Method for estimating characteristics of a communication channel and associated computer program

Abstract

A method for estimating characteristics of a communication channel comprising the following steps: - receiving, at a first communication device (2) and via a configurable surface (4), pilot signals from a second communication device (6); - estimating a first angle (θ g ) defining a direction of the first communication device (2) with respect to the configurable surface (4); - determining a second angle (θ h ) defining a direction of the second communication device (6) with respect to the configurable surface (4) and which minimizes a value calculated based on a Hermitian inner product between a first matrix comprising the received pilot signals and a second matrix calculated based on the first and second angles; - determining a first delay associated with the path between the first communication device (2) and the configurable surface (4), and a second delay (τ h ) associated with the path between the second communication device (6) and the configurable surface (4), that minimize a distance calculated based a difference between a first vector of complex gains computed based on possible respective values of the first delay and the second delay, and a second vector of complex gains estimated based on the first and second angles.

Description

[0001]Method for estimating characteristics of a communication channel and associated computer program Technical field of the invention The invention relates to the field of wireless communications.It is directed in particular to a method for estimating characteristics of acommunication channel and to an associated computer program.State of the art In order to enhance the coverage provided by base stations in wireless communications, it has been proposed to insert a configurable surface in the communication path between the base station and user equipments such as mobile phones and other electronic devices with means to wirelessly communicate with the base station. Such a configurable surface (e.g. a RIS or Reconfigurable Intelligent Surface)includes a plurality of configurable elements that may each alter the incidentelectromagnetic signal. The effect of each configurable element on the electromagnetic signal is generally considered as a phase shift. Thanks to such a configurable surface, wireless communication is possible between a base station and a user equipment (via the configurable surface) even though the direct path (or line-of-sight path) between the base station and user equipment is blocked, for instance. However, the use of a configurable surface complicates channel estimation,which is of the utmost importance to correctly configure the communication devices toobtain efficient wireless communications between them. Summary of the invention In this context, the invention provides a method for estimating characteristics ofa communication channel between a first communication device and a second communication device and via a configurable surface having a plurality of configurable elements, comprising the following steps: -receiving pilot signals from the second communication device at the firstcommunication device and via the configurable surface; -estimating at least one first angle defining a direction of the first communicationdevice with respect to the configurable surface;- determining at least one second angle defining a direction of the secondcommunication device with respect to the configurable surface and which minimizes a value calculated based on a Hermitian inner product between a first matrix comprising the pilot signals as received at the first communication device and a second matrix calculated based on the at least one first angle and on the at least one second angle; -determining a first delay associated with the path between the firstcommunication device and the configurable surface, and a second delay associated with the path between the second communication device and the configurable surface, that minimize a distance calculated based on at least one difference between a first vector of complex gains computed based on possible respective values of the first delay and the second delay, and a second vector of complex gains estimated based on the at least one first angle and the at least one second angle. Thus, an efficient method is provided for channel estimation in the presence of a configurable surface. The second matrix may for instance be calculated based on a Hadamard productbetween a matrix comprising steering vectors from the first communication device to the configurable surface that are estimated based on the at least one first angle, and a matrix comprising steering vectors from the configurable surface to the second communication device that are estimated based on the at least one second angle. Precisely, the second matrix may be a product of the transpose of said Hadamardproduct by a configuration matrix representative of respective configurations of theconfigurable surface during the transmission of pilot signals; said value may then beequal to the opposite of the square of the module of said Hermitian inner product divided by the square of a norm of the second matrix. The first matrix comprises for instance K x N elements representing respectivelypilot signals received on an antenna of the first communication device on K subcarriers at N times. The first communication device may comprise a plurality of antennas. In this case,the step of estimating the at least one first angle may comprise:- for each of a plurality of configurations of the configurable surface, transmitting,from the first communication device to the second communication device via the configurable surface, a plurality of test signals respectively produced using distinct precoding matrices;- measuring, by the second communication device, values respectivelyrepresentative of a quality of transmission of the test signals; -estimating the at least one first angle based on the measured values.According to another possibility, the first communication device comprising a firstantenna and other antennas, the step of estimating the at least one first angle may comprise: -for each one of the other antennas, determining