domain: spi phys

text:
Thomas Geoffrey Decker
email: thomas.decker@onera.fr

Robin William Devillers

Stany Gallier

Experimental visualization of aluminum ignition and burning close to a solid propellant burning surface

Visible images of burning solid propellants loaded with aluminum particles are presented. The images are recorded at high acquisition frame rate (up to 33kHz) with excellent sharpness, enabling the study of aluminum ignition and combustion close to the propellant burning surface. The article focuses on two aspects: the aluminum aggregate ignition and the alumina breaking and migration on the aggregate surface. The article presents new ways of studying aluminum agglomeration and combustion by applying image processing algorithms on state-of-the-art image series.

Introduction

Solid Rocket Motors (SRM) are widely used in military and civilian applications. They are highly reliable, require little maintenance, and are readily available even when stored for a long time. A solid propellant is a solid material used to generate thrust by its combustion. It is composed of a fuel binder and oxidizing particles. Metal particles, usually aluminum, are added to increase the propulsion performances with additional combustion heat release. While the fuel and the oxidizer burn at the propellant surface, the aluminum particles burn in the gas flow produced by the fuel/oxidizer combustion. The aluminum particles are subject to complex phenomena prior to their combustion in the gas flow [START_REF] Price | Combustion of aluminized solid propellants[END_REF][START_REF] Babuk | Formation of condensed combustion products at the burning surface of solid rocket propellant[END_REF]. They follow an accumulation-aggregationagglomeration mechanism [START_REF] Maggi | Combustion of metal agglomerates in a solid rocket core flow[END_REF][START_REF] Ao | Aluminum agglomeration involving the second mergence of agglomerates on the solid propellants burning surface: experiments and modeling[END_REF]. The particles accumulate in the solid propellant pockets [START_REF] Cohen | A pocket model for aluminum agglomeration in composite propellants[END_REF], they aggregate while being attached to the burning surface and finally agglomerate when they ignite on the burning surface or in the gas flow. The aluminum particles are referred as aggregates (on the burning surface, with a coral-like shape, eventually morphing into a spherical one), and agglomerates (in the gas flow, with a spherical shape). The resulting droplets can reach hundreds of micrometers in diameter [START_REF] Babuk | Nanoaluminum as a solid propellant fuel[END_REF], while the virgin particle size is usually between 5 and 50µm. An oxide (alumina) cap is attached to the burning aluminum droplet. The droplet combustion produces heat as well as alumina, with some parts being evacuated in the gas flow as smoke while another portion increases the size of the oxide cap.

The inert alumina droplets produced during the aluminum combustion influences the stability and the performances of the SRM, depending on their size [START_REF] Salita | Deficiencies and requirements in modeling of slag generation in solid rocket motors[END_REF][START_REF] Li | Effects of particle size on two-phase flow loss in aluminized solid rocket motors[END_REF]. The particles often follow a trimodal distribution [START_REF] Zarko | Formation of al oxide particles in combustion of aluminized condensed systems[END_REF] when captured with collection techniques ([2, 10, 11]). The lower and higher modes of the size distribution are respectively attributed first to alumina smokes and second to the aluminum agglomerates and coarse oxide, but the intermediate mode (4 -8µm) is not fully understood [START_REF] Zarko | Formation of al oxide particles in combustion of aluminized condensed systems[END_REF], and doubts remain about the production of those alumina droplets. The alumina production mechanism during the aluminum droplet combustion is considered in many studies [12,[START_REF] Karasev | Formation of charged aggregates of al2o3 nanoparticles by combustion of aluminum droplets in air[END_REF]. But its production close to the surface when the aluminum is still attached to the propellant has never been studied to the authors' knowledge. No model for oxide-cap formation during the aggregation-agglomeration mechanism has been published. This formation is crucial because the alumina migration to form an oxide cap influences the aluminum ignition on the burning surface while the size of the resulting oxide cap influences the aluminum combustion along the droplet lifetime [12,[START_REF] Beckstead | Correlating aluminum burning times[END_REF][START_REF] King | Aluminum combustion in a solid rocket motor environment[END_REF].

Two phenomena associated with the alumina production and oxide cap formation on the burning surface are studied with image processing: the aluminum aggregate ignition and the alumina layer breaking and migration. This study shows new ways of studying physical phenomena associated with aluminum agglomeration and combustion in solid propellants.

Experimental setup and data

Shadowgraphy was used to visualize accurate details above the solid propellant surface during combustion [START_REF] Devillers | 7th European Conference for Aeronautics and Space Sciences[END_REF]. Here a similar optical set-up was used without back illumination to improve the contrast between aluminum and alumina. A high-speed camera acquires frames to target physical phenomena on the solid propellant burning surface. The acquisition rate was adjusted up to 33kHz, and the recorded images size depends on the frame rate. The spatial resolution is about 3.2µm/px.

Two solid propellants are studied (P1 and P2). Their compositions are similar. Both include a trimodal repartition of Ammonium Perchlorate (AP) particles, a hydroxyl-terminated polybutadiene (HTPB) binder and approximately 20% of aluminum particles. They only differ in the initial size of the aluminum particles. The P1 initial aluminum particles size is approximately 30µm while the P2 is approximately 15µm. In order to capture the aluminum particles or agglomerates as clearly as possible, propellants are beveled. The cam-era views the propellant slightly from the top with an angle around 45 • . Heated aluminum and alumina are clearly visible because of their incandescence.

The P1 propellant is studied at two initial pressures, 5 and 10 bar. It is recorded at 14kHz in order to capture the aluminum ignition of the aggregates. The P2 propellant is studied at one initial pressure, 5 bar. It is recorded at 33kHz in order to capture the aluminum breaking and migration. Image examples are presented in figures 1, 2, and 3. The surface on the image of the P1 propellant at 10 bar is brighter than at 5 bar (the experimental setup is kept identical). The solid propellant flames are closer to the surface with increasing pressure. The aluminum close to the surface is therefore hotter, i.e. brighter.

Image processing 3.1 Aggregates detection

The first studied phenomenon is the aluminum aggregates ignition on the burning surface of the propellant. The objective is to automatically detect and track the aluminum aggregates and agglomerates on the propellant surface and in the gas flow. The number of captured images for the P1 propellant at the initial pressures of 5 and 10 bar being approximately 2000 and 2500, automatic algorithms are needed. The following processing steps were used:

Step 1 -Top-hat filtering The Top-hat transform [START_REF] Dougherty | SPIE[END_REF] extracts elements from given images. The transform depends on a structuring element, usually a disk. The bright objects with much smaller sizes are considered as part of the background. Therefore, only the aggregates with sufficient sizes can be easily detected.

Step 2 -Thresholding A simple thresholding of the resulting image enables the detection of the aggregates and agglomerates on the burning surface. The threshold choice is a compromise in order to avoid merging separate aggregates into a single detected object.

