PhD Giulia Fornasa

MSc Marc Clement

PhD Emilie Groyer

BSc Anh-Thu Gaston

PhD,* † Jamila Khallou-Laschet

BSc Marion Morvan

MSc Kevin Guedj

DVM Srini V Kaveri

PhD, ¶ Alain Tedgui

MD Jean-Baptiste Michel

PhD,* † Antonino Nicoletti

MD Giuseppina Caligiuri
email: giuseppina.caligiuri@inserm.fr

A CD31-derived peptide prevents angiotensin II-induced atherosclerosis progression and aneurysm formation

INTRODUCTION

Complex inflammatory processes underlie the progression of atherosclerosis towards its complications [START_REF] Libby | Inflammation in atherosclerosis: from pathophysiology to practice[END_REF] such as coronary plaque thrombosis [START_REF] Hansson | Inflammation, atherosclerosis, and coronary artery disease[END_REF] and abdominal aortic aneurysms (AAA) [START_REF] Hellenthal | Biomarkers of abdominal aortic aneurysm progression. Part 2: inflammation[END_REF] .

Several antigens become immune targets in atherosclerotic patients [START_REF] Caligiuri | Evidence for antigen-driven T-cell response in unstable angina[END_REF][START_REF] Caligiuri | Autoreactive antibody repertoire is perturbed in atherosclerotic patients[END_REF] possibly because the regulation of immune responses is defective [START_REF] Caligiuri | Tregs and human atherothrombotic diseases: toward a clinical application? Arteriosclerosis, thrombosis[END_REF][START_REF] Mallat | The role of adaptive T cell immunity in atherosclerosis[END_REF] . The trans-homophilic [START_REF] Newton | Residues on both faces of the first immunoglobulin fold contribute to homophilic binding sites of PECAM-1/CD31[END_REF] inhibitory immunoreceptor CD31 (PECAM-1) [START_REF] Newman | Switched at birth: a new family for PECAM-1[END_REF] is expressed exclusively and constitutively by the cells of the blood-vessel interface and may therefore play a major role in vascular homeostasis [START_REF] Newman | Signal transduction pathways mediated by PECAM-1: new roles for an old molecule in platelet and vascular cell biology[END_REF] . Notably, experimental studies have shown that CD31 signaling is necessary to prevent blood leukocyte cell-cell adhesion [START_REF] Brown | Apoptosis disables CD31mediated cell detachment from phagocytes promoting binding and engulfment[END_REF] , chronic inflammatory diseases 12 , and platelet thrombosis [START_REF] Falati | Platelet PECAM-1 inhibits thrombus formation in vivo[END_REF] .

We previously observed that a reinforcement of the physiologic CD31 T-cell regulatory pathway, operating before the development of the disease, prevents plaque development in atherosclerosisprone mice [START_REF] Groyer | Atheroprotective effect of CD31 receptor globulin through enrichment of circulating regulatory T-cells[END_REF] . However, this approach requires the presence of the trans-homophilic CD31 extracellular domains [START_REF] Groyer | Atheroprotective effect of CD31 receptor globulin through enrichment of circulating regulatory T-cells[END_REF] which are typically lost on peripheral T-cells of mice [START_REF] Caligiuri | Reduced immunoregulatory CD31+ T cells in the blood of atherosclerotic mice with plaque thrombosis[END_REF] and patients [START_REF] Caligiuri | Reduced immunoregulatory CD31+ T cells in patients with atherosclerotic abdominal aortic aneurysm[END_REF] that have already developed atherosclerotic complications. Recently, a new therapeutic option has arisen from our latest data showing that a truncated extracellular CD31 fragment is indeed expressed by Tcells that apparently lack CD31 [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] and that a CD31-derived peptide is able to engage this fragment.

In particular this peptide showed an immunosuppressive effect in vivo through restoration of the CD31 inhibitory pathway [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] . The aim of this study was therefore to evaluate whether restoring the CD31-mediated regulatory pathway with this peptide could harness the inflammatory responses underlying atherosclerosis progression and aneurysmal complication in an experimental model. We chose to test this hypothesis in aged apolipoprotein E knockout (ApoE KO) mice submitted to chronic infusion of angiotensin II because, as in patients [START_REF] Montecucco | The renin-angiotensin system modulates inflammatory processes in atherosclerosis: evidence from basic research and clinical studies[END_REF] , angiotensin II promotes atherosclerotic progression and AAA formation via its pro-inflammatory effect in this model [START_REF] Guzik | Role of the T cell in the genesis of angiotensin II induced hypertension and vascular dysfunction[END_REF][START_REF] Wang | TGF-beta activity protects against inflammatory aortic aneurysm progression and complications in angiotensin II-infused mice[END_REF] .

CVR-2011-1155R1

METHODS

Peptides. The murine synthetic CD31 peptide (aa 551-574, MW 2606.0) (purified or 5,6-FAM-conjugated, >95% pure) was synthesized by Genosphere (France) or Mimotopes (Australia) and dissolved at 1 mg/ml in sterile PBS (DMSO 0.5%). Endotoxin levels were consistently < 0.01 ng/μg of peptide as determined by the LAL test.

Mice. Male, 28-week old ApoE KO mice (B6.129P2-Apoe tm1Unc /Crl, Charles River France) were maintained on a regular chow diet under standard conditions. The experiments were repeated four times and included 2 groups (n =8-10 mice/group) assigned to the administration of 50 µl of either the peptide solution ("peptide" group) or of vehicle alone ("control" group). The dose of the murine CD31 peptide (1.5 mg/Kg/d) was chosen on the basis of our previous in vivo studies [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] . The treatment was administered subcutaneously, for 28 days during which Angiotensin II (Sigma, #A9525) was infused (1 mg/kg/d) using osmotic mini-pumps (Alzet, #2004) as previously described [START_REF] Daugherty | Angiotensin II promotes atherosclerotic lesions and aneurysms in apolipoprotein E-deficient mice[END_REF] . At the end of the study, mice were euthanized by exsanguination under anesthesia (i.p. injection of Ketamine-HCl 100mg/Kg and Xylazine 20 mg/kg). Blood was withdrawn from the right heart ventricle and collected in heparinized and EDTA tubes for blood cell and plasma analysis. The heart and the aorta were dissected for AAA assessment, measurement of plaque size and phenotypic analysis. Four additional mice of the "control" group received a single injection of AAA and atherosclerotic lesions. The presence of an AAA was blindly assessed by two investigators (A-T. G. and A. N.). Plaque size was measured on oil-red-O stained frozen crosssections of the aortic root, as previously described [START_REF] Caligiuri | Reduced immunoregulatory CD31+ T cells in the blood of atherosclerotic mice with plaque thrombosis[END_REF] . Morphometric analysis was performed on Masson's trichrome stained slides. Adventitial cell infiltrate was calculated as the fraction of the CVR-2011-1155R1 4 total surface area of the tissue outside the external elastic lamina occupied by nuclei (black); plaque extracellular matrix density was calculated as the ratio between the green-stained surface area and the surface of the plaque. All computer-assisted image analyses were performed using the Leica Qwin® software.

