M.D Jebrane Bouaoud
email: jebrane.bouaoud@gmail.com

Matthieu Olivetto

Sylvie Testelin

Stephanie Dakpe

Jeremie Bettoni

Bernard Devauchelle

Fraser syndrome: review of literature illustrated by an historical adult case

Keywords: Fraser syndrome, cryptophthalmos, syndactyly, Rare conditions Genetic, autosomal recessive

Fraser syndrome (cryptophthalmos-syndactyly syndrome) is a rare autosomal recessive malformation disorder. The first description of the syndrome was reported by George Fraser in 1962. The diagnostic is based on major criteria and minor criteria established by van Haelst et al., In 2007. Unilateral or bilateral cryptophthalmos, syndactyly, unilateral renal agenesis and genital anomalies are the most frequent anomalies. Several maxillofacial, oro-dental, ear-nose-throat, hormonal and anorectal disorders are reported. Cardiac malformations, and musculoskeletal anomalies are uncommon. The syndrome id related to mutations in three different genes (FRAS1, FREM2, and GRIP1) resulting in failure of the apoptosis program and disruption of the epithelial-mesenchymal interactions during embryonic development. Prenatal diagnosis is based on detection of renal agenesis and laryngeal atresia together with a family history. Most of the fetuses with severe anomalies are terminated or resulted in stillbirth. All patient or pregnancy with a diagnosis of FS should be referred to expert centers. For the management, a collaborative approach of anesthetists, ENT, maxillofacial surgeons, geneticists is necessary. In vivo and in vitro research models are available to better understand the underlying etiology.

Introduction

Fraser syndrome (FS), also known as cryptophthalmos-syndactyly syndrome (OMIM #219000, http://omim.org/entry/219000), is an autosomal recessive malformation disorder. This Syndrome is characterized by cryptophthalmos, syndactyly, and abnormalities of the respiratory and urogenital tract [START_REF] Fraser | Our genetical 'load'. A review of some aspects of genetical variation[END_REF][START_REF] Slavotinek | Fraser syndrome and cryptophthalmos: review of the diagnostic criteria and evidence for phenotypic modules in complex malformation syndromes[END_REF][3] . The diagnostic is established by clinical examination and is based on major criteria (cryptophthalmos; syndactyly; ambiguous genitalia, urinary and respiratory tract anomalies and an affected sibling) and minor criteria (congenital nose and ears malformations; skull ossification defects; Anorectal anomalies and umbilical hernia) 3,[START_REF] Thomas | Isolated and syndromic cryptophthalmos[END_REF] . While FS shows an interfamilial highly variable phenotype ranging from minor symptoms to lethal malformations like renal agenesis, there is a strong phenotypic similarity exists within a family 3 .

Numerous case reports of FS are published in literature since the first description of the syndromic association of cryptophtalmos-syndactily by George Fraser in 1962 [START_REF] Fraser | Our genetical 'load'. A review of some aspects of genetical variation[END_REF] . Most of them are clinical descriptions of fetuses from terminated pregnancy or stillbirth. The few reports of alive patients are usually pediatric cases.

Here, we provide a review of the epidemiology, the clinical presentation, the management, the physiopathology and the genetics of this syndrome especially for head and neck disorders. This review is supported by one new historical case of an adult patients with FS, never published before and managed by the maxillofacial Surgeon General Gustave Ginestet [START_REF] Brue | Gustave Ginestet (1897-1966), doctor general. Life and work of a pioneer of cosmetic and reconstructive maxillofacial surgery[END_REF]6 before the first publications of FS by George Fraser in 1962.

Epidemiology and survival

FS is a rare disorder. A large epidemiological study in a European population showed a minimal estimated prevalence of 0.2 cases of FS per 100 000 births and statistically more cases in west part of Europe compared to the rest of Europe (p=0.0003) [START_REF] Barisic | Syndrome: Epidemiological Study in a European Population[END_REF] . This prevalence represents a minimal estimate given that most of the fetuses with severe anomalies were terminated or resulted in stillbirth without syndrome diagnosis [START_REF] Barisic | Syndrome: Epidemiological Study in a European Population[END_REF] . Regarding alive patients with FS, 25% die within the first year of life, in most cases due to airways or urinary tract anomalies [START_REF] Boyd | Fraser syndrome (cryptophthalmos-syndactyly syndrome): a review of eleven cases with postmortem findings[END_REF] . Only n=3 FS patient's aged more than 20 years old are published in literature (Table1) [START_REF] Slavotinek | Fraser syndrome and cryptophthalmos: review of the diagnostic criteria and evidence for phenotypic modules in complex malformation syndromes[END_REF][START_REF] Impallomeni | Fraser syndrome in a 96year-old female[END_REF][START_REF] Zhang | Cryptophthalmos: a report on three sibling cases[END_REF] . At all, the prognosis for survival in individuals born with this condition is in general poor [START_REF] Fraser | Syndrome: Two millennia of cryptophthalmos from Pliny the Elder to FRAS, FREM and GRIP: A historical perspective[END_REF][START_REF] Comstock | Prenatal Death in Fraser Syndrome[END_REF] .

Clinical presentation and diagnosis

Diagnostic criteria

In 1986 Thomas et al., were the first authors to report the criteria establishing the diagnosis of FS [START_REF] Thomas | Isolated and syndromic cryptophthalmos[END_REF] .

In 2007, after analyzing 59 cases of FS, van Haelst and the Fraser Syndrome Collaboration Group have confirmed the clinical utility of these criteria and included the airway tract and urogenital anomalies in the major criteria whereas mental retardation and clefts were removed from this list 3 (table 2). At all, FS can be diagnosed, if two major and one minor criteria or one major and four minor criteria are present 3 . All studies agreed that there was marked clinical variability and that none of the major criteria are mandatory for diagnosis. For some authors, within a family, the phenotype and the degree of severity of the disease are strongly concordant [START_REF] Abdalla | Fraser syndrome: Phenotypic variability and unusual findings in four Egyptian families[END_REF] .

Clinical presentation

The frequency of the most reported congenital anomalies in published Series of FS are summarized in table 3 [START_REF] Slavotinek | Fraser syndrome and cryptophthalmos: review of the diagnostic criteria and evidence for phenotypic modules in complex malformation syndromes[END_REF][3][START_REF] Thomas | Isolated and syndromic cryptophthalmos[END_REF][START_REF] Barisic | Syndrome: Epidemiological Study in a European Population[END_REF][START_REF] Gattuso | The clinical spectrum of the Fraser syndrome: report of three new cases and review[END_REF][START_REF] Eskander | Fraser syndrome: a new case report with review of the literature[END_REF] . Unilateral or bilateral cryptophthalmos, syndactyly, unilateral renal agenesis and genital anomalies are the most frequent anomalies reported in literature. Apart cryptophtalmos other maxillofacial and oro-dental findings reported are facial asymmetry, upward slanting palpebral fissures, hypertelorism, tongue of hair extending from the anterior hairline to the forehead, the eyebrows and the upper-outer edge of the orbit, broad nose and/or nasal bridge (8-84%), short neck, cleft lip and palate (11%), high arched palate (12%), malocclusion, dental crowding, fusion of primary teeth, dental hypoplasia, supragingival calculus, microdontia, retained deciduous teeth, hypodontia and short roots 2,16-18 (Figure1a and 1b). Airway disorders (laryngeal compromise) are found in 21-83% of the cases of FS [START_REF] Alvaréz-Neri | Airway features in Fraser syndrome: Case report and literature review[END_REF] . Subglottic stenosis and laryngeal webs or laryngotracheal atresia are the most frequent laryngotracheal disorder. Other rare ear-nose-throat anomalies are malformed and/or low set ears, meatal stenosis or dysplastic pinna and hypoplastic notched nares or choanal stenosis or atresia [START_REF] Ford | ENT manifestations of Fraser syndrome[END_REF] .

