s k . ( 3
)
By definition, the AWGN is invariant under rotation such that, for simplicity of notation, n may stand for n • e jθ for any θ fixed. The received symbol should be studied through its amplitude and phase as

|r k | = (|s k | + n k ) • e j( s k +φ k ) = (|s k | + (n k )) 2 + (n k ) 2 E s + (n k ) (4)
r k = arg[(|s k | + n k ) • e j( s k +φ k ) ] = s k + φ k + arctan (n k ) |s k | + (n k ) s k + φ k + (n k ) √ E s . (5)
These first-order approximations are tight for a high SNR scenario [START_REF] Fu | Exact phase noise model and its application to linear minimum variance estimation of frequency and phase of a noisy sinusoid[END_REF], [START_REF] Krishnan | Soft metrics and their performance analysis for optimal data detection in the presence of strong oscillator phase noise[END_REF]. By Eq. ( 2), the likelihood function follows a bivariate Gaussian distribution and is thus expressed by

p(r k |s k ) = exp - 1 2 (|r k | - √ E s ) 2 σ 2 n + ( r k -s k ) 2 σ 2 g + σ 2 n /E s 2π σ 2 n (σ 2 g + σ 2 n /E s ) . (6)
This expression, originally derived in [START_REF] Krishnan | Constellation optimization in the presence of strong phase noise[END_REF], can be exploited in our study to approximate the BER of a PSK. With respect to the ML decision rule for a PSK, the detected symbol is

ŝk = argmax s ∈ C p(r k |s k ) = argmin s ∈ C ( r k -s k ) 2 , (7)
which enables to derive the SEP as follows

P se = 1 -Pr( ŝk = s k |s k ) = 1 -p - π M < r k -s k < π M = 2Q π M σ 2 g + σ 2 n /E s . ( 8
)
To directly relate the BER to the SEP, we shall make two commonly used assumptions. First, the bit labeling of the constellation satisfies a Gray coding. Furthermore, misdetections

10 0 32PSK -σ 2 g = 1x10 -3 16PSK -σ 2 g = 2x10 -3 QPSK -σ 2 g = 2.5x10 -2
Eb/N 0 (dB) only occur on the nearest neighbors of the sent symbol. Finally, the BER of a PSK affected by Gaussian PN is approximated by

P g be,PSK 2 log 2 (M ) Q π M σ 2 g + 1 2•log 2 (M ) 1 E b /N0 , (9)
where the average bit energy E b satisfies E s = E b log 2 (M ) and the noise power spectral density is defined by N 0 = 2σ 2 n . The BER performance of PSK for arbitrary orders of modulation and PN variances are illustrated in Fig. 1. As exhibited, the closed-form expression holds accurate approximations of the BER at high SNR.

B. DPSK over Wiener phase noise

DPSK enables a non-coherent demodulation at the receiver. As a consequence, estimation of the carrier phase is not required. Moreover, a differential modulation is not subject to the cumulative nature of the PN, and only slightly to the CFO. This robustness is achieved at the expense of a BER performance degradation. Yet, the stronger these impairments, the more valuable it seems to opt for differential encoding. The pending question is when DPSK is more robust than PSK. Therefore, let us derive the performance of PSK and DPSK when the PN is described by the sum of a Wiener and a Gaussian PN. The optimum decision for a DPSK receiver [START_REF] Proakis | Digital Communications, ser. McGraw-Hill series in electrical and computer engineering : communications and signal processing[END_REF] is given by

δθ = argmin δθ ∈ C ( r k -r k-1 ) -δθ 2 . ( 10
)
With regard to the PN model in Eq. ( 2) and to the high SNR approximation in Eq. ( 5), we have which is directly equivalent to

r k -r k-1 δθ k + δφ w,k + φ g,k -φ g,k-1 + (n k -n k-1 ) √ Es , (11)
r k -r k-1 δθ k + φ eq,k ,
where φ eq ∼ N (0,

σ 2 w + 2σ 2 g + 2σ 2 n /E s ). (12)
Thereupon, the BER for a DPSK subject to Gaussian and Wiener PN may be approximated by