estimations of the pilot signalreceived at the concerned other antenna based on the pilot signal received at the first antenna and for various possible values of the angle defining the direction of the first communication device with respect to the configurable surface; -estimating the at least one first angle as the possible value for which a distancebased on differences, for the various other antennas, between the pilot signal received at the concerned antenna and the determined estimation of the pilot signal received at the concerned antenna is minimum. Transmitting the pilot signals may comprise transmitting a pilot signal at each ofa plurality of times, and the configurable surface may then be respectively configuredin a plurality of distinct configurations at said plurality of times. For instance, the first communication device is a base station and / or the second communication device is a user equipment. The second angle ^^^may for instance be determined (using a maximum likelihood estimation) as ^^^ ^^ ^^^ where ^^is said on said atleast one first angle, ^^(^^ , ^^) is a matrix of steering vectors depending on possiblevalues for the second angle, ^ is a matrix which columns respectively define variousconfigurations taken by the configurable surface during the receiving step and ^^^is another angle defining the direction of the second communication device with respect to the configurable surface and concurrently determined. The first delay and the second delay may then be determined (using another maximum likelihood estimation) as where ^^is the first a of the first communication device, ^^is the second vector of complex gains for an antenna a ofthe first communication device, A is a subset of antennas (e.g. a pair of antennas)among antennas of the first communication device, c is the celerity of light in vacuum,^^^ is an inner radius of the far-field region and ^^^ is a cell radius.In order to perform channel estimation in a simpler manner once a first channelestimation has been made as proposed above, the method may further comprise thefollowing steps: -selecting a plurality of configurations;- transmitting further pilot signals at a plurality of times respectively associatedwith the selected configurations, the configurable surface being configured at each time in the selected configuration associated with the concerned time; -determining an updated value of the at least one second angle which minimizesa further value calculated based on a Hermitian inner product between a third matrix comprising said further pilot signals received at the first communication device and a fourth matrix calculated based on the at least one first angle and on the updated value of the at least one second angle. The invention also provides a computer program comprising instructionsexecutable by a processor (e.g. a processor of the first communication device) andsuitable to implement a method as proposed above when these instructions areexecuted by the processor. The invention also provides a (non-transitory) computer readable medium storing such a computer program. Detailed description of embodiments of the invention Other possible features of the invention will appear upon reading the descriptionbelow, made with reference to the appended drawings where :- Figure 1 is a schematic representation of a system in which the invention maybe implemented; -Figure 2 is a flow chart showing the main steps of a possible embodiment of amethod according to the invention;- Figure 3 represents exchanges between a base station and a user equipmentvia a configurable surface in the context of a first embodiment of a step of estimating angles; -Figure 4 represents exchanges between the base station and the userequipment via the configurable surface in the context of a possible variation of this first embodiment; -Figure 5 represents exchanges between the base station and the userequipment via the configurable surface in the context of another possible variation of this first embodiment. Figure 1 shows a communication system including a first communication device 2 (here a base station), a configurable surface 4 (here a RIS or Reconfigurable Intelligent Surface) and a second communication device 6 (here a user equipment). The method described below could however be implemented in a communicationsystem including a further communication device, or further communication devices.For instance, in a typical situation, the communication system includes a base station and a plurality of user equipments. It is considered in the present example that the base station 2 includes M antennas, the user equipment 6 includes one antenna and the configurable surface includes N configurable elements (for instance configured as a matrix of configurable elements with Ny columns and Nz lines, such that Ny×Nz = N). Propagation of electromagnetic waves in the communication channel betweenthe base station 2 and the user equipment 6 via the configurable surface 4 can bemodelized by the following equation for each antenna a of the base station 2 and eachsubcarrier: ^ ^ where response from the base station antenna a to the configurable surface 4, ^^is a vector of N complex elements representing the channel response from the configurable surface 4to the user equipment 6, ⊙ is the Hadamard product, ^^,^ is the path delay of the pathbetween base station antenna a and the configurable surface 4, ^^ is the path delayof the path between the configurable surface 4 and the user equipment 6, are angles representing the direction of the base station 2 relative to thesurface 4 (or Angle of Departure from the configurable surface 4), (^^, ^^) are angles representing the direction of the user equipment 6 relative to the configurable surface4 (or Angle of Arrival to the configurable surface 4), ^^ is a vector of N complexelements respectively representing phase shifts applied by the N elements of the configurable surface 4 (^th^is for instance the ncolumn of a codebook ^ ∈ ℂ^×^), ^^is the complex signal transmitted for the kth subcarrier and ^^,^ is a complex AdditiveWhite Gaussian Noise (AWGN) for the base station antenna a. This model is particularly appropriate when the configurable surface 4 is in thefar-field region of both the