A Vindication

Rémy Duthille

Thomas Spence

has long been recognized as one of the very few late-eighteenth-century champions of women's rights. E. P. Thompson noted that

record on women's rights in order to answer feminists' charges that Spence was merely reproducing a "patriarchal" pattern. This article will start by a critical survey on the historiography that criticized Spence's representation of women in The Rights of Infants. The second section will broaden the perspective by discussing other works by Spence because it is misguided to assume that The Rights of Infants contains Spence's definitive statement on women and their rights. This pamphlet, and others, raise the question of women's agency. To what extent did he conceive women as agents rather than as passive beneficiaries of rights? How far does his commitment to gender equality translate into a greater share of political activity? The final section will examine Spence's pronouncements on the family, marriage and divorce, to examine his alleged maintenance of "patriarchy".

The critical conversation on The Rights of Infants 3

In the 1980s and 1990s, critics searching for Spence's pronouncements on women concentrated on The Rights of Infants. This pamphlet, like many others by Spence, is a charge against landlords fattening themselves on the labour of their tenants, and a defense of a universal right of subsistence. In the preface, dated 19 March 1797, Spence specifically attacked Thomas Paine, who had defended a measure of redistribution and land reform in Agrarian Justice earlier in the year. 1 Spence bitterly arraigned Paine for falling short of advocating his own land plan: while Paine was right to justify the principle of equal right to the land, his plan falls short of the people's just claims: "The poor, beggarly stipends which [Paine] would have us to accept of in lieu of our lordly and just pretensions to the soil of our brith are so contemptible and insulting". Spence knew full well that the author of Rights of Man was a big name, that his pamphlet would sell and therefore that his half-way measures would outshine Spence's own "plan of enjoying man's right, which [he had] been publishing in different ways for more than twenty years" (Spence 1982, 47). The pamphlet proper is a dialogue between "Aristocracy" and "Woman." Woman advocates Spence's land plan on the grounds that every "infant" has a right to live:

Ask the she-bears, and every she-monster, and they will tell you what the rights of every species of young are. -They will tell you, in resolute language and actions too, that their rights extend to a full participation of the fruits of the earth. They will tell you, and vindicate it likewise by deeds, that mothers have a right, at the peril of all opposers, to provide from the elements the proper nourishments of their young." (48)

4
This right involves a right to means of subsistence, which in turn entails common ownership of the land and universal dividends. Despite its title, then, the pamphlet is not concerned with childhood or childcare as such, but rather with the ultimate consequences of the newborn's right to subsistence. "Woman" is the children's advocate and, to Aristocracy's "sneering" question: "And is your sex also set up for pleaders of rights?" she proudly answers: "Yes, Molochs! Our sex were defenders of rights for the beginning." Since men, "like he-asses," suffer to be imposed upon and bear oppression without repining, then it is up to women to speak up for universal rights: "we, even we, the females, will vindicate the rights of the species and throw you and all your panyers in the dirt" (49). 2 The second half of the pamphlet consists in "Woman"'s impassioned speech. She defiantly tells the aristocracy ("ladies and gentlemen", "my good gentlefolk") Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000 that the people are going to expropriate them and hand over the land to the parishes. Women are to play the central role in the process:

We women (because the men are not to be depended on) will appoint, in every parish, a committee of our sex (which we suppose our gallant lock-jawed spouses and paramours will at least, for their own interest, not oppose) to receive the rents of the houses, and lands already tenanted, and also to let, to the best bidders, on seven years leases such farms and tenements as may, from time to time, become vacant. ( 51)

The rents will cover all the government's expenses, and any surplus will be redistributed to every man, woman and child in the community. "Woman" insists that "all this is done for the sake of system, not revenge or retaliation" (52): the former landowners and the rich will keep all their moveable property. Should they resist the appropriation of land, however:

If, by foolish and wicked opposition, you should compel us, in our own defence, to confiscate even your moveables, and perhaps also to cut you off, then let your blood be upon your own heads, for we shall be guiltless. It will therefore be your interest and wisdom to submit peaceably and fraternize chearfully with us as fellowcitizens. (52) This language harks back to the Terror and the sans-culotte argument that the aristocracy must be exterminated for resisting the Revolution; the guillotine is the condign punishment of those who refuse to "fraternize". The use of the word is particularly revealing as Spence includes women in such fraternization. Spence's pamphlet ends in a rejection of the "pretended philanthropy of the great" and a defense of "the rights of the human species": the final message is that the poor are entitled to justice and equality, not charity (51, 53). Barbara Taylor recognized that this pamphlet held out a promise "of earthly selffulfilment" that was extended to women. While acknowledging that in his utopian polity, Spensonia, men and women would enjoy the same political rights, she insisted on the exclusion of women from councils owing to their domestic chores. Moreover, she commented, "a woman's marital status would in all respects […] be equal to that of her husband." But Taylor adds a parenthesis that carries the weight of her argument: "(except apparently the domestic workload)" (Taylor 8). David Worrall too set about "reading carefully through what Spence does and does not say" (Worrall 31) and took him to task what what he did not say. He duly noted that in Spence's plan the surplus produce from the parishes "would be shared out exactly equally whether male or female; married or single; legitimate or illegitimate; from a day old to the extremest age". But he stressed that Spence clung to a patriarchal model, first because parish dividends would be paid to the male head of each family, secondly because The Rights of Infants is framed as a dialogue between "Aristocracy" and "Woman", the latter generic character defending the rights of women as mothers (not as human beings), and presenting women as close to Nature and ultimately relegated to the care of children. The economic and social dependency of women, then, would not change in Spensonia. In Spence's eyes women were only useful as a revolutionary vanguard, and possibly as cannon fodder. While Spence "drew a quick political lesson from events like the women's march on Versailles in 1789" it is even unclear, for Worrall, whether Spence imagined women would really act or whether he tried to shame men out of their political apathy and into virile revolutionary action. Worrall, however, had to concede that " [p]erhaps what is most important about Spence's discussion of women is his ability to figure their Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000 agency at all" (31-32). Anna Clark expanded the argument and suggested that by taking on a female persona in The Rights of Infants, Spence tried to shame and goad men into action (Clark 1999, 149). As will be argued later, imagining female agency and adopting a woman's voice (however generic) was a crucial achievement which in itself makes it very difficult to portray Spence as an unqualified upholder of the patriarchal status quo.

9

Malcolm Chase adopted a more nuanced approach, underlining that Spence's position changed over time. While women were not mentioned in his 1775 lecture, The Rights of Infants was seen as a turning point because this pamphlet brought out a defence of women's full political rights. Chase perceived in the 1797 pamphlet "the germ of a concept of male oppression, and an admission that masculine brutishness and turpitude lay at the root of inequality." He also noted close affinities between Spence's ideal of equality between the sexes and that of (unnamed) seventeenth-century radicals, but wisely refrained from inferring a direct "influence." 3 Judgments have become more positive recently. In 2011, Jon Mee, referring to The Rights of Infants, argued that female equality was "a cause treated more positively in the popular radical movement than is sometimes allowed" (Mee 126). Mee's was a remark in a general discussion of popular radical culture, and it was not elaborated on: this begs the question of how positively women's rights are treated by Spence. As for Arianne Chernock, she recognized that Spence's essentialist argument presenting men as mothers (in Rousseau's sense) is "problematic" but noted that his vision of the positive transforming potential of women's feminine sensibility was in itself crucial and significant in the reform movement of the times . She enlisted him among the "radicals who, if they did not make feminism a priority, at least supported women's rights (Chernock 4)."

Chernock's judgment is valid to a certain extent. Spence was not a feminist indeed, in the sense that he did not make women's liberation a priority and that he did not think gender difference was the root of oppression (the fundamental cause of oppression and inequality, both economic and political, was private ownership of land). Chernock, however, retains much of Barbara Taylor's scepticism about Spence's ulterior motives and suggests that he may have been uncomfortable with the idea of enfranchising conservative women or those who might be influenced by their husbands.

Supposing the pamphlet to be a piece of opportunistic propaganda, then why should it reveal what Spence really thought about women? He presents "Woman" as a mother and a wife. It does not follow that he thought that motherhood was the essence of womanhood, or that all Englishwomen were wives and mothers. He knew very well that was not the case: the pamphlet contains the phrase "men or female; married or single" (Spence 1982, 51). Rather, it suggests that Spence found it politically expedient to appeal to maternal instinct and the defence of children. It should be noted here that some Frenchwomen did justify their revolutionary commitment by their role as mothers, but according to Dominique Godineau, who undertook a systematic survey of Parisian women's political activities during the Revolution, this was not the dominant rationale, and though all the lower-class women of Paris were housewives and were vitally affected by the issue of subsistence, this issue was not central to the struggle of the more politically conscious women (Godineau 1989;Godineau 1988, 352). Spence, then, was not mimicking the actual discourse of Parisian revolutionary women. The context of the war may offer an explanation for his focus on motherhood. Women's role as child-bearers was exalted during the war "when the size and health of the population was a particularly significant issue" (Macleod 28), both in France, with the concept of "republican motherhood" Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000 and in Britain, in the loyalist propaganda and in the highly visible contribution of women to the war effort, through charity work and activities such as knitting and sewing for soldiers, which tied in nicely with their roles as mothers and housewives . Since female support for the war was publicized, for instance in the form of addresses or subscription lists in the newspapers, Spence could not have been unaware of it. His pamphlet, in that context, may be explained as an attempt to reclaim women's maternal role for his own purposes, against conservative appropriations of it. [START_REF] Spence | division of the parish surplus among the "inhabitants of every description, and whether they be men, women or children, legitimate or illegitimate[END_REF] Chernock's contention that Spence had a "reductive understanding of woman as a figure naturally sympathetic to revolution" leads her to wonder "whether Spence himself would have supported those women who did not exhibit "revolutionary" sentiments", women like the conservative controversialist Hannah More (124). This argument proves too much: if Spence was not ready to enfranchise conservative women, then why would he support male universal suffrage in the first place? He knew full well that many men were loyalists, and yet he fought for the enfranchisement of all men, including loyalists. Spence did portray women as "naturally sympathetic to revolution" (Chernock 124) but it does not necessarily follow that he believed that all women, in 1797, were ready to engage in revolutionary action. A more likely interpretation is that he believed that women, like men, could be educated and might become aware of their true interests, which were best defended in his land plan.