Figure 5 shows steps 1 and 2 for the P1 propellant at 5 bar, compared to the color scale limited original image shown in figure 4.

Steps 3 and 4 -Detection and tracking

The resulting thresholded image is binary. The aggregates and agglomerates are easily detected. Metrics are automatically calculated, such as the area, the circularity, the mean and the maximum intensity.

The resulting detections are tracked on successive images to analyze the behavior of aggregates on the solid propellant surface. Thanks to the significant frame rate, a simple Intersect-Over-Union (IOU) threshold is employed. Two tracked aggregates at 5 and 10 bar can be visualized in figures 6a and 6c).

Alumina detection

The second studied phenomenon is part of the aggregate ignition, it is the alumina breaking and migration. The objective is to detect and track alumina on the surface of aluminum aggregates. In order to study the phenomenon, the frame rate is much higher, 33kHz. We focus here on one sequence of approximately 300 frames where the alumina encapsulating an aggregate breaks up and migrates.

A Top-hat transform is applied, followed by a thresholding. An example is shown in figure 7 for propellant P2 at 5 bar with (a) Top-Hat transform and (b) Threshold image. Figure 7 zooms on a igniting aggregate on the propellant surface.

The detection algorithm can segment the main alumina surface surrounding the aluminum collapsing into a lobe (on the left-hand side) but also isolated alumina portions moving on the aluminum surface (on the righthand side) that will eventually reach the forming oxide cap.

Several metrics are automatically calculated, such as the area, the circularity, the mean and the maximum intensity. The main alumina surface is easily tracked over time, as the largest detection. We follow other alumina detections with the IOU calculation. Here, the minimum IOU is fixed very low because of the rapid motion of the alumina zones compared to their size. Figure 8a shows the evolution of the main alumina layer that initially surrounds the whole liquid aluminum, and figure 9a shows successive positions of a single alumina portion.

Results and discussion 4.1 Aggregates ignition

Here are comments on the aggregate ignition on the surface by analyzing two aggregates tracked other time (figures 6a and 6c). The metrics are plotted in figure 6b.

The growth of the detected areas of the two aggregates on the burning surface (see images 1 to 4 from figure 6a and images 1 to 3 from figure 6c) can be observed with the area. Only fragments of the aggregated are detected for the first detection because the overall aggregate is not bright enough at this early heating stage. The detections grow with time as more and more portions of the aggregates become sufficiently bright.

The increase in temperature of a tracked aggregate is not only synonymous with an increase of the detected area but also a steady increase in the mean intensity (see images 1 to 4 from 6a and 1 to 3 from figure 6c). The mean intensity slowly increases from 2.5 to 4.0ms for the aggregate at 5 bar (blue plot) while the intensity increase happens from 1.1 to 2.0ms at 10 bar (red plot). The intensity spike happening around 0.3ms in the red plot corresponds to a burning droplet passing nearby in its upwards movement.

When the aggregates are ignited and transformed into agglomerates, they establish a diffusion flame with the surrounding gas (see image 6 from 6a and image 5 from figure 6c). The diffusion flame establishment corresponds to an increase in area, an increase in mean intensity and a decrease in circularity. Simultaneously, the newly formed agglomerates leave the surface and move in the gas flow. The movement in the gas flow is visible with the vertical velocity increase starting at 5ms at 5 bar and 4.2ms at 10 bar.

The metrics are calculated for each tracked aggregate on the burning surface detected for at least five frames. 786 aggregates were tracked at 5 bar and 1259 at 10 bar. Two estimates are calculated for each tracks

• The track duration time gives the estimate of the ignition time τ • A mean intensity Imean is calculated over the complete track Distributions for the two estimated are presented in figures 10a and 10b. To avoid visualizing the threshold effect with a spike of distribution on the lowest values, the distribution of the ignition time is presented as a cumulative. The ignition time τ is globally lower at 5 bar than at 10 bar. The aggregates ignition is faster with increasing pressure. A shorter ignition delay leads to less agglomeration. It is consistent with the physics of aluminum agglomeration in solid propellants, agglomerates are smaller with increasing pressure [START_REF] Pokhil | Combustion of metal powders in active media[END_REF][START_REF] Sambamurthi | Aluminum agglomeration in solid-propellant combustion[END_REF].

The mean intensity I mean is globally increasing with increasing pressure. Propellant flames get closer to the burning surface with increasing pressure, leading to a more efficient aggregate heating (i.e. brighter detections).

Overall, tracking aluminum aggregates on the burning surface enables the study of physical phenomena associated to aluminum agglomeration, ignition, and combustion on the solid propellant burning surface. It helps understand the importance of the aggregates' temperature on its ignition. The study of the detected area shows that the aggregates are not homogeneous in temperature. Data also show the importance of temperature in the aggregates ignition. With increasing pressure, the solid propellant flames are closer to the burning surface, the aggregates are hotter, resulting in a decreasing ignition time.

A more quantitative study is required to compare the ignition time of the aggregates to their residence time on the propellant surfaces. Models would have to include ignition delay if its time range is comparable to the residence time on the burning surface. A more detailed study could put into equation the ignition time depending on physical parameters such as pressure, the propellant constitution or the aggregate size.

Alumina breaking and migration

The second focus is on the alumina breaking and migration of an aluminum aggregate attached to the solid propellant burning surface. The alumina breaking and migration exposes the liquid aluminum to the surrounding oxidizing gas. Therefore, the liquid aluminum starts to burn and establishes a diffusion flame (see images 4 to 6 from figure 8a). We focus on two tracks, the main alumina surface that initially surrounds the whole aluminum aggregate and an isolated alumina portion moving rapidly on the liquid alumina surface. Metrics associated with the two tracks are presented in figures 8b and 9b.

The main alumina surface follows a first period of ∼ 7ms where it keeps a circular shape but seems to have a variable temperature (i.e. a variable mean intensity in figure 8b). The exothermic production of alumina is a possible explanation of the increased temperature (i.e. an increased mean intensity in figure 8b between 2.5 and 5ms) prior to the alumina breaking. Price et al. [START_REF] Price | Combustion of aluminized solid propellants[END_REF] demonstrated that the encapsulating alumina cracks due to the expanding liquid aluminum. The liquid aluminum finds itself partially exposed, resulting in the production of additional alumina.

Then, the alumina surface breaks up on the top of the aggregate (where it is supposed to be hotter), a local temperature increase occurs due to the released liquid aluminum combustion, and the circular alumina surface retracts. The alumina break up happens at ∼ 7ms. The alumina may move on the aluminum surface as small portions. The phenomenon is very rapid, as shown in figure 9b (the total duration of the alumina movement being only a few ms). The alumina may also be ejected as small drops (see images 3 and 4 from figure 9a).