Blood cells and plasma analysis. Blood was centrifuged at 900 g for 30 minutes to separate plasma. The Th1/Th2/Th17 CBA kit (BD Biosciences) was used to measure cytokines in the plasma samples. Cholesterol was measured using Infinity® Cholesterol-Liquid reagents and an Olympus AU-400 multiparametric analyzer. Leukocyte pellets were stained with CD3-Alexa Fluor®700, CD4-PerCP, CD8-Pacific Blue, CD19-APC, CD69-PE-Cy7, CD115-PE, Ly-6G-APC-Cy7, CD31-FITC, (all from BD Biosciences) or with anti-mouse CD4-PerCP, CD25-APC (clone PC61, BD) and intracellular FoxP3-PE (clone PE-FJK-16s, eBiosciences). Analysis was performed using a LSRII ® flow cytometer and BD FACSDiva® Software 6.0.

T-lymphocyte function. TCR stimulation. CD4+ splenocytes (CD4 T Lymphocyte

Enrichment Set, BD Biosciences) were plated at 0.2x10 6 cells/well in U bottom 96-well plates (Costar®) pre-coated with anti-mouse CD3 antibody (BD Biosciences) and cultured for 3 days in the presence of 1 µg/ml anti-mouse CD28 antibody (BD Biosciences) and different concentrations of the CD31 peptide. Cytokines were measured in the supernatants using the Th1/Th2/Th17 CBA kit (BD, Biosciences) and T-cell proliferation was assessed using the CellTrace TM CFSE Cell Proliferation Kit (Invitrogen). Phospho-SHP2 was evaluated by flow cytometry on TCR-stimulated splenocytes as detailed in the supplementary method section. Antigen-specific stimulation. Four individual ApoE KO male mice aged 24 weeks were immunized (4 footpads) with 100 µg autologous oxidized (ox) LDL (prepared as previously described [START_REF] Caligiuri | Phosphorylcholine-targeting immunization reduces atherosclerosis[END_REF] ) in complete Freund's adjuvant.

Ten days later, the animals were euthanized and the popliteal and axillary lymph nodes draining the immunization sites were collected. Single cell suspensions obtained from pooled lymph nodes from each mouse were stained with CFSE (5 µM) and plated in complete medium in 96-well plates CVR-2011-1155R1 5 (round bottom, 2x10 5 cells/well) in the presence of oxLDL (1 µg/ml) and in the presence of increasing doses of CD31 peptide (0, 12.5, 25, 50 and 100 µg/ml). Culture supernatants were harvested four days later for soluble CD31 analysis and cells were submitted to cytometry to analyze the CFSE-based proliferation index within the CD4+ lymphocyte gate. The mean fluorescent intensity of surface CD31 was analyzed in the same wells and soluble CD31 concentration was assessed in the supernatants (supplementary methods).

Macrophage function.

Bone marrow-derived macrophages were differentiated and IFNprimed as previously described [START_REF] Khallou-Laschet | Macrophage plasticity in experimental atherosclerosis[END_REF] . Cells were then cultured in complete medium and stimulated with 100 ng/ml angiotensin II in the presence of increasing doses (0, 25, 50µg/ml) of CD31 peptide. Differences between groups were analyzed by Student t-test or chi-squared test, as appropriate.

Differences were considered statistically significant when the p value was ≤0.05.

CVR-2011-1155R1

6

RESULTS

Loss of T-cell extracellular CD31 and development of AAA

Plaque-infiltrating leukocyte analysis showed that CD4 + cells were all positive for intracellular CD31 but not all of them co-expressed extracellular CD31 (supplementary Figure 1a). The lack of extracellular CD31 was also specifically observed on peripheral blood CD4+ T lymphocytes and associated with the development of an AAA (supplementary Figure 1b and1c).

CD31 peptide treatment reduces AAA formation and plaque growth

Since AAA development was associated with the loss of extracellular CD31 on CD4+ T-cells we reasoned that this receptor could be shed from mouse leucocytes as we have previously described for human cells [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] . Accordingly, we evaluated the therapeutic potential of a CD31-derived peptide, which is able to restore the lost inhibitory function in vitro and in vivo 17 in this model. CD31 peptide treatment significantly reduced the incidence of AAA formation (Figure 1a) and the extent of atherosclerotic lesions (Figure 1b and1c). Aortic root adventitial cell infiltrate was associated with the presence of an AAA (Figure 1d and1e) and was also reduced in peptide-treated mice. The peptide stabilized the phenotype of the plaques as determined by higher extracellular matrix density (44.52 ± 5.5 vs 31.61 ±4.9 a.u, p=0.05), lower expression of VCAM-1 and higher SMA content (supplementary Figure 2). Fibrillar collagen was more abundant in the aortic root plaques and significantly higher at the site of the abdominal aorta that is prone to dissection in this model, suggesting that the peptide treatment confers a higher resistance against rupture to the arterial wall (supplementary Figure 3). Furthermore, the presence of T-cells (CD4+), macrophages (Mac3+) and MMP9 within the plaques was also blunted by the treatment (supplementary Figure 2). CD31treatement did not affect body weight (34.8 ± 0.8 vs 36.4 ± 0.9 g), lipoprotein profile (supplementary Figure 4) or plasma levels of total cholesterol (11.9 ± 0.75 vs 10.9 ± 0.6 mmol/l), HDL (1.2 ± 0.1 vs 1.1± 0.1 mmol/l), and triglycerides (1.1 ± 0.1 vs 1.2 ± 0.1 mmol/l). No CVR-2011-1155R1 7 differences could be found between the two groups in terms of total IgG and IgM and of specific anti-oxLDL IgG and IgM serum levels (supplementary data, Figure 5) or circulating blood cell count (supplementary Table 1).

CD31 peptide modulates the peripheral T-cell compartment in vivo and directly inhibits T-cell responses in vitro

Peptide-treated mice showed increased CD4 + CD25 + FoxP3 + (Tregs) and reduced CD69 + (recently activated) T-cell % in the peripheral blood (Figure 2a). The treatment decreased plasma levels of IL-2, IFN, IL-4 and IL-6 (Figure 2b) but not those of TNF, IL-10 or IL-17A (data not shown).

We therefore assessed if the peptide exerts direct T-cell suppressive effects in vitro. Our data show that, as for human cells [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] , the peptide reduces mouse T-cell proliferation in response to TCR engagement (Figure 3a). In addition, it inhibited the production of IL-2, IFN, IL-4, IL-6, TNF and IL-10 (Figure 3b). To assess whether the peptide triggered the physiological T-cell CD31 inhibitory signaling, we evaluated the levels of the SHP2 phosphorylation [tyrosine (Y) 542] in TCRstimulated splenocytes. Similar to the specific control (antibody-mediated cross-linking of surface CD31) a significant increase in intracellular SHP2 pY542 was induced by the peptide, in a dosedependent manner (Figure 3c).