FS is classed among the hormonal disorders of sex development caused by hypogonadism [START_REF] Hutson | Malformation syndromes associated with disorders of sex development[END_REF] .

Reported genital anomalies are cryptorchidism and pseudo hermaphroditism for males and masculinization of the external genitalia in females with clitoral hypertrophy, vaginal atresia, labial fusion and gonadoblastoma [START_REF] Frazer | XX CHROMOSOMES AND RENAL AGENESIS[END_REF][START_REF] Greenberg | Gonadal dysgenesis and gonadoblastoma in situ in a female with Fraser (cryptophthalmos) syndrome[END_REF] . Among anorectal disorders, anal atresia/stenosis are the most common. Colonic atresia, diastema of the pubic symphysis, displacement of the umbilicus and common mesentery have also been reported to illustrate abdominal anomalies associated with FS [START_REF] Narang | Fraser-cryptophthalmos syndrome with colonic atresia[END_REF] .

Cardiac malformations, and musculoskeletal anomalies are uncommon 7 . A part syndactyly, musculoskeletal abnormalities associated with FS include skull ossification defect, diastasis of the pubic symphysis, bilateral hip dysplasia and genu valgum [START_REF] Price | The Presence of Bilateral Hip Dysplasia and Genu Valgum in Fraser Syndrome[END_REF] .

Complementary exam

The diagnosis of FS is based on the clinical exam. Complementary exams are realized to research organ malformations. An abdominal echography is realized to investigate the urinary and genital tracts. Skull ossification defects are evaluated with radiographies and/or CT-scan (computerized tomography).

Physiopathology and genetics

FS is an autosomal recessive malformation disorder [START_REF] Francannet | Fraser syndrome with renal agenesis in two consanguineous Turkish families[END_REF] . The incidence of consanguinity in families with FS is estimated reaching 15% to 30% [START_REF] Slavotinek | Fraser syndrome and cryptophthalmos: review of the diagnostic criteria and evidence for phenotypic modules in complex malformation syndromes[END_REF][START_REF] Thomas | Isolated and syndromic cryptophthalmos[END_REF][START_REF] Barisic | Syndrome: Epidemiological Study in a European Population[END_REF][START_REF] Martínez-Frías | Fraser syndrome: frequency in our environment and clinical-epidemiological aspects of a consecutive series of cases[END_REF] . This syndrome seems to be related to a failure of the apoptosis program and to the formation of large blisters during embryonic development due to defects in epidermal adhesion (disruption of the epithelial-mesenchymal interactions) [START_REF] Short | Let's stick together: the role of the Fras1 and Frem proteins in epidermal adhesion[END_REF][START_REF] Pavlakis | The role of Fras1/Frem proteins in the structure and function of basement membrane[END_REF][START_REF] Hines | Syndactyly in a novel Fras1rdf mutant results from interruption of signals for interdigital apoptosis[END_REF] . Indeed, in embryos, the Fraser complex (FC) mediates epithelial-connective tissue interactions. This complex is composed of the Fras1/Frem family of Extra Cellular Matrix proteins [START_REF] Pavlakis | The role of Fras1/Frem proteins in the structure and function of basement membrane[END_REF] . These proteins have also been reported to mediate both the initiation of the mammalian kidney and glomerular maturation and integrity [START_REF] Pitera | Fras1, a basement membrane-associated protein mutated in Fraser syndrome, mediates both the initiation of the mammalian kidney and the integrity of renal glomeruli[END_REF][START_REF] Pitera | Generation of mice with a conditional null fraser syndrome 1 (Fras1) allele[END_REF] . At all, Loss of expression of FC components leads to FS [START_REF] Hiroyasu | A New Component of the Fraser Complex[END_REF] .

Mutations in three different genes (FRAS1, FREM2, and GRIP1) have been identified causing FS [START_REF] Van Haelst | Molecular study of 33 families with Fraser syndrome new data and mutation review[END_REF][START_REF] Mcgregor | Fraser syndrome and mouse blebbed phenotype caused by mutations in FRAS1/Fras1 encoding a putative extracellular matrix protein[END_REF][START_REF] Jadeja | Identification of a new gene mutated in Fraser syndrome and mouse myelencephalic blebs[END_REF][START_REF] Shafeghati | Fraser syndrome due to homozygosity for a splice site mutation of FREM2[END_REF][START_REF] Vogel | Mutations in GRIP1 cause Fraser syndrome[END_REF][START_REF] Schanze | Fraser syndrome due to mutations in GRIP1-Clinical phenotype in two families and expansion of the mutation spectrum[END_REF] .

Fraser syndrome-1 (FRASRS1) is caused by homozygous or compound heterozygous mutation in the FRAS1 gene (Fraser extracellular matrix complex subunit 1, OMIM * 607830) on chromosome 4q21. At all, 27 mutations of FRAS1 gene have been reported [START_REF] Hoefele | Expanding the mutation spectrum for Fraser syndrome: identification of a novel heterozygous deletion in FRAS1[END_REF][START_REF] Nayak | Variable presentation of Fraser syndrome in two fetuses and a novel mutation in FRAS1[END_REF] . Most of them are truncating mutations.

The mutational spectrum includes nucleotide substitutions, splicing defects, a large insertion, small deletions/insertions and a recently reported large deletion.

Fraser syndrome-2 (FRASRS2) is caused by mutation in the FREM2 gene (FRAS1 related extracellular matrix protein 2, OMIM * 608945) on chromosome 13q13.

Fraser syndrome-3 (FRASRS3) is caused by mutation in the GRIP1 gene (glutamate receptor interacting protein, OMIM * 604597) on chromosome 12q14.

Prenatal diagnosis

Renal anomalies, syndactyly and cryptophtalmos are present in more than 90% of cases of prenatal and postnatal fetal phenotype. However, they are rarely found on prenatal ultrasound because oligohydramnios, which is frequent, hampers the prenatal recognition of the cardinal FS diagnosis criteria [START_REF] Tessier | Fraser syndrome: features suggestive of prenatal diagnosis in a review of 38 cases[END_REF][START_REF] Bernardo | Prenatal diagnosis of Fraser syndrome: a matter of life or death?[END_REF] . Thus, prenatal diagnosis of FS is often based on detection of some of the more easily detectable minor criteria, such as renal agenesis and laryngeal atresia, together with a family history.