The small tracked alumina portion also has a variable temperature (i. e. a variable mean intensity) as shown in figure 9b. It seems that its temperature decreases when it is moving from the top of the liquid aluminum to the main alumina surface, meaning that the aluminum aggregate has a vertical temperature gradient. It confirms the analysis in the previous section that the aggregate temperature is not homogeneous.

The movement of alumina on the liquid aluminum stops at ∼ 14ms. The reason attributed here is that the aluminum of this aggregate does not produce enough heat. The alumina produced on the liquid aluminum surface tempers the combustion and slowly passivates the aggregate. It is visually observed that some igniting aggregates can be passivated. Another ignition needs to occur to finalize the transition from aggregate to agglomerate.

Overall, significant alumina production occurs on the liquid aluminum surface, during the residence of the aluminum aggregate on the solid propellant burning surface. The produced alumina then migrates into the oxide cap. Therefore, a portion of the final residue is produced when the aluminum aggregate is attached to the propellant burning surface. This study shows the importance of physical phenomena associated to aluminum on a solid propellant surface, influencing the size of the resulting alumina cap, and affecting the stability of a SRM.

Conclusion

Visible images of burning solid propellants loaded with aluminum particles were presented. Physical phenomena associated with alumina production were studied thanks to high-speed recording, excellent spatial resolution, good image clearness, and new algorithms using a Top-hat transform.

Different stages of the aggregated aluminum ignition were shown at two initial pressures, 5 and 10 bar. Aggregate temperature increases before it ignites and transforms into a spherical agglomerate. It was found that the ignition time decreases with increasing pressure. The mean intensity of the aggregates increases with increasing pressure, meaning that the aggregates are hotter on the burning surface. Increased pressure leads to closer solid propellant flames to the burning surface and the aggregates.

The alumina breaking and migration were observed thanks to a test at a very high frame rate of 33kHz. An alumina portion was even tracked on a liquid aluminum droplet. Small aluminum/alumina drops were observed being ejected in the gas flow during the surrounding alumina surface migration. A significant production of alumina occurs on the liquid aluminum surface. To the authors' knowledge, those phenomena were never studied in the literature. This study shows the importance of the The study showed the importance of the aggregates' temperature during their ignition. The study also showed that aggregates ignite with a delay, depending on pressure. With refined data analysis, quantitative data about the temperature gradient depending on pressure or aggregate size could be calculated. Its influence on the aluminum aggregate ignition delay could also be investigated. Quantitative data on the aggregate temperature gradient and its ignition delay will be useful for future aluminum agglomeration models.

Figure 1 :

 1 Figure 1: Image of the P1 propellant at the initial pressure of 5 bar. Agglomerates are visible in the gas flow, and aggregates (igniting or not) on the burning surface.

Figure 2 :

 2 Figure 2: Image of the P1 propellant at the initial pressure of 10 bar.

Figure 3 :

 3 Figure 3: Image of the P2 propellant at the initial pressure of 5 bar. Aggregates transforming into agglomerates are visible on the left and in the middle.

Figure 4 :

 4 Figure 4: Image of the P1 propellant at the initial pressure of 5 bar with a limited color-scale.

Figure 5 :

 5 Figure 5: Thresholding following the Top-hat transform application on the image of the P1 propellant at the initial pressure of 5 bar.

Figure 6 :

 6 Figure 6: Tracking and physical metrics of two aggregates/agglomerates of the P1 propellant at the initial pressures of 5 and 10 bar.

Figure 7 :

 7 Figure 7: (a) Top-hat transform application on the zoomed image on an aggregate of the P2 propellant at the initial pressure of 5 bar, (b) Thresholding of the resulting image

Figure 8 :

 8 Figure 8: Tracking and physical metrics of the main alumina surface of an aggregate of the P2 propellant at the initial pressure of 5 bar (thumbnails zoomed).

Figure 9 :

 9 Figure 9: Tracking and physical metrics of a moving alumina portion of an aggregate of the P2 propellant at the initial pressure of 5 bar (thumbnails zoomed).

Figure 10 :

 10 Figure 10: Distributions for the tracked aggregates at 5 and 10 bar. (a) Mean Intensity distribution, (b) Ignition time cumulative distribution

Acknowledgment

Thomas Decker's PhD is financed by ONERA and ArianeGroup. S. G. thanks DGA (French Procurement Agency) for funding.


L Alaus

G Villemaud

P F Morlat

J M Gorce

WLAN PREAMBLE DETECTION METHODS IN A MULTI-ANTENNA, MULTI-STANDARD SOFTWARE DEFINED RADIO ARCHITECTURE

Keywords: SDR receiver, SIMO, wideband sensing, WLAN

This paper presents a comparison of different detection methods which could be used to sense a frequency band in order to select a particular channel and a particular communication standard in a wideband melted signal. Here we focus on a generic WLAN receiver based on SDR principles, capable of sampling several overlapping channels to demodulate simultaneously concurrent users possibly using different waveforms.

Introduction

Software Defined Radio (SDR) is a well-known concept, particularly promising to combine numerous communication standards in a single receiver [START_REF] Mitola | The software radio architecture[END_REF]. Thus, this powerful approach could be associated with multi-antenna principles to enhance terminal capabilities by the way of SIMO or MIMO algorithms, naturally offering interference rejection possibilities. In order to tend to a really cognitive system, a first step is to allow a wideband detection of all received signals (supposing wideband front-ends), enabling an efficient characterization of all possible standards. This paper presents in the first part the general structure of a SDR testbed dedicated to combine multi-antenna, multistandard and multi-channel approach. This supposes to have several antennas, with several RF front-ends and wideband ADC, enabling to sample more than only one channel. Then it appears possible to numerically select the desired channel and also characterize the standard used. Moreover, this system could allow the test of interference cancellation techniques on adjacent channels, combined with multi-antenna algorithms [START_REF] Mary | Reduced Complexity MUD-MLSE Receiver for Partially-Overlapping WLAN-Like Interference[END_REF]. Then the second part will focus on the first and fundamental step of the digital receiver: detection and characterization of present signals. Therefore different methods to detect and also analyze the quality of particular frames in melted signals are discussed. The aim is there to provide a good trade-off between precision and computation cost, to offer a fast decision of the presence of useable information and, in case of several emitters, the quality of each link. Of course, the idea is to characterize the signal before any demodulation step to automatically choose which numerical blocks have to be processed to recover data. For a practical case of study, two cohabitating standards (without any cooperation) of WLAN systems are used, 802.11b and 802.11g. Three families of detection methods have been explored: correlators with period detection, cyclostationarity and second order moment estimator detector. To compare those methods, an indoor environment was simulated with 802.11b and 802.11g frames emitted, and one or two antennas at the receiver. AWGN or multipath channel were observed with interferer along seven different overlapping channels. Results are discussed in terms of performance versus complexity. Finally, the impact of using a multi-antenna algorithm associated with these methods was investigated by the way of a SMI approach [START_REF] Morlat | Performance Validation of a multi-standard and multi-antenna receiver[END_REF].