The peptide was also able to suppress the CD4+-specific immune response directed against ox-LDL, a major atherosclerosis-related antigen (Figure 4a). Interestingly, the expression of CD31 extracellular domains at the cell surface was reduced after antigenic T-cell stimulation, concomitantly with an increase in soluble CD31 concentration in the supernatants, further adding to the evidence that CD31 shedding is driven by (antigen-specific) TCR-mediated T-cell activation (Figure 4b and4c).

CVR-2011-1155R1

8

CD31 peptide prevents angiotensin II-induced macrophage activity in vitro

While T cells are certainly involved in the acceleration of plaque formation in the angiotensin II infusion model, macrophages may play a more important role in AAA formation [START_REF] Saraff | Aortic dissection precedes formation of aneurysms and atherosclerosis in angiotensin II-infused, apolipoprotein E-deficient mice[END_REF][START_REF] Uchida | Total lymphocyte deficiency attenuates AngII-induced atherosclerosis in males but not abdominal aortic aneurysms in apoE deficient mice[END_REF] . We therefore assessed whether the peptide is able to bind to macrophages in vivo and to exert a direct effect on angiotensin II-induced macrophage activation, in vitro. Fluorescent peptide tracking showed that plaque-infiltrating and peri-aneurysmal macrophages could indeed be targeted by the peptide, in vivo (Figure 5). In vitro, the CD31 peptide reduced intracellular MMP-2/9 activity (Figure 6a and 6b) and release of IL-6, MCP-1, MIP-1 and MIP-1 in the culture medium (Figure 6c). The concentrations of IL-1, IL-1, IL-12 and RANTES were not affected by the peptide (data not shown).

CVR-2011-1155R1

9

DISCUSSION

The present study provides further evidence for a protective role of T-cell CD31 against atherosclerotic complications, such as AAA. Indeed, as in patients [START_REF] Caligiuri | Reduced immunoregulatory CD31+ T cells in patients with atherosclerotic abdominal aortic aneurysm[END_REF] , the presence of an AAA was linked to the loss of CD31 on both plaque-infiltrating and peripheral T-cells in angiotensin IIinfused apoE KO mice. We also found that the incidence of AAA correlated with adventitial cell infiltration at the level of the aortic root, distant from the abdominal aorta. While such a perivascular leukocyte infiltration had previously been described at the site of aneurysm formation [START_REF] Saraff | Aortic dissection precedes formation of aneurysms and atherosclerosis in angiotensin II-infused, apolipoprotein E-deficient mice[END_REF] , our findings suggest that the adventitial inflammatory process induced by angiotensin II extends to the whole arterial tree and contributes to both the acceleration of plaque-growth (aortic root) and the occurrence of wall dissection/aneurysm formation (abdominal aorta) depending on site-specific hemodynamics and leukocyte environment. In support of this hypothesis, the CD31-peptide treatment effectively reduced perivascular inflammation and equally protected against aneurysmal complications and atherosclerosis progression in this study.

Although the CD31 peptide can potentially act on CD31-positive cells other than leukocytes (platelets and endothelial cells), in this study we focused our attention on its putative effect on the cells of the immune system. Indeed T-cell activation is a key cellular process linking the hypertensive and pro-inflammatory effects of angiotensin II [START_REF] Guzik | Role of the T cell in the genesis of angiotensin II induced hypertension and vascular dysfunction[END_REF][START_REF] Crowley | Lymphocyte responses exacerbate angiotensin II-dependent hypertension[END_REF][START_REF] Marvar | Central and peripheral mechanisms of T-lymphocyte activation and vascular inflammation produced by angiotensin II-induced hypertension[END_REF] . Our data suggest that the inhibition of T-cell activation achieved in vivo [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF][START_REF] Chen | Administration of a CD31-derived peptide delays the onset and significantly increases survival from lethal graftversus-host disease[END_REF] by the CD31 peptide prevents the angiotensin II-driven inflammatory vascular damage. However, the T-cell suppression cannot explain, alone, the anti-inflammatory and protective effect of the peptide in this model because angiotensin II receptors are expressed both by T lymphocytes and macrophages [START_REF] Shimada | Binding sites for angiotensin II in human mononuclear leucocytes[END_REF] . The latter are particularly relevant in angiotensin II-driven arterial wall dissection and AAA formation [START_REF] Saraff | Aortic dissection precedes formation of aneurysms and atherosclerosis in angiotensin II-infused, apolipoprotein E-deficient mice[END_REF][START_REF] Uchida | Total lymphocyte deficiency attenuates AngII-induced atherosclerosis in males but not abdominal aortic aneurysms in apoE deficient mice[END_REF] . Interestingly, the peptide was found to bind to both plaque and adventitial macrophages, which were both reduced by the treatment. In addition, the peptide inhibited macrophage collagenolytic activity and the release CVR-2011-1155R1 10 of IL-6 and MCP-1 by angiotensin II-stimulated inflammatory macrophages, possibly explaining the resistance of the aortic wall to dissection in peptide-treated mice [START_REF] Tieu | An adventitial IL-6/MCP1 amplification loop accelerates macrophage-mediated vascular inflammation leading to aortic dissection in mice[END_REF] .

In agreement with our findings in human lymphocytes [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] , our in vitro data suggest that restoring CD31-driven intracellular SHP-2 phosphorylation in activated leukocytes constitutes a novel immunomodulatory strategy. Interestingly, it has recently been shown that the CD31-SHP2 pathway simultaneously inhibits tyrosin kinase-dependent activation while promoting T-cell survival via the Erk/MAP kinase pathway [START_REF] Ma | Ig gene-like molecule CD31 plays a nonredundant role in the regulation of T-cell immunity and tolerance[END_REF] . The latter is also involved in extrathymic Treg induction [START_REF] Nishihara | IL-6-gp130-STAT3 in T cells directs the development of IL-17+ Th with a minimum effect on that of Treg in the steady state[END_REF] and function [START_REF] Adler | Activation of MAP kinase p38 is critical for the cell-cycle-controlled suppressor function of regulatory T cells[END_REF] . This may account for the enrichment of the Treg peripheral pool that we have observed in treated mice and represent an additional immunoregulatory mechanism exerted by the peptide.

As compared to other potential immunosuppressive atheroprotective agents, such mycophenolate mofetil [START_REF] Van Leuven | Mycophenolate mofetil (MMF): firing at the atherosclerotic plaque from different angles?[END_REF] , anti-CD3 [START_REF] Sasaki | Oral anti-CD3 antibody treatment induces regulatory T cells and inhibits the development of atherosclerosis in mice[END_REF][START_REF] Steffens | Short-term treatment with anti-CD3 antibody reduces the development and progression of atherosclerosis in mice[END_REF] and anti-CD20 [START_REF] Ait-Oufella | B cell depletion reduces the development of atherosclerosis in mice[END_REF] antibodies, the peptide that we used in this study induces a "targeted" immunosuppressor effect because it does not cause lymphocyte depletion and reduces the release of selected disease-related cytokines . Moreover, since disease severity is linked to the extent of CD31 shedding from leukocytes [START_REF] Caligiuri | Reduced immunoregulatory CD31+ T cells in patients with atherosclerotic abdominal aortic aneurysm[END_REF] , which can be easily measured in plasma samples [START_REF] Fornasa | TCR stimulation drives cleavage and shedding of the ITIM receptor CD31[END_REF] , the dosing of the peptide could be finely adjusted to optimize the benefit/risk ratio of its use as a drug. Peptide-treated mice (n=8) showed significantly reduced (*p<0.01) cell infiltration as compared to control mice (n=8). Interestingly, a higher adventitial nuclear density was correlated with the presence of abdominal aortic aneurysms (AAA, red dots; no AAA, green dots).