Aside from the presence of oligohydramnios, prenatal diagnosis can be sometimes challenging to establish especially if no previous child is affected [START_REF] Rousseau | Prenatal diagnosis and intrafamilial clinical heterogeneity of Fraser syndrome[END_REF][START_REF] Berg | Prenatal detection of Fraser syndrome without cryptophthalmos: case report and review of the literature[END_REF] .

The prognosis of pregnancies with FS is poor and dependent on the predominant anomalies.

Termination of pregnancy may be recommended when diagnosis is made early, especially in the setting of renal agenesis or laryngeal atresia [START_REF] Tuuli | Odibo AO. 128 -Fraser Syndrome[END_REF] . In European countries, a large proportion of pregnancies in this situation, up to 82% of cases, are medically interrupted. In all cases, prenatal diagnosis of FS should be guided by a genetic counselling [START_REF] Fraser Syndrome | Atlas of Genetic Diagnosis and Counseling[END_REF] .

Molecular diagnosis

The antenatal and post-natal diagnosis of FS could be realized by targeted sequencing of a panel of genes including FRAS1, FREM2 and GRIP1 genes [START_REF] Kornacki | Prenatal diagnosis of Fraser syndrome using routine ultrasound examination, confirmed by exome sequencing: Report of a novel homozygous missense FRAS1 mutation[END_REF] .

Management of head and neck disorders

General management

All patient or pregnancy with a diagnosis of FS should be referred to expert centers (https://www.orpha.net/consor/cgi-bin/Clinics_Search.php?lng=EN) [START_REF] Fraser Syndrome | Atlas of Genetic Diagnosis and Counseling[END_REF] . A Collaborative approach of experts' anesthetists, ENT, maxillofacial surgeons, geneticists is necessary.

Anesthesia

Although low incidence of complications was reported for general anesthesia in FS patients, all were related to the management of airways. Indeed, after reviewing n=125 general anesthesia for FS patients, Mathers et al., reported a high incidence (20%) of difficult or impossible tracheal intubation due to glottic stenosis [START_REF] Mathers | Delivery of anesthesia and complications for children with Fraser syndrome: a review of 125 anesthetics[END_REF] .

Airways

Airway compromises represent a risk factor for death in infancy and early childhood, and appropriate management may be difficult due to the high incidence of recurrence, especially in the case of laryngeal webs [START_REF] Alvaréz-Neri | Airway features in Fraser syndrome: Case report and literature review[END_REF][START_REF] Somme | Prenatal Assessment and Perinatal Management of Suspected Airway Compromise in the Fetus and Neonate[END_REF][START_REF] Izadi | Fraser syndrome with laryngeal webs: Report of two cases and a review of the literature[END_REF] . Tracheostomy at birth could be necessary to keep the airway and preserve the patient's life [START_REF] Crowe | Impossible laryngeal intubation in an infant with Fraser syndrome[END_REF] . In other cases, laryngotracheal alterations should be researched to anticipate a difficult/impossible intubation [START_REF] Okumus | Resuscitation failure due to Fraser syndrome in a newborn undiagnosed in the prenatal period[END_REF] . Direct laryngoscopy can be realized to evaluate the severity of glottic web according to Cohen's classification [START_REF] Cohen | Congenital glottic webs in children. A retrospective review of 51 patients[END_REF] and subglottic stenosis according to the Cotton-Myer scale [START_REF] Myer | Proposed grading system for subglottic stenosis based on endotracheal tube sizes[END_REF] . Endoscopic airway measurement combining optical endoscopic instruments with open source image processing can also be useful to accurately obtain airway dimensions [START_REF] Francom | Clinical validation and reproducibility of endoscopic airway measurement in pediatric aerodigestive evaluation[END_REF] . All cases should be personalized managed. Although no guidelines can be given due to the small number of cases published in the literature, the cricotracheal resection seems to be an adequate alternative for surgical management in glottic-subglottic stenosis and severe laryngeal webs [START_REF] Alvaréz-Neri | Airway features in Fraser syndrome: Case report and literature review[END_REF] .

Ophthalmic malformations

Cryptophtalmos

Cryptophthalmos, especially the eyelid defect, represents a challenge in surgical reconstruction and visual rehabilitation [START_REF] Sullivan | Eyelid and fornix reconstruction in bilateral abortive cryptophthalmos (Fraser syndrome)[END_REF] . Saleh et al., published in 2009 a series of 13 eyes from 7 patients with FS with the aim to optimize visual potential for these patients [START_REF] Saleh | A surgical strategy for the correction of Fraser syndrome cryptophthalmos[END_REF] . The cryptophthalmos was complete in 3 eyes and abortive in 10 eyes. They concluded that the periocular surgical management of these type of complex cases should be planned using a systematic approach. Surgical steps should include dissection of corneal adhesions from keratinized cornea, mucous membrane graft, Mustarde eyelid switch flap with subsequent division, and further lower lid augmentation as required. Lessa et al., presented in 2011 present a two-stage surgical reconstruction procedure for correction of the upper eyelid and ocular bulb anomalies in cryptophthalmos (Mustardé's technique with fixation of the lower eyelid transposed flap to the levator muscle) [START_REF] Lessa | Two-stage reconstruction for eyelid deformities in partial cryptophthalmos[END_REF] .

Lacrimal system dysgenesis and dacryocystoceles

Syndromic congenital nasolacrimal duct obstructions are not very common in FS patients [START_REF] Ali | Lacrimal Drainage Anomalies in Fraser Syndrome[END_REF] . Nasal endoscopic endonasal evaluation should be realized to research dacryocystoceles and realize drainage and marsupialization if necessary [START_REF] Falls | Endoscopic Management of Lacrimal System Dysgenesis and Dacryocystoceles in Fraser Syndrome: A Case Report and Literature Review[END_REF] .

Dental care

Self-dental cares can be difficult and/or impossible for FS patients especially when a mental retardation is present. Furthermore, cardiac abnormalities have been observed in 6 to 13% patients with FS 2,7 . Thus, FS patients have a predisposition to infective endocarditis [START_REF] Hassona | Oral healthcare in Fraser syndrome[END_REF] . Moreover, it seems to be an association between the presence of dental plaque, periodontal disease, and chronic lung disease (especially pneumonia). Therefore, the establishment of oral health protocols with a goal of reducing the biofilm is essential. The dentists should realize the periodontal treatment with the clinical use of chlorhexidine and Povidone-iodine (PVP-I) [START_REF] De Oliveira | Fraser Syndrome-Oral Manifestations and a Dental Care Protocol[END_REF] . The rehabilitation of occlusion with for example the placement of dental implants should be favorised [START_REF] Gallottini | Oral manifestations and rehabilitation in Fraser syndrome: A case report[END_REF] .