Structure of the SDR receiver

Global multi-* approach

A common view of the future for wireless communications is the trend toward systems enabling a fusion of numerous standards, always offering the highest quality. Some devices already propose several integrated functionalities by the way of hardware duplication, even in a single chip package. Of course the idealist vision of universal software radio is very seducing, but yet actual limitations in sampling capabilities can not let imagine it for high frequency systems. Even though, SDR principles are mostly applicable to design flexible multi-standard transceivers, requiring a large scale RF part and powerful common digital processing resources. Based on well-known considerations, this part describes the use and merging of some popular concepts in the field of converged wireless systems, placed from the receiver point of view, and targeting a flexible test platform for such structures. Let us now list the most meaningful principles used in our general approach.

Multi-standard approach -To achieve the wireless convergence, as said above, a SDR architecture with a common baseband processing seems very appealing. This implies that all parts of the receiving process are done numerically, except the downconversion. In this way, each technology will no longer relies on a particular chip, but on a software package, allowing dynamical changes, parallel decoding, and also update or new bundle downloads. Then a particular attention should be paid on calculation resources, assuming a maximum reuse of basic functions for all standards (FFT, filtering...) and a precise dimensioning to achieve real time operations. This relies both on computation capabilities and on RF Front-end design. SDR proposals often suggest direct conversion architectures, arguing that heterodyne systems can not fit every standard needs. Thus, zero or lowIF designs are generally preferred, all possible RF bandwidths being transposed to the same low frequency band before sampling. These simple and cost effective architectures greatly impact on baseband signal properties, inducing numerical compensation to be processed. Multi-antenna approach -This is a very hot topic in the area of wireless systems. Even from the only receiver point of view, multiplying antennas offers a high potential to compensate radio channel fading and interference. Indeed, receiving several copies of the same signal allows spatial diversity, with possible spatial rejection, or combined spacetime processing. In large angular spread configurations (e.g. urban or indoor), a great benefit could also be taken from time or polarization diversity. All incoming works on wireless applications deal with at least both space and time combiners from the simplest forms (antenna switch, FIR...) to advanced techniques like space-time coding (Alamouti code, Trellis or block-coding for MIMO systems). Then these popular techniques have to be evaluated in realistic environments enabling an efficient tradeoff between expected performances and the increase of RF needs (multiple front-ends, power consumption...) as well as calculation needs (DSP, FPGA, processor with also an impact on energy management).

Multi-channel approach -

There we talk about multiple frequency channel approach. Classical receivers, after selection of its allowed channel for communication, operate a frequency tuning in its RF part to only filter this chosen band, naturally operating an adjacent channel rejection. A global supervision of the network is needed to ensure that all co-and adjacent channel interference are efficiently reduced. A very relevant example is the 2.4 GHz bandwidth for 802.11 systems: this 84 MHz large band is shared between up to 14 overlapping 22 MHz channels. Therefore frequency-reuse is a hard point for dense networks, usually leading to high interference levels. Numerous interference rejection or multiuser detection techniques are well-known, generally dedicated to a single channel filtering. We discuss herein the opportunity of a wider sampling, offering a larger numerical information of the desired signal together with interferers. Then different techniques of interference mitigation, rejection (co-or adjacent channel), or parallel decoding can be involved. Of course, this principle comes with consequences on RF specifications (wideband operation) and digital processing (several potential additional noises).

Global combined approach -

Of course all those multi-* approaches already offer meaningful performances separately. Nevertheless combining these seducing principles in a global test platform allow evaluating all possible trade-off between joint or dissociated processing. Indeed this platform must be able to support additional technologies like CDMA or OFDM. A general scheme of such a platform is described in the following part (Fig. 1), with a particular attention paid on RF architecture choice and numerical compensation techniques [START_REF] Morlat | Global system evaluation scheme for multiple antennas adaptative receivers[END_REF].

General architecture discussion

The key point of such a multi-* architecture is obviously the analog to digital converter. Because a sampling frequency of few GHz is unachievable, the conversion implies a limited bandwidth. The agility of a receiver is then driven by two features: the carrier frequency tuneless and the maximal bandwidth. The first allows the receiver to process many standards as a function of the frequency band. On the opposite, the second allows the receiver to manage simultaneously several signals of same technology over adjacent channels. Note that both may converge in a near future because the radio bands are saturated and several standards should be called for co-existing on the same band. In co-existing systems, interference plays a major role in limiting the overall capacity. There is no doubt that all techniques of interference mitigation are going to be studied in depth. The SDR framework offers a first way to increase this capability. Indeed, the use of a high sampling frequency permits interference cancelling of adjacent channels by the use of multi-user detection. Multi-antennas is also a very complementary technology to avoid or mitigate interference. Finally, a full and efficient agility depends on both RF frontend features and numerical processing. RF Front-End features -To properly balance subsystem performance we must be aware of the limitations of the analog RF front-end considering that compensation can be made numerically. In most systems, the receiver tends to be more complex than the transmitter. The first challenge of receiver design is the Dynamic Range. RF front-end of a receiver must separate a desired signal typically from -130 dBm to -70 dBm, from a background RF environment that may be in the relative range from -20 dB to 0 dB. In many systems, the RF front-end also sets the system signal to noise ratio and should be designed to add minimal noise. Thus the ADC ADC ADC overall system must have a considerable dynamic range to accommodate both the high-power background signals and the lowestpower desired signal. Dynamic range is limited at the bottom of the range by noise that enters the system through thermals effects of the components or through nonidealities of the ADC, such as quantization noise or sampling aperture jitter. Low level signals can be masked by this noise. Dynamic range is limited at the high-end by interference. The source of this interference could be co-channel, adjacent channel, or self induced by the transceiver. High interference levels may cause the receiver to become more non-linear and introduce cross products (spurious components), which may inhibit the detection of low-level signals or reduce the desired signal bit error rate (BER). Simply attenuating the high-level signal before they drive the receiver into a non-linear operating region is insufficient since low-level desired signals also present will be attenuated until masked. The tunable radio frequency receiver consists in an antenna connected to a RF bandpass filter (BPF). The BPF selects the signal and the low noise amplifier (LNA) with the automatic gain control (AGC) raises the signal level for compatibility with the ADC. The BPF bandwidth relative to the carrier frequency must be highly selective and today it is impossible to design a filter at RF or microwave frequencies. Whatever the technology, it is clearly impractical. Firstly, the difficulty in designing a tuned radio frequency receiver is the limitation of the ADC, which must handle high frequency signals. In addition, to give the bandwidth and rolloff limitations of the RF filter, the sampling rate of the ADC must be high enough to avoid significant aliasing. The consequence of high sampling rate conversion is high power consumption. The ADC must accommodate multiple signals over the wide bandwidth of the RF filter (in tens of megahertz) with dynamic range of 100 dB and its non-idealities, such as jitter, lead to distortion of the signal. Numerical processing -In such a framework, the signal of interest reaches the processor, over-sampled and mixed with other interfering signals. Thus, several functions have to be implemented in a multi-* SDR numerical receiver: signal detection, synchronisation, downsampling, RF impairment mitigation, beamforming, etc … The complexity of the digital receiver is strongly related to the efficiency of the RF front-end. For multiple antennas, the balance between the RF front-end and numerical processing increases further. For each data channel, a digital demodulation is needed, providing an equivalent narrow-band signal. The over-sampling eases the time synchronisation and mitigation, but in turns is subject to an increase of the sampling noise due to possible high power adjacent channels. This loss of efficiency may be compensated by the use of multiuser detection techniques taking into account adjacent channels and several standards. In this context, the multiple antennas architecture appears promising, because more signals can be separated. The counterpart is the need of a multi-channel ADC.