14 How opportunistic was the pamphlet, then? Interpretation is delicate. We cannot probe Spence's heart, and part of the argument depends on the pamphlet's implied audience and what Spence thought about it. Did he calculate that there was a constituency of women that he could win over to this cause by specifically feminist arguments? This might have been the case, but it doesn't imply he was insincere, especially because the argument that women must have the vote on account of their children appears elsewhere, in pamphlets that do not specifically target women, but have a male implicit reader. If his feminist proposals were opportunistic, then he should have dropped them when addressing men, who were presumably the majority of his audience and certainly his implied readers. Given the prevalence of "rough" types of masculinity in his plebeian environment, the rhetoric of manly superiority pandering to misogynistic or patronizing attitudes would have made more strategic sense. Plebeian clubs, including Spencean clubs, were ruled by an artisan masculine ethos that incorporated elements of aggressive virility which could degenerate into drinking contests, brawls and violent behaviour. Members of the plebeian societies and followers of Spence were thus viewed as "unrespectable" by the authorities and the loyalists. Spence certainly rejected his opponents' polished, urbane, Addisonian ideal of the "independent gentleman", pouring scorn on "our now-a-days so much boasted gentlemen of independent fortunes". 4 On the face of it, Spence's plebeian, rough masculine environment was no natural constituency of feminism, and argument addressing supposedly feminist sensibilities in such a social milieu seem doomed to failure. This leaves us with the hypothesis that Spence included provisions for women in his constitutional plans to appeal to women. This would mean he was addressing a mixed audience, writing to men and women, which is in itself significant and sets him apart from other radical writers of the time who wrote for males only.

Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000

Women's agency and women's rights in Spence's writings

Whatever ulterior motives Spence might have had, The Rights of Infants is significant as a speech act. Spence's "Woman" is not a female allegory of Britannia, the republic, liberty or anything else. In his prosopopoeia this male writer adopted a female persona to make a serious political argument. This seems to be unique in the abundant literature of the 1790s. Inventing a credible popular voice to achieve a potent "vernacular voice" was notoriously difficult for radicals and anti-Jacobins as well. Hannah More, who is sometimes seen as a feminist, staged dialogues between male characters. Even Wollstonecraft addressed middle-class women and did not try to impersonate labouring women.

As Worrall noted, the question of women's agency is central in The Rights of Infants.

Examples of Frenchwomen's activism during the Revolution, such as the march to Versailles on 5-6 October 1789, must have inspired Spence. He is exceptionally favourable to poor women's political agency in The Rights of Infants when compared to Burke and even Wollstonecraft. Edmund Burke's evocation of the royal family's return to Paris under watchful escort on 6 October 1789 has remained famous: "the royal captives who followed in the train were slowly moved along, amidst the horrid yells, and shrilling screams, and frantic dances, and infamous contumelies, and all the unutterable abominations of the furies of hell in the abused shape of the vilest of women" (Burke 63). As critics have noted, though Mary Wollstonecraft had dismissed this passage in her Vindications of the Rights of Men in 1790, in her Historical and Moral of the French Revolution she depicted the Parisian working women in pejorative terms that were reminiscent of Burke's harpies: "the lowest refuse of the streets, women who had thrown off the virtues of own sex without having power to assume more than the vices of the other". 5 In Spence's Rights of Infants, on the contrary, "Woman" seems to have retained "female" maternal sensibility and taken on "manly" fortitude, sturdiness and courage. In stark contrast with Burke's and Wollstonecraft's degrading representations Spence exalts a politically-conscious, vocal and respectable lower-class woman who stands up for her own and her family's rights. "Woman"'s opening invocation of "the she-bears, and every she-monster" might be read as a rejection of social stigma, of stereotypical opprobrium, and as a defence of lower-class women's dignity.

Spence's sympathy for lower-class women must have originated in his own experience of poverty which, as he himself declared, had awakened his sense of injustice. His childhood was spent in miserably poor circumstances in Newcastle; his mother, Margaret Flet, a native of the Orkneys, "was an industrious woman, and kept a stall for the sale of stockings" (Rudkin 15). Spence knew what working hard and struggling for subsistence meant. He might also have been aware that women played political roles at a local level: in the late eighteenth century some women ratepayers attended vestry meetings and had the right to vote on matters directly affecting the community (Eastwood 47). Further research is needed to determine whether this was the case in Newcastle and whether Spence could have been aware of it. It may be supposed, however, that he had some knowledge of women's political involvement in Newcastle. From 1769 on a wave of Wilkite agitation gathered momentum; national grievances, in the context of the incipient American War, and the dispute around the Town Moor coalesced in 1775 and a

Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000 radical opposition set the tone of politics until well into the 1780s. In 1782 a group of women "proposed forming a 'patriotic association in defence of their liberties' and addressing the queen" in support for a motion to end the war (Wilson 426).

18 Spence looked beyond his own immediate experience for other examples of popular agency. In Pig's Meat he published long extracts from "The History of the Rise and Fall of Masaniello." Masaniello was a fisherman who had led a revolt in Naples in 1647 (Spence 1794, III.22-55, 67-98, 123-136). 6 The participation of women is noted several times in this account, but their behaviour is not praised as such and at times it can also be understood as evidence of the fickleness of public opinion. Significantly Masaniello's revolt was sparked off by a new tax on food. Spence must have known that women were particularly active in food riots. Women's closeness to nature and maternal nature is not essential to his argument on the right to the fruits of the earth; rather Spence must have appealed to popular notions of justice, what E. P. Thompson famously called "the moral economy of the English crowd." 7 Spence's political consciousness was first stirred during the controversy over the enclosure of the Newcastle town moor. Several provisions in his projects of constitutions such as The Constitution of Spensonia (1803) address popular grievances with legislation on hunting and against the engrossing and forestalling of corn (Art.39, 40, 42, in Spence 1982, 109-110).

19 How is the issue of women's agency and political rights treated elsewhere in Spence? David Worrall finds that "[r]eferences to women are infrequent" in Spence's works apart from The Rights of Infants (Worrall 31). But Spence does mention women very frequently indeed compared to his contemporaries Price, Priestley, Paine, or Cartwright-or to the French, American, or (unwritten) British constitutions of his times, or ours for that matter. The civic humanist tradition emphasized the necessity of virtue, an etymologically manly quality. In the eighteenth century the idea gained hold that women's and man's virtues were essentially different and incompatible (on the complexity of French conceptions of vertu, see Linton 2001). There is a misogynistic streak in much republican writing which saw any woman's political involvement as morally and politically dangerous. This is especially true in the writings of some English Commonwealthmen, such as James Burgh, whose Political Disquisitions (1774-1776) warn against the effeminizing influence of women, the deleterious advice giving by royal favourites such as Charles II's mistresses or the marquise de Pompadour in France. Attacks on effeminacy mediated anxieties about rivalry with France, imperial concerns and alleged aristocratic corruption. 8 John Wilkes's libertinism and homophobia were also a consequence of the gendered construction of the opposition between the manly independent elector and the effete courtier (McCormack 86-92;[START_REF] Clark | The Chevalier d'Eon and Wilkes: Masculinity and Politics in the Eighteenth Century[END_REF]. Positions on women's political rights, then, did not always tally with conventional divisions between radical and conservative. Edmund Burke admitted that educated women were part of the British public whose views constituted a real public opinion that should be heeded by legislators. John Thelwall, a self-proclaimed Jacobin and an ardent defender of male universal suffrage, ridiculed Burke's suggestion, reducing it to a preux chevalier's unguarded expression of gallantry (Thelwall 397). It is in France that the misogynist nature of republican ideology was most visible, because the French revolutionaries refused to grant citizenship to women. It has been argued that the ancien régime public sphere, which tolerated and even accommodated the political expression of at least some aristocratic women in salons, was more open to women than the new republican public sphere which emerged out of the French Revolution. Joan Landes claimed that the public sphere was reconstructed along masculinist lines, not just without women, but against them (Landes).

Spence seems to be indebted to the civic humanist tradition inasmuch as he repeatedly insisted that all men should actively participate in political life as both citizens and soldiers. In his earlier work he depicted scenes involving men and boys engaged in military exercises on the parish common while old men, women and children sat watching them:

And now you shall witness with your own eyes that force is as unlikely to succeed against us as your secret corruption. Therefore you must go with me to-morrow to a neighbouring parish about two miles off, it being their general review day, when all the men thereof are to go through their military exercise. Every parish has a general field day once in a quarter of a year appointed by act of parliament […].

