Youcef Messai

Bertrand Vileno

David Martel

Philippe Turek

Eddine Mekki
email: mekki.djameleddine57@gmail.com

Milling effect on the photo-activated properties of TiO 2 nanoparticles: electronic and structural investigations

Keywords: Titania nanoparticles, ball milling, photo-catalytic properties, photo-generated radicals, electronic paramagnetic resonance spectroscopy

Commercial PC105 titanium dioxide nanoparticles were studied under mechanical milling process. The effect of milling time and speed on the structural and electronic properties of TiO 2 powder was then investigated using X-ray powder diffraction (XRD), dynamic light scattering (DLS), transmission electronic microscopy (TEM), electron paramagnetic resonance (EPR) and UV-visible spectroscopy. The related photo-catalytic properties of the milled nanoparticles were probed following the degradation rate of methylene orange (MO) under UV-light irradiation and through EPR spinscavenging approach. Comparison with pristine powder shows that milled nanoparticles are significantly less reactive upon illumination, despite decreased radius and hence, higher specific area. Such low yield of reactive species is attributed to the apparition of the amorphous TiO 2 and brookite phase upon milling, as well as increased charge carrier recombination as pointed out by the presence of sacrificial electron donor.

Introduction

Nowadays, nanoparticles (NPs) find numerous and increasing uses in many fields of technology. This trend is foreseen to considerably expand in the near future, ranging from biology to medicine, energy storage, environment, pigment or cosmetic industries [START_REF] Mozafari | Nanomaterials and nanosystems for biomedical applications[END_REF][START_REF] Zhang | [END_REF][3]. This wide variety of applications is undoubtedly related to their peculiar characteristics that include particle shape, specific area, charge, chemistry, dispersion and/or agglomeration characteristics, aggregate size and shape distribution, solubility and porosity [4][5][6][7].

Remarkably, the research towards the development of highly active heterogeneous photo-catalysts, naturally oriented towards transition metal oxides (TMOs, such as TiO 2 , ZnO, SnO 2 ) that are semiconductors (SC) with a gap allowing good absorption of light in the UV and/or in the near-visible range. These SC-based NPs often exhibit improved photocatalytic properties due to enhanced surface/volume ratio.

Electronic supplementary material: The online version of this article (https:// doi.org/ 10.1007/ s12034-018-1572-8) contains supplementary material, which is available to authorized users.

When combined with the so-called methods of advanced oxidation processes (AOP) [8], these materials are known to be efficient decontaminant:neutralizing bacteria and viruses [9,10], as well as degrading organic pollutants within air and water [11]. Such high applicative potential involves various processes ranging from photolysis via H 2 O 2 [12], to Fenton or photo-Fenton effect [13], where photo-mediated reactive oxygen species (ROS) are playing central role.

Among TMOs, TiO 2 is considered as one of the most promising for wide environmental-and energy-applications, because of its suitable valence and conduction band positions, long-term stability, cost-effectiveness and strong oxidizing power [14]. It is a polymorphic material with three main distinct phases [15]: anatase (tetragonal phase, I4 1 /amd space group, indirect band gap, E g = 3.2 eV), rutile (stable tetragonal phase, P4 2 /mnm space group, direct band gap, E g = 3.0 eV) and brookite (stable orthorhombic phase, Pbca space group, direct band gap E g = 3.3 eV) [16,17].

1

While with a higher surface adsorption capacity to hydroxyl groups, anatase was shown to present lower charge carrier recombination rate than rutile [18,19]. Indeed, the lifetime of photo-generated electrons and holes in anatase is about an order of magnitude greater than one of the rutile. This greatly promotes their contribution to surface chemical reactions [20]. Moreover, the average effective mass of photo-generated electrons and holes in anatase displays smaller value in comparison to rutile and brookite [21]. The transfer rate of photo-generated electrons and holes being inversely proportional to their effective masses [17], the photo-excited charge carriers of anatase is thus transferred faster to the semiconductor surface [22]. These facts bear out the idea that TiO 2 in its anatase form shows better photo-catalytic performance than rutile and brookite [12,23,24]. Regarding the present study, it was shown that ROS are photo-generated via TiO 2 NPs suspension under UV illumination [25,26].

There are several methods to prepare TiO 2 NPs, such as sol-gel [27], micro emulsion [28], hydro-and solvo-thermal [29] precipitations or co-precipitations [30,31]. Mechanical milling (MM) is also widely used, as it is a cheap, efficient and relatively simple technique to handle. During the process, powder particles are subjected to severe mechanical deformations and are repeatedly deformed, heat-treated (cooling and warming), welded and fractured, inducing their gradual refinement to nanometer scale [22,[START_REF] Koch | Nanostructured materials: processing, properties, and applications[END_REF][START_REF] Shokrollahi | [END_REF][34]. Consequently, unusual properties could appear via the emergence of structural defects that can be charged or not.

Although numerous articles report on the correlation between photo-catalytic activity and the physical properties [35,36] (particle size [37], crystal structure [38,39], surface area [40]), recent investigations challenged such conclusions [41,42]. Among the available experimental approaches, MM at high energy is an established method to modify physical properties [43], aiming to improve the material properties. Nevertheless, the consequences of milling on TiO 2 NPs are still debated. Rezae et al [44] showed that MM for 6 h causes a complete conversion of the anatase phase to the brookite and rutile phases. Other recent studies indicate that milling of TiO 2 NPs results in an amorphous material [45,46], which is photo-catalytically inactive [47]. Moreover, Bégin et al [45] observed the degradation of the photo-catalytic properties of TiO 2 NPs after MM and attributed it to new channels of radiative recombination produced upon milling. Indeed, partial amorphization of NP surfaces induces an increase of surface defect density and offers electron/hole (e -/ h + ) recombination pathways. The e -/ h + recombination rate in presence of amorphous phase occurs more quickly when compared to any pure crystalline phase [36]. Such conclusions were also achieved in very recent work by Aggelopoulos et al [48], comparing ZnO and TiO 2 NPs. Nevertheless, Saitow and Wakamiya [46] showed an impressive 130-fold enhancement of the photo-catalytic properties of NPs TiO 2 prepared by planetary ball milling, pointing to the controversy of scientific debate. Such enhancement was attributed by the authors to the disordered, amorphous state together with the srilankite phase of TiO 2 NPs produced upon milling.

The present work deals with the effects of MM conditions (time and speed) on anatase TiO 2 NPs through the resulting structural modifications and electronic properties as well as the photo-catalytic activity towards MO degradation. The structural and morphological properties of the studied NPs were investigated by classical X-ray diffraction (XRD), transmission electron microscopy (TEM) and dynamic light scattering (DLS). The electronic properties were analysed by means of UV-visible spectroscopy of the solid state. Additionally, electronic paramagnetic resonance (EPR) spectroscopy was performed to probe the photo-mediated reactive species by using spin-scavenging approach via 4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPOL) reduction [49]. All the obtained results are compared with the properties of pristine TiO 2 nanoparticles.