Research model for FS

In vivo/animal models

The bl ('blebbed') mouse model (http://omim.org/entry/219000) In 1990, in a letter to the editors, Winter hypothesized that FS in human might be homologous to one of the mouse 'bleb' mutants phenotype [START_REF] Winter | Fraser syndrome and mouse "bleb" mutants[END_REF] . Few years later in 1994, the genetic background of this 'blebbed' murine phenotype, has been more characterized by Darling and Gossler, especially the mutations in at least 5 loci, including bl [START_REF] Darling | A mouse model for Fraser syndrome?[END_REF] .

Then two major events confirmed that the bl mouse is a model for FS in humans. Firstly, the screening of the DNA from bl/bl mice and the identification of a mutation in the Fras1 gene that resulting in premature protein termination [START_REF] Mcgregor | Fraser syndrome and mouse blebbed phenotype caused by mutations in FRAS1/Fras1 encoding a putative extracellular matrix protein[END_REF] . Second, the demonstration that Fras1 deficiency (bl/bl homozygous embryos) results in cryptophthalmos, renal agenesis and blebbed phenotype in mice [START_REF] Vrontou | Fras1 deficiency results in cryptophthalmos, renal agenesis and blebbed phenotype in mice[END_REF] .

Given these elements, the authors concluded the perturbation in the composition of extracellular space underlying epithelia by loss of Fras1 function characterize the blebbed phenotype in mice and FS in humans.

Regarding the implication of GRIP1 in the FS, Takamiya et al., showed in 2004 that Grip1 is required for normal cell-matrix interactions during early embryonic development and that there is a direct functional link between the multi-PDZ domain protein GRIP1 and Fras1 66 . In 2006, Kiyozumi et al., report that Frem1 (FRAS1 related extracellular matrix protein 1, OMIM * 608944), Fras1, and Frem2 proteins are localized to the basement membrane, and that their basement membrane localization is simultaneously impaired in FS model mice (Grip1-mutant 'eye blebs' mice) [START_REF] Kiyozumi | Breakdown of the reciprocal stabilization of QBRICK/Frem1, Fras1, and Frem2 at the basement membrane provokes Fraser syndrome-like defects[END_REF] .

The Frem2 gene was reported as a cause of FS not linked to FRAS1 by Jadeja et al., in 2005 after performing linkage analysis in the 'myelencephalic blebs' (my) mice [START_REF] Jadeja | Identification of a new gene mutated in Fraser syndrome and mouse myelencephalic blebs[END_REF] . This model showed a phenotype similar to that of Fras1-mutant mice. At all, an article published in 2005 by Smyth and Scambler reviews the genetics of FS and of its homologs in the blebs mouse mutants [START_REF] Smyth | The genetics of Fraser syndrome and the blebs mouse mutants[END_REF] .

The fused pulmonary lobe 'fpl' mutant rat model

Fused pulmonary lobes (fpl) mutant rats exhibit similar phenotypes to FS [START_REF] Aoyama | Heritable pulmonary lobation anomaly in the rat[END_REF] . Based on this observation, Kiyozumi et al., have sequenced the DNA of the fpl/fpl mutant mice. They found that the fpl gene harbors a nonsense mutation that introduced a stop codon in FS-associated gene Frem2.

Thus, the Fpl mutant was defined as a first rats model of human FS [START_REF] Kiyozumi | Fused pulmonary lobes is a rat model of human Fraser syndrome[END_REF] .

Zebrafish model

Zebrafish seems to be an ideal genetic model to understand the pathology and the genetic heterogeneity underlying FS [START_REF] Hiroyasu | A New Component of the Fraser Complex[END_REF] . In 2011, Talbot et al., have shown that zebrafish fras1 mutants exhibit defects in facial epithelia and facial skeleton which participated to the comprehension of the developmental basis of facial defects in FS [START_REF] Talbot | fras1 shapes endodermal pouch 1 and stabilizes zebrafish pharyngeal skeletal development[END_REF] . The potential involvement of several other genes such as Hemicentin1 (HMCN1), Furin, and Fibrillin2 that interact in basement membrane anchorage has been proposed based on the study of zebrafish, suggesting further genetic heterogeneity for FS [START_REF] Carney | Genetic analysis of fin development in zebrafish identifies furin and hemicentin1 as potential novel fraser syndrome disease genes[END_REF] .

Zebrafish have also allowed the identification of novel component of the FC complex (the protein AMACO, an extra cellular matrix protein encoded by the VWA2 gene) [START_REF] Richardson | AMACO is a novel component of the basement membrane associated Fraser complex[END_REF] .

In vitro model

Four human cell lines derived from male FS patients are proposed by the Coriell Institute for Medical Research (New Jersey, United Stated, https://www.coriell.org/OmimNum:219000; Table 4).

New historical case of adult FS

Presentation

We report the case of an adult untreated patient with FS from the personal collection of the Surgeon General Gustave Ginestet and never published before. This patient presented some malformations classically described in the syndrome but also some specific maxillofacial characteristics. The patient presented bilateral complete cryptophthalmos, bilateral coloboma of eyelid, bilateral and asymmetric cleft (on the right side the cleft was complete reaching the lip, the maxillary and palate while the cleft was limited to the lip on the left side), short philtrum. Nasal anomalies were a broad nose with midline groove towards the tip, hypoplastic nasal alae and widely set nostrils. The other maxillofacial disorders were facial asymmetry, musculo-skeletal abnormalities (hypoplasia of orbital bones), hypertelorism, a tongue of hair extending from the anterior hairline to the forehead, the eyebrows and the upper-outer edge of the orbit, a short neck, upward slanting palpebral fissures.

The dental exam found dental hypoplasia and microdontia (Fig1a, 1b).

Maxillofacial management

This patient was surgically managed by the maxillofacial surgeon General Gustave Ginestet. Thus, he was operated several times (multi-step strategy) for its maxillofacial disorders before the first description of cryptophtalmos-Syndactily syndrome by George Fraser in 1962 1 (Fig1c, 1d and Fig2).

Firstly, the patient was operated to repair the bilateral cleft with primary cheiloplasty and rhinoplasty (Fig 1c ,1d). Then, several other rhinoplasties and cheiloplasties were realized (Fig2). Briefly, bilateral local foreheads, orbital flaps were prepared and progressively modified until allowing reconstruction of the nasal base with the two nostrils, the tip and the supra tip. The final result is very interesting (Fig2c, 2d)."