Accordingly when next morning came, which was exceedingly fine, we went to the military ground of the aforesaid parish, which was very neat and convenient and tolerably large, surrounded with several rows of trees, with seats underneath for the spectators and kept entirely for that and such like public uses. The parish bells rung merrily, numbers of spectators from the neighbouring parishes, with all the old men, women, and children that could get from the same parish were solacing themselves in the morning sun around the place. Presently the men of the parish appeared, those who had good horses on horseback, those of a colour together, others trailing field-pieces of brass, and others with muskets. The boys too were classed according to their sizes, with small muskets and cannon suitable to their strength, and the whole with proper officers, colours, music, and an uniform dress, which last was peculiar to the parish […]. They made a gallant appearance and all in their most happy countenances, as if going to some agreeable sport. 9 In this idyllic setting women and girls, together with the elderly, are literally watching the martial show from the sidelines. The utopian scene appears decidedly conservative here, replicating the gendered categories of eighteenth-century England, and even the social distinctions which were visible in militia musters through the distinction between the affluent men on horseback and the rank-and-file walking behind them. This scene would not be amiss in a loyalist description of a perfect English village attending the militia's drilling at the time of the American War or the French Wars.

Such neatly gendered utopian scenes are absent from his later work. Spence's thought developed in the direction of gender equality. Women are not mentioned in his 1775 lecture to the Newcastle Philosophical Society, published as "The Real Rights of Man" (Spence 1982, 1-5). Recently a copy of the original version of the lecture, long thought to be lost, was found; it revealed that the original title was "Property in Land Every One's Right ". Alastair Bonnett cautiously comments that "[g]iven Spence's limited but steadfast support for female suffrage (he supported it at the parish level but opposed at the national level) the gender neutrality of the title may or may not have been deliberate" (Bonnett 135). This caution is commendable: Spence used gender-neutral pronouns later in his career, and in 1775 he had hardly begun his research in the English language. But Spence may have been aware of the issue of women's rights. The 1793 edition of the lecture was accompanied by "Queries sent to the Philosophical Society, in Newcastle, on the 26 th of December, 1775, by the Rev. Mr. J. Murray, on account of Mr. Spence's expulsion". The fourteenth query reads: "Is it implied in the nature of the social compact, that the one half of the contractors should have no right of possessions?" (Spence 1793, 33) This query suggests that by 1775 Spence had drawn the egalitarian implications of the social contract: if men's property was guaranteed by the social contract why should not women's property guaranteed as well since men and women were equally rational creatures and co-contractors?

Spence explicitly defended women's rights only later. In The Constitution of a Perfect Commonwealth (1798), he distinguished between "local" and "proprietory" citizens. While only men ("every man") enjoyed the voting rights of local citizens, "[e]very man, woman, and child is a proprietary citizen in the parish or district in which they have acquired the title of local citizen, either on account of their own residence, if adults, or of their parents, if infants." Women and children, as well as men, enjoy economic rights in the form of a share of the revenue of the parish (Spence 1982, 61-62). 10 By that time, however, Spence was already considering that women could deliberate and vote, since the women in The Rights of Infants threaten with "appoint[ing], in every parish, a committee of our own sex" and are ready to do the business of the parish that is neglected by men.

In The Constitution of Spensonia (1803), he defended votes for women, and therefore a fully universal adult suffrage (Spence 1982, 104-118). A striking feature of the declaration of rights at the beginning of the book is its floating semantics. Spence seems to be groping his way toward a gender-neutral vocabulary. Some articles, relative to judiciary guarantees especially, have "every man" or "a man" (art. [START_REF] Spence | division of the parish surplus among the "inhabitants of every description, and whether they be men, women or children, legitimate or illegitimate[END_REF]16), echoing the phraseology of the English common law. Article 16 reads: "Every man being supposed innocent until he has been declared guilty, if it is judged indispensable to arrest him all severity not necessary to secure his person ought to be be strictly repressed by the law." There are also negative clauses based on articles of the French Declaration of the Rights of Man, as in article 22: "no one can be deprived of the smallest portion of his property without his consent, except when the public necessity, legally ascertained, evidently require it, and on condition of a just and previous indemnification." Article 13 reads: "No person can be accused, arrested, or confined but in cases determined by the law, and according to the form which it prescribes. Every citizen summoned or seized by the authority of the law ought immediately to obey, he renders himself culpable by resistance" (art.13). Finally, Spence uses indeterminate, gender-neutral words such as "every individual" (art.34) or "those who…" (art.15): "The right of presenting petitions to the depositories of public authority belongs to every individual" (art.34). The first article, which stated that "all men are equal by nature and before the law", was reworded to read "all human beings." This disparate, changing vocabulary suggests that Spence's thinking was still in flux as he was working his plan out and moving toward gender equality.

Spence fell short of advocating absolute equality, however, as article 5 testifies:

Female citizens have the same right of suffrage in their respective parishes as the men: because they have equal property in the country and are equally subject to the law and, indeed, they are in every respect, as well on their own account as on account of their children, as deeply interested in every public transaction. But in consideration of the delicacy of their sex, they are exempted from, and are ineligible to, all public employments." (Spence 1982, 107) Justifications for women's suffrage here seem to stem partly from a democratic version of the neo-Harringtonian idea that land ownership confers political rights; 11 partly from a more general argument that every person concerned with public affairs ought to have the vote. In The Constitution of Spensonia, everyone, including women, children, and criminals, enjoy "a share of the parish revenue" (105). Each person enjoys this right because they belong to humankind. In later editions of the pamphlet, Spence wrote that "all human beings are equal by nature and before the law, and have a continual and inalienable property in the earth, and its natural productions" (104). If the vote derives from landed property and landed property is a right of every human being, then ultimately women are entitled to the vote as adult human beings.

The object of article 5 was not to grant full equality, but on the contrary to differentiate between men and women. It sounds as if children were virtually represented by their mothers and not by their fathers-as if, therefore, women were even more entitled than men to have the vote. This extra justification for women's votes is in contrast with their exclusion from public employments. Spence's consideration for "the delicacy of their sex" can easily be dismissed as a supremely sexist and patronizing instance of false gallantry. Mary Wollstonecraft already ranked "delicacy of sentiment" among "those pretty feminine phrases, which the men condescendingly use to soften our slavish dependence" (Wollstonecraft 82). Wollstonecraft's claim can be substantiated by many examples of French legislators justifying women's exclusion from the suffrage and a differentiated education for girl by considerations on women's delicate constitutions and their natural vocation for marriage and household management. A shining exception is Condorcet, who defended women's suffrage and demolished such arguments as early as July 1790; in the Convention only Gilbert Romme and Pierre Guyomar proposed enfranchising women (Fauré;Condorcet; on Mirabeau and Talleyrand's stance against women).

Spence's use of "delicacy" was similar to that of French legislators who naturalized the difference between men and women. This is impossible to vindicate, even in Spence's own system of thought. Women, he writes, are "exempted." In his 1755 Dictionary of the English Language Samuel Johnson defined "exemption" as "immunity, privilege, freedom from imposts or burdensome employments." This concept sits uneasily with Spence's general rejection of privileges. One argument however may somehow mitigate our judgment. In Spence's polity, women have voting rights at the parish level, where the literally vital questions of subsistence and everyday life would be debated and solved. Executive functions are derivative and burdensome. Ideally they are confined to mere execution with no space for personal (and potentially arbitrary) interpretation. Spence had no truck for a strong government devising policies and pushing them through the medium of a parliament and local agencies. In his utopian polities the reality of power is lodged with the parish councils, not with male law-enforcement officers or even the central government. 12 Giving the vote to women in the parish councils and excluding them from executive functions did not mean confining them to the lowest political echelon, but ensuring they had a say in the assembly that legislated for the community's fundamental concerns.

Spence on marriage and the family

A final argument that must be confronted is the notion that Spence's utopia would leave women's subordinate position in a patriarchal society essentially unchanged. It should be noted, however, that "patriarchy" did not entail the subjection of women only. As Ann Hughes wrote in a recent study of the English Revolution of the 1640s:

Early modern England is sometimes described, in short-hand form, as a patriarchal society, where patriarchy is understood as the domination of men over women. Patriarchy should, however, be defined more specifically as a form of power based on fatherhood, giving some men authority over children, younger and poorer men, as well as over women. It was by no means a system that benefited all men. (Hughes 19) Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000

Many men -those who never married (up to a fifth of the male population) and the poor -never achieved the ideal of "self-sufficiency seen as crucial to manhood" (19).

Spence defended one aspect of "patriarchy" as defined above: he saw marriage as the natural wish of every girl-and boy. If women are condemned to the marital state in his utopia, so are men. Arguably, this leaves Spence's utopias vulnerable to a queer critique of heteronormativity even more than to a feminist critique. In The Constitution of a Perfect Commonwealth (1798) Spence argued that the current system of private property not only compromised the wellbeing and happiness of individuals of both sexes, but degraded their morals, in all social classes. He deploys the language of sensibility to denounce the ills begotten by marriages of convenience:

Does not the pride and etiquette of birth and family act the inexorable tyrant over their most tender feelings, destroy love and friendship, and even dissolve the brotherly ties of blood by unnaturally erecting one in every brood of children into a lordly tyrant over the rest? (Spence 1982, 55) The perpetrators of such a system were also its victims. They were turned into "unnatural monsters." The children of "the labouring class" did not fare better: they were brought up to become "whores and soldiers" (56). One of the arguments in favour of his plan is that it would "be a great improvement in the morals of this class." In particular, a parish dividend of £ 10 a year per person would teach young unmarried women habits of household economy. They would be encouraged to "become notable housewives, as the prospect of marriage, in such a land of bliss, would soon open to their views." Spence waxes lyrical on the blessings of conjugal love: "The whole horizon of love will glow with felicity, no more to be clouded with ill-boding and gloomy apprehension" (56).