Channel detection and characterization

Different methods

The first and fundamental step of signal processing is to detect that an interesting signal is present. Designers must pay attention to avoid expensive algorithms if there is nothing to receive all the time. Numerous methods exist to detect a desired signal, and the overall complexity essentially depends on the amount of known information and the amount of desired information. The use of singularities in a particular standard eases the detection, but that supposes a multiplication for each targeted standard. On the other hand, blind techniques are hard to implement and offer poor information on the signal quality. Let us now list the most useful techniques. Energy based signal detection -Usually, standard detectors use power detection methods to distinguish the offset of energy, characteristic of the presence of a signal. The detection is based on some function of the received samples which is compared to a threshold. Energy detectors are often used due to simplicity and good performance, but offer limitation in the case of spread signals and produce an important level of false detections.

Matched filter and correlation detection method -

The crosscorrelation is a measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. If a signal is correlated with itself (autocorrelation), then the maximum value of the correlation can be found at a time shift of 0. If this maximum is above a known threshold, the detection is proved. The most utilized technique provides a matched filter and a correlation detection method that carries out a correlation on a received signal with known periodic codes inserted as in the case of a 802.11b preamble. Cyclostastionarity Detection -A cyclostationary signal is a signal which contains a hidden periodicity [START_REF] Gardner | The Cumulant Theory of Cyclostationary Time-Series, Part I : Foundation[END_REF][START_REF] Gardner | The Cumulant Theory of Cyclostationary Time-Series, Part II : Development and Applications[END_REF]. A time-series x(t) contains a second order periodicity with frequency "a" if and only if there exists some stable Quadratic Time Invariant (QTI) transformation of x(t) into y(t) such that y(t) contains first-order periodicity with frequency a. The most obvious QTI transformation is a simple square modulus. Then cyclostastionarity detection becomes simple periodicity detection [START_REF] Burel | Detection of Spread Spectrum Transmissions using Fluctuations of Correlation Estimators[END_REF]. Moreover, calculating the different cyclic autocorrelation functions and identifying the non-zero values is also used to underline a cyclostastionary signal and detect the cyclic period, but this process is much more complex.

Of course various combinations of these techniques could be used depending on the desired complexity. In a multi-antenna context, some benefits could also be taken from the different copies of the signal, but considering that the synchronization is not yet performed. Until detection is proved and synchronization achieved, the full benefit of spatial diversity could be taken as describe in the following part.

Case of study

Our actual case of study is based on 802.11b and 802.11g standards. As said previously, if considered as in a noncooperative behaviour, those two protocols presents high levels of interference in the 2.4 GHz ISM band, with strongly overlapping channels. We are then developing a multi-* SDR receiver with 4 antennas at 2.4 GHz with a 80 MHz sampling offering an actual 40 MHz baseband. Thus we could find several overlapping channels with both possible standards in the sampled signal. Figure 2 presents the main numerical blocks required for one arm of this receiver. Therefore, the first method is based on a classical correlation of the received signal and a reference one, but enhanced by a periodicity detection (CPD), allowing a good separation of both kinds of signals. This prevents problems on defining a detection threshold. The second method is based on cyclostationarity detection [START_REF] Gardner | The Cumulant Theory of Cyclostationary Time-Series, Part II : Development and Applications[END_REF][START_REF] Gardner | The Cumulant Theory of Cyclostationary Time-Series, Part I : Foundation[END_REF]. Here the detection is based on the periodicity of higher order moments, and could be performed in time domain or in frequency domain based on the nullity of these moments at cyclic frequencies. Then, the third method considers fluctuations of second order moment estimators [START_REF] Burel | Detection of Spread Spectrum Transmissions using Fluctuations of Correlation Estimators[END_REF], detecting variation of those estimators corresponding to the symbol period.

For each method, an important consideration is to find a useable period of the signal depending of the waveform. As exposed on figure 3, the DSSS used for 802.11b present a 11 µs periodicity while the OFDM preamble of 802.11g could be characterized by a 16 µs format. (lower)

Results

To compare those methods, an indoor environment was simulated with 802.11b and 802.11g frames emitted, and one or two antennas at the receiver. AWGN or multipath channel were observed with interferer along seven different overlapping channels. Results presented on figure 4 are quite equivalent in terms of performances, but an important difference to be noticed is on complexity (Table 1). Hence, the CPD is the most robust in front of noise or interference with a low complexity but could not offer information of the better present mode, if both 802.11b and 802.11g standards are present. Frequency cyclostationarity and estimator detection characterize the quality of each signal with relatively good thresholds (ratio versus interferer considering SNR on figure 4). Thus, the estimator method is less complex but also less accurate. After all, the use of multi-antenna capabilities by the SMI algorithm notably enhances performances of such methods with only two antennas.

Conclusions

SDR concept combined with multi-channel and SIMO processing in the same terminal is a very promising issue to develop future wireless receivers ensuring high data rate and robust transmissions. The aim of this work was to present a global SDR system designed to combine several multi-* capabilities in a single receiver. Then we expose performances of different detection techniques to choose channels of interest and characterize the standard to deal with. Therefore, the CPD is the most robust in front of noise or interference with a low complexity and estimator detection characterize the quality of each signal with relatively good thresholds. Obviously, combining multiple antennas enhances performances of such methods with modest additional computation cost. Incoming works are dealing with more analysis and estimation of WLAN performances in a multi-channel configuration. Studies about implementation of more efficient multi-antenna algorithms in order to permit better interferers mitigation could also be interesting.

Figure 1 :

 1 Figure 1: General architecture of a multi-* SDR receiver

Figure 2 :

 2 Figure 2: General structure of the software WLAN receiverBy the way, the first block consists on the characterization of potentially interesting signal. We then estimate the costperformances trade-off of different detection methods.