Conclusion

Fraser syndrome (FS) was first described in 2 pairs of siblings by George Fraser in 1962. To date, more than 250 patients have been described in the literature. The clinical variability associated with FS supports the genetic heterogeneity of the syndrome. To our knowledge, there have been only n=3 previously reported cases of a patient fulfilling the diagnostic criteria for FS and surviving over the age of 20 years. Numerous clinical trials and research models are available to better characterize this syndrome in clinical, pathophysiological and genetic terms. Gustave Ginestet before the first publications of FS by George Fraser in 1962. 1a and 1b: The patient presented some maxillofacial malformations classically described in the FS: bilateral complete cryptophthalmos, bilateral coloboma of eyelid, the eyebrows and the upper-outer edge of the orbit, upward slanting palpebral fissures, a tongue of hair extending from the anterior hairline to the forehead, facial asymmetry, hypertelorism, bilateral and asymmetric cleft (on the right side the cleft was complete reaching the lip, the maxillary and palate while the cleft was limited to the lip on the left side), short philtrum, a short neck. Nasal anomalies were a broad nose with midline groove towards the tip, hypoplastic nasal alae and widely set nostrils. Dental anomalies were dental hypoplasia and microdontia. All these elements are particularly suggestive of the FS; 1c and 1d: bilateral cleft repair with primary cheiloplasty and rhinoplasty. (FS: Fraser Syndrome)

Figure and table legends

Figure 1 .

 1 Figure 1. Historical case of an adult patient surgically managed by the maxillofacial surgeon General

Figure 2 .

 2 Figure 2. Multi step surgical strategy realized by the maxillofacial surgeon General Gustave Ginestet

Table 1 .

 1 Adult cases (age>20 years old) of Fraser Syndrome reported in literature. (NA: non-available)

Table 2 .

 2 Diagnostic criteria for Fraser syndrome published by Van Haelst et al.,2007.

Table 3 .

 3 Frequency of the most reported congenital anomalies for published series of patient with Fraser syndrome.

Table 4 .

 4 Human cell lines derived from male FS patients proposed by the Coriell Institute for Medical Research (New Jersey, United Stated, https://www.coriell.org/OmimNum:219000) (LCL: Lymphoblastoid Cell lines; DNA: deoxyribonucleotidic acid; YR: years; FW: fetal weeks).

Acknowledgments

The authors thank the French association of face surgeons "AFCF: Association Française des Chirurgiens de la Face" for giving opportunity to study the Surgeon General Gustave Ginestet archives.

All

authors have viewed and agreed to the submission.

Key historical events

The first description of the cryptophtalmos-syndactily syndrome was reported in 2 pairs of siblings by George Fraser in 1962 [START_REF] Fraser | Our genetical 'load'. A review of some aspects of genetical variation[END_REF] . Several key events have contributed to this description. In 79 AD, Pliny the Elder (Gaius Plinius Secundus) reports in his Book VII of his "Naturalis Historia" the observation of a couple having three children born with an eye covered by a skin membrane [START_REF] Fraser | Syndrome: Two millennia of cryptophthalmos from Pliny the Elder to FRAS, FREM and GRIP: A historical perspective[END_REF][START_REF] Plinius | Pliny the Elder)[END_REF] . This is the first report of "hidden eyes" with a family history. In 1872, Zehender and Manz introduced for the first time the term cryptophthalmos ("hidden eye") to describe the case of a six-month old girl [START_REF] Manz | Eine missgeburt mit hautüberwachsenen augen oder kryptophthalmus[END_REF] . In 1902, Golowin reports the first case of an alive adults with cryptophthalmos and having an affected sister [START_REF] Golowin | Beiträge zur Anatomie und Pathogenese des Kryptophthalmus congenitus[END_REF] .

In 1906 Asayama reported consanguine mice with cryptophthalmos which can be regarded as the first cases of the blebbing mutants in mice [START_REF] Asayama | Vererbung von kryptophthalmus[END_REF] . The older literature on cryptophthalmos with associated malformations was reviewed by Duke-Elder in 1963 [START_REF] Duke-Elder | Normal and Abnormal Development[END_REF] .


Julien Mazuet
email: julien.mazuet@univ-ubs.fr

Michel Narozny

Catherine Dezan

Jean-Philippe Diguet

A seamless DFT/FFT self-adaptive architecture for embedded radar applications

Keywords: FPGA, DPR, radar, QoS, DFT

Radar is one of the domains where adaptability is paramount and algorithms must be adapted to system state. However, most systems include static implementations on FPGA or ASIC to process the massive amount of data from multiple sensors in parallel. The classic approach is to configure hardware logic through registers to switch radar modes, requiring to hardwire all configurations. In embedded systems, FPGA dynamic partial reconfiguration (DPR) is a promising solution to reuse scarce resources. In this paper, we use DPR for radar processing in order to switch between a classic discrete Fourier transform (DFT) sum and a fast Fourier transform (FFT) to enhance Doppler extraction. Our study explores the pros and cons of both methods. Based on these observations, we propose a new architecture and decision method that relies on Radar QoS for enabling an efficient self-adaptive solution. Finally, we provide a case study and a hardware-in-loop simulation with a reconfigurable radar implementation.

I. INTRODUCTION

Modern embedded radar applications require high performance architectures. This point is specially critical in small aircraft and unmanned aerial vehicles. But a radar system can inherently leverage data parallelism, which can be efficiently implemented on a FPGA [START_REF] Yang | Implementation architecture of signal processing in pulse Doppler radar system based on FPGA[END_REF]. For instance, active electronically scanned array (AESA) radar have multiple channels which can be processed independently by HW accelerators [START_REF] Rao | Digital beam former architecture for sixteen elements planar phased array radar[END_REF]. Besides, these applications have strong performance and latency constraints. Furthermore, a radar system has different modes [START_REF] Chamouard | Radars aéroportés multifonctions[END_REF], like high pulse recurrence frequency (PRF) and low PRF, or more complex modes like search and tracking or airair and air-ground. These modes have different motivations and requirements. The mode adaptation is often ensured by runtime software adaptation and hardware reconfigurations through dedicated registers. However, this approach means that configurations are simultaneously implemented within the same programmable logic (PL). Important configuration changes result in the PL overuse. Consequently, designers must limit the performances of the target algorithms to fit with available PL resources. In that perspective, using DPR appears as a promising solution. However, this approach requires a specific methodology to allow an efficient collaboration between application experts who can determine the algorithm choices and specify the reconfiguration decision making with hardware experts who can design highly optimized architectures using CAD tools. In this work we apply this methodology to design the first solution that fully benefit of FFT and DFT compliant configurations to mitigate the tradeoff between resolution and latency according to user requirements.

Section II presents a state of the art on DFT in the radar domain, and the use of reconfiguration. Section III details the DFT algorithm in the context of radar systems and explains the two main methods to compute it. Section IV proposes a methodology to take efficient reconfiguration decisions at runtime. A methodology to create an adaptive reconfigurable DFT for radar, is described in section V. Section VI shows and comments the results obtained through a hardware in the loop (HIL) implementation on a case study. Section VII concludes the paper and draws directions for future work.