This vision was "patriarchal" to the extent that Spence saw the family as the basic structure and the male as head of the household. But he certainly wished to eradicate negative aspects of the patriarchal model outlined by Hughes: to end the poorer and younger men's dependency on older and richer men, and to redress the balance of power in the married couple. He collapsed the difference between legitimate children and bastards, stating in 1803 that everybody had an equal claim to a share of the rent, "every man, woman, child, whether born in wedlock or not (for nature and justice know nothing of illegitimacy)." His ideal constitution had a provision for "every widow or unmarried woman or woman separated from her husband." 13 Here as on many other issues, Spence remains frustratingly laconic. He insists on removing the stigma attached to bastards: children born out of wedlock and their mothers should be treated respectfully, like any other individual. In a British context this was very progressive, considering the humiliating treatment single mothers and their children were subjected to when they claimed relief.

To assess the significance of Spence's commitment to equality and women's rights it is useful to stress that he insists on rights but does not dwell on the specific problems of those women and children and especially on the problem of the father's acknowledgment of his children. In this he adheres to the spirit of the French legislators but ignores issues that were treated by Olympe de Gouges. The idea that "nature and justice know nothing of illegitimacy" was the rationale for major reforms in family and inheritance law during the French Revolution. The abolition of privileges (4 August 1789) had paved the way to the equal treatment of all children, the abolition of primogeniture and the equal sharing of inheritance among all children, including daughters. The law of 12 brumaire an II (2 November 1793) guaranteed that natural children who were legally acknowledged by their father would enjoy the same inheritance rights as legitimate children. 14 In practice, however, French law tolerated the continuance of discriminatory practices and not all "bastards" benefited from the new clauses, if only because fathers could not be forced to acknowledge their children. Article XI of Olympe de Gouges's Declaration of the Rights of Woman and the Female Citizen (1791) states that: "The free communication of thoughts and opinions is one of the most precious rights of woman, since that liberty assures the recognition of children by their fathers. Any female citizen thus may say freely, I am the mother of a child which belongs to you, without being forced by a barbarous prejudice to hide the truth" (Levy, Applewhite, & Johnson 91). Sexual liberty (though not licentiousness) is as a corollary to liberty of speech: a woman must have the right to name her child's father. Gouges added that a married man's bastard is deprived of his/her inheritance by "barbaric laws". She proposes a "social contract" whereby "our property belongs directly to our children, from whatever bed they come, and [...] all of them without distinction have the right to bear the name of their fathers and mothers who have acknowledged them" (94; see also Duhet,. The last clause is essential: the parents must acknowledge the child. The emphasis is strikingly different in Spence.

Whereas Gouges insists on the woman's sexual freedom and the man's responsibility to acknowledge the child, in order to safeguard the child's inheritance, Spence adopts a male point of view: he argues that unmarried mothers should not bear a stigma and should enjoy equal rights, but does not suggest that the father has a duty to acknowledge the child. Contrary to Gouges he is not concerned with inheritance, presumably because all individuals are provided with a basic subsistence income in his land plan.

35 In his defence of divorce, he endeavours to adopt the point of view of both men and women; his argument rests on equality between the spouses and on the right of women, as well as men, to initiate divorce proceedings. While he may have been indebted to Milton or others, he kept abreast of the news and his apology of divorce, in 1800, contributed to ongoing debates. A bill which "would have made adultery a crime for the first time since Cromwell" failed in the British Parliament. 15 Spence praised the "facility of divorce which the French now allow" (Spence, The Political Works of Thomas Spence 76). The French law on divorce was predicated on a the idea that marriage was a civil contract: this secularized vision of marriage had long been brooding in the French Enlightenment -Montesquieu and Diderot shared it, among others -but it was enshrined only in 1791, in article 7 of the new Constitution: "The law recognizes marriage only as a civil contract" (Dessertine 208). The law of 20 September 1792 made the dissolution of marriage possible by mutual consent, on the basis of a simple assertion by one of the spouses, of any of seven possible motives, including dementia, physical abuse, abandonment for more than two years, absence for more than five years, or "déréglement notoire des moeurs" (adultery). There had been much agitation in favour of the divorce law, and on 1 April 1792 the Legislative Assembly had admitted a delegation of women who claimed the right to divorce (Ronsin 321). Though Spence did not spell out the justified causes for divorce in so much detail, he clearly accepted some provisions of the French law (on dementia, physical abuse and adultery):

[U]nder our unalterable establishment what a dreadful thing it is to make a wrong choice where there is no remedy nor redress for life. It is enough to make one shudder to think of being indissolubly bound to a spendthrift, a drunkard, a sluggard, a tyrant, a brute, a trollop, a vixen. What signifies reforms of government or redress of public grievances, if people cannot have their domestic grievances redressed? (76)

Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000

Spence recognized that an Englishman's home should not be his castle, and that domestic despotism or marital strife, whether the fault lay with the husband or the wife, was unacceptable. He suggested that marriage should be founded on love. Adopting a male point of view, he argued that divorce would give every man a fair chance of achieving love with his loved one:

The matrimonial couples need not always now be chiding each other to no purpose about misconduct, for as they know they can part so easily they must if they wish to continue together study to make each other happy by sobriety, industry, civility, etc. Gross faults will not always be borne with now by either side therefore disgraceful bickerings will cease and the nuptial state will become like a continual courtship, because a good husband or good wife will be valued, and used as they deserve through fear of being lost.

[…] Another good effect must also flow from such known possibility of separation.

Men will no longer be afraid to give a beloved woman a fair trial of domestic life, though formerly she may have borne but a loose character, by which many will be reclaimed, the number of single women lessened, and the state of society much mended. ( 76)

He adhered to an ideal of marital bliss that unfortunately he could not achieve in his own marriage. Olive Rudkin wrote that "[m]arriage did not bring happiness to Spence. He was "unfortunate" in his choice of a [first] wife." His second wife was described as a "termagant" (Rudkin 24,89). In the passage marriage appears as an ideal that everybody should strive for : even women "of loose character" and, possibly, prostitutes, can be "reclaimed". The condition of "single women" is not an enviable one, even in Spence's ideal utopia. Such a passage shows that Spence was indebted to a moral ethos of family life and domestic virtue.

Thomas Spence does not qualify as a feminist according to late-20th or early-21thcentury standards. But why should he ? It would anachronistic to dismiss his advanced views or his failure to develop a full critique of patriarchy by holding him to our standards, without remembering that he wrote on many social and economic issues, some pertaining to women specifically, that were entirely neglected by other reformers of his time (and later). His defence of women's suffrage was predicated on the fundamental equality of all human beings, although a gendered notion of republican virtue and female "delicacy" remained present and limited their active political participation. Spence's position, however, changed and he paid increasing attention to gender equality. Perhaps he could have been convinced in time that women could hold political office.

BIBLIOGRAPHY

  Blakemore, Steven. Crisis in Representation: Thomas Paine, Mary Wollstonecraft, Helen Maria Williams, and the Rewriting of the French Revolution. Madison, NJ : Fairleigh Dickinson University Press, 1997. Bloquet, Josée. "'La société n'a pas intérêt à ce que des bâtards soient reconnus' (Napoléon)". Napoleonica. La Revue 14 (2012): 50-73. Thomas Spence on Women's Rights: A Vindication Miranda, 13 | 0000

Thomas Spence défendait les droits politiques et économiques des femmes. Il était l'un des très rares pamphlétaires de son époque à demander le vote des femmes. Certains historiens ont cependant décelé chez lui une vision patriarcale, voire rétrograde. Contre ces interprétations anachroniques, cet article s'emploie à dégager l'évolution de la position de Thomas Spence, de plus en plus favorable à l'égalité entre les sexes, tout en soulignant que Spence n'envisageait pas de confier aux femmes de fonctions exécutives et n'était pas féministe au sens où on peut l'entendre de nos jours.

INDEX personnescitees Thomas Spence

Mots-clés: vote, féminisme, suffrage universel, droits civiques, droits économiques, égalité, utopie Keywords: suffrage, feminism, universal suffrage, civil rights, economic rights, equality, utopia


François Dehmas
email: francois.dehmas@cea.fr

Valérian Mannoni
email: valerian.mannoni@cea.fr

Vincent Berg
email: vincent.berg@cea.fr

Turbo-FSK, a physical layer for LPWA: Synchronization and Channel estimation

Keywords: LPWA, OFDM, Turbo Codes, FSK, Zadoff-Chu, Constant Envelope I

Turbo Frequency Shift Keying (Turbo-FSK) has been considered as a promising physical layer for low power wide area applications. Its constant envelope at the transmitter combined with performance close to the Shannon's limit enable to achieve a high energy efficiency. However, results published so far in the literature for this waveform have assumed perfect synchronization and channel estimation. This paper, presents a synchronization and channel estimation approach based on a specifically built preamble and adapted to the performance of the new modulation. Simulations have been performed for both time and frequency synchronization as well as channel estimation. Less than 1 dB degradation in comparison to perfect detection is achieved for the most severe types of channels.

INTRODUCTION

Machine type communications (M2M) are rapidly expanding such that more than twenty billion devices are expected to be connected through wireless systems by 2020 [START_REF] Gartner | Gartner Says 8.4 Billion Connected "Things" Will Be in Use in 2017[END_REF]. Low Power Wide Area (LPWA) network technologies constitutes an important part of the Internet of Things (IoT) by providing a long range and low power wireless connectivity alternative to current generations of cellular systems (2G, 3G and 4G) [START_REF] Raza | Low Power Wide Area Networks: An Overview[END_REF]. LPWA is a generic term for a group of technologies that enable wide area communications at low cost and long battery life (Sigfox, LoRa, RPMA, NB-IoT, Weightless-P, IEEE 802.11ah) [START_REF] Raza | Low Power Wide Area Networks: An Overview[END_REF]. Among them, LoRa and NB-IoT are two leading emergent technologies [3]. When 5G IoT connectivity is considered, LPWA is predicted to represent approximately 10% of the overall IoT connections [START_REF] Rebbeck | Low-Powered Wireless Solutions Have the Potential to Increase the M2M Market by Over 3 Billion Connections[END_REF].