base station 2 and the user equipment 6, and considersnon-line-of-sight paths as part of the noise ^^,^. In the present example, an orthonormal frame of reference (O, x, y, z) is used, where (Oy) and (Oz) are parallel to the horizontal side and the vertical side of the (rectangular) configurable surface 4, respectively, and (Ox) is normal (i.e.perpendicular) to the configurable surface 4. In this case, the angles mentioned abovecan be defined as follows: -^^ is the elevation of the direction of the base station 2 relative to theconfigurable surface 4, i.e. the angle between this direction and the axis (O, z);- ^^ is the azimuth of the direction of the base station 2 relative to theconfigurable surface 4, i.e. the angle between the projection of this direction in theplane (O, x, y) and the axis (O, x); -^^ is the elevation of the direction of the user equipment 6 relative to theconfigurable surface 4, i.e. the angle between this direction and the axis (O, z);- ^^ is the azimuth of the direction of the user equipment 6 relative to theconfigurable surface 4, i.e. the angle between the projection of this direction in theplane (O, x, y) and the axis (O, x). In other embodiments, the situation described above can be represented using a 2D model including the base station 2, the configurable surface 4 and the user equipment 6 in a plane, such that the direction of the base station 2 relative to the configurable surface 4 and the direction of the user equipment 6 relative to theconfigurable surface 4 may each be represented by a single angle (e.g. formedbetween the concerned direction and a direction normal to the direction of extensionof the configurable surface 4 in the plane just mentioned).Using the amplitude ^^,^(^^,^ , ^^) and phase ^^,^(^^,^ , ^^) of the overall channel(complex) gain = ^^,^(^^,^ , ^^)^^^^,^(^^,^,^^)and steering vectors ^^^^^, ^^^, ^^(^^ , ^^) between the base station antenna a and the configurablesurface 4 and between the configurable surface 4 and the user equipment 6, the equation above can be written as follows: ^^^ ^^ ^ where ⊗ is the Kronecker product, G represents the overall antenna gain (ordirectivity, a fixed parameter possibly measured beforehand or given by the manufacturer of the antenna), ^^is the frequency of the kthsubcarrier, ^^the ^ corresponding free-space wavelength (hence ^^= ^^ where ^ denotes the celerity oflight in vacuum), ^^is the horizontal spacing between two elements of the configurable surface 4 and ^^is the vertical spacing between two elements of the ^ configurable surface 4, with ^^^^^≤ ^ and ^^≤ ^ . For further explanations on this equation, reference can be made for instance to the article “RIS-Aided Wireless Communications: Prototyping, Adaptive Beamforming,and Indoor / Outdoor Field Trials”, by Pei, Xilong, et al. in IEEE Transactions onCommunications, Vol. 69, no. 12, 1 Dec. 2021, pp. 8627–8640.Thus, knowing the configuration of the system and the corresponding fixed parameters, the channel may be estimated by estimating the following parameters (orcharacteristics): ^^,^ , ^^, ^^, ^^ , ^^ , ^^ . Estimating parameters ^^,^ needs onlyestimating a parameter ^^ for a single antenna (for instance ^^,^ = ^^ for antenna 1)as parameters ^^,^ for other antennas can be derived from parameter ^^ knowing thegeometrical relationship between antennas. Figure 2 is a flow chart showing the main steps of a possible embodiment of amethod for estimating these characteristics.This method starts with a step S2 of transmission of a collection of K x N pilotsignals from the user equipment 6 to the base station 2 via the configurable surface 4:this set comprises N time-symbols, with each symbol encompassing the K subcarriers. In the present example, each pilot signal is a “1”, such that the matrix X representing pilot signals is a K x N matrix with all elements equal to 1. When transmitting the nth time-symbol, the configurable surface 4 is configuredin accordance with vector ^^ , i.e. the N configurable elements of the configurablesurface are respectively configured to apply a phase shift given by the correspondingelement of the vector ^^. As already indicated, ^^ is for instance the nthcolumn of acodebook ^ ∈ ℂ^×^.The configurable surface 4 is thus configured in N distinct configurations over thetransmission of the pilot signals.The pilot signals transmitted from the user equipment 6 are thus received (via the configurable surface 4) at the base station 2. For each antenna a of the basestation 2 (^ ∈ [1.. ^]), the received signal can be written in matrix form as follows (theN columns of the matrix respectively corresponding to the N time-symbols, each column comprising K elements corresponding to the K subcarriers): ^^^^ ^^ ^where diag(v) is the diagonal^^ = ^ ^^^^ ^= ^,^ , … ,^,^^ ^^is a complex Additive White Gaussian Noise matrix. The pilot signal matrix X is absent from the formula giving ^^ due to its particularform (all elements being equal to “1”) used in the present case as explained above. The method of Figure 2 then comprises a step S4 of estimating angles ^^ , ^^.The obtained estimated values for angles are respectively noted ^^^, ^^^. As explainedabove, these angles ^^ , ^^ define the direction of the base station 2 with respect to theconfigurable surface 4.Several possible ways of estimating angles ^^, ^^ are described below, withreference to Figures 3 to 5 in particular. Although in the present embodiment the step S2 is performed before the step S4, it should be noted that, in some embodiments, the step S2 described above could be performed between the step S4 and the step S6. The method of Figure 2 then comprises a step S6 of estimating respective values^^^ , ^^^ (for the angles ^^ , ^^ ) that maximize a normalized Hermitian inner productbetween a matrix of signals received at the base station 2 (by a given antenna, hereantenna 1) and a matrix including estimations of these signals computed (based onthe formula above giving ^^) taking into account (for steering vectors of the matrix ^^)the estimated angle values ^^^, ^^^ and considering (for steering vectors of matrix ^^)the possible values of angles ^^ , ^^.This is for instance performed by first computing, using estimated angle values^^^, ^^^, the estimated matrix ^^