II. STATE OF THE ART

Reconfigurable FPGA have been strongly used to efficiently implement signal processing applications [START_REF] Tessier | Reconfigurable Computing Architectures[END_REF] but few works have addressed the question of radar [START_REF] Seguin | A Dynamically-Reconfigurable Phased Array Radar Processing System[END_REF]- [START_REF] Harb | Dynamically reconfigurable architecture for a driver assistant system[END_REF]. In radar tracking systems, the environment is composed of targets, clutter and other perturbations, which can be characterized by computing a range-Doppler map of the radar signal (i.e. a discrete version of the time-frequency analysis first described in [START_REF] Ville | Theory and Applications of the Notion of the Analytic Signal[END_REF]). In practice, this function is composed of a matched filter and a series of Fourier transforms. This transform is the core of our study, it can be performed with different methods [START_REF]Chapter 17: Doppler Processing[END_REF]. The main methods are the FFT [START_REF] Lush | Airborne radar analysis using the ambiguity function[END_REF], [START_REF] Klilou | Real-time parallel implementation of Pulse-Doppler radar signal processing chain on a massively parallel machine based on multi-core DSP and Serial RapidIO interconnect[END_REF] and the classic DFT summation [START_REF] Inggs | Commensal radar: Range-Doppler processing using a recursive DFT[END_REF], [START_REF] Shin | Timing Analysis of Doppler Filter Bank with Parallel Processing Configuration[END_REF]. The two approaches present different characteristics in terms of throughput, latency, processing and memory resources, that can benefit to different phases of application scenarios. In the context of multi-channel radars, the range-Doppler function becomes a major concern [START_REF] Antonio | MIMO Radar Ambiguity Functions[END_REF]. Indeed, although the AESA spatial degrees of freedom give extra information on the targets, this function must be computed for every channel, consuming a lot of logic resources. In this context, the DFT method used for the range-Doppler transform is fixed at design time. Hence, the system cannot benefit from different DFT architectures. DPR, which is proved to be particularly efficient in the signal processing field [START_REF] Choi | An Reconfigurable FIR Filter Design on a Partial Reconfiguration Platform[END_REF]- [START_REF] Michael Feilen | Real-time signal processing on low-cost-FPGAs using dynamic partial reconfiguration[END_REF], permits to overcome this limitation.

The first contribution of this paper is a reconfigurable architecture which allows to use the proper version of DFT algorithms according to application needs, without the resource consumption overhead. This architecture limits the impact of the reconfiguration time by performing an original progressive reconfiguration that opens new perspectives. The second contribution is a method to take the reconfiguration decision at the right time in a radar application.

III. DFT OPTIONS FOR RADAR PROCESSING

A. DFT algorithm

The DFT algorithm (defined by Eq. ( 1)) is used to extract the spectral distribution of a discrete signal.

A k = N -1 n=0 W kn N a n where W kn N = e -i 2π N ×kn (1)
This equation allows the DFT computation of any size N of discrete signal. However, all the temporal samples a n are required to compute a single spectral sample A k , k ∈ [0, N [. This algorithm is well known and many implementations exist in the literature, with complexities going from O(N log(N )) for the FFT to O(N 2 ) for a direct implementation of Eq. ( 1). However, in some applications, this direct DFT implementation can be useful to order certain operations.

B. DFT concerns in radar processing

The DFT in radar processing is used to extract a Doppler frequency from the temporal signal. To this end, the system downsamples the input data and performs a DFT over the different sub-signals. The combination of a matched filter and this transform is known as 'range-Doppler processing'. Fig. 1-a) depicts this downsampling and the DFT processing to illustrate our statements. This manipulation is known as a 'corner turn' in radar and sonar domains [START_REF] Lush | Airborne radar analysis using the ambiguity function[END_REF], [START_REF] Klilou | Real-time parallel implementation of Pulse-Doppler radar signal processing chain on a massively parallel machine based on multi-core DSP and Serial RapidIO interconnect[END_REF]. Fig. 1 a) shows that to complete the first DFT, we need to wait for (N -1)×M +1 points to arrive. However, some DFT algorithms allow to begin the computation earlier. If we can process the input data as soon as we receive it, it is possible to reduce the DFT latency. Otherwise, we have to wait for a significant amount of data to arrive, which leads to a higher latency. This latency depends on the algorithm used for DFT.

C. Discrete Fourier transform for dataflow

An important property of the direct implementation of DFT, which we refer to as DFT in the rest of this paper, is its ability to process inputs equally in any order. It is widely used in radar systems to overcome the difficulty of processing the data in a different order from arrival (Fig. 1-a)).

Consuming the data in the natural order of arrival minimizes latency since computations start earlier and the O(N 2 ) computations are then covered as the data comes in. However, all partial sums of Eq.(1) need to be stored locally in the FPGA for every output, in order to keep the short latency benefit. But in contrast with FFT, DFT can compute a selected part of the spectral domain from the full time domain, reducing the number of computation while ensuring spectral accuracy. Hence, DFT allows to adapt the size of the explored spectrum to available storage and logic resources on FPGA. Eventually, we can summarize as follows:

• pros: dataflow processing, low latency, no need to buffer the input data, possibility to compute a selected interval • cons: high DSP and BRAM consumption per output sample, limited range-Doppler exploration because of the limited output samples D. Fast Fourier transform for block processing In contrast to DFT, FFT algorithms use more efficiently both processing and memory resources, by means of computation results reuse. However, a drawback of FFT is the inability to process the inputs in order of arrival. With the DIF FFT algorithm for instance, N 2 +1 input samples are required before the first computation can start. The main issue is the latency penalty. A second one is the incapacity to store all the input samples in the FPGA ( N 2 × number of distance gates × number of channels). Hence, an external DDR memory is used and introduces an additional latency, but it also free up resources that can be used to compute the full spectral domain. Eventually, we can summarize as follows:

• pros: low resources consumption per output sample, full size range-Doppler exploration • cons: high latency, data buffering is mandatory

E. Conclusion on DFT algorithms for radar applications

At radar startup, the system does not know the exact position of the tracked objects in Doppler and space domains. At this time of the mission, it is critical to have information on the full space to emphasize detection. Moreover, the latency is not critical since no tracking is launched, thus a FFT is the right solution. Once detection is successful the system has to start tracking, which requires other algorithms (e.g. angle of arrival estimation, filtering with Kalman filters). The latency constraint is strengthened. Furthermore, the system now has a precise estimation of the target range and speed. So, the extensive overview on the range-Doppler domain can be exchanged for reduced latency, allowing the system to perform additional required functions. This trade-off on the exploration space of the two algorithms is illustrated in Fig. 1-b).

This describes the original idea of our study, but we still need to define the reconfiguration decision-making.

IV. QOS AWARE RECONFIGURATION CONTROLLER Upon startup, the system uses the FFT algorithm. Once detection is successful, we could change for the DFT algorithm. However, a successful detection cannot guarantee a positive detection in the next radar coherent processing interval (CPI). Indeed, a poor signal to noise ratio (SNR) or signal to clutter ratio (SCR) may result in the loss of the target. Such changes in SNR and SCR can come from radar cross section (RCS) changes, fluctuation loss or environment configuration.