For these systems, long range is achieved by ensuring a very low level of sensitivity at the receiver obtained by ensuring Quality of Service (QoS) for poor levels of Signal-to-Noise Ratio (SNR). The low energy consumption requirement directly results from the necessity to have a long battery life. At the physical layer, this is achieved by selecting an energy efficient modulation combined with an efficient usage of the Power Amplifier (PA), the most power-consuming component of the transmission chain [START_REF] Raab | Power amplifiers and transmitters for RF and Microwave[END_REF]. The efficiency of the PA is highly dependent on the peak power of the signal [START_REF] Miller | Peak power and bandwidth efficient linear modulation[END_REF]. Constant envelope modulations are thus of prime importance, as they allow for large PA efficiency gains.

Turbo Frequency Shift Keying (Turbo-FSK) is a new waveform introduced in [START_REF] Roth | Turbo-FSK: A New Uplink Scheme for Low Power Wide Area Networks[END_REF] that combines an orthogonal modulation with a convolutional code. Its receiver relies on turbo processing to meet a performance close to Shannon's limit for low spectral efficiency. Furthermore, the waveform exhibits a constant envelope (i.e. it has a peak to average power ratio (PAPR) equal to 0 dB). Turbo-FSK is therefore well adapted to future LPWA systems notably for the 5 th generation of cellular systems.

As Turbo-FSK proposes to improve energy efficiency to within a few dB of Shannon's limit, expected signal-to-noise ratio at the receiver should be well below 0dB. This imposes significant performance constraints on both synchronization (time and frequency) and channel estimation at the receiver. However, results published so far in the literature for the waveform [START_REF] Roth | Turbo-FSK: A New Uplink Scheme for Low Power Wide Area Networks[END_REF][8] have assumed perfect synchronization and channel estimation. Hence, a new approach of synchronization and channel estimation based on a preamble and adapted to the performance of the new modulation is here proposed and evaluated.

The paper is structured as follows: Section II presents the principles of Turbo-FSK. In Section III, a structure of preamble adapted to the new waveform is presented. Synchronization and channel estimation algorithms are described and individually evaluated. Performance comparison to perfect synchronization and channel estimation is given in Section IV. Section V concludes the paper.

II. PRINCIPLES OF TURBO-FSK

In this section, a brief introduction of the Turbo-FSK scheme presented in [START_REF] Roth | Turbo-FSK: A New Uplink Scheme for Low Power Wide Area Networks[END_REF] is given. The structure of the transmitter (Fig. 1) is composed of λ stages, each one encoding a differently interleaved version of the ܳ input information bits. At each stage information bits are grouped into ܰ blocks of ݍ bits ( ܳ = ܰ ݍ ), and each block is sequentially encoded using a parity accumulator. The resulting ݍ + 1 bits of each block are then mapped to a complex codeword of the so called coplanar FSK alphabet [START_REF] Roth | The Physical Layer for Low Power Wide Area Networks: A Study of Combined Modulation and Coding Associated with an Iterative Receiver[END_REF] (i.e. mapped to NL-PSK subsets of ܰ ୄ -FSK possible symbols, ݍ + 1 = log ଶ ሺܰ ܰ ୄ ሻ ). Thanks to the accumulator, every consecutive Coplanar FSK symbol is related to the previous ones. The output of each encoder is then a set of coplanar FSK codewords. A Parallel-to-Serial Conversion follows to transmit the FSK codewords through the channel.

The receiver, depicted in Fig. 2, includes a Serial-to-Parallel Conversion, to reconstruct the emitted λ stages. A soft FSK detector estimates the probabilities of each possible codeword.

Then these probabilities feed the decoder, which uses them as channel observation, while output of the other decoders will be used as a priori information. A modified BCJR algorithm [START_REF] Bahl | Optimal decoding of linear codes for minimizing symbol error rate (corresp.)[END_REF] is used to decode the trellis, and the A Posteriori Probabilities (APP) of the information bits are computed. For detailed explanations about the receiver's computations, the reader is invited to refer to [START_REF] Roth | The Physical Layer for Low Power Wide Area Networks: A Study of Combined Modulation and Coding Associated with an Iterative Receiver[END_REF].

Asymptotic performance for perfect interleaving can give near error free performance for an energy per information bit over the spectral density of noise ܧ( ܰ ⁄ ) of less than 0.3dB and 1.35dB with block size Q limited to 1000 bits when assuming perfect synchronization and channel estimation [START_REF] Roth | The Physical Layer for Low Power Wide Area Networks: A Study of Combined Modulation and Coding Associated with an Iterative Receiver[END_REF].

Digital baseband front-end can be implemented similarly to Orthogonal Frequency Division Multiplexing (OFDM) systems using fast Fourier transform (FFT) and inverse FFT (IFFT) respectively at the receiver and the transmitter [START_REF] Roth | The Physical Layer for Low Power Wide Area Networks: A Study of Combined Modulation and Coding Associated with an Iterative Receiver[END_REF]. The size of the transform is denoted ܰ and the frequencies spacing, which is also the symbol rate before cyclic prefix addition, is Δ݂. Thus the sampling rate is ܰΔ݂.

III. SYNCHRONIZATION AND CHANNEL ESTIMATION

A. Preamble based dectection

A preamble-based synchronization has been considered. The preamble shall allow to get time and frequency synchronization while tolerating carrier frequency offset (CFO). In order to keep the low-power advantage of the waveform we imposed for the preamble to have a constant envelope. As a consequence, constant amplitude, zero autocorrelation (CAZAC) sequences have been considered as these are well adapted. Zadoff-Chu (ZC) sequences [START_REF] Chu | Polyphase codes with good periodic correlation properties[END_REF] are an example of such sequences and have already been widely used in cellular systems [START_REF]3rd Generation Partnership Project (3GPP) Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (Release 10)[END_REF].

A preamble adapted to Turbo-FSK is thus proposed. It is composed of a ZC sequence = ݏ( , ݏ ଵ , … , ݏ ே ିଵ ) repeated ܰ times and weighted by another constant amplitude sequence = ݓ( , ݓ ଵ , … , ݓ ே ೌ ିଵ ) such that the complete preamble is equal to ⊗ , where ⊗ is the Kronecker vector product (Fig. 3).

The sequence is defined as a modified ZC sequence whose phase is scaled to fit the number of frequencies ܰ ୄ and spectrally translated to fit the spectrum location of the FSK waveform:

ݏ = ܣ exp ቆ-݆ ߨ݊ ଶ ܰ ୄ ܰܰ ቇ × exp ൬݆ 2ߨ݂ ݊ ܰΔ݂ ൰ ( 1
)
where ܣ is a constant amplitude scaling, ݂ is the upper frequency of the FSK baseband signal, ݊ ∈ ൳0, ܰ -1൷.

Let define as the cumulative product of a ZC sequence:

ݓ = ෑ exp ቆ-݆ ߨ݅ ଶ ܰ ቇ ୀ (2) for ݊ ∈ ۤ0, ܰ -ۥ1
To the contrary of the aforementioned cellular systems [START_REF]3rd Generation Partnership Project (3GPP) Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (Release 10)[END_REF] whose synchronization sequences are transmitted in the frequency domain, the resulting preamble ⊗ has a constant envelope. It exhibits properties that are exploited in the next sections of this paper.

B. Turbo-FSK Synchronization

As Turbo-FSK should provide quality of service for low levels of SNR, preamble synchronization has to be performed using a cross-correlation between the received signal and a relatively long sequence in order to extract signal information from noise. However, in presence of significant amount of CFO (i.e. CFO > 10 ppm) the cross-correlation peak is significantly degraded.

Instead, we suggested to cross-correlate the received signal with the shorter sequence . The result of this cross-correlation is then differentially cross-correlated to the sequence. More explicitly, if ]݇[ݎ is the received signal at instant ݇, cross-correlation with sequence is calculated for every instant k:

ܿሾ݇ሿ = ݏ * ݎሾ݇ + ݊ሿ ே ିଵ ୀ (3)
where ሺ•ሻ * stands for complex conjugate.

Differential cross-correlation on the resulting signal is then equal to:

݀ሾ݇ሿ = ݓ ାଵ ݓ * ܿൣ݇ + (݊ + 1)ܰ ൧ܿ * [݇ + ݊ܰ ] ே ೌ ିଶ ୀ ( 4
)
By construction of , the sequence ሺݓ ାଵ ݓ * ሻ ஸழே ೌ ିଵ is also a ZC sequence but truncated by its last element. Detecting the peak in ݀ሾ݇ሿ at position ݇ gives the synchronization time at the receiver. Using ܰ ୄ = 32, ܰ = 128, ܰ = 32, ܰ = 128, Δ݂ = 15 kHz Fig. 4 gives an example of a resulting ݀ሾ݇ሿ signal (without any noise) where we can observe a unique cross- correlation peak that is more than 30 dB above the rest of the cross-correlation lags. As a unique peak is present, no start of frame delimiter is required to detect the beginning of the payload thus reducing the signaling overhead.

CFO estimation is evaluated on the samples ܿሾ݇ ሿ, ܿൣ݇ + ܰ ൧, … , ܿൣ݇ + ሺܰ -1ሻܰ ൧ using the Mengali estimator [START_REF] Mengali | Data-aided frequency estimation for burst digital transmission[END_REF].