Materials and methods

MM

Anatase TiO 2 (PC105) NPs were purchased from Crystal Global. Average NP size is of ca. 25 nm, surface area estimated at ca. 90 m 2 g -1 and the weight purity is of ca. 95%. Samples of PC105 (1.7 g) with a ratio of 97:3 from ball masses vs. NP powders was charged under an Ar atmosphere in high-energy planetary ball mill (FRISCH premium line). Milled NPs were successfully obtained with two speed conditions ( = 200 and 400 rpm) and four different milling times (t = 1, 3, 5 and 7 h) for each speed.

XRD

TiO 2 NPs XRD spectra were carried out with a panalytical Phillips X'Pert Pro diffractometer, equipped with a CuKα 1 anticathode (λ = 0.15406 nm). The XRD patterns were recorded between 20 and 90 • with a monitoring step of 0.03 • .

DLS

A Zetasizer Nano ZS (Malvern, λ = 633 nm) and a disposable folded capillary cell were used to measure the hydrodynamic diameter of the aggregated TiO 2 NPs in aqueous suspension. All the hydrodynamic diameter distributions correspond to number distributions.

TEM

The morphology and crystalline structure of TiO 2 NPs were studied with a Tecnai G2 20 Twin TEM. An aqueous suspension of TiO 2 (0.1 g l -1 ) was sonicated for 15 min to reduce the granulation. Five microlitres of this suspension was deposited onto a grid covered by a thin carbon film.

Optical characterization

Band gaps were determined via optical measurements. UVvisible spectra of TiO 2 powders were recorded at room temperature in reflection mode in the range of 200-800 nm with a JASCO V-750 spectrometer, equipped with an integrating sphere model #ILN-725.

Photo-catalytic activity

2.6a MO degradation: Aqueous suspensions (250 ml) of TiO 2 NPs (200 mg l -1 ) and 45 μM of MO (purchased from Aldrich) were prepared. Prior to any illumination step, the suspensions were stirred in the dark for 30 min. The suspensions were subsequently irradiated with a UV lamp (Vilber Lourmat VL-215-BL, λ max = 365 nm, P = 60 W) located at 15 cm from the sample to avoid heating of the suspension and pigment bleaching. The suspensions were stirred during the whole experiment and the temperature was kept at 298 ± 2K. Two and a half millilitres of the working solution was repeatedly withdrawn from the working suspension, centrifuged and the supernatant was analysed by UV-visible spectroscopy performed in transmission mode with a JASCO V-750 spectrometer. The present experimental data show the decay of the absorbance recorded at the wavelength of λ = 480 nm (see supplementary figure S1b) and normalized to the value obtained prior to the first illumination. The adsorption of the MO onto the NPs surfaces was found to be negligible (<5% of the dye concentration after 3 h in contact with the TiO 2 suspension), the threshold being reached after 30 min (data not shown).

2.6b EPR spin-scavenging: Experimental protocol was derived from the existing methodology described elsewhere [50,51]. Continuous-wave (cw) EPR spectra were recorded at room temperature using an X-band ECS 106 (Bruker-Biospin GmbH, Germany) spectrometer equipped with a regular TE102 resonator. This setup was used to record the conventional field-swept spectra from the aqueous suspensions containing TiO 2 suspensions (0.1 g l -1 ) and 200 μM of TEMPOL (purchased from Aldrich) in ultrapure water (18.2 M cm -1 ). TEMPOL is a paramagnetic probe (i.e., active) known to react with small-sized radicals leading to diamagnetic and hence, EPR silent byproducts [50]. Therefore, its decay is testimony of the photo-mediated generation of reactive species. The EPR spectrum of 200 μM prior illumination is presented in supplementary figure S1a. Ethylenediamine tetraacetic acid (EDTA, purchased from Aldrich) was also used in this work as electron sacrificial donor. Prior to measurements, the solutions (1 ml) were sonicated (15 min in a sonicator bath). Afterwards, the solutions were immediately transferred into thin-wall glass capillaries (Hirschmannrin caps, 50 μl), which were sealed at both ends. Illumination of the sealed capillaries was performed outside the cavity with a UV light source Vilber Lourmat T-4.L (λ max = 365 nm and E(1 cm) ≈ 1.5 mW cm -2 measured with a power meter 1936-C Newport). The EPR spectra were recorded after each irradiation step. The main experimental parameters were: microwave power of 2 mW, time constant of 40 ms, conversion time of 80 ms and sweeping of 100G leading to ca. 80 s of accumulation per scan. All experiments were performed at room temperature (295 ± 2K).

EPR measurements at low temperature

Sixty milligrams of TiO 2 powder were introduced in a 4 mm outer diameter quartz tube and degassed for ca. 10 min at room temperature. The cw-EPR spectra were recorded at 25K with a micro X-EMX spectrometer (BrukerBiospin GmbH, Germany) equipped with a high sensitivity resonator (4119HS-W1, BrukerBiospin GmbH, Germany) and liquid He cryostat (ESR900, Oxford Instrument).

Results and discussion

Structural properties

XRD patterns of TiO 2 NPs are shown in figure 1a andb for the two values of milling speed ( = 200 and 400 rpm, respectively), different milling times (1-7 h) and the reference sample (t = 0 h).

Several diffraction peaks are observed for = 200 rpm (figure 1a) at the following angular positions: 2θ = 25, 37.8, 48.5, 53.95, 55, 62.6, 68.9, 70.1, 75 and 82 • . These peaks were identified according to the JCPDS card as the (101), (112), ( 200), (105), (211), (204), (116), (220), ( 215) and (303) Bragg's planes of the anatase TiO 2 structure. The relative ratios between peaks, for a given sample, are almost constant. Furthermore, new peaks were detected for the two longer milling times (t = 5 and 7 h), where the small bump detected around 2θ = 30.8 • can be testimony of brookite phase [41]. Clearly, the more the NPs were milled, the more the data appeared noisy and present a significant baseline at small angles, indicating the rising of an amorphous state.

In contrast, for the high energy milling at = 400 rpm (figure 1b), the peak intensities decrease rapidly. After 1 h milling, the similar amorphous finger print is rising together with a peak close to 2θ = 30.8 • , pointing to brookite phase.

NPs characterization

Average of the grain sizes D of NPs TiO 2 were estimated with Scherrer formula, equation (1) [52,53].