Figure 3 :

 3 Figure 3: Frame structure for 802.11b (upper) et 802.11g (lower)

CPD


I Burciu
email: ioan.burciu@insa-lyon.fr

G Villemaud

J Verdier

Multiband Simultaneous Reception Front-End with Adaptive Mismatches Correction Algorithm

Keywords: multistandard simultaneous reception, adaptive systems, least mean square methods I

This paper addresses the architecture of multistandard simultaneous reception receivers and aims at improving the performance-power-complexity trade-off of the front-end. To this end we propose a single front-end architecture offering lower complexity and therefore lower power consumption. In order to obtain the same performance as the state of the art receivers, a light weight adaptive method is designed and implemented. It uses a mix of two digital implemented algorithms dedicated to the correction of the frontend IQ mismatches. A study case concerning the simultaneous reception of 802.11g and UMTS signals is developed in this article.

INTRODUCTION

The multiple functionalities characteristics imposed to the devices of the wireless telecommunications embedded domain have lead to the development of several dedicated standards. Depending on the type of the implemented service, a decision is made concerning the type of wireless telecommunication standard. For example the 2G standards are used for the voice communication, the WiFi is used for data transfer or a more general standard, like the 3G UMTS, is used for simultaneous data and voice transfer. Meanwhile, when implementing a multiservice simultaneous treatment device, the dedicated standards stack-up is generally chosen in order to have a good power-performance trade-off.

When designing a wireless telecommunications embedded device, the main goal is the good performance-powercomplexity trade-off [START_REF] Li | A System Level Energy Model and Energy-Quality Evaluation for Integrated Transceiver Front[END_REF]. The state of the art of the multiband simultaneous receivers is using the technique of the dedicated front-end stack-up. If we take into account the parallelization level of this type of architecture, it becomes obvious the interest of designing a unique front-end capable of simultaneously receiving two signals [START_REF] Evans | Development and Simulation of a Multi-standard MIMO Transceiver (Report style)[END_REF]. Such a multiband simultaneous reception single front-end architecture was proposed in [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. A comparative study between this architecture and the front-end stack-up [START_REF] Burciu | Low Power Multistandard Simultaneous Reception Architecture[END_REF] shows a power reduction of 20% in favor of the proposed architecture, as well as a complexity gain due to the use of fewer components (image rejection filters and frequency synthesizers). Meanwhile, while evaluating the performances of the proposed architecture, we can observe an important sensitivity to the IQ mismatches of the orthogonal translations [START_REF] Traverso | Decision Directed Channel Estimation and High I/Q Imbalance Compensation in OFDM Receivers[END_REF] [START_REF] Rudell | Frequency Translation Techniques for High-Integration High-Selectivity Multi-Standard Wireless Communication Systems[END_REF]. In fact, as shown in [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF], for a level of IQ mismatches going from zero to a realistic level [7] (1 o of phase imbalance and 0.3 dB of gain imbalance) the signal's quality can be degraded up to six times.

In order to mitigate the influence of the IQ mismatches on the reception quality of the useful signal, an adaptive digital algorithm was developed. This method is context-aware and is based on a mix between an iterative light weight algorithm and a more complex SMI [START_REF] Gantz | Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference[END_REF] (Single Matrix Inversion) algorithm. By mixing these two methods, we take advantage of the low consumption of the LMS (Least Mean Squares) iterative algorithm [START_REF] Widrow | The complex LMS algorithm[END_REF] and of the fast convergence characteristics of the more power greedy SMI. The results show a perfect mitigation of the effects of the IQ mismatches by the adaptive algorithm. In other words, when integrating this algorithm, the proposed architecture has the same performance as the font-end stack-up. This paper is composed of three parts. Following this introduction, section II describes the double IQ multistandard front-end architecture. Section III details the IQ mismatches and their impact on the quality of reception when using a double IQ front-end architecture. It is also dedicated to the implementation of the adaptive mismatches correction algorithm and to the results of the entire multiband simultaneous reception structure. Finally, conclusions of this study are drawn.

II. UNIQUE FRONT-END DEDICATED TO THE MULTIBAND SIMULTANEOUS RECEPTION

A. Double orthogonal translation front-end architecture

In wireless telecommunications, the integration of IQ baseband translation structures in the receiver chain has become a common procedure [START_REF] Traverso | Decision Directed Channel Estimation and High I/Q Imbalance Compensation in OFDM Receivers[END_REF]. It is generally used in order to reduce the bandwidth of baseband signals treated by the ADC. The orthogonal frequency translation is also used to eliminate the image frequency signal during the translation steps of heterodyne front-end architectures [START_REF] Rudell | Frequency Translation Techniques for High-Integration High-Selectivity Multi-Standard Wireless Communication Systems[END_REF]. This image frequency rejection technique consists in using two orthogonal frequency translations stages followed by a signal processing technique. It relies on the orthogonalization of the useful signal and the image frequency band signal during the translation from the RF to base band domain. Even though the spectrums of the two signals are completely overlapped after the first frequency translation, the orthogonalization allows the baseband processing to theoretically eliminate the image frequency component while reconstructing the useful one. Starting from this monostandard image rejection architecture, the double orthogonal translation technique is implemented in a novel multistandard simultaneous reception architecture [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. The choice of the standards used for the study case is WLAN (802.11g) and WCDMA-FDD, representitive of the OFDM and CDMA techniques, as well as for the severe constraints they impose. Several simulation of the structure presented in Fig. 1 were performed using the ADS software provided by Agilent Technologies [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. One of this series of simulations concerns the BER (Bit Error Rate) evolution of the two study case standards when being simultaneously received either by a structure using the heterodyne front-end stack-up architecture or by the proposed double IQ architecture. The blocks used during the simulations have the same typical metrics in both cases. The performance of the two architectures during the simultaneous reception of the two standards is almost identical. Meanwhile, these simulations do not take into account the orthogonal mismatches of the IQ translation blocks.This sensible matter concerning the mitigation of the IQ mismatches impact is amply treated in section III.

B. Comparative power-complexity study

One of the most important issues when designing a radiofrequency front-end is the performance-power-complexity trade-off [START_REF] Li | A System Level Energy Model and Energy-Quality Evaluation for Integrated Transceiver Front[END_REF]. This section is therefore dedicated to a comparative overall power-complexity evaluation between the heterodyne front-end stack-up and the proposed architecture. Table 1 presents the results of a bibliographic study, concerning the state of the art of the blocks used by the two structures [START_REF] Burciu | Low Power Multistandard Simultaneous Reception Architecture[END_REF]. It summaries the numbers of elements used by each structure, as well as their individual power consumption along with the supply voltage. We can then conclude that the proposed architecture needs fewer components than the frontend stack-up as it doesn't need image rejection filters and it uses two times less frequency synthesizers. Therefore, the complexity comparison is favorable to the proposed structure, especially because the image rejection filters are not on-chip integrated elements. For our study case and for the power consumption levels presented in Table 1 the overall consumption comparison shows that our structure consumes This means a 20 % of gain in favor of the single front-end structure assessed in this paper.It can be observed that the power reduction comes essentially from the use of two times less frequency synthesisers, while using the same number of other components.