This synchronization algorithm has then been simulated and performance in terms of Packet Error Rate (PER) has been measured (assuming perfect channel estimation) in order to evaluate the performance loss due to the synchronization (for both time and frequency errors) on the receiver. The results are given in Fig. 5. The following assumptions have been taken for the simulations: ܰ ୄ = 32 , ܰ = 16 , ߣ = 4 , Q = 1008 information bits, Δ݂ = 15 kHz, additive white Gaussian noise (AWGN) channel. ܰ is chosen equal to 32 to support a CFO ~ 15 kHz (16 ppm when in 868 or 915 MHz ISM bands).

Using these assumptions, performance loss introduced by the synchronization algorithm is less than 0.1 dB when ܰ is equal to 128 at PER = 1%. With a lower value (ܰ ܽ = 64), the loss is 1.4 dB due to a lower correlation peak causing more miss detections.

In Fig. 6, the accuracy of the CFO estimation has been given using the remaining error in CFO of the 99% quantile as a function of ܧ /ܰ for an initial frequency error of respectively 0 Hz and 15 kHz. In both cases, the remaining error is the same, about 50 Hz for an ܧ ܰ ⁄ ≈ 1dB meaning that phase rotation is still superior to 2ߨ with a typical frame length of 1008 bits. This will be compensated thanks to channel estimation and further described in section IV.

C. Turbo-FSK channel estimation

Channel estimation is another mandatory operation at the Turbo-FSK receiver since coherent reception is required for the linear modulation detection (phase estimation are necessary) and for log-likelihood ratio estimations required for the BCJR algorithm [START_REF] Roth | The Physical Layer for Low Power Wide Area Networks: A Study of Combined Modulation and Coding Associated with an Iterative Receiver[END_REF]. The channel is assumed constant over the duration of a packet (a few 10s of ms). As the demodulation is performed in the frequency domain as is often the case in OFDM, the widespread frequency domain channel estimation approach has been considered.

Pilots for channel estimation have also been constrained to have a constant envelope. As for time and frequency synchronization, a modified time domain ZC sequence is considered to guarantee constant amplitude in the time domain and a good repartition of the power in the frequency domain. The following channel estimation sequence has been considered: If = ሺܲ , … , ܲ ேିଵ ሻ ் is the discreet Fourier transform (DFT) of  , we get:

 = ܣ exp ቆ-݆ ߨ݊ ଶ ܰ ୄ ܰ ଶ ቇ × exp ൬ ݆2ߨ݂ ݊ ܰΔ݂ ൰ (5)
ܴ = ܪ ܲ + ܤ (6)
where = ሺܪ , … , ܪ ேିଵ ሻ ் is the DFT of the channel impulse response and = ሺܤ , … , ܤ ேିଵ ሻ the DFT of the complex additive white Gaussian noise with a variance ߪ ଶ .

Different channel estimators have been compared. The least square (LS) estimator:

= diagሺሻ ିଵ [START_REF] Roth | Turbo-FSK: A New Uplink Scheme for Low Power Wide Area Networks[END_REF] where diag() stands for diagonal matrix with the vector on its diagonal.

The linear minimum mean square error estimator (LMMSE) [START_REF] Savaux | LMMSE channel estimation in OFDM context: a review[END_REF]:

= ሺ + ߪ ଶ ሺdiagሺሻdiagሺሻ ு ሻ ିଵ ሻ ିଵ (8)
where is the covariance matrix of the DFT of the channel.

An approximation of the LMMSE estimator avoiding noise power and covariance matrix estimation, can be considered supposing a uniform channel and a given (target) SNR [START_REF] Edfors | OFDM channel estimation by singular value decomposition[END_REF].

A pragmatic improvement of LS estimator (called LS filtered in the following) has also been considered. In this case, the LS estimate is windowed in the time domain to retain only the most significant taps of the channel impulse response and filter out the noise on the channel estimate. This is equivalent to filter the frequency response of the channel to reduce the noise level and take into account the correlation between neighboring frequency taps.

Using an extended typical urban (ETU) channel [START_REF]3rd Generation Partnership Project (3GPP) Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (Release 10)[END_REF], we compared the root mean square error (RMSE) of the channel estimate for the different channel estimation approaches in Fig. 7. Ideal LMMSE assumes perfect knowledge of the covariance matrix of the channel as well as the noise power. The performance of the simple LS filtered solution is close to the performance of the LMMSE assuming a uniform channel (<1dB) and significantly outperforms the LS estimate with a gain larger than 5 dB.

In terms of PER, performance is even closer when LS filtered and LMMSE are compared (Fig. 8). For these simulation scenarios, the pilot sequence is repeated 64 times and averaged to improve the performance of the estimator. Except the LS estimator that has a loss of 1.4 dB in comparison to the reference (perfect channel estimation), the other estimators have a very limited loss between 0.2 dB (LMMSE) and 0.3 dB (LMMSE with uniform assumption). Consequently, the LS filtered solution is chosen, as it is a good compromise between complexity and performance.

IV. OVERALL PERFORMANCE OF TURBO-FSK

The main issue to consider in the overall performance of the Turbo-FSK receiver is the influence of the CFO on the channel estimation. The accuracy of the CFO estimation has been evaluated as not sufficient to consider channel estimation only on a preamble for performance over the entire packet. The probability of a phase rotation greater than 2ߨ over the 30 ms duration of the packet is expected to be significant (greater than 1% as seen in section II.B).

To address this issue, a second CFO estimation is made on the distributed pilots used for channel estimation also using the Mengali algorithm [START_REF] Mengali | Data-aided frequency estimation for burst digital transmission[END_REF]. Distributed pilot symbols have been regularly spaced over the entire transmission burst. Three different cases have been considered: one pilot symbol every 6 symbols, one pilot symbol every 10 symbols and one pilot symbol every 20 symbols. The preamble is made of ܰ × ܰ = 130 × 32 samples. A second CFO correction is done followed by channel estimation on the averaged distributed pilot symbols. Channel and CFO are both assumed constant over the duration of the burst.

For AWGN channel, the loss of ܧ /ܰ for PER levels of 1% is less than 0.2 dB when one pilot symbol every 6 symbols (Fig. 9) is considered. When the loss of energy introduced by the addition of pilot samples is considered, a penalty of 10log ଵ ሺ6 5 ⁄ ሻ = 0.8 dB should be added to the performance loss giving an overall performance loss inferior to 1 dB when both synchronization and channel estimation are taken into account. Similarly, when one pilot symbol every 10 symbols is considered, a loss of 0.4 + 10log ଵ ሺ10 9 ⁄ ሻ = 0.9 dB is observed: i.e. the same energy per bit has to be transmitted for both cases. When less pilot symbols are considered, the loss is more important (>1.4 dB for one pilot every 20 symbols).

For ETU channel (Fig. 10), similar conclusions can be drawn: the loss of energy efficiency is less than 1.0 dB when compared to perfect synchronization and channel estimation.

V. CONCLUSION

Thanks to its performance very close to Shannon's limit and its constant envelope modulation, Turbo-FSK is a waveform that is well adapted to future LPWA systems notably massive machine type communication applications of the fifth generation of cellular systems. However, the impact of synchronization and channel estimation have so far not been considered on the performance of the Turbo-FSK receiver. This paper demonstrated that using preamble and distributed pilot symbols, performance degradation in required energy per information bit due to imperfect synchronization and channel estimation is fairly limited: less than 1dB for AWGN and ETU channels. The preamble and the pilots have been specifically designed to have a constant envelope which is of prime importance for energy efficiency at the transmitter. The preamble has also correlation properties such that the use of extra signaling (SFD) is avoided and CFO is tolerated. This approach is thus particularly well adapted to the selected LPWA scenario.

Future work should consider extension of the presented channel estimation scheme to support mobility scenarios.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Architecture of the Turbo-FSK transmitter.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Preamble structure.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Paquet Error Rate (PER) with synchronization for different preamble lengths, AWGN channel, perfect synchronization is referred as Reference.

Fig. 7 .

 7 Fig. 7. RMSE of channel estimators in ETU channel (perfect synchronization)

Fig. 9 .

 9 Fig. 9. PER for AWGN channel including synchronization, CFO estimation and correction, channel estimation.

Fig. 10 .

 10 Fig. 10. PER for ETU channel including synchronization, CFO estimation and correction, channel estimation.

PER

ACKNOWLEDGMENT

The research leading to these results was supported by the French Agence Nationale de la Recherche (ANR), under grant agreement ANR-16-CE25-0002 (project EPHYL).


Alexis Landrault

Ludovic Pellier

Alexandre Richard

Christian Jay

Michel Robert

Daniel Auvergne

An I.P. Migration and Prototyping Strategy Using Transistor Level Synthesis

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-265 --265 -Abstract-Designers are today facing two challenges of conflicting objectives. In one hand they need to design for optimum performance and in the other hand they need to design in a minimum time frame ("time to market") while using the latest upto-date available technology. It becomes necessary for the designers to very quickly prototype IP blocks for any given technology. This paper describes a new approach based on transistor level layout synthesis for CMOS IP cores rapid prototyping (~100k transistors).

Index Termslayout synthesis, virtual library, prototyping, technology migration, incremental optimization, transistor level, analytical modeling I. INTRODUCTION TANDARD cell libraries have been successfully used for years. However with the emergence of new technologies and the increasing complexity of designs, this concept becomes less and less attractive. Most of the time, cells are too generic and not well suited to the block being created. As a result the final design is not well optimized in terms of timing, power and area. Depending on the target application, today's SoC may need to integrate the same IP block optimised using different criteria's (Platform based design [START_REF] Sangiovanni -Vincentelli | Platform-Based Design: A Path to Efficient Design Re-Use[END_REF], [START_REF] Reinhardt | Implementing a Migration-Based IP-Reuse Strategy[END_REF]). Standard approaches try to resolve this problem by providing the designer with multiple libraries containing cells optimized under specific electrical constraints. As a consequence, IP's generated using such a library will, most of the time, respect one specific constraint but will be over-fitted regarding other constraints. Moreover the development needed for every new technology and the maintenance of these standard libraries are very costly in term of time and in term of human resources . This can seriously impact time -to-market consideration during migration process.