D = K λ β cos θ , ( 1
)
where K = 0.94, θ is the angle of diffraction, λ the X-ray wavelength, β the full-width at half-height of a peak corresponding to a given orientation. The grain sizes were also assessed from TEM observation and are summarized in table 1. The curves resulting from Grain size (nm) DRX (200 rpm) 23 18 13 13 13 Grain size (nm) ± σ via TEM (200 rpm) 19.9 ± 6.9 14.9 ± 5.1 11.9 ± 3.9 12.8 ± 5. TEM data analysis and representing the grain size distribution (fitted with Gaussian functions) for all the samples milled at = 200 and 400 rpm are given in supplementary figure S2. Accordingly, the grain size varies between 5 and 45 nm. Whatever the XRD or TEM data, grain size significantly decreases from ca. 20 to 12 nm after 3 h of milling at the lowest speed. At the highest speed, a similar trend is observed with a decrease from ca. 20 to 10 nm. The average size of the grain deduced from TEM observations is in good agreement with the one calculated from XRD using Scherrer formula (table 1).

Figure 2 shows the TEM micrographs of TiO 2 NPs for various conditions of milling times (t = reference, 1, 3, 5 and 7 h) and speeds ( = 200 and 400 rpm). During MM, the NPs are subjected to severe mechanical deformations, leading to a progressive evolution of their shape and mean grain size. However, it seems that experiments at higher grinding times would have produced more uniform size distribution and homogeneous spherical shapes. This trend is expected when the high energy ball milling process reach a steady state, where a balance happens between cold welding and fracturing operations [54]. It is to be noticed that these effects are sharper at higher speed (see figure 2).

It is also known that one of the possible consequences of the MM process is the appearance of amorphous and/or unstable phases [55]. It was therefore, interesting to appreciate and observe these phases. For this purpose, TEM images were interpreted by means of a fast Fourier transform (FFT) for milling speed condition, = 200 rpm. Figure 3 shows the FFT of an amorphous grain (single spot) and well-defined crystalline grains (spots distributed with respect to the crystal symmetry). Two lattice spacings of 0.35 and 0.9 nm are measured, which are assigned to the (101) of anatase and (100) plane of the brookite phase [56], respectively, revealed after 3 h milling [57].

DLS analysis

It is known that the transition metal oxides aggregate considerably in aqueous solution [58,59]. As the yield of reactive species is influenced by the available surface and the surface states, the knowledge of the characteristics of the aggregation state is required. For this purpose, both milled and reference samples were characterized by DLS to estimate the hydrodynamic diameter of aggregated NPs. All data were fitted with a Gaussian function and for clarity purpose, only the resulting fits are represented in figure 4.

The materials before milling (t = 0) in suspension have an average diameter of ca. 1 μm (figure 4). Notably, this size remains constant (ca. 550 nm) for all milled TiO 2 NPs i.e., similar to 3 and 7 h milling times as well as reference sample (figure 4b). Moreover, although the particle sizes obtained for both milling speeds and equivalent milling times are similar (see table 1), the subsequent hydrodynamic diameter do not present the same similarities. This suggests a considerable influence of the milling condition on the nature of the NPs surface states that drive the aggregation phenomenon. However, the milling process induced a slight shift of the absorption edge towards higher wavelength, regardless of the speed. Consequently, as MM generates different type of defects (such as surface, lattice strain, vacancy, interstitial, dislocation, grain boundary, etc.), additional states appear within the band gap of TiO 2 , create band tails extending of the valence and conduction band edges [60]. Two important parameters are naturally impacted by this physical situation, namely the optical gap (E g ) and the Urbach energy (E u ) pointing to changes in the electronic structure (doping, disorder, etc.). To assess E g and E u , the absorption coefficients F(R) are deduced from the reflectance curves, according to the Kubelka-Munk equation [61][62][START_REF] Kortüm | Reflectance spectroscopy: principles, methods, applications[END_REF]:

Optical properties and electronic structure

F (R) = (1 -R) 2 2R , ( 2
)
where R is the reflectance, and F (R) is equivalent to the absorption coefficient (α). The band gap, E g is evaluated through the Tauc plot on the linear part of (αhν) n ∝ hν -E g (where n = 1/2 for indirect band gap) for (αhν) 1/2 = 0 (see figure 6). The Urbach energy, E u is given by the following phenomenological relation [START_REF] Grundmann | The physics of semiconductors-an introduction including[END_REF], where α 0 and E 0 are constants related to the studied material:

α = α 0 exp hv -E 0 E u . ( 3
)
Figure 7a and b represent the respective variations of E g and E u as a function of milling time for both the values of . It is observed that as expected, E g and E u have opposite evolution curves. Nevertheless, the more the value of is high, the more its influence is obvious for E g , rather than for E u . Finally, the influence of grain size on the variations of the Urbach energy, E u and the optical band gap, E g is highlighted in figure 7c and d. Although the displayed results are rather scattered, they show clear trends in the evolution of these parameters: for both speeds, E g and E u have regular and opposite behaviours. In summary, regardless of the applied speed, the milling of TiO 2 powder affects the light absorption properties of the powder. Furthermore, it is shown in figure 5 that from about 400 nm, the absorption curves are more spread out toward higher wavelength as the milling time increases. This is attributed to the formation of novel electronic states in the band gap at the TiO 2 nanoparticles surface [START_REF] Indris | [END_REF], in agreement with the observed increase of Urbach energy together with the milling time. In TiO 2 , Ti 4+ is surrounded by six oxygen ions forming the TiO 6 octahedral [66], high energy ball milling alters the arrangement of oxygen ions around Ti 4+ leading to either oxygen vacancies, while breaking the Ti-O bonds [67], or phase changes. This broadens the valence and conduction band edges, decreasing the gap energy, while increasing the Urbach energy [68]. As indicated by the XRD and HRTEM data comparison, it can be assumed that this process starts at the particle surfaces and propagate increasingly to the NP core as a function of energy.

Photo-catalytic properties and ROS generation

As already mentioned, the radical photo-generation is related to surface reactions. Therefore, the morphology of the NPs, the crystal phase as well as the surface states are the major parameters influencing the generation rate of the photomediated ROS. Semiconductors in aqueous suspension are known to generate reactive species upon illumination with photon energy equal or higher to the energy band gap. The photo-generated electrons and holes oxidize and reduce rapidly the molecular oxygen and water as shown in the following equations (5-7) [69], allowing the ROS generation such as O •- 2 and HO • , whose rate competes with the electronhole recombination (equation ( 6)).