The decision to reconfigure the system requires a more accurate QoS indicator than the simple Boolean one. We need a value which reflects the probability to successfully detect the target. A good solution is to use the probability of detection (P d ), which is in practice unknown but can be approximated from a quantifiable variable. One possible approach is to record the positive and negative detections of the target, and compute the target detection frequency. To use this approach, we need to ensure that the plots (i.e. positions where detection is positive) come from the same object. This can be achieved by a probabilistic data association filter (PDAF) [START_REF] Bar | The probabilistic data association filter[END_REF]. This filter uses the log-likelihood of the innovation ( ) computed by a Kalman filter to determine if the plot is likely to be related to the observed target. The PDAF associates the plots to a track with a validate function V (k) described in Eq. [START_REF] Rao | Digital beam former architecture for sixteen elements planar phased array radar[END_REF].

V (k) = 1, if (k) γ 0, if (k) < γ (2) L q (k + q) = 1 q q i=1 V (k + i) (3)
Where : (k) : log-likelihood of the innovation at plot k γ : validation threshold

The detection ratio over q samples is given by Eq. ( 3). The target detection is confirmed when the frequency exceeds a defined threshold λ, so we can simply define the QoS criterion as the detection ratio: f QoS (k + q) = L q (k + q). A PDAF is required in any radar tracking system, so the QoS function does not introduce a computational overhead.

The required configuration s k can take one of the two states of S : {S DF T , S F F T }, which are the DFT and the FFT respectively, depending on the QoS criterion. Eq. (4, 5) describe the state of the configuration with regard to the QoS criterion. Fig. 2 gives another representation of this system through a cyclic graph and a transition hysteresis.

s k = S DF T , if S DF T • ā + S F F T • b S F F T , if S DF T • a + S F F T • b (4)
Where:

a = b = f QoS (k + q) < λ (5)
SDF T SF F T a ā b b f QoS (k + q) λDF T λF F T λ S F F T S DF T Transitions from Eq. (5)
Transitions from Eq. ( 6)

Fig. 2. Control graph and associated transition hysteresis

A transition based on Eq. ( 5) induces a risk of constant reconfiguration. For example, with λ = 2. 5 3 , if the QoS value follows the sequence: [ 3 5 , 2 5 , 3 5 , 2 5 ], the reconfiguration happens at every radar CPI. Therefore, we adopt an hysteresis model with two different thresholds λ for the two state changes. λ F F T is used for the transition from DFT to FFT and λ DF T for the reconfiguration from FFT to DFT. With λ DF T > λ F F T , the transition functions are given by Eq. ( 6).

a = f QoS (k + q) λ F F T ; b = f QoS (k + q) λ DF T (6)
Fig. 2 shows that Eq. ( 6) results in a more stable controller, which is unlikely to cause ceaseless reconfigurations. This automaton is synchronous with the radar CPI end.

It is worth mentioning that the QoS criterion is specific to one target and must be computed independently for every distinguished target. Once all the criteria are computed, an external operator can choose where to place the DFT window at reconfiguration time. In this study, we suppose this operator wants the window to be centered on the last detected plot.

Since the concept and the benefits of the DFT reconfiguration have been exposed, we present an architecture allowing to efficiently implement a reconfigurable DFT.

V. IMPLEMENTATION OF A RECONFIGURABLE DFT A. Problem of channel reconfiguration

In a radar system, the data is processed from the sensors to the software in a dataflow way. The reconfiguration of part of this processing flow requires to interrupt the flow. The DPR introduces a delay which is not compliant with most of radar systems that may lose the track of targets during the interruption. However, we consider multi-channel radar, whose channels can be processed independently when DFT is performed. Hence, it provides an opportunity to reconfigure channels by blocks, from one single channel, up to all channels. Nevertheless, the number of channels to reconfigure at the same time determines the number of resources to reconfigure. Reconfiguration time increases linearly with the reconfigurable partition (RP) size. Our reconfiguration paradigm can be formalized as the following problem. Determine the best tradeoff between stopping the process for a long time to reconfigure all the channels and reconfiguring only one channel at a time, but running in a degraded mode with the other channels. Fig. 4 shows a sixteen sensors radar system which implements DFT reconfiguration, where each RP performs four DFT to divide the reconfiguration time in four steps. During this process, the radar system is still running with 3/4 of the channels.

B. Data reordering

As introduced in Sec. III, DFT and FFT inputs are not processed in the same order. For the DFT, samples are processed in arrival order without having to reorder input data. Unlike DFT, FFT receives the data after downsampling, and thus store batches of data in DDR until it has enough data in the processing core. It means that a switch is required before the reconfigurable DFT to act either as a passthrough or as a store and load device. Fig. 3-a) represents this block which uses a small amount of resources, thus we keep it out of the RP. However, this block is mandatory when using FFT, to deal with the 'corner turn', but AXI (Data) is used only with the FFT configuration. An additional AXI lite slave port is required to configure the switch block in FFT or DFT modes.

C. Architectures of DFT/FFT configurations

An efficient DPR requires that the configurations sharing the same RP have similar amount of resources since the RP is sized for the worst case, so a mismatch may result in an excessive waste of hardware resources.

The DFT uses a lot of memory but only few DSP per channel whereas an efficient FFT implementation demands a lot of memory but also a lot of DSP. So we can balance the resource consumption disparity by implementing n DFT per FFT block. This implies no latency issue since most of this latency is due to data movements with the FFT model. Fig. 3b) shows how the configurations design can balance resources usage by using the same FFT core for n = 3 channels.

It is important to note that if only the FFT needs to access to the DDR for the Data though an AXI (Data) bus, the situation is different for the DFT since only the DFT needs to read the coefficients from the DDR using an AXI (Coeff) bus which is unused with the FFT configuration. Merging the AXI (Coeff) and AXI (Data) requires more Mux resources and architecture complexity, hence we keep a solution with two distinct bus.

A second consideration is the DDR bandwidth limit. Indeed, the pipelined versions of the FFT can read a new input at each clock cycle. If we can read up to N values per clock cycle from the DDR, it is useless to implement more than N FFT.

D. Conclusion on the DFT implementation

Multiple parameters impact the implementation results (e.g., DFT window size, computations parallelism, reconfiguration speed and channel number per FFT). Therefore, the design space exploration is made by means of a HLS specification that allows to get resource / performance estimations in a reasonable amount of time. In this study, we implement a versatile IP resulting in different implementation from preprocessing directives. We have three distinct configurable specifications: a DFT, a wrapper to the FFT of Xilinx with the pipeline configuration, and a homemade pipelined FFT with resources consumption and latency close to the proprietary IP. We implement our own pipelined FFT on Vivado HLS to generate a HLS synthesis estimation of resources consumption. Indeed, the Vivado FFT uses incorrect precomputed HLS results with the tool current version (2019.1) as indicated in Table I as the HLS estimation quality. Our HLS code allows to choose the number of channels per FFT in the reconfigurable IP.

VI. CASE STUDY A. System description

To study the performance of our architecture, we implement the system described in Fig. 4 on a ZCU102 board. This board includes a Zynq Ultrascale+ circuit, two DPR are attached to the ARM (PS) processor and FPGA (PL) respectively.