Designers must be able to handle and quickly evaluate the design performance in the newest technology. Fast prototyping enables to increase the control on the trade-off between parameters such as speed, area and power consumption.

In this paper, we describe an investigation towards the use of transistor level layout synthesis to avoid employing a standard cell library and to allow designers to very quickly prototype "application-fitted" IP blocks for any given technology. It avoids the costs due to developing a standard cell library and mostly allows a quick evaluation of the performances of different flavours of a same IP.

The paper is organized as follows. In section II, we describe the standard cell approach and the newly emerg ing flows. In section III, we present our new flow based on transistor level layout synthesis and all the currently developed tools. And finally in section IV, we analyze the results obtained with this new "transistor level layout synthesis" tool called I 2 P 2 before to conclude in section V.

II. DESIGN METHODOLOGIES

A. The standard cell based approach

In the "Standard Cell" flow [START_REF] Mcmillen | An Industrial View of Electronic Design Automation[END_REF], the layout of the design is directly generated from a behavioral description. First, it proceeds to a logical optimization and maps the Boolean equation to the target library. Then after placing and routing all the pieces of layout, representing the individual precharacterized cells, the final layout is generated. The use of standard cells presents a wellunderstood trade-off. On the positive side, a standard cell library normally provides a set of prepackaged functionalities. Each cell is speed and power characterized. Furthermore, the existing industrial EDA tools are relatively well adapted to this approach.

On the other hand some drawbacks appear: • With new UDSM technologies where interconnects are of significant importance. It is more difficult to predict the cell drive and to satisfy the timing constraints. Various iterations are needed between each point-tool of the flow. This can seriously damage the flow convergence. • In fact, it is well known that the quality of designs highly depend on the library that is being used [START_REF] Keutzer | Improving Cell Library for synthesis[END_REF] and of the variety of functionalities and sizes for each primitives gates [START_REF] Keutzer | Impact of Library Size on the Quality of Automated Synthesis[END_REF]. Most of the designers recognize that standard cell libraries are populated with "too generic" cells [START_REF] De Dood | Approach makes most of synthesis, place and route -Liquid Cell ease the flow[END_REF], and that significant improvements can be achieved just by resizing some existing cells (drive continuity) or by adding a few customized cells (design dependency) in the initial library.

B. New alternatives

New emerging approaches are proposed by industrial companies so as to avoid these problems .

• Timing consistency problem is resolved by using tools built around a unified data model [START_REF] Coudert | Physical design closure" Monterey design system[END_REF]: data requirements relative to the physical design can be reached quickly by the tools thanks to this unique data structure.

• Problem concerning "drive continuity" is partly resolved by using the "Liquid Library" [START_REF] De Dood | Putting Automated Libraries into the Flow[END_REF] concept: In this approach, a static base library is used for design synthesis. Then the structural representation is placed and routed. Usually during the optimization step, we notice that some cells of the base library are not well suited to the design. Afterward needed design dependent cells are automatically generated by a "cell Factory" and are Engineering Change Order (ECO) placed (if possible) in the design.

Nevertheless, one main drawback still exists on these approaches : they are based on an already existing target library populated by a few hundred of logic gates specified to satisfy very specific areaperformance tradeoffs. Consequently, the resulting IP block structures are forced to stay within the predetermined library precluding an optimal solution based on the total available design space of the available transistor structures.

Furthermore, the effectiveness of the standard flow methodology is highly dependent on the library development and process migration, which is costly.

III. AN ADAPTIVE LIBRARY CONCEPT BASED ON LAYOUT SYNTHESIS

We propose a standard cell independent based approach, working at transistor level. Theoretically, layout synthesis offers the possibility of overcoming deficiencies of the standard cell approach. The idea is that from a structural HDL description of a circuit, a synthesis tool would generate the optimized layout for the specified technology and timing constraints.

The main motivations for this approach are:

• First to avoid supporting the library and standard cell generation. This dependency is very costly in term of time (around 6 months to develop and characterize a library) and in term of human resources (around 5 people/month) while it only requires less than a day, using I 2 P 2 , to migrate to a new process by creating a new technology file.

• Secondly t his approach enables to work at transistor level. Using the proposed methodology, each transistor can be individually sized or re-sized continuously (no discrete size limitations) at every stage of the flow.

Although this approach is not based on a standard cell library, we have to supply the logical synthesis commercial tool with a functionality set. We call this set the "virtual library". To each function, we associate a virtual cell that can be considered as a set of connected transistors (at symbolic level, no layout generated). Virtual cells appear as an interface between synthesis, place and route and the layout generation. The vast set of functionalities in the virtual library is expected to imply less transistor count in the design.

The proposed flow takes as input a behavioral description of the circuit function (VHDL or Verilog). It is composed of the following steps:

• During the first one a high-level logic synthesis and optimization, and a technology mapping are realized using the virtual library. • A transistor level layout synthesis step, at which the layout of the circuit is generated, using a set of constraints, a structural description of the design and the virtual library as inputs. This includes placement, routing, timing analysis, optimization and physical layout generation.

We develop a tool which achieves this last step. As it is illustrated in the Fig. 1, the "transistor level layout synthesis" tool starts from a structural description of the circuit and generates the layout. This approach is constituted of two major steps.

• The first one consists in creating the virtual cells from their functionality, resulting in an associated transistor network.

• The second phase achieves placement and routing based on physical estimations obtained from the targeted layout style. Timing analysis and optimization is realized during theses two steps. This feature enables, step-by-step, more optimized and refined performance results regarding initial design constraints. Information exchanged between these tools is made through the common data structure as it is shown on the Fig. 2. The physical layout of each row is then automatically generated, with full respect of the technology rules.

The main problems to be addressed in constructing such a flow are as follows. It is firstly necessary to provide a transistor netlist with an optimal number of transistors for the required functionality. Another challenge is to predict and optimize the timing and power characteristics of the circuit before the final layout availability. The last challenge consists in generating a dense layout of the netlist, based on well-specified technology rules.

The main goal of our approach is to deal with all these problems and to converge to the best solution.

Let us now consider in more detail the different steps of this layout synthesis approach.

A. Layout style

As virtual cells don't have predefined layout, it is necessary to deal with layout generation. The chosen style for the transistor-level generation is a variant of the popular "linear-matrix" [START_REF] Lopez | A Dense Gate-Matrix Layout for MOS VLSI[END_REF]. The layout of the circuit is constructed by a sequence of NMOS and PMOS transistor rows. This style is principally characterized by the minimization of the space between the two N and P diffusion zones. Routing is realized over the diffusion zones (gain in terms of area) and avoids the use of metal 2 to save the porosity of each row and to facilitate the routing step.

Fig. 3. Layout Style

This style has been chosen because it's perfectly adapted to software implementation (regular style with vertical placement of the poly grid) [START_REF] Moraes | Pre-Layout Performance Prediction For Automatic Macro-Cell Synthesis[END_REF]. As described on Fig. 3, all the ports are placed at the center between N and P diffusions. Although our choice of topology was initially chosen to generate combinatorial cells, sequential elements such as DFF have been also fully generated using this layout style (more complex style should be used for sequential elements in order to reach quite the same area as standard cells). With respect to this style, a temporary layout can be very quickly generated for each virtual cell needed in the design. This layout used only for the prediction of the cell size and the port location will be then deleted (the final detailed layout of the design will be done only at the very end of the flow). These accurate estimations of the width, the height and the port position will then be used by place, route and timing analysis tools during all the block generation steps.

B. "Virtual Library" a new concept

The synthesis flow presented here is based on virtual libraries, using transistors generated (at symbolic level first to fill the data structure) on the fly instead of using a static set of pre-characterized cells. We have to keep in mind that, at this level, no layout is generated. Layout will be generated only for cell size prediction (temporary and then deleted) and at the very end of the flow (section III-C) at row-level.

The set of cells constituting the "Virtual Library" is mostly composed of complex gates. As a consequence the number of cells available is virtually unlimited (in terms of logical functionality). The constraints are only fixed by the target technology and performance limitations (maximum number of serial transistors).

In addition, as the final layout will be automatically generated, the driving capability of all these "virtual cells" can be continuously adapted, at the contrary of the discrete drive possibility offered in usual standard cell design.

1) Logic Optimization / Technology Mapping: the library free technology-mapping problem concerns the ability to use complex gates instead of using pre-characterized libraries. The main problem with "Virtual Libraries" is that the number of cells available can be very high and we can assume that the logic synthesis commercial tools are not especially well adapted to this kind of library.

In Table 1, we give an illustration of the number of different logic functions available in CMOS technology for a given limitation of N and P transistors in series For instance, for a maximum of four serial transistors (for each plan, N and P) we may dispose of a library with 3503 different functionalities. Moreover, we have a continuous sizing for each logical function that results in an almost infinite number of elements, considering the continuous transistor sizing facility.

Several approaches to realize technology mapping onto Virtual Library have already been proposed [START_REF] Abouzeid | Logic Synthesis for Automatic Layout[END_REF], [START_REF] Reis | The Library Free Technology Mapping Problem[END_REF], either as industrial products or in academic tools. Once the technology mapping on the virtual l ibrary cells has been completed, each logical function is transformed into the corresponding transistor network that is associated to a virtual cell. The network creation consists of generating a BDD for each virtual cell used in the design. Then an optimization of this BDD allows the generation of a transistor netlist for the circuit.