III. ADAPTIVE ALGORITHM DEDICATED TO THE CORRECTION OF ORTHOGONAL MISMATCHES

This section is addressing the impact of the orthogonal mismatches on the quality of the useful signal in a multiband double orthogonal translation structure. It also presents a dedicated adaptive MMSE (Minimum Mean Square Error) algorithm used to mitigate this impact.

A. IQ mismatches

The double orthogonal translation technique allows a theoretically perfect rejection of the image band signal for a case study where the quadrature mounted mixers are perfectly matched -no phase or gain mismatch. Nevertheless, design and layout defaults, such as different line lengths between the two branches and non identical gain of the mixers, generate phase and respectively gain mismatches [START_REF] Traverso | Decision Directed Channel Estimation and High I/Q Imbalance Compensation in OFDM Receivers[END_REF]. Therefore, in a real case scenario where the gain and the phase mismatch can go up to 0.3 dB and respectively 1 degree [7], the image band signal is not completely rejected. In fact the metric used to quantify this rejection, the image rejection ratio (IRR), depends on the gain and phase mismatches between the two branches of the IQ translation structures [START_REF] Rudell | Frequency Translation Techniques for High-Integration High-Selectivity Multi-Standard Wireless Communication Systems[END_REF]. While evaluating the IRR of the double orthogonal translation, we choose to ignore the IQ mismatches of the block used to translate the signal in the base band domain because of the low frequency of their input signal. Supposing that the first IQ stage has a gain mismatch ΔA and a phase mismatch Δθ, the final IRR can be modeled by the equation:

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ Δ + - Δ + + Δ Δ + + Δ + + = ) cos( ) A 1 ( 2 ) A 1 ( 1 ) cos( ) A 1 ( 2 ) A 1 ( 1 log 10 ) ( 2 2 θ θ dB IRR (1)
For the levels of phase and gain mismatch of 1 o and 0.3 dB respectively, the theoretical IRR rejection is 28.97 dB. In the followings we assume that the mismatches of the orthogonal translation blocks integrated in the multiband simultaneous reception architecture can reach this level. Therefore the 28.97 dB of IRR represent the minimum rejection that the complementary signal undergoes when one of the signals is received. For our study case -simultaneous reception of UMTS and WLAN -this level of rejection is clearly not sufficient. In fact, the worst case scenario implies a WLAN signal having a -80 dBm power level and a UMTS signal with a -30 dBm power level at the antenna. For this case we consider an automatic gain control stage (AGC) that amplifies of 30 dB the signal on the WLAN dedicated branch and of 0 dB the signal on the UMTS dedicated branch. For these given conditions the WLAN quality of service imposes that the front-end rejects the complementary UMTS signal under the power level of the thermal noise on the WLAN dedicated branch. This means an IRR of 41 dB that has to be realized by the double orthogonal translation structure in order to have the same performances as the front-end stack-up architecture. For the scenario presented above, several simulations show a normalized WLAN BER that can go from 1 to 6 when the phase and gain mismatch go from 0 to 1 o and 0.3 dB respectively [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF].

B. Adaptive digital Algorithm

In order to mitigate the influence of the IQ mismatches on the quality of the signals processed by the proposed receiver structure, a digital adaptive method has been implemented. It is composed of a mix between a light power consumption iterative LMS algorithm and a power greedier SMI algorithm. The scenario considered here involves a continuous reception of a WLAN signal while the UMTS signal at the antenna has a random power level. It is also supposed that the IQ mismatches have a slow variation during the reception.

Based on (1) and on the system model presented in [START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF] The α/β ratio is directly proportional with the IRR, as it represents the attenuation of the image band signal compared to the useful baseband signal. In the followings, we choose to focus on the reception of the WLAN signal and to consider the UMTS signal as interference, the UMTS dedicated method being analog to that used for the WLAN. For this study case, the adaptive correction method is estimating β by a weight w.

Figure 1 .

 1 Figure 1. Double orthogonal frequency translation front-end dedicated to the multistandard simultaneous reception.This new architecture considers the image band signal as a useful signal. In order to fulfill this condition the local oscillator used during the first of the two orthogonal translations is ably dimensioned. Its frequency is set in such a manner that each of the two useful signals has a spectrum that occupies the image frequency band of the other.The architecture and the spectrum evolution of such a receiver, able of treating simultaneously two standards, are developed in Fig.1. As it can be observed, the parallelization of the input stages imposes the use of two dedicated antennas, two dedicated RF band filters and two dedicated LNAs. The gain control stage is realized by the input stages, each LNA being dedicated to the gain control of one of the signals. Once separately filtered and amplified, an addition of the two signals is made. The output is then processed by a double orthogonal translation structure. As the frequency of the first oscillator is chosen in such a manner that each of the two signals occupies a spectrum in the image band of the other, a complete overlapping of the spectrums can be observed in the intermediate frequency domain. After the second orthogonal frequency translation and after the digitalization of the four resulting signals, two basic processing chains are implemented. Each of them reconstructs one of the two useful signals, while rejecting the other.The choice of the standards used for the study case is WLAN (802.11g) and WCDMA-FDD, representitive of the OFDM and CDMA techniques, as well as for the severe constraints they impose. Several simulation of the structure presented in Fig.1were performed using the ADS software provided by Agilent Technologies[START_REF] Burciu | A 802.11g and UMTS Simultaneous Reception Front-End Architecture using a double IQ structure[END_REF]. One of this series of simulations concerns the BER (Bit Error Rate) evolution of the two study case standards when being simultaneously received either by a structure using the heterodyne front-end stack-up architecture or by the proposed double IQ architecture. The blocks used during the simulations have the same typical metrics in both cases. The performance of the two architectures during the simultaneous reception of the two standards is almost identical. Meanwhile, these simulations do not take into account the orthogonal mismatches of the IQ translation

Figure 2 .

 2 Figure 2. Digital context-aware method used to mitigate the influence of IQ mismatches in a double orthogonal translation receiver.

  , the two signals s BBWLAN and s BB UMTS , obtained after the digital demodulation presented in Fig.1, can be modeled by: WLAN and s RF UMTS are the baseband translation of the RF signals at the output of the automatic gain control stages. The α and β coefficients depend directly of the gain mismatch ΔA and of the phase mismatch Δθ:

Figure 3 .

 3 Figure 3. WLAN BER evolution during a multiband simultaneous reception for different values of the gain control and for two configuration depending on the implantation of the adaptive IQ mismatches corection method.

TABLE I

 I

	.	BASIC ELEMENTS USED BY THE TWO ARCHITECTURES
			Stack-up Double IQ Power//Supply
			Quantity	Quantity	mW//V
	LNA UMTS		1	1	7.2//1.8
	LNA WLAN		1	1	8//1
	RF Filter		2	2	-
	IF Filter		2	0	-
	Mixer		6	6	5.6//-
	RF-Frequency Synthetizer	2	1	42//3
	IF-Frequency Synthetizer	2	1	20//-
	Baseband-Amplifier WLAN	2	4	10//-
	Baseband-Amplifier UMTS	2	0	5//-
	ADC WLAN		1	4	12//2.5
	ADC UMTS		2	0	11//1.8

216 mW while the state of the art architecture uses 284 mW.