The input signal is a synthetic radar signal, transporting information on a target through delay, Doppler frequency and direction (phase shift). This signal is injected at the DFT Switch input of Fig. 4. The filtering is a simple beamformer which projects the signal in a spatial direction, and write the result to the PS DDR memory. The detection is then performed with a CA-CFAR [START_REF]Chapter 16: Constant False Alarm Rate Detectors[END_REF] (Cell-Averaging Constant False Alarm Rate) implemented in software. The reconfiguration controller defined in Section IV is implemented in software as well.

We use the Gazebo simulator [20] to compute the target movement and provide a graphical output for the HIL demonstrator. The simulator sends the target position and speed to a Python 3 process that generates the signals. This process sends the signal through an Ethernet link to the board. The reconfigurable modules of the FPGA computes the DFT and the static part filters the data with the beamforming. Detection is executed by the Zynq ARM as well as the reconfiguration controller (described in Sec. IV) which is updated accordingly. The board sends the output signal and the detection plots to our Python 3 interface through Ethernet, for graphical plots.

B. PCAP API improvement

DPR is performed through the processor configuration port (PCAP). But we have modified the Xilinx PCAP API to add a non-blocking reconfiguration command. When the reconfiguration is launched, the task is suspended. When the PCAP is done, a CSUDMA interruption resumes the task. Furthermore, this API greatly reduces the reconfiguration time by avoiding data cache flush. Unlike the Xilinx API, we control the memory range and flush operation out of the reconfiguration time. The impact on performance is given in the Sec. VI-E.

C. Scenario description

We choose to highlight our architecture benefits in terms of performance and adaptability. Without loss of generality and to avoid interference with phenomenons out of the scope of this paper, the scenario features one target in white noise, without clutter. This simplification does not invalidate the key concept since the DFT reconfiguration process would be the same with a target in a clutter. Besides, changing the architecture to a multi-target version would only add a selection method which is application specific and usually implemented out of the radar system itself. However, the simplification results in a simpler QoS function. The association result is considered as correct when a plot is detected. We fix the QoS thresholds λ DF T = 3 5 and λ F F T = 1 5 . This configuration implies that the target is still present in the DFT scope (and will likely be detected again) if at least three detections were successfully performed in the last five radar CPI. However, if less than two detections are successful, the system should explore the entire rangespeed space. To observe the reconfiguration stability, we use the Swerling I model of RCS [START_REF] Swerling | Probability of detection for fluctuating targets[END_REF].

The scenario is composed of three phases depicted in Fig. 5. At the beginning of the mission, the target is distant. The radar system does not know the target position in the range-Doppler space and is in FFT configuration. At first, the RCS ensures a good SNR. At this time of the mission, our system should detect the target and switch to DFT configuration. Later, the target orientation changes, lowering the RCS. The SNR falls, leading to the target loss. The system should then switch to FFT configuration. The target speed direction changes in the time it was lost. When the target is close to the radar, the system detects it again (at a different place in the range-Doppler map), it should switch to DFT configuration and the mission ends. We use this scenario to test our HIL system and provide a demonstration video available online [START_REF] Mazuet | HIL demonstration of the DFT/FFT selfadaptive radar architecture[END_REF].

D. Implementation results

As we stated in Sec. V-D, the whole architecture is generated with HLS codes. The main parts are the DFT Switch and the different configuration of DFT. The implementation can be parameterized with six variables: (1) N s is the maximum signal size (radar CPI), (2) N d is maximum DFT size, (3) N c is total number of channels, (4) N df ts is number of samples per DFT, (5) N ipc is channels per IP, (6) N f f t is FFT per IP (FFT mode). The first three parameters depend on the application. We choose the parameters as follow in our case study:

(1) N s = 16000

(2)

N d = 1024 (3) N c = 16
The next parameters need exploration to choose the best channels slicing and to control its impact on the radar performances. In a first step, we carry out different Vivado HLS synthesis to observe the number of DFT we can implement for one FFT to have equivalent resources usage. The DFT and FFT sizes result in an optimal ratio of four DFT per FFT (resource consumption from logical synthesis in Table I). Furthermore, the maximum DDR bandwidth allows us to read up to 4 values per clock cycle. Therefore, we implement one FFT per IP, for a total of four IP. We determine the best configuration: (4) N df ts = 1024

(5) N ipc = 4 (6) N f f t = 1 In our study, the PRF is not a relevant parameter and remains unchanged. The two important observed metrics are Previous HLS estimation quality: Accurate Approx. False the latency and the size of the speed-range domain.

The full architecture is depicted in Fig. 4. The input signal is injected to the DFT Switch and the matched filter is performed beforehand by a Python 3 code. This architecture is based on the parts described in Sec. V. Decouplers are connected to the RP to guarantee isolation at reconfiguration time. These decouplers can isolate the four partitions independently to allow the reconfiguration of only a subset of the channels.

E. Performance results

With this configuration, the observed system response meets the expected response described in Sec. VI-C. We measured a latency of 6.6ms for the DFT configuration, which coincides with the sum of the CPI and the beamformer latencies, so DFT latency is negligible compared to the other latency sources. However, with the FFT configuration, the latency is higher with a total of 9.3ms. The major improvement offered by this architecture is the 2.7ms measured gain on the system latency when using DFT instead of FFT, 2.7 6.4 × 100 = 42% of the CPI in our example. It means that the system is more responsive and this time is available for complex algorithms for tracking.

The RP reconfiguration time of each reconfigurable DFT block takes from 4.4ms to 5.8ms with the Xilinx PCAP API, and 2.2ms to 2.8ms with our modified API. This reconfiguration time is smaller than the CPI of 6.4ms, enabling to reconfigure without interruption of the radar processing flow. Indeed, although an expected degradation of the signal quality is observed during the four cycles needed to reconfigure all the RP, the radar signal consistency is preserved.

VII. CONCLUSION

To the best of our knowledge this paper presents the first self-adaptive architecture in the embedded radar field that tracks the best trade-off between latency and detection space by means of smooth DFT / FFT reconfiguration per channels group. Our reconfigurable architecture allows to take full benefit of the conventional DFT and FFT respective strengths. The decision method is the first contribution detailed in Sec.IV, it relies on the use of QoS specific to our Radar application. The second contribution is a dynamically reconfigurable architecture which is optimized for the implementation of DFT / FFT configurations as well as fast and flexible enough to avoid interruption of the radar function during transitions.

Through a case study implemented by means of a realistic HIL approach, we demonstrate the efficiency of the architecture implementation. Our solution is valid for a large range of radar applications and can be parameterized to fit with different system configurations (e.g. number of channels, ranges, etc.). In real-life applications, it is possible to observe objects at different speeds and ranges. So a future work will allow to isolate and process several areas in the range-speed map. The proposed approach remains relevant, but modifications have to be considered in the DFT IP and in the downstream processing.

Fig. 1 .

 1 Fig. 1. Constitution of a range-Doppler radar map. a) down-sampling and DFT. b) Representation of the computing capacities of DFT and FFT.

Fig. 3 .

 3 Fig. 3. a) Switch block to adapt input data ordering for DFT. b) The two configurations of the DFT IP.