TiO 2 + hν → e -+ h + , ( 4
)
e -+ O 2ads → O •- 2 , ( 5
)
h + + H 2 O ads → OH • , (6)
e -+ h + → hν(recombination). (7) Remarkably, other ROS can arise from the reactions described above (equations (5-7)), such as hydrogen peroxide and singlet oxygen [70,71]. Oxidation and reduction processes occur at the particle surface/solvent interface. The average lifetime of the photo-generated ROS being extremely short (from ns to μs at room temperature) when compared to the time of experiment, their evolution rate was estimated following two indirect methods: (i) the study of the degradation of the MO using UV-visible spectroscopy and (ii) spin-scavenging EPR technique using TEMPOL as paramagnetic probe. Figure 8 shows the decay of the normalized absorbance (A(t)/A 0 ) recorded at λ = 480 nm for the reference sample and for all milled samples at the different speed and time conditions. We notice that for both milling speeds, the normalized MO kinetic of degradation (A(t)/A 0 ) slows down when the milling time increases. Interestingly, no photo-catalytic activity is detected (up to 210 min of illumination) for the highest energy milling ( = 400 rpm) and for a milling time of 3 h and more (figure 8b).

To confirm this result, EPR spin-scavenging investigation was achieved [50,72]. The experiment was performed for the TiO 2 NPs, for the reference sample and for all the milling conditions. Figure 9 shows the decay of the EPR-normalized intensity I (t)/I 0 of TEMPOL as a function of the illumination time.

Similar to the MO degradation experiment, TEMPOL concentration decays as a function of UV-exposure time and the respective kinetics slow down when the milling time and/or speed is increased. The reduction of TEMPOL into EPR silent byproducts is mainly attributed here to HO • , H • and/or e - [50]. At the highest milling speed and above 1 h of milling time, I (t)/I 0 curve remains flat despite 90 min of UV exposure in the presence of TiO 2 NPs. When compared to the In several studies, the amorphous phase is defined as a catalytically photo-inactive [47,73,74], due to a higher e -/ h + recombination rate [36]. However, even in the most altered structure investigated in this study (i.e., 7h milling at = 400 rpm), TiO 2 NPs do not appear fully inactive. Indeed, when supplementing the aqueous suspension of NPs with a sacrificial electron donor (such as EDTA), significant reduction of TEMPOL is observed (figure 10), yet delayed when compared to non-supplemented experiment (figure 9). The presence of such electron donor will neutralize the photogenerated holes, limiting e -/ h + recombination rate and therefore, increasing the lifetime of the photogenerated electrons available for TEMPOL reduction through direct pathway or indirect one (H • , HO • ) [50]. Considering the EPR kinetics, with or without EDTA, it appears that the MM does not hamper the overall generation of excitons, but rather drastically increases the recombination rate through newly generated electron traps. These new electronic levels arise from a modification of the electronic level distribution due to the presence of amorphous phase and thus, prevent the formation of reactive species and lead to the degradation of the photo-catalytic properties.

Finally, low temperature EPR (T = 25K) was also used to confirm how MM induces structural alteration of the NPs. On one hand, the EPR fingerprint of nano-TiO 2 in its anatase form [75][76][77] in the g = 2 region appears severely affected by MM (see supplementary figure S4) and is attributed to an increase in the amorphous phase and to induced disorder during milling. On the other hand, EPR spectra with larger sweep range (see supplementary figure S5) exhibit: (i) signals at g = 4.31 testimony of metallic high spin state attributed to Fe(III), and (ii) broad line ascribed to metallic contaminations [78]. Noteworthy, each of such tampering hallmarks is increasing with milling time and speed.

Conclusion

Structural consequences of planetary ball-milling process on TiO 2 NPs are manifold. Significant amorphization of TiO 2 related to the milling time and speed was demonstrated by TEM and XRD, while a weak phase transformation from anatase to brookite was observed. Such phase transformations play in favour of a degradation of the photo-catalytic activity. The diminution of grain size as a function of milling time and speed were characterized by TEM, while the hydrodynamic diameters obtained in aqueous suspension by DLS were determined. These later appear smaller at = 200 rpm and unchanged ca. at = 400 rpm. Such evolutions would suggest an increase in the photo-mediated generation of radicals for the lowest milling speed by increasing their respective available surfaces and an equivalent yield for the highest speed. However, the photogeneration activity assessed by MO degradation and EPR spin-scavenging are unquestionable and point toward a drastic degradation of the photo-catalytic activity concluding that no detectable activity for higher milling speed and milling time ≥3 h. The photo-catalytic activity seems to be affected much earlier than the occurrence of structural changes. However, the use of a sacrificial electron donor allows restoration of the activity, thus, pointing e -/ h + recombination as the limiting process. Finally, EPR at low temperature illustrated the disruption of anatase phase fingerprint as a function of both milling speed and time, and points towards metallic contamination.

Figure 1 .

 1 Figure 1. XRD patterns of NPs TiO 2 before milling and at various milling times for the milling speed (a) 200 and (b) 400 rpm.

Table 1 .

 1 Grain sizes as a function of milling time for the speeds = 200 and 400 rpm. Milling time (h

  nm) ± σ via TEM (400 rpm) 19.9 ± 6.4 15.4 ± 6.2 10.5 ± 3.6 -9.8 ± 2.9

Figure 2 .

 2 Figure 2. TEM images showing the morphology of TiO 2 NPs before and after milling t = 0 (reference), 1, 3, 5 and 7 h with speed = (a) 200 and (b) 400 rpm. Scale bar corresponds to 20 nm.

Figure 5

 5 Figure 5 displays the diffuse reflectance properties, for commercial (reference sample) and milled TiO 2 NPs at all rotation speeds and milling times. Typical fingerprint of TiO 2 NPs crystallite in the UV range is obtained.However, the milling process induced a slight shift of the absorption edge towards higher wavelength, regardless of the speed. Consequently, as MM generates different type of defects (such as surface, lattice strain, vacancy, interstitial, dislocation, grain boundary, etc.), additional states appear within the band gap of TiO 2 , create band tails extending of the valence and conduction band edges[60]. Two important parameters are naturally impacted by this physical situation, namely the optical gap (E g ) and the Urbach energy (E u ) pointing to changes in the electronic structure (doping, disorder, etc.). To assess E g and E u , the absorption coefficients F(R) are deduced from the reflectance curves, according to

Figure 3 .

 3 Figure 3. High-resolution TEM images of NPs TiO 2 (after 3 h of milling at = 200 rpm) showing the crystalline anatase (A), brookite (B) and amorphous (Am) phases. The insets correspond to the local FFT and the scale bars correspond to 5 nm.

Figure 4 .

 4 Figure 4. Distribution of the hydrodynamic diameter in an aqueous suspension of milled compounds and reference sample (0.1 g l -1 ), with = (a) 200 and (b) 400 rpm.

Figure 5 .

 5 Figure 5. UV-visible spectra for milling time t = 0 (reference), 1, 3, 5 and 7 h, at = (a) 200 and (b) 400 rpm. The maximum absorbance obtained at 335 nm for pristine NPs was used as a reference to normalize all of the milled absorbance spectra. For non-normalized spectra, see supplementary figure S3.

Figure 6 .