CVR-2011-1155R1

LEGENDS

1. 5

 5 mg/Kg fluorescent (5,6-FAM-conjugated) peptide, 30 minutes before euthanasia (day 28). All the investigations conformed to the Directive 2010/63/EU of the European Parliament and formal approval was granted by the Local Animal Ethics Committee (Comité d'éthique Bichat -Debré).

  Macrophage intracellular MMP-2/9 activity was quantified by flow cytometric detection of a fluorescent enzyme substrate, according to the manufacturer's instructions (Invitrogen). Briefly, 10 µg/ml fluorescein-conjugated DQ TM type IV collagen, analog of the MMP-2/9 natural substrate, were added to stimulated macrophages for six hours and the fluorescence derived from the enzymedriven hydrolysis of the fluorescein-conjugated DQ TM was quantified by flow cytometry. IL-1, IL-1, IL-12/IL-23p40, RANTES, IL-6, MCP-1 and MIP-1 and MIP-1 (CBA flex sets, BD Biosciences) were measured in the culture supernatants from each condition. Individual mouse data (n =4), expressed as Median Fluorescence Intensity (MFI) have been used for statistical analysis. Statistical Analysis. Data are expressed as means ± SD unless otherwise indicated in the text.

Figure 1 .

 1 Figure 1. CD31 peptide-treatment prevents plaque growth and aneurysm formation. a. The

Figure 2 .

 2 Figure 2. Immunoregulatory effects of the CD31 peptide in vivo. a. The percentage of Tregs (CD25 + FoxP3 + ) was increased while the relative fraction of activated T-cells (CD69 + ) CD4 + Tcells among total blood CD3 + T-cells was diminished by the peptide treatment (*p<0.05). b. Plasma

Figure 3 .

 3 Figure 3. The CD31 peptide inhibits TCR-stimulated T cell responses in vitro and drives

Figure 4 .

 4 Figure 4. oxLDL stimulation drives the cleavage and shedding of CD31 and the CD31 peptide

Figure 5 .

 5 Figure 5. The CD31 peptide binds to plaque-infiltrating and peri-aneurysmal adventitial

Figure 6 .

 6 Figure 6. The CD31 peptide inhibits macrophage response to angiotensin II. a. Representative

ACKNOWLEDGEMENTS

We thank Devy Diallo (Inserm U698) for his help with the lipoprotein profile analysis and Mary Osborne-Pellegrin (Inserm U698) for her help in editing the manuscript.

CONFLICT OF INTEREST

None declared.

CVR-2011-1155R1

FUNDING

This work was supported in part by the "Fondation de France" (Engt 2008-002724), the "Agence Nationale de la Recherche" (project "RELATE" and project "BROSCI"), the "Fighting Aneurysmal Disease" (FAD, #217) European integrated project (Health-F2-2008-200647). G.F. was the recipient of grants from the "Groupe de Reflexion sur la Recherche Cardio-Vasculaire", "Féderation Française de Cardiologie" and "Fondation pour la Recherche Médicale". M.C. is the recipient of a doctoral grant provided by the "CODDIM" from the Region île de France.


G L Gattobigio

A Couvert

G Reinaudi

B Georgeot

D Guéry-Odelin

Optically guided beam splitter for propagating matter waves

Keywords: numbers: 37.27+k, 37.10.Gh, 05.45.-a, 67.85.-d

We study experimentally and theoretically a beam splitter setup for guided atomic matter waves. The matter wave is a guided atom laser that can be tuned from quasi-monomode to a regime where many transverse modes are populated, and propagates in a horizontal dipole beam until it crosses another horizontal beam at 45 o . We show that depending on the parameters of this X configuration, the atoms can all end up in one of the two beams (the system behaves as a perfect guide switch), or be split between the four available channels (the system behaves as a beam splitter). The splitting regime results from a chaotic scattering dynamics. The existence of these different regimes turns out to be robust against small variations of the parameters of the system. From numerical studies, we also propose a scheme that provides a robust and controlled beam splitter in two channels only.

Matter-wave interferometry has the potential of being several orders of magnitude more sensitive than optical interferometry. Many demonstrations have been made of its use as high-precision gravimeters or gyrometers [1]. Its development requires the coherent manipulation of matter waves with atom optical elements. In this respect, the achievement of beam splitters for atoms moving in free space was essential [2][3][4][5][6][7][8].

To optimize the sensitivity of an atomic interferometer, one needs large angle beam splitters with atom wave packets into superposition of two narrow momentum distribution with large momentum separation. Narrow distribution yields good fringe contrast [9]. A few strategies are currently explored or envisioned to increase the enclosed area: the enhancement of the interaction time based on large momentum beam splitter [7,8,10], atom interferometry experiments placed in a reduced gravity environment [11,12], or the use of slow atoms in a guided environment.

In this Letter, we shed light on the physics of matter wave splitting in a crossing guide configuration. Confined geometry for atom interferometry are promising in terms of compactness and portability. The wide variety of techniques available to design potentials and guides for the external degrees of freedom has been used to investigate the operation mode of different type of beam splitters. One should distinguish those involving a trap [10,[13][14][15][16][17][18] and those based on combinations of waveguides [19][20][21][22][23]. So far, the former have been investigated with Bose-Einstein condensate (BEC) while the latter were studied in the thermal regime. In this work we report on the study of an all-optical beam splitter structure for propagating matter waves both experimentally and numerically and in both regimes (i.e. various initial transverse modes of the guide from the multimode to the monomode limit [24]). This problem amounts to a quantum scattering problem in confined environment in which chaotic behavior can emerge [25][26][27].

The beam splitter is obtained by combining two guides which provide a potential structure where four paths are available for the matter wave. In our experimental setup, we use two dipole beams crossing at 45 o in an horizontal plane (see Fig. 1). This X configuration has four channels [28]. Optical confinement has many advantages: it can be applied to atoms with no permanent magnetic moment (e.g., ytterbium and alkaline-earth), which is particularly interesting for metrology, an extra magnetic field can be used to tune the interactions (Feshbach resonance) and the focus position can be easily moved [29,30]. Furthermore, the crossing region has a confinement strength larger than that of the guides. As a result the setup is robust against low frequency noise. This is to be contrasted with other Y geometries where the connection zone between the guides implies an important lowering of the potential strength [19][20][21]31].