P w be,DPSK 2 log 2 (M ) Q π M σ 2 w + 2σ 2 g + 1 E b /N0 1 log 2 (M ) . ( 13
)
To establish a comparison with the PSK modulation, we consider a genie estimation at the PSK receiver. With one pilot symbol, the receiver is able to estimate and compensate perfectly the Wiener process. The pilot period is defined by T , such that if k = n•T then φ w,k+1 = δφ w,k . The estimation problem in presence of Wiener PN exceeds the scope of this paper, but is addressed in [START_REF] Munier | Estimation of phase noise for qpsk modulation over awgn channels[END_REF]. Though the derivation is not developed here, the BER for a PSK in this case is given by

P w be,PSK 1 T -1 T -1 k=1 2 log 2 (M ) • Q π M k • σ 2 w + σ 2 g + T /(T -1) E b /N0 1 2•log 2 (M ) . (14)
Figure 2 confronts the performance of a 16PSK to the ones of a 16DPSK for Gaussian and Wiener PN. The PSK receiver presents a pilot density of 10% with a genie estimation. Conversely, the DPSK receiver does not implement any channel estimation. Figure 2 shows that analytical expressions are tight to the simulation results. Moreover, Fig. 2 confirms an aforementioned intuition. The DPSK presents a loss in BER performance, still, when considering stronger Wiener PN then it is more robust than the PSK.

IV. LINK ADAPTION A. Estimation of thermal and phase noise variances

To improve spectral efficiency, practical communication systems implement adaptive modulation scheme [START_REF] Technologies | LTE and the Evolution to 4G Wireless: Design and Measurement Challenges[END_REF]. Namely, the modulation order is inferred from a SNR estimation. In the case of a channel dominated by Gaussian PN, the analytical approximation of the BER in Eq. ( 9) enables to determine the greatest value of M while maintaining the error rate below a fixed target. Figure 3 depicts the modulation scheme regions for M -ary PSK, i.e. the highest modulation order M achieving BER < 10 -4 given E b /N 0 and σ 2 g . It is shown that the performance is highly related to the PN variance, which should necessarily be considered in the link adaptation to maintain robustness.

Such link adaptation requires an estimation of σ 2 n and σ 2 g . This may be realized by inserting N pilot samples possibly distributed and known from the receiver denoted s = (s 1 , s 2 , ..., s N ) and by deriving the appropriate estimators. From Eq. ( 6), the joint likelihood function of the N received samples r = (r 1 , ..., r N ) is given by

p N (r|s, σ 2 n , σ 2 g ) = N k=1 p(r k |s k , σ 2 n , σ 2 g ). (15)
We derive the ML estimate of the covariance matrix for the multivariate normal distribution [START_REF] Moon | Mathematical Methods and Algorithms for Signal Processing[END_REF]. It yields here the ML estimators of σ 2 n and σ 2 g expressed by

σ2 n = 1 N N k=1 (|r k | -E s ) 2 , σ2 g = 1 N N k=1 ( r k -s k ) 2 - σ2 n E s . (16)
Writing these estimators as χ 2 (N ) distributions enables us to quantify their performance in terms of bias and dispersion respectively with the means and variances given by

E[σ 2 n ] = σ 2 n V[σ 2 n ] = 2σ 4 n N , E[σ 2 g ] = σ 2 g V[σ 2 g ] = 2(σ 2 g +σ 2 n /Es) 2 N + 2σ 4 n N Es . (17)
Since these estimators are unbiased and the regularity conditions clearly satisfied in Eq. ( 6), we may compare the estimators to their Cramer-Rao Lower Bounds (CRLB) [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF] written as

V σ2 n ≥ 2σ 4 n N , V σ2 g ≥ 2(σ 2 g + σ 2 n /E s ) 2 N . (18)
It follows easily that the thermal noise variance estimator is efficient in the sense of achieving the CRLB cf. [START_REF] Moon | Mathematical Methods and Algorithms for Signal Processing[END_REF]. As for the PN variance, the estimator is tight to the CRLB but does not reach it. However, both estimators demonstrate the smallest Mean Square Error (MSE) among any unbiased estimators. From Eq. ( 15), it is straightforward that the joint density p N belongs to the exponential family such that S = (

N k=1 (|r k | - √ E s ) 2 , N k=1 ( r k -s k ) 2
) is a complete sufficient statistic for parameter (σ 2 n , σ 2 g ). By the Lehman-Scheffé theorem, the unbiased estimators (σ 2 n , σ2 g ), defined upon S, are respectively the unique Minimum-Variance Unbiased Estimators (MVUE) of σ 2 n and σ 2 g .