ACKNOWLEDGMENT

The authors wish to acknowledge the assistance and support of the Orange Labs Grenoble.

In order to do this estimation it uses the two signals from the output of the digital demultiplexing stage and a known training sequence -two long preamble symbols of the WLAN signal. Once the estimation is finished, the weight is multiplied with the s BB UMTS signal and the result is subtracted from s BB WLAN , as shown in Fig. 2. In this manner, the interfering s RF UMTS component of the s BB WLAN signal becomes insignificant.

The estimation is realized by a context-aware method using either a LMS or a SMI algorithm [START_REF] Gantz | Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference[END_REF] [START_REF] Widrow | The complex LMS algorithm[END_REF]. The LMS algorithm is an iterative method that uses the MMSE technique in order to minimize the difference between the received signal and a training sequence. For our study case, each of the iterations implies the following operations:

where s REF WLAN is the training sequence of the WLAN signal and μ is the algorithm step size. A trade-off has to be made when choosing μ because a large step size leads to a bad estimation precision while a small one leads to a slow convergence of the algorithm. Simulations show that the algorithm manages to mitigate the influence of IQ impairments. In addition, for a continuous WLAN and UMTS simultaneous reception, LMS manages to adapt to the slow IQ impairments variation.

The major drawback of this algorithm is the small precision of the evaluation to the absence or to the week power level of the complementary UMTS signal. But this is not a major problem for this input power level case. The real inconvenient is the fact that, if the power level on the UMTS dedicated branch changes from -107dBm to a significant level, the LMS algorithm has to converge once again in order to offer a good precision. Simulation shows that, in order to converge to an estimation of β allowing a supplementary 20 dB of IRR, the algorithm needs up to 10000 samples. Knowing that the two WLAN preamble symbols provide 128 samples of training sequence per frame, it takes up to 80 frames for the algorithm in order to grant a sufficient precision. We conclude that this algorithm can provide an adaptive mitigation of the influence of the IQ impairments, but it cannot manage an arbitrary power variation of the complementary signal.

In order to overcome this sensitivity of the LMS algorithm to the absence of signal at the output of the UMTS dedicated branch, a solution is the use of this adaptive algorithm only when the complementary signal sbb UMTS has certain power level. But this means that during the absence of the UMTS signal, the algorithm can not adapt the w estimation to the variation of the IQ mismatches. Therefore, each time the UMTS signal power changes from an insignificant to a consistent level, the LMS has to converge in order to evaluate once again the IQ mismatches that could have changed during the absence of the UMTS signal. The solution that has been choose in order to adapt to this UMTS signal fluctuating power level is to use a SMI algorithm [START_REF] Gantz | Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference[END_REF]. The advantage of this algorithm is its estimating performance when using a relatively small training sequence -128 samples of the two WLAN preamble symbols for our study case. Compared to the continuous estimation approach of the LMS algorithm, the SMI has a block adaptive approach. Instead of using an iterative approach in order to estimate w, it uses the entire training sequence for a matrix inversion operation. Simulations show that a training sequence of 128 samples is sufficient for the SMI algorithm in order to realize a supplementary 20 dB rejection of the UMTS complementary signal. However, the main drawback of this type of algorithm is its complexity and power consumption compared to the LMS. By consequence, the optimum solution for an adaptive IQ mismatch correction algorithm is a context-aware method depending on the power level P UMTS of s BB UMTS :

• If the current P UMTS is bigger than a choosen detection level, the decision on which algorithm to be activated depends on the P UMTS level of the previous frame:

o If it was smaller than the detection level, the SMI is activated in order to find the optimum w weight by using only one 128 samples training sequence.

o If it was bigger than the detection level, the LMS algorithm is activated in order to be able to adapt to the IQ mismatches slow variation.

• If P UMTS is smaller than a trigger level, none of the two algorithms is activated in order to estimate the w weight.

This context-aware adaptive method was implemented using Matlab software. In order to have more eloquent results, it was incorporated in a co-simulation platform which also includes the UMTS and WLAN transmission sources, as well as the model of the analog double orthogonal front-end. This platform is composed of two E4438C Signal Generators, of a 89600 Vector Signal Analyzer and it uses the Advanced Design System software, all provided by Agilent technologies [10]. The measurements were made by using a line of sight channel close to the AWGN conditions. During this measurements campaign we focused on the WLAN reception while the UMTS signal is considered as interfering. In order to validate the context awareness of the adaptive method, the source generating the interfering signal is arbitrarily turned on. The power level for this source is chosen in such a manner that the UMTS interfering signal has a power level of -30 dBm at the input of the receiver. Fig. 3 presents several BER evolutions as function of the WLAN signal's SNR (Signal to Noise Ratio). These results reveal that, for different levels of the gain control and therefore of the interfering signal, the influence of the IQ mismatches is mitigated by the digital adaptive method. In fact the performance of a single WLAN dedicated front-end and that of the proposed multiband simultaneous reception structure are practically identical when the adaptive method is used. In the same time, we can observe a shift between the curves characterising the BER evolution when the adaptive method is implemented and when the multiband receiving structure doesn't use any digital correction method. This shift can go up to 20 dB, depending on the attenuation of the UMTS interfering signal by the gain control stage.

Finally the proposed adaptive method manages to offer up to a supplementary 20 dB of the complementary signal rejection when implemented in a multiband double orthogonal translation structure. In other words, our structure has the same performance as the front-end stack-up structure [START_REF] Evans | Development and Simulation of a Multi-standard MIMO Transceiver (Report style)[END_REF], independently of the IQ mismatches.

IV. CONCLUSIONS

This article is focused on a novel context-aware adaptive method dedicated to the mitigation of the IQ mismatches impact in a multiband double orthogonal translation front-end. The theoretical results related to this digital processing technique were validated by measurement. During this measurement campaign, a performance comparative study is realized between the front-end stack-up receiver and the single front-end multiband receiver integrating this digital adaptive method. For this purpose, the radiofrequency platform is integrating a real communication channel and realistic models of the two multiband simultaneous reception front-ends compared here. The reception measured performances are practically identical when the two structures are used. This implies that, when integrating the adaptive method, the proposed single front-end architecture has the same performance as the dedicated front-end stack-up. If we also take into account the complexity gain as well as the 20% of power reduction, the proposed receiver structure offers a significantly improved performance-consumption-complexity trade-off when compared to state of the art of the multistandard simultaneous reception architecture.

The follow-ups of this work would consist in a powerperformance study concerning the length optimization of the training sequence used by the SMI algorithm.