2) Timing & Power Modeling, Transistor Sizing: in this section, we will summarize the problem of timing analysis (already presented in one of our previous work [START_REF] Landrault | A design approach of reusable cores based on transistor level synthesis[END_REF]) using transistor sizing in association with the inherent problem concerning the transistors structure modeling. In [START_REF] Daga | A comprehensive delay macromodeling for submicron CMOS logics[END_REF], [START_REF] Brglez | A Neutral Netlist of 10 Combinatorial Benchmark Circuits and a Target translator in Fortran[END_REF], [START_REF] Auvergne | Signal transition time effect on CMOS delay evaluation[END_REF] it has been shown that it is possible to develop a simple analytical model of the performance of CMOS gates with a good accuracy compared to electrical simulations. An efficient implementation of this model has been integrated. Concerning the problem of transistor sizing, [START_REF] Cremoux | Path Resizing Based on Incremental Technique[END_REF] and [START_REF] Cremoux | Path Selection for Delay and Power Performance Optimization[END_REF] show that for most of the circuits, a local re-sizing of only a few selected transistors in the circuit can significantly reduce the power consumption.

C. Place and Route, Layout generation

The place and route and layout generation tools of the "transistor level layout synthesis" approach have been vastly presented in previous work [START_REF] Landrault | A design approach of reusable cores based on transistor level synthesis[END_REF]. In this section, we will briefly recapitulate the strategy of these tools .

1) Virtual cell Place and Route: placement and routing steps is performed from the "Virtual Cell" structural netlist representation. These operations use the predictive analytical models presented in the previous paragraph and is composed of three steps.

• First, a placement based on an iterative partitioning and global routing between each partition is performed [START_REF] Fiduccia | A linear-time heuristics for improving network partitions[END_REF]. Then cells are placed in each partition to allow rows creation. A global routing step is lastly done to generate virtual channels.

• Secondly, we create the symbolic view of each virtual cell (using the Euler trail solution [START_REF] Riepe | Transistor level microplacement and routing for two dimensional digital VLSI cell synthesis[END_REF]). Afterward the symbolic transistors rows are created then optimized (flipping, merging etc …) and routed ("inner Row" maze routing).

• Finally, all the remaining connections are routed by a virtual channel router using detail routing algorithms (constraint graphs and multi-layer maze router).

2) Layout generation: the layout generation of each row requires as inputs the symbolic view of each row and the technology rules for the targeted process. From a constraint graph, we obtain a "compacted" layout inherent of the "linear-matrix" style. The main advantage offered by this procedure is the technology independence (rules are described in an user file).

IV. RESULTS AND VALIDATION

A. The implementation

As said previously, in order to converge most efficiently during the optimization phase, the architecture of the software prototype is based on a unique data-structure done in C++. This prototype integrates plug and play facilities to ease the exchange of the different "engines" under development

B. Validation strategy

Validations have been done in a 0.13µm CMOS technology. The comparison has been done with respect to the standard flow using an In-House library. We have run our prototype on some industrial and ISCAS85 circuits. We proceed to various comparisons on transistor number (logic synthesis efficiency), transistor density (area), timing and power performances (transistor width) to evaluate our tool.

C. Logic synthesis and associated area

The technology mapping step has been completed using Design Compiler (Synopsys). The number of transistors required in the final netlist is the benchmark metric to evaluate the impact of using a virtual library for the mapping. Moreover we obtain a first estimation of the final circuit area, given by the sum of the cells area. The results given in the Table 2 illustrate the decrease of the number of transistors required to realize the same circuit with our prototype, compared to a standard approach. Actually, the transistor number is decreased by an average of 27 %. Meanwhile the circuit area is not reduced in the same amount (i.e. equivalent area for smallest circuits). The reason is that automatically generated cells are not as small as standard cell.

Standard

D. Flow validation versus standard approach

To evaluate the whole flow of our approach versus the standard approach, we run a set of benchmarks on different circuits that should reach the same timing constraint for both approaches . The benchmark metric is the sum of the transistors width and the final area: As shown in the two tables above, the areas obtained with both methods are similar except for the Mult32 circuit. This degradation is due to the complexity of the place and route step which increases the interconnect length and so impacts the results in area and timing (developed place and route tools are not yet as efficient as commercial ones). The Fig. 4 represents an area and an average transistor width comparison for circuits satisfying almost the same timing constraint:

Standard approach Virtual approach

Average transistor width comparison shows a significant advantage for the presented approach compared to the standard cell implementation (average reduction around 50% improvement). This result shows clearly that the possibility to resize smartly only needed transistor (specific and continuous transistor resizing) allows to significantly reduce the global width of the transistors. As a direct effect, we can expect to obtain a substantial power dissipation reduction compared to standard cell approaches (validation concerning power reduction is currently in progress using commercial power estimation tools ).

Additionally, by reducing the number of transistors required to realize the same circuit (section IV-C), we can expect significant power reduction. Indeed, with new UDSM technologies, leakage current becomes of significant importance even if the transistor is not toggling.

E. Run time analysis

These results concerning area, timing and power are quite encouraging mostly if we consider the facility obtained in generating and migrating macro-blocks in very short time intervals as shown in Table 5 These results, obtained on UltraSparc II 480Mhz machine, strengthen one of the main advantages offered by this approach: the possibility to quickly prototype IP block. Moreover, we remove the time associated to the development of a library and this enables fast technology migration every time a new technology is available.

F. Layout example and migration facilities

On the example given in Fig. 5, a benchmark circuit done in a 0.13µm CMOS technology synthesized with our transistor-level layout generator is presented: We have validated the migration possibilities of our methodology by evaluating the performance of benchmark circuits in new process available. Using I 2 P 2 , it only requires few time to migrate to a new process. Apart from the time necessary to update the technology file (half a day), the circuits have been migrated from one process to another in a very short time as shown in the Table 6.

Circuit

G. Improvement and future work

We pointed out previously that the physical layout generation can strongly impact the final circuit. In fact the results of the comparison between the area of individual virtual cells compared with the standard cells (for the same functionality and the same technology) show almost equivalent results for combinatorial cell but prove a significant difference for sequential element. The high complexity of the intra cell interconnections of the flip-flop and our choice of topology (initially chosen to generate combinatorial cell) can explain this difference that can be overcome by revisiting some of the algorithms of the physical generation.

Moreover, the first validations of our place and route tool versus Magma's highlight some light degradation on complex circuits. Some place and route algorithms should be improved so as to reach the same area as we could get using industrial tools.

V. CONCLUSION

In this paper, we have presented an original alternative to the classical standard cell based layout synthesis. By using a "virtual cell library", we obtain a physical generation at the transistor level, integrating the different steps of physical layout generation, performance estimation and optimization. This may give great facilities in quickly evaluating and prototyping different flavors of IP b locks by using the latest available technology and moreover it removes the time and the prohibitive costs associated to the development of a standard library. We show that our tool which can be seen as an "IP Prototyper" is able to handle simple blocks (order of complexity ~10K to 100k transistors).

Fig. 1 .

 1 Fig.1. I 2 P 2 description.

Fig. 2 .

 2 Fig.2. I 2 P 2 architecture.

Table1.

  Number of logic functions available for a given limitation of serial transistors.

Fig 5 .

 5 Fig 5. Layout of the c3540 (2998 transistors) circuit Fig 4. Area and average transistor width comparison.

I 2 P 2

	Circuit	Transistor number	Area (mm 2 )	Transistor number	Area (mm 2 )
	C3540	3860	0.0061	2998	0,0060
	C5315	4712	0.0095	4518	0,0092
	C6288	9876	0.0151	7424	0,0150
	C7552	7008	0.0116	5902	0,012
	Uniphy	30168	0.0473	13952	0,026
	Mult32	47586	0.0785	40354	0.086

Table 2 .

 2 Logical synthesis and associated area.

Table 3 .

 3 Standard flow results

	Circuit	Average transistors width (µm)	Area (mm 2 )	Density (tr/mm 2 )	Timing performances (ps)
	C3540	0.957	0.008	374750	1653
	C5315	0.869	0.013	362462	1736
	C6288	0.832	0.020	371200	5389
	C7552	0.855	0.016	368880	3474
	Uniphy	1.003	0.065	214650	1773
	Mult32	0.851	0.104	388020	9312
	Circuit	Average transistor width (µm)	Area (mm 2 )	Density (tr/mm 2 )	Timing performances (ps)
	C3540	0.357	0.0072	416390	1690
	C5315	0.308	0.013	347540	1650
	C6288	0.459	0.018	412450	4870
	C7552	0.347	0.016	368880	2030
	Uniphy	0.486	0.031	450060	1850
	Mult32	0.368	0.119	339110	12930

Table 4 .

 4 I 2 P 2 flow results

Table 5 .

 5 : I 2 P 2 tools: run time

	Circuit	Transistors count	Run time (mn)
	C3540	2998	3
	C5315	4518	5
	C6288	7424	8
	C7552	5902	6
	Uniphy	13952	15
	Mult32	40354	65

Table 6 .

 6 I 2 P 2 migration from 0.18µm to 90nm.

		Density (tr/mm 2 )	Density (tr/mm 2 )	Density (tr/mm 2 )	Time needed
		0.18 um	0.13 um	90 nm	(min)
	C3540	199870	416390	832780	3
	C5315	173770	347540	728950	5
	C6288	206220	412450	857170	8
	C7552	190390	368880	725690	6
	Uniphy	211393	450060	872000	15
	Mult32	184270	339110	733710	65

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