 6 Figure 6. Variation of the band gap (E g ) according to Kubelka-Munk approach for milled TiO 2 NPs at = (a) 200 and (b) 400 rpm, E g is estimated by the intercept of the Tauc plot of (αhν) 1/2 ∝ hν -E g and the energy axis.

Figure 7 .

 7 Figure 7. Variations of the band gap (E g , black square) and Urbach energy (E u , blue circle) with the milling time (upper panel) and resulting grain size (lower panel) for the two milling speeds: (a and c) 200 and (b and d) 400 rpm. Dashed lines are indicated as guide for the eyes.

Figure 8 .

 8 Figure 8. Photo-catalytic degradation, over time, of methylen orange in aqueous solution in the presence of TiO 2 NPs, for the milling times: t = 0 (reference), 1, 3, 5, 7 h at = (a) 200 and (b) 400 rpm.

Figure 9 .

 9 Figure 9. Evolution of TEMPOL-normalized EPR intensity, I (t)/I 0 as a function of time exposure to UV-light for the TiO 2 NPs aqueous suspension (0.1 g l -1 ), I 0 being the intensity obtained prior to illumination. The data presented illustrate different milling speeds = (a) 200 and (b) 400 rpm and milling times (1, 3, 5 and 7 h) as well as non-milled NPs (reference). XRD investigation presented in this work, the degradation of the photo-catalytic properties coincides with the apparition of the amorphous phase of TiO 2 and surface states modification. Hence, neither the shift of the hydrodynamic diameter towards lower values (as shown in the DLS investigation, figure 4) nor the appearance of brookite phase (see XRD pattern of figure 1) influence neither the MO degradation nor the TEMPOL reduction.In several studies, the amorphous phase is defined as a catalytically photo-inactive[47,73,74], due to a higher e -/ h + recombination rate[36]. However, even in the most

Figure 10 .

 10 Figure 10. Evolution of normalized TEMPOL EPR intensity, I (t)/I 0 as a function of UV exposition time for the TiO 2 NPs (milled at 400 rpm for 7 h) in aqueous suspension (0.1 g l -1 ), where I 0 is the EPR intensity obtained prior to illumination: with (filled circle) or without (filled square) sacrificial donor EDTA at 0.1 M, pH = 6.5.

Acknowledgements

This study was supported by the CNRS (Centre National de la Recherche Scientifique) and Université de Strasbourg. We gratefully acknowledge Dr Marc Schmutz for his kind help in the TEM experiments. The authors thank the French Ministry of Research and the REseauNAtional de Rpeinter-Disciplinaire (RENARD, Fédération IR-RPE CNRS #3443).


Stefan Weithoffer
email: weithoffer@eit.uni-kl.de

Matthias Herrmann
email: herrmann@eit.uni-kl.de

Claus Kestel
email: kestel@eit.uni-kl.de

Norbert Wehn
email: wehn@eit.uni-kl.de

Advanced Wireless Digital Baseband Signal Processing Beyond 100 Gbit/s

The continuing trend towards higher data rates in wireless communication systems will, in addition to a higher spectral efficiency and lowest signal processing latencies, lead to throughput requirements for the digital baseband signal processing beyond 100 Gbit/s, which is at least one order of magnitude higher than the tens of Gbit/s targeted in the 5G standardization. At the same time, advances in silicon technology due to shrinking feature sizes and increased performance parameters alone won't provide the necessary gain, especially in energy efficiency for wireless transceivers, which have tightly constrained power and energy budgets.

In this paper, we highlight the challenges for wireless digital baseband signal processing beyond 100 Gbit/s and the limitations of today's architectures. Our focus lies on the channel decoding and MIMO detection, which are major sources of complexity in digital baseband signal processing. We discuss techniques on algorithmic and architectural level, which aim to close this gap. For the first time we show Turbo-Code decoding techniques towards 100 Gbit/s and a complete MIMO receiver beyond 100 Gbit/s in 28 nm technology.

I. INTRODUCTION

The first generations of mobile communication systems have shifted the communication from landline to handheld devices, followed by the third (3G) and fourth (4G) generations, which marked the advent of the mobile internet. The amount of devices, which will mostly be wirelessly connected, is expected to increase to 50 billion in the year 2020.

While the fifth generation (5G) of mobile communications systems is being standardized by the 3GPP, the monthly data traffic per smartphone is estimated to increase to 18 GB per month in 2021 [START_REF] Lundvall | Ericsson Mobility Report[END_REF]. The rapid increase in both data volume and data rate (or throughput) is a continuation of the evolution from 3G to 4G networks, and the downlink data rate, for example, will be at least 20 times higher compared to 4G LTE-A [START_REF] Young | Telecom Experts Plot a Path to 5G[END_REF].

Beyond 5G, which will have data rates in the order of tens of Gbit/s, the throughput requirements for mobile communication systems will be higher than 100 Gbit/s. Figure 1 illustrates this evolution of the peak downlink data rate in the context of the 3GPP mobile communication standards. The main contributers to this trend are applications like streaming video, which make up over 50% of the annual mobile traffic increase.

At the same time, the latency is becoming more and more constrained. This is evident from Figure 2, which illustrates the trend towards roundtrip latencies in the order of µs. Accordingly, the evolution of the length of the Transmission Time Intervalls (TTIs), in which the transmission of a data block is organized on the physical layer, shows the same trend. The shrinking latencies are expected to enable a range of applications, which have been described by the term Tactile Internet, i.e. remote driving, free-viewpoint video, machine-tomachine or smart grid synchronization [START_REF] Fettweis | The Tactile Internet: Applications and Challenges[END_REF]. To satisfy this ever increasing demand for higher data rates 978-1-5386-0446-5/17/$31.00 c 2017 IEEE many wireless communication standards, e.g. WiFi, LTE or WiMAX, adopted multiple input multiple output (MIMO) techniques. This technological innovation has vastly improved the spectral efficiency and thus been a key enabler for today's data rates of several Gbit/s. To achieve even higher data rates, higher frequency ranges that offer more bandwidth, must be exploited. A recent example is the WiGig standard (IEEE 802.11ad) that already utilizes carrier frequencies in the 60 GHz band to achieve a maximum throughput of almost 7 Gbit/s. However, utilizing MIMO techniques in millimeter wave systems is still a great challenge and currently a very active research field (e.g. [START_REF] Heath | An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems[END_REF]) and a promising approach to achieve data rates of 100 Gbit/s and more.