B. Is the phase noise a cumulative process?

As illustrated in Fig. 2, the DPSK should be favored at the detriment of PSK only if the cumulative nature of the PN is non-negligible. Hence, the link adaptation problem can be expressed as a simple detection problem: is the cumulative process of the phase noise strong enough to advantage a differential modulation. Let formulate the corresponding binary hypothesis test as

H 0 : Gaussian PN, if σ 2 w /σ 2 g < λ fixed, H 1 : Wiener PN, otherwise. (19)
The link adaptation decision δ is then expressed by

δ(r) = PSK, if S(r) < ϕ(λ) DPSK, otherwise , (20)
where r = (r 1 , ..., r N ) is a received sequence of N consecutive pilots, S denotes a sufficient statistic of the received pilots sample and ϕ is a test threshold function of λ. Fortuitously, this problem has been extensively studied in the financial field under a different name: random walk hypothesis for stock market prices [START_REF] Charles | Variance ratio tests of random walk: An overview[END_REF]. Numerous statistical tests have been designed, yet, one in particular has retained most of the attention: the variance ratio test [START_REF] Charles | Variance ratio tests of random walk: An overview[END_REF], [START_REF] Lo | Stock market prices do not follow random walks: Evidence from a simple specification test[END_REF]. This test relies on the fact that the variance of the random walk increments increases linearly with p the sampling interval. Applied to our context, this is expressed by

V [φ k+p -φ k ] = p • σ 2 w + 2σ 2 g , (21)
which is denoted further by σ 2 ∆p . Letting σ 2 w = λ • σ 2 g and summing over p, the statistical test becomes where σ2 ∆p is the estimator of σ 2 ∆p and evaluated by

S(r) = M p=1 σ2 ∆p σ2 ∆1 < ϕ(λ) = λ • M (M + 1) + 4M 4λ + 2 , (22)
σ2 ∆p = 1 N -p N -p k=1 ( r k+p -s k+p ) -( r k -s k ) 2 . (23)
The upper bound of summation M satisfies 1 < M < N , and is optimized heuristically 3 . Figure 4 depicts the mean probability of taking decision δ(r) = H 1 and thus use DPSK. Several pilot lengths are considered and λ is set to 1/2 as in Fig. 2 . As exhibited, the longer the pilot sequence, the more accurate the test. The performance degradation caused by an incorrect decision should be evaluated to properly specify the length of the training sequence. Due to space limitation, it is not carried out here but using the proposed framework, it is straightforward to derive.

V. CONCLUSION In this paper, we have addressed the problematic of link adaption for phase modulated signals affected by PN. We have first considered PSK modulations impacted by a Gaussian PN and provided the closed-form approximation of the BER. Optimum ML estimators of thermal and phase noise variances have been derived to propose a link adaptation scheme. Exploiting estimations of both the SNR and the PN variance proved to be essential to maintain robustness. Then, the PN has been described with a more realistic model: a sum of a Gaussian and a Wiener process. Performance of PSK and DPSK were compared in order to determine when the use of a differential modulation is beneficial. Accordingly, we proposed a simple detection test, inspired from the financial field, to perform the link adaptation and exploit the most robust modulation between PSK and DPSK. Nevertheless, these results remain an analytical analysis and it is of particular interest to investigate this adaptation problem under practical implementation considerations.

Fig. 1 :

 1 Fig. 1: Analytical and simulated BER performance of M -ary PSK affected by Gaussian PN with variance σ 2 g

Fig. 2 :

 2 Fig. 2: Analytical and simulated BER performance of 16PSK and 16DPSK for Gaussian PN (σ 2 g = 10 -3 , σ 2 w = 0) and Wiener PN (σ 2 g = 10 -3 , σ 2 w = σ 2 g /2)

Fig. 3 :

 3 Fig. 3: Modulation Scheme Regions for M -ary PSK: highest modulation order M achieving BER < 10 -4 as a function of E b /N 0 and the inverse PN variance 1/σ 2 g

Fig. 4 :

 4 Fig. 4: Mean probability of taking decision δ(r) = H 1 when λ = 1/2 for different lengths of pilot sequence N

Flicker noise is diregarded in this study.

The upper bound M in Eq. 22 must be large enough to yield a robust test. However, as the sampling interval p gets bigger, the dispersion of σ2 ∆p in Eq. 23 increases. Thus, if M is too large, the test is defined upon unreliable estimations.

ACKNOWLEDGMENT

The research leading to these results received funding from the French National Research Agency (ANR-17-CE25-0013) within the frame of the project BRAVE.