We produce a rubidium-87 BEC in a crossed dipole trap (located at A in Fig. 1) using two focussed laser beams (wavelength of 1070 nm, waist of w 1 ≃ 35 µm) [24]. Beams L 1 and L 2 originate from the same laser but have a frequency difference of 80 MHz to wash out possible interferences. Atoms are prepared in the |F = 1, m F = 0 internal state through a spin distillation process implemented during the evaporative cooling stage [32]. The guided atom lasers are realized by outcoupling atoms from the BEC in the horizontal dipole beam of the trap either by applying a time-dependent magnetic field gradient or by reducing the intensity of the non horizontal beam of the crossing dipole trap [24,[32][33][34][35][36].

Although atom-atom interactions may not always alter dramatically the coherence [37], theoretical studies of cold atoms interferometers based on guiding potentials show that they can affect dramatically the contrast of the expected interference signal [38,39]. To reduce the role played by interactions we perform the outcoupling very slowly. The low atomic density of the propagating beam makes this system nearly interaction-free [24,32]. The propagating matter wave is charaterized by its atom flux (∼ few 10 5 atoms/s), its mean velocity (13 ± 2 mm.s -1 ) and the mean excitation number n associated to the transverse modes.

Experiments are carried out at a fixed power P 1 = 140 mW of the guide beam L 1 which corresponds to a measured transverse frequency of about 300 Hz and a depth of 10 µK. The crossing beam L 2 has a waist w 2 = 70±5 µm and an adjustable power P 2 . Atoms propagate for a time long enough to obtain clear information on the asymptotic output channels. In practice, the crossing between L 1 and L 2 beams is at 700 µm downstream from the BEC. The beam propagates during 200 ms, and we take an absorption picture after a few ms time-of-flight.

In a first set of experiments, we prepare the propagating guided atom laser in the ground state of the transverse confinement ( n ≃ 0). In this transverse monomode regime, we observe three different regimes (I), (II) and (III) depending on P 2 /P 1 (see Fig. 2). Images (I) belong to the weak defect regime for which the beam is transversally excited after passing through the interaction region. The coherent excitation of the transverse modes is induced by the weak coupling between the longitudinal and transverse degrees of freedom in the crossing guide region. As illlustrated in Fig. 2, the larger P 2 /P 1 , the stronger the coupling and the larger the number of transverse modes populated downstream from the crossing region. Image (II) corresponds to the splitting regime where atoms can explore the four channels provided by our X shape geometry. It corresponds to a much stronger coupling between the different degrees of freedom and the corresponding classical dynamics becomes chaotic (see below) [27,40]. Images (III) illustrate the switch regime where atoms go into one arm of the beam L 2 with a 100 % efficiency [20,21]. The center of mass motion is excited as a result of momentum transfer of the longitudinal incident momentum on the transverse degrees of freedom of the output channel guide. We plot a boundary between (I) and (II) in Fig. 2 (middle) when less than 80 % of the atoms continue their propagation in the original guide L 1 , and between (II) and (III) when more than 80 % of the atoms are deviated to the guide L 2 . The error bars show the typical size of the transition regions.

We also have investigated experimentally this dynamics for various values of the initial mean quantum number n of the transverse states by adjusting the fraction of condensed atoms from which the guided atom laser is produced [24]. For n = 10 more than hundreds of transverse levels are populated since one has to take into account the degeneracy, while one transverse state is populated for n = 0. The results are summarized in Fig. 2 (middle). We observe that the three regimes are still present. However, the transverse oscillations can be observed only for low incoming mean transverse excitation (compare images (IIIa) and (IIIb) taken for different values of n ). In previous experiments where the splitting of a beam of cold atoms was carried out, it was im- possible to observe this transverse excitation since many transverse states were populated and these oscillations were thus washed out [19,20,22,23]. The boundaries between the different regimes appear to be very robust against n and a slight misalignement of the crossing beam. This is to be contrasted with the interaction of a guided atom laser with an out-of-center vertical potential [27]. The boundaries remain nearly unchanged when the crossing is misaligned by a tenth of the waist of the beams. For each set of data the alignment was checked before and after the data acquisition. We estimate that the maximum relative change of the beam positions is below 2 µm.

To interpret the splitting regime, we have computed the dynamics of 2D quantum wavepackets using the split-Fourier algorithm [START_REF]few hundreds of nm) and the long interaction time makes this kind of calculation unrealistic in 3D with the currently available supercomputers[END_REF] and developed a direct simulation Monte Carlo (DSMC) method where atoms are evolved according to classical mechanics (see Fig. 2 (bottom)). The three regimes observed experimentally can be reproduced by numerical simulations and turn out to be generic. Each point in Fig. 2 (bottom) corresponds to the results obtained for an initial state that coincides with the n th transverse eigenstate. We observe that the boundaries deduced from classical and quantum simulations are very close. The fact that the boundaries are not exactly the same in classical and quantum dynamics is somehow expected since the equations fulfilled by the center of mass of the packet are different in classical and quantum mechanics. Indeed, the external potential is not anymore harmonic in the crossing guide region. The error bars on the experimental data are such that one cannot distinguish the classical or quantum nature of the motion at low n. Numerics confirm the robustness of the existence of the boundaries. However, their precise positions can depend on several parameters such as small misalignment of the crossing beams, a residual longitudinal acceleration and/or the relative waist size of the two beams. Many of these parameters cannot be measured accurately. Consequently and to avoid the use of too many free parameters, we do not fit the experimental data with the numerics but use the numerics to identify the underlying physics and confirm its generic character and its robustness.

Figure 3 provides a typical experimental example of the dynamics of the splitting regime. The guided atom laser that enters the crossing region remains partially trapped (larger density) and then the contamination of all available branches is observed. We have plotted in Fig. 4 the output channels obtained from a simulation relying on classical mechanics (using different color for the different output channels) for different initial conditions of the transverse phase space. We clearly identify a chaotic region with a fractal structure in which a very small change in the initial condition changes the output channel. This is the signature of a chaotic dynamics [25]. We have also checked that Lyapunov exponents become positive in this parameter region. To further characterize this zone, we have verified that the set of boundaries between the four accessible output channels as a function of the initial conditions displays a fractal structure. For a wide variety of fixed transverse velocity v y in regime (II), we find a fractal dimension of ξ ≃ 0.85 revealing a strong fractality of the basin boundaries, usually associated with chaotic scattering. Furthermore, numerics seem to indicate that the fractal Wada property [25,[START_REF] Kennedy | [END_REF]43] (every point on the boundary of a basin is on the boundary of all basins) can be fulfilled in this system. The distribution of trapping times in the vicinity of the crossing guide region is found to exhibit an exponential decay.

Interestingly the population in a given channel can be reduced by adding a small extra gradient ; this happens in the experiment if the beams are not perfectly horizontal. In our nearly horizontal configuration, a gradient that corresponds to a hundredth of the gravity strength is sufficient to dissymmetrize dramatically the population in the output channels. In this way one can populate only two channels and realize a two-channel beam splitter. This effect has been checked numerically and explains the variation of the populations in the different channels seen in the experimental results (compare image (II) of Fig. 2 and images of Fig. 3). A beam splitter experiment for a thermal cloud accelerated by gravity in a quasivertical configuration has been discussed in [22,44]. Note that the possibility of realizing a coherent beam splitter using the transient dynamics of a chaotic system has been addressed in another context with amplitude modulated optical lattices [45].

The X configuration that we have investigated thus exhibits two regular regions separated by a chaotic region. Actually, the numerical simulations reveal the existence of other splitting region at even higher power ratio P 2 /P 1 that were not investigated in our experiment. These splitting regimes are undesirable for interferometry since the relative phases of the matter wave in the different output channels can be affected in an uncontrollable manner from run to run. A possible solution as investigated numerically in [46] consists in adding a dedicated extra potential to decrease the coupling between FIG. 3: (color online) Example of experimental splitting dynamics illustrating regime (II) (see Fig. 2). Time evolution is directly visible in the succession of absorption images.The images show a larger density at the crossing point which is attributed to the complex dynamics that traps the atoms there for some time. Atoms that escape from this region populate all available channels. the longitudinal and transverse degrees of freedom.

In the following, we propose an alternative scheme using a transverse momentum kick transferred to atoms before they enter the crossing region. The power ratio is chosen to be in regime (III) (the switch guide regime). Different experimental techniques can be used to achieve such a transfer: Bragg or Raman transitions, Bloch oscillations [START_REF] Cohen-Tannouji | Advances in atomic physics: an overview[END_REF]. In our simulation, we add an instantaneous transverse momentum upstream to account for the momentum kick. Figure 5 summarizes our numerical results. Each asymptotic output channel obtained here from a classical simulation is represented by a different color as a function of the velocity kick value and the "phase" i.e. the position before the crossing at which the momentum transfer is performed. Using the prediction of the simulations relying on classical physics as guidelines for quantum simulations, we conclude on the feasibility of re-directing atoms in guide L 1 with an efficiency larger than 96 %. This technique enables to switch from guide L 2 to L 1 without changing in time the guide characteristics [20,21]. This also means that if the incoming wave packet is prepared in a linear superposition with equal weight of the states with and without the proper transverse momentum kick, the wave function can be split into two coherent wave packets that propagate in the two guides L 1 and L 2 . Interestingly enough, the domain of useful parameters in momentum kick and phase to realize such a guided matter wave beam splitter is relatively large. This shall ensure the robustness of the method. The splitted beams are for each guide in an excited state that is responsible for their transverse oscillation (see image (III) of Fig. 2). An out-of-guide axis potential with an appropriate strength can be used to remove the remaining transverse dipole oscillation [27].

In conclusion, this Letter reports on the realization of all-optical guided beam splitter devices. Such tools are important for the development of guided atomic optics which has a huge potential for applications, in particular for inertial sensors. In addition, it was shown recently that there exists a direct mapping between waveguide theory and spin chain transport [START_REF] Makin | [END_REF], opening possible applications of our scheme in solid state physics.

2 gFIG. 1 :

 21 FIG. 1: (color online) Schematic of the matter wave guided beam splitter setup based on two crossing dipole beams in a horizontal plane. Atoms are outcoupled from a BEC located at point A and propagate in the beam L1 towards point B where beam L2 crosses beam L1.

FIG. 2 :

 2 FIG.2:(color online) Propagation of an atom laser in a X shape guide structure. Top: Three regimes are experimentally observed depending on the power ratio associated with each guide: (I) weak defect regime where the excitation of transverse modes downstream from the crossing increases with the power ratio P2/P1, (II) splitting regime where atoms explored all the available channels, and (IIIa/b) switch regime where all atoms are directed into guide L2. The mean transverse excitation numbers of the incoming beam are n ≃ 0.3 (IIIa) and n ≃ 10 (IIIb). Middle: Experimental diagram that summarizes the observed regime depending on both the power ratio P2/P1 and the mean transverse populations. The boundaries of the three regimes turn out to be robust against the population of the transverse modes. Bottom: Numerical simulations confirming this robustness; red solid line: quantum simulations, blue dotted line: classical simulations. Wave packets are started 150 µm before the crossing, with initial longitudinal velocity 10 mm.s -1 , for w1 = 45 µm, w2 = 41 µm.

10 FIG. 4 :

 104 FIG.4:(color online). Left: colors associated with the different output channels. The arrow indicates the propagation direction of the incoming atoms. The overlap region between the guide is represented as a dark blue disk. Right: Output channels associated to different initial phase space conditions of the transverse degree of freedom in regime (II) (see Fig.2). Each classical trajectory started at the bottom of the guide, 150 µm before the crossing, with initial velocity 10 mm.s -1 , for w1 = 45 µm, w2 = 41 µm, P2 = 0.143 W= 0.8 P1.

FIG. 5 :

 5 FIG. 5: (color online). Left: Output channels for a classical trajectory started at the bottom of the guide, between 100 µm and 200 µm before the crossing, with initial longitudinal velocity 10 mm.s -1 , and an initial transverse velocity between -25 mm.s -1 and 25 mm.s -1 , with w1 = 45 µm, w2 = 41 µm, P2 = 0.365 W= 2.04 P1. Right: center of mass motion of numerically simulated quantum wave packets. The one with initial parameters of point C (150 µm before defect, no transverse velocity) is deviated in the second guide at 99.9 % (green curve). In contrast, the one with initial parameters of point D (154.75 µm before defect, transverse velocity of 15.5 mm.s -1 ) ends up at 96.2 % in the initial beam (blue curve).

We thank R. Mathevet and T. Lahaye for useful comments at the early stage of this work. We acknowledge financial support from the Agence Nationale de la Recherche (GALOP project), the Région Midi-Pyrénées, the university Paul Sabatier (OMASYC project), the NEXT project ENCOQUAM and the Institut Universitaire de France. We thank CalMiP for the use of their supercomputers.


Charles Blandin
email: charles.blandin@inria.fr

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

Alexey Ozerov
email: alexey.ozerov@inria.fr

Multi-Source TDOA estimation using SNR-based angular spectra

Keywords: Multiple source localization, TDOA estimation, signal-to-noise ratio, angular spectrum

This paper deals with the localization of multiple sources from two-channel mixtures recorded in a reverberant environment. We introduce new angular spectrum-based methods relying on the signal-to-noise ratio (SNR) to estimate the time difference of arrival (TDOA) of each source. We propose and compare five ways of estimating the SNR in each time-frequency point and in each direction, using beamforming techniques and statistical models. Large-scale evaluation considering a high number of situations shows the effectiveness of the proposed approach compared to state-of-the-art angular spectrum-based techniques.

INTRODUCTION

Recorded signals are often a mixture of several sound sources such as speech, music or noise. Source localization is the task of estimating the direction of arrival (DOA) of each source. It has potential applications in many domains such as videoconferencing, surveillance, or blind source separation.