Transceivers to support such high data rates must be extremely power/energy efficient. The available power budget is typically limited to some Watts for digital baseband processing due to thermal power density contraints. E.g., if we target a throughput of 100 Gbit/s in a 1 W power envelope, only 10 pJ energy is available to process a single bit [START_REF] Kienle | On Complexity, Energy-and Implementation-Efficiency of Channel Decoders[END_REF]. For comparison, in 28 nm technology, a 64 bit double precision floating point operation consumes about 20 pJ and transferring 256 bits over a 40 mm wire on a chip costs about 10 nJ. For the future, progress in microelectronics will yield some improvements in the three important metrics, i.e. area, energy, and frequency. Extrapolating down from 28 nm to 7 nm technology will bring approximately a factor 12x reduction in area, a factor 4x in energy efficiency, and a factor 3x in (maximum operating) frequency [26] [12]. Due to the fact that area density increases faster than the improvement in energy efficiency, power density will be one of he biggest challenges and is already a big issue in today's technologies and known as "dark silicon phenomenon" [START_REF] Shafique | The EDA challenges in the dark silicon era[END_REF]. Thus, for digital baseband signal processing beyond 100 Gbit/s, the improvement in energy efficiency from new silicon technology has to be complemented with improvements on the algorithmic and the architectural level.

Advanced channel coding and modulation are major sources of complexity in digital baseband signal processing and largely contribute to the overall power consumption, area, and most important to the overall latency. The computational workload of channel decoding in today's 3GPP standards is already in the order of 100 Giga operations per second. Thus, in this paper we focus on advanced channel coding and MIMO detection schemes and the challenges for 100 Gbit/s implementation.

II. CHANNEL CODING FOR 100 GBIT/S

Advanced channel codes like Turbo-Codes and LDPC codes combine randomness with limited locality (i.e. interleaver for Turbo-Codes, Tanner graph for LDPC codes, respectively) and some structures with iterative decoding techniques to achieve near channel capacity. However, energy efficient, low latency, and high throughput implementations require highly parallel architectures with large data locality, large regularity and a minimum of control flow. Thus, there is an inherent discrepancy between the information theoretical and the implementation objectives. To bridge this gap, a joined consideration of code, decoding algorithms and architectures is mandatory and parallelism has to be exploited on all levels [START_REF] Scholl | Advanced iterative channel coding schemes: When Shannon meets Moore[END_REF]. The three prominent channel codes, namely Turbo-Codes, LDPC-Codes and the more recently discovered Polar codes [START_REF] Arikan | Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels[END_REF], largely differ in this respect:

• Turbo-Code decoding is inherently serial and is mainly performed on data-flow graphs; • LDPC-Code decoding is inherently parallel and is mainly performed on a data-flow graph; • Polar code decoding is inherently serial and is performed on a code tree structure.

Thus, the challenges for decoder implementations achieving 100 Gbit/s and beyond are fundamentally different between Turbo-Codes, LDPC codes and Polar codes. This is illustrated in Table I. It contains projections of selected high throughput state-of-the-art decoder implementations down to 7 nm technology utilizing the scaling factors of the previous section. Note, that each design features different kind of codes, code block lengths and code rate flexibility, and communications performance is not considered. Thus, a direct comparison is not possible. However, the elemental conclusions that emerge from this table are:

• For a given communications performance LDPC code decoders show a distinct throughput advantage over Turbo and Polar code decoders, due to the inherently parallel nature of the LDPC code decoding (belief propagation algorithm). • Existing Turbo-Code decoders cannot achieve 100 Gbit/s even in 7 nm technology. • Turbo and Polar codes offer built-in flexibility with respect to code block sizes and code rates. • Power density is the biggest challenge for existing decoders exceeding the 100 Gbit/s barrier.

The two most prominent techniques to achieve high throughput on architectural level are spatial parallelism and functional parallelism (pipelining). Pipelining has some efficiency advantages compared to spatial parallelism, but is limited in its applicability if control-flow and feedback loops play a major role. Channel decoding is mainly data-flow dominated. Thus, to achieve throughput beyond 100 Gbit/s, data-flow and tree structures can be flattened, or "unrolled", and pipelined respectively. This approach produces large locality on the layout level, but comes at the cost of decrease in flexibility. Note, that an early VLSI implementation of a Turbo-Code decoder also used iteration unrolling [START_REF] Jezequel | Turbo4: a high bit-rate chip for turbo code encoding and decoding[END_REF].

A. High Throughput Turbo-Code Decoding

In a basic Turbo-Code decoder, two component decoders process a complete code block alternatingly and exchange extrinsic data through an interleaver/de-interleaver. Commonly, one highly parallelized, monolithic BCJR decoder core functions alternatingly as component decoder 1 and 2 [START_REF] Berrou | Near Shannon Limit Error-Correcting Coding and Decoding: Turbo-Codes[END_REF] the BCJR algorithm is inherently sequential and thus, achieving a throughput of tens of Gbit/s is a challenging task for Turbo-Code decoders.

Turbo-Code decoder architectures for high throughput decoding employ one of the following approaches to parallelize the code block processing on component decoder level: Parallel Map (PMAP): The complete code block is split into sub-blocks, which are processed in parallel on multiple subdecoder cores. The spatial parallelization approach is used in most reported state-of-the-art architectures [START_REF] Ilnseher | A 2.12Gbit/s Turbo Code Decoder for LTE Advanced Base Station Applications[END_REF], [START_REF] Shrestha | High-Throughput Turbo Decoder With Parallel Architecture for LTE Wireless Communication Standards[END_REF], [START_REF] Belfanti | A 1Gbps LTE-advanced turbo-decoder ASIC in 65nm CMOS[END_REF]. Fully Parallel Map (FPMAP): Splitting the code block into sub-blocks of size one in combination with shuffled decoding [START_REF] Zhang | Shuffled Iterative Decoding[END_REF] leads to the FPMAP architecture [START_REF] Maunder | A Fully-Parallel Turbo Decoding Algorithm[END_REF]. It has been demonstrated to achieve a very high throughput, however at the cost of a decreased area efficiency and flexibility [START_REF] Li | VLSI Implementation of Fully Parallel LTE Turbo Decoders[END_REF]. Pipelined Map (XMAP): The data block is split into subblocks, which are decoded in a pipeline that implements an unrolling of the recursive state metric calculations [START_REF] May | A 150Mbit/s 3GPP LTE Turbo Code Decoder[END_REF], [START_REF] Weithoffer | On the applicability of trellis compression to Turbo-Code decoder hardware architectures[END_REF]. The X-shaped pipeline structure, that gives the architecture its name, has been proven optimal with respect to the amount of state memory storage [START_REF] Mansour | VLSI architectures for SISO-APP decoders[END_REF]. For large degrees of parallelism, the splitting of the code block into (small) sub-blocks necessitates additional calculations to compute estimates for the state metrics at the sub-block borders in order to mitigate a degradation of the Frame Error Rate (FER) performance [START_REF] May | A 150Mbit/s 3GPP LTE Turbo Code Decoder[END_REF]. This, in turn, limits the maximum degree of parallelization for the PMAP and XMAP architectures because of the increasing length of the necessary acquisition calculations [START_REF] May | A 150Mbit/s 3GPP LTE Turbo Code Decoder[END_REF]. For the same reason, the FPMAP, which essentially works on sub-blocks of size 1, needs up to three times more decoding iterations as PMAP/XMAP decoders. This effect is expected to be even more pronounced at high code rates close to 1. Note, however, that one full decoding iteration for the FPMAP has only a two clock cycle latency, which is substantially shorter than for PMAP/XMAP decoders.

Considering the state-of-the-art Turbo-Code decoders in Table I, it becomes clear, that even assuming 7 nm technology, a throughput beyond 100 Gbit/s is not attainable with stateof-the-art monolithic decoder cores and improvements on different design levels are mandatory.

A solution to increase the throughput for state-of-the-art LTE Turbo-Code decoders, which requires minimal changes to the decoder architecture and is applicable to all decoder types, is Iteration Balancing [START_REF] Weithoffer | Latency Reduced LTE-A Turbo-Code Decoding with Iteration Balancing on Transport Block Level[END_REF]. For iteration balancing, the iteration control, which is used to terminate the decoding process early in the event of successful decoding, is extended to the Transport Block (TB) level. It makes use of the fact, that the transmission data in LTE is organized in TBs, which consist of several code blocks. Instead of specifying a maximum budget n max HI of iterations that the decoder can spend for the decoding of individual code blocks, the iteration budget now considers the complete TB. Thereby, the decoder can make use of iterations that are saved by terminating the decoding process early for some code blocks. By distributing the saved iterations, the overall number of iterations needed to decode the complete TB can be reduced. For a TB size of 97896 bit, i.e. 16 code blocks of 6144 bit (coded: 18432 bit), a reduction of up to 30% without sacrificing FER performance has been shown for the architecture from [START_REF] Ilnseher | A 2.12Gbit/s Turbo Code Decoder for LTE Advanced Base Station Applications[END_REF]. This translates to an increase in throughput of about 42%. Also note, that, because of the higher dynamic range, the potential increase in minimum throughput -and with it the architecture efficiency -increases for larger TBs.

Throughput can be further increased by spatial parallelization, i.e. several decoder cores are instantiated, each of them processes a single code block individually. However, this decreases the architectural efficiency whereas the latency of a single code block is not reduced. Another possibility is functional parallelization that exhibits a much better architectural efficiency than spatial parallelization. Here, the various decoding iterations are unrolled and the individual iteration stages are pipelined. Instead of calculating a complete iteration in parallel as with the FPMAP architecture, a fully pipelined decoder would still calculate the recursions sequentially while the data travels through the pipeline. Since the XMAP architecture already follows a pipelining approach for the MAP decoder, it is best suited as basis for this unrolled architecture. Figure 3 illustrates this new approach and contrasts it with the straightfoward decoder parallelization. It is easy to see that this streaming-like approach increases the architecture efficiency by using less extrinsic memory. Since the extrinsic memory makes up a significant percentage of XMAP decoders, a) the architectural efficiency is much better. Furthermore, the fully unrolled architecture is highly data-flow oriented. The unidirectional routing and high data locality allows efficient placement & routing with modern synthesis tools and greatly reduces wiring congestions. Table II lists synthesis results for a prototype of an unrolled XMAP Turbo-Code decoder in 28 nm Fully Depleted Silicon On Insulator (FD-SOI) technology under worst case power/voltage/temperature (PVT) conditions, and gives estimates for area and throughput. The synthesis results for the decoder, that consists of 12 half-iteration stages and supports a information block length of 64 bit show, that unrolling of the decoding iterations is a promising approach towards very high throughput Turbo-Code decoders. Extrapolating these number to 7 nm technology results in a throughput of about 140 Gbit/s.

MEM 1 MEM 2 MEM 3 MEMp ⇧/⇧ 1 ⇧/⇧ 1 ⇧/⇧ 1 ⇧/⇧ 1 . . .

B. High Throughput LDPC Decoding

Unlike Turbo-Codes, LDPC decoding is inherently parallel. The decoding is based on the iterative message exchange between the check and variable node sets of the Tanner Graph. The calculations for the check and variable nodes can easily be done in parallel and the decoder throughput is only limited by the data exchange between the node sets. Similar to the fully unrolled approach for Turbo-Code decoders discussed in the previous section, the iterative decoding of LDPC codes can be unrolled to a fully pipelined decoder. In [START_REF] Balatsoukas-Stimming | A Fully-Unrolled LDPC Decoder Based on Quantized Message Passing[END_REF], [START_REF] Schläfer | A New Dimension of Parallelism in Ultra High Throughput LDPC Decoding[END_REF] and [START_REF] Scholl | Advanced iterative channel coding schemes: When Shannon meets Moore[END_REF], the Tanner graph is mapped directly into hardware for each iteration and the individual iteration stages are connected via pipeline registers. However, the number of iterations and the code block size have to be fixed for this approach. With this approach, throughput in the order of hundreds of Gbit/s (160 Gbit/s for 28 nm FD-SOI), and energy efficiency in the order of single digit pJ/bit (6 pJ/bit in 28 nm FD-SOI) are possible in future technologies. The rows for references [START_REF] Schläfer | A New Dimension of Parallelism in Ultra High Throughput LDPC Decoding[END_REF], [START_REF] Balatsoukas-Stimming | A Fully-Unrolled LDPC Decoder Based on Quantized Message Passing[END_REF] in Table I show the projections to 7 nm technology.

However, achieving these throughput numbers with an increased flexibility with respect to code rates and block size, however, remains still an open topic for research.

C. High Throughput Polar Code Decoding

Polar Codes, invented 2008 by Erdal Arikan, are the first codes proven to achieve channel capacity for Binary Symmetric Memoryless Channels (BSMC). They belong to the class of multilevel concatenated codes and use the phenomenon of channel polarization to maximize coding efficiency which distinguishes them from the similar Reed-Muller-Codes.

In contrast to Turbo-Codes and LDPC codes, polar codes exhibit a quite regular structure. But at the same time the recursive nature of polar codes hinders an efficient parallelization. The standard decoding algorithm, namely successive cancellation and its derivatives, work on a code tree structure. Although successive cancellation has a low implementation complexity, the decoding itself is inherently serial and limits the throughput. A possibility to increase the throughput is the unrolling of the traversal on the tree. This results in a data-flow architecture that can be pipelined in a similar way as described above [START_REF] Giard | High-Speed Decoders for Polar Codes[END_REF]. This approach can achieve a throughput far beyond 100 Gbit/s, however results in a big power density challenge, is limited to the fast simplified successive cancellation algorithm, i.e. without list/CRC, and has no flexibility at all. Omitting the pipeline register results in a pure combinatorial decoder without any registers [START_REF] Dizdar | A High-Throughput Energy-Efficient Implementation of Successive Cancellation Decoder for Polar Codes Using Combinational Logic[END_REF] which largely reduces the power, but also largely reduces the throughput.