This problem is particularly difficult in the two-channel under-determined case, when three or more sources must be localized from only two sensors. Localization is often achieved by finding time difference of arrival (TDOA) between channels for each source [START_REF] Knapp | The generalized crosscorrelation method for estimation of time delay[END_REF][START_REF] Schmidt | Multiple emitter location and signal parameter estimation[END_REF]. Usually, this problem is addressed using the short-time Fourier transform (STFT). Let X(t, f ) = [X 1 (t, f ), X 2 (t, f )] T and S n (t, f ), n = 1, . . . , N be respectively the STFT of the observed signals and the n-th source signal in time frame t and frequency bin f . The mixture can be modeled as the sum of a direct part and a reverberated part B(t, f ):

X(t, f ) = N n=1 d τn (f )S n (t, f ) + B(t, f ) (1)
where τ n is the TDOA of source n and

d τ (f ) = [1, e -2iπf τ ] T (2)
This work was supported in part by French ANR project ECHANGE and by the Quaero Programme, funded by OSEO.

is the steering vector associated with TDOA τ . Each TDOA thus translates into an expected phase difference 2πf τ at each frequency f . Three different approaches have been proposed in the literature. A first one [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequency masking[END_REF][START_REF] Faller | Source localization in complex listening situations: Selection of binaural cues based on interaural coherence[END_REF][START_REF] Arberet | A robust method to count and locate audio sources in a multichannel underdetermined mixture[END_REF] is to convert the observed phase difference into a TDOA in each time-frequency bin and to build a histogram of the TDOAs whose peaks point to the sources. This approach is restricted to small microphone spacings for which little or no spatial aliasing occurs. A second possibility [START_REF] Izumi | Sparseness-based 2ch BSS using the EM algorithm in reverberant environment[END_REF][START_REF] Sawada | Grouping separated frequency components by estimating propagation model parameters in frequency-domain blind source separation[END_REF] is to alternately cluster the timefrequency bins into sources and update the source TDOAs according to the observed phase differences. It does not suffer from spatial aliasing but necessitates an initial guess of the source TDOAs due to local optima. A third approach [START_REF] Knapp | The generalized crosscorrelation method for estimation of time delay[END_REF][START_REF] Schmidt | Multiple emitter location and signal parameter estimation[END_REF][START_REF] Nesta | Cumulative state coherence transform for a robust two-channel multiple source localization[END_REF] is to build a function of TDOA that we call angular spectrum, whose peak(s) indicate the TDOA(s) compatible with the observed phase difference in each time-frequency bin, and to sum this function over all bins. In the following, we consider the latter approach which is applicable to any microphone spacing and does not necessitate any prior guess of the source TDOAs.

A limitation of current angular spectrum-based methods is that they essentially assign the same weight to all observed phase differences, whether they result from the direct sound of single source or from a mixture of direct and reverberated sound and/or several sources 1 . In [START_REF] Arberet | A robust method to count and locate audio sources in a multichannel underdetermined mixture[END_REF], a signal-to-noise ratio (SNR)-like confidence measure was proposed to weight the information provided in each time-frequency bin in the specific context of histogram-based localization in instantaneous mixtures and was shown to greatly improve localization performance.

In this paper, we propose to use the SNR in each timefrequency point to construct an angular spectrum and define five ways of estimating the SNR in a convolutive mixture using beamforming techniques and statistical models. In section 2, we describe the five proposed SNR-based angular spectra. We evaluate the performance of the proposed approaches and compare them to existing angular spectrum-based methods in section 3. Finally, we conclude in section 4.

SNR-BASED ANGULAR SPECTRA

In a given time-frequency bin (t, f ), we define the SNR(t, f, τ ) associated with TDOA τ as the ratio between the signal power E τ in this direction and the noise power E b (power in all other directions). The SNR is then supposed to take large values in the direction of a given source in the time-frequency bins where this source is predominant. We propose to build an angular spectrum by summing the estimated SNRs over all time-frequency bins and all TDOAs:

Σ(τ ) = (t,f ) SNR(t, f, τ ) (3)
The source TDOAs are then estimated by selecting the values of τ corresponding to the J highest peaks of Σ(τ ). The choice of J leads to a trade-off between recall and precision , as described in section 3.

In order to estimate SNR(t, f, τ ), we propose three different approaches. The first one, that we call a posteriori, uses beamforming to estimate the source power and considers the residual power as noise. The second one, that we call a priori, jointly estimates the source and noise powers in the maximum likelihood (ML) sense, under a diffuse noise model. We then combine these two models to define a third approach based on frequency weighting of the a posteriori SNR.

Estimation of a posteriori SNR

From now on, we consider a single time-frequency bin (t, f ) and omit its indices for simplicity. The power associated with TDOA τ can be estimated as the power of the output of a Delay-and-Sum (DS) beamformer or a Minimum Variance Distortionless Response (MVDR) beamformer, respectively given by [6]

E (DS) τ = d τ H Φ xx d τ 4 (4)
E (MVDR) τ = (d τ H Φ -1 xx d τ ) -1 (5)
where Φ xx denotes the empirical mixture covariance matrix that can be computed as described in [START_REF] Duong | Spatial covariance models for under-determined reverberant audio source separation[END_REF]. We write E b = E X -E τ where E X = 1 2 tr( Φ xx ) represent the total power. We obtain two ways of estimating the SNR for TDOA τ

SNR DS = d τ H Φ xx d τ 2tr( Φ xx ) -d τ H Φ xx d τ ( 6
)
SNR MVDR = (d τ H Φ -1 xx d τ ) -1 1 2 tr( Φ xx ) -(d τ H Φ -1 xx d τ ) -1 (7)
Figures 1 (A) and (B) show the angular spectra obtained respectively with SNR DS and SNR MVDR . As compared to the DS beamformer, MVDR beamformer appears to provide better noise elimination and enhances the peaks.

Estimation of a priori SNR by ML under a diffuse noise model.

In the a posteriori approach, the SNR is generally overestimated at low frequencies. Indeed, the observed phase differences are small so that Φ xx becomes similar to d τ d τ T for all τ . This can be addressed by modeling both the source and the noise as random variables. We assume that in each timefrequency point, one source S of TDOA τ is predominant, and that S and noise B follow independent zero-mean Gaussian distributions. The mixture X = d τ S + B then follows a zero-mean Gaussian distribution with covariance matrix

Φ xx = v s d τ d τ H + v b Ψ (8)
where v s et v b represent respectively the source variance and the noise variance, and Ψ is the covariance matrix of a diffuse noise [4, 2]

Ψ = 1 sinc(2πf d c ) sinc(2πf d c ) 1 ( 9
)
where d is the distance between the two microphones, c is the soundspeed and sinc(.) = sin(.) (.) . We estimate v s and v b in the ML sense using the closed form algorithm in [START_REF] Duong | Spatial covariance models for under-determined reverberant audio source separation[END_REF]

v s v b = (diag(Λ 1 ) diag(Λ 2 )) -1 diag(A -1 Φ xx (A H ) -1 ) (10)
where diag(.) denotes the column vector of diagonal entries of a matrix, A is the matrix whose columns are the eigenvectors of d τ d τ H Ψ -1 , and Λ 1 , Λ 2 are equal respectively to A -1 d τ d τ H (A H ) -1 and A -1 Ψ(A H ) -1 . Non-negativity is imposed by setting v s to zero and v b to 1 2 tr(Ψ -1 Φ xx ) when v b or v s from (10) is negative [START_REF] Duong | Spatial covariance models for under-determined reverberant audio source separation[END_REF]. We then compute the SNR by:

SNR APR = v s v b (11)
This method effectively addresses the SNR overestimation problem at low frequencies but results in slightly wider peaks, so that the resulting spectrum is not much different (see figure 1 (C)).

Estimation of a priori SNR by frequency weighting of a posteriori SNR

We now want to combine both approaches to obtain an angular spectrum with the global shape of a priori SNR and the precision of a posteriori SNR. In order to do so, we express the relationship between these two forms of SNR, in the simple case where the input signal consists in a single source of TDOA τ = 0 and a diffuse noise. Φ xx is then given by [START_REF] Sawada | Grouping separated frequency components by estimating propagation model parameters in frequency-domain blind source separation[END_REF]. By plugging (8) into ( 6) and ( 7), we obtain:

SNR DS = 1 + 2 SNR priori + sinc(2πf d c ) 1 -sinc(2πf d c ) (12)
SNR MVDR = 1 + 2 SNR priori + sinc(2πf d c ) 1 -sinc(2πf d c ) (13)
where SNR priori = v s /v b . By inverting these equations, we obtain a new way of computing a priori SNR by frequency weighting of a posteriori SNR, for both SNR DS and SNR MVDR :

SNR DSW = W d (f )SNR DS + W d (f ) -1 (14) SNR MVDRW = W d (f )SNR MVDR + W d (f ) -1(15) where W d (f ) = 1-sinc(2πf d c ) 2
is a frequency-dependent factor reducing the weight of low frequencies. Figure 1

EXPERIMENTAL EVALUATION

We evaluated the five proposed methods on a large number of configurations, involving two to six sources, six reverberation times (from 50 ms to 750 ms), four microphone spacings (from 5 cm to 1 m), four distances between the sources and the center of the microphone pair (from 20 cm to 2 m), several source DOAs, and three source types (male speech, Recall, precision and F-measure for J J opt (A, N, d) averaged over all configurations. female speech and music). 4446 mixtures of 11 s duration were generated in total using impulse responses simulated via the Roomsimove toolbox2 for a room of dimensions 4.45 m × 3.55 m × 2.5 m. Matlab code implementing the five proposed methods is available 3 . We compared these methods with three existing angular spectrum methods GCC-PHAT [START_REF] Knapp | The generalized crosscorrelation method for estimation of time delay[END_REF], MUSIC [START_REF] Schmidt | Multiple emitter location and signal parameter estimation[END_REF], and cSCT [START_REF] Nesta | Cumulative state coherence transform for a robust two-channel multiple source localization[END_REF]. The parameters of cSCT were fixed by interpolation of the values chosen by the author for other configurations.

Evaluation was made in terms of recall, precision and Fmeasure. An estimated TDOA τ is considered to be a correct estimate of a true TDOA τ if c d (ττ ) ≤ γ with γ a constant set in our experiments to 0.05. For N sources, if we select the TDOAs corresponding to the J highest peaks of the angular spectrum, and we note I J the number of correct TDOAs, we define the recall R, the precision P and the F-measure F by R(J) = IJ N , P(J) = IJ J and F(J) = 2 R(J)×P(J) R(J)+P(J) respectively [START_REF] Van Rijsbergen | Information retrieval, 2nd Edition[END_REF].

Figure 2 (A) shows the average F-measure as a function of J for N = 6 sources. For all evaluated algorithms, excepted MUSIC and GCC-PHAT, the F-measure reaches its maximum for J equal to the number of sources N . The best F-measure is obtained by SNR MVDRW and SNR DSW which provide respectively an improvement of 0.06 and 0.04 compared to cSCT.

In the following, we fix the number of selected peaks to a value J = J opt (A, N, d) for each algorithm A, each number of sources N and each distance between microphones d, so as to maximise the F-measure averaged over all other parameters. Indeed, preliminary experiments showed that these parameters have the most important effect on the value of J opt . The resulting average recall, precision and F-measure are presented in table 1. The best recall, precision and F-measure are obtained by SNR MVDRW and SNR DSW .

Figure 2 shows the F-measure obtained as a function of microphone spacing d and reverberation time RT 60 for speech sources. All methods provide poorer results with microphone spacings smaller than 15 cm or with larger reverberation time. SNR MVDRW the other evaluated methods for most microphone spacing and for all reverberation times. The two principal reasons are that it is robust to high reverberation thanks to MVDR beamforming, and to small microphone spacing thanks to frequency weighting.

CONCLUSION

We proposed five new angular spectrum methods using SNR to estimate TDOAs in two-channel under-determined mixtures. Large-scale evaluation showed that two of the proposed angular spectra, based on frequency weighting of SNR estimated by beamforming techniques outperform state-of-theart methods in most configurations. Future work will focus on summing a nonlinear function of SNR in each time-frequency point and in using other information such as harmonicity to improve TDOA estimation.

  (D) shows the shape of W d (f ) for different values of d. Angular spectra obtained with SNR DSW and SNR MVDRW are represented in figure 1 (E) and (F).

Fig. 1 .

 1 Fig. 1. Angular spectra produced by SNR DS (A), SNR MVDR (B), SNR APR (C), SNR DSW (E) and SNR MVDRW (F) for three female speech sources placed at 50 cm from the center of the microphone pair, with d = 15 cm and a reverberation time of 500 ms. (D) represents the weighting factors W d (f ) for different microphone spacings d.

Fig. 2 .

 2 Fig.2. Average F-measure of the evaluated algorithms as a function of the number of selected peaks J for all 6-source mixtures (A) and as a function of microphone spacing d (B) and reverberation time RT 60 (C) with J = J opt for all speech mixtures.

Table 1 .

 1

	SNR DS MVDR APR DSW MVDRW PHAT GCC MUSIC cSCT
	R 0.41 0.58 0.64 0.63	0.66	0.56	0.58	0.61
	P 0.48 0.61 0.66 0.67	0.69	0.65	0.24	0.64
	F 0.43 0.59 0.65 0.65	0.67	0.58	0.34	0.62

MUSIC[START_REF] Schmidt | Multiple emitter location and signal parameter estimation[END_REF] attenuates the effect or reverberation or interfering sources by denoising in the parameter domain but the output spectrum does not depend on the resulting signal-to-noise ratio

http://www.irisa.fr/metiss/members/evincent/software

http://bass-db.gforge.inria.fr/bss locate

ACKNOWLEDGEMENTS

The authors would like to thank F. Nesta for sharing his cSCT code, and N. Ito discussion during the course of this work.