Belief propagation is a further decoding option [START_REF] Abbas | High-Throughput and Energy-Efficient Belief Propagation Polar Code Decoder[END_REF]. This algorithm works on the factor graph. The belief propagation is alike to LDPC decoding parallel. However, the decoding requires a very large number of iterations to be competitive in communications performance, which prohibits an unrolling of the iterations. Implementation results for the discussed decoding methods projected to 7 nm technology are listed in Table I.

III. MIMO RECEIVERS

MIMO techniques in combination with bit-interleaved coded modulation enable the transmission of independent and separately encoded data streams from each antenna in the same frequency band. In return, the receiver needs to perform computationally complex MIMO detection to separate the data streams and to generate bitwise log-likelihood ratios (LLRs) for the subsequent channel decoder. Since both MIMO detector and channel decoder must jointly meet the requirements with regard to throughput and energy efficiency the design of a MIMO receiver is particularly challenging. As argued in Section II very high throughput channel decoders employ fully pipelined architectures, thus requiring LLR values for a complete code block per clock cycle. In the following we discuss challenges for high throughput MIMO detection matching the full pipeline utilization of the channel decoders.

Advanced MIMO detectors traverse a tree structure to find a shortest path. Although a tree has a high regularity and large data locality, the actual detection of the best path in this decision tree is difficult to parallelize. Exhaustive search, i.e., computation of all paths and selection of the minima allows for a maximum parallelism but is infeasible due to the large tree size. Therefore, advanced detection algorithms, like the sphere decoding, use sophisticated pruning techniques to limit the number of visited tree nodes to a very small subset. However this adaptive pruning at runtime requires a control driven sequential processing of an unpredictable number of nodes which limits parallelism. As a consequence sphere decoders are limited to throughputs below 1 Gbit/s on current silicon technology [START_REF] Adeva | Optimizing a pipelined MIMO sphere detector for energy efficiency[END_REF].

List Fixed Complexity Sphere Decoding (LFSD) has been introduced as an approach to overcome the complexity problem by performing an exhaustive search on a constrained tree only. This subtree is defined at design time by fixing the number of nodes per layer and thus the number of paths to a small subset. For the first time we propose to apply the concept of "unrolling" (as described in the context of iterative decoders) to the different layers of the tree. The resulting deeply pipelined architecture with a directed data-flow from the root to the leave layer is depicted in Figure 4. However, this comes again at the cost of reduced flexibility with respect to the number of antennas and modulation and some degradation of the communications performance. . Other approaches that have been introduced for maximum throughput are k-best detection [START_REF] Wong | A VLSI architecture of a K-best lattice decoding algorithm for MIMO channels[END_REF] and its soft-output extension, the path preserving trellis-search (PPTS) detector [START_REF] Sun | Trellis-Search Based Soft-Input Soft-Output MIMO Detector: Algorithm and VLSI Architecture[END_REF]. In [START_REF] Sun | High-Throughput Soft-Output MIMO Detector Based on Path-Preserving Trellis-Search Algorithm[END_REF], the authors present a fully parallel PPTS detector in 65 nm technology that achieves a throughput of 6.4 Gbit/s. However, this detector suffers in area efficiency, especially for higher order modulations (> 16 QAM).

Faster MIMO detection is limited due to the fact that MIMO detection operates on transmission vectors that typi-cally consist of a small number of bits. As a consequence even the deeply pipelined MIMO detector achieves much lower throughput compared to a deeply pipelined channel decoder, that operates on much larger code blocks. However, since the different transmission vectors associated with one code block can be considered independent, the detection can be performed in parallel on multiple detectors. E.g., assuming a 160 Gbit/s LDPC decoder with a code block size of 672 bit, as presented in the previous section, and a 4 ⇥ 4 64 QAM transmission system, a complete code block can be mapped on 28 independent transmission vectors, each 24 bits respectively. Thus, we can use 28 MIMO detectors in an array structure to match the throughput requirements of the channel decoder. Such a detector array is shown on the left side of Figure 5. Each detector is highlighted with a different color. The detectors are implemented as deeply pipelined LFSD with list size 16, performing the detection of all transmission vectors associated with a complete code block in each clock cycle. The total area requirement of the detectors in 28 nm FD-SOI technology is 4.3 mm 2 and the maximum operating frequency under worst case conditions is 240 MHz, resulting in a throughput of approximately 160 Gbit/s. The right side of Figure 5 depicts the aforementioned deeply pipelined LDPC decoder in the same technology. Here, each color highlights the groups of variable and check nodes associated with one iteration. The decoder features 10 iterations and supports a code rate of 5/8, which is slightly different to the LDPC decoder in [START_REF] Scholl | Advanced iterative channel coding schemes: When Shannon meets Moore[END_REF] (9 iterations, code rate 13/16). The area of the LDPC decoder core is 3.3 mm 2 .

The detector array can be interconnected via a fixed interleaving network to the LDPC decoder, resulting in a fully pipelined MIMO-BICM receiver. The total area requirement of the MIMO-BICM receiver is approximately 8 mm 2 and the resulting energy efficiency about 25 pJ/bit in 28 nm technology (6 pJ/bit extrapolated to 7 nm).

IV. CONCLUSION

In this paper, we discussed challenges and limitations for state-of-the-art channel decoding and MIMO detection in wireless digital baseband signal processing with throughput requirements of 100 Gbit/s and more. We showed, that improvements in silicon technology alone will not provide the necessary gains in terms of throughput and energy efficiency. The remaining performance gaps must be closed on the algorithmic and the architectural level. We demonstrated that flattening/unrolling of data-flow and tree structures in the channel decoder and the MIMO detector are a promising approach, however at the cost of flexibility. For the first time we have shown Turbo-Code decoding techniques towards 100 Gbit/s and a complete MIMO receiver beyond 100 Gbit/s in 28 nm technology.

ACKNOWLEDGMENT

We gratefully acknowledge financial support by the DFG (project-ID: 2442/8-1) and the EU (project-ID: 760150-EPIC). .

Fig. 1 .

 1 Fig. 1. Throughput Evolution in 3GPP Mobile Communication Standards

Fig. 2 .

 2 Fig. 2. Roundtrip Latency and TTI Length Evolution in 3GPP Mobile Communication Standards

1 Fig. 3 .

 13 Fig. 3. Multiple Decoder case and Unrolled Iterations.

Fig. 4 .

 4 Fig. 4. Deeply pipelined, "unrolled" architecture for LFSD.

Fig. 5 .

 5 Fig. 5. MIMO-BICM receiver for throughput of 160 Gbit/s: MIMO detector array (left), LDPC decoder (right)

Code Ref.

Code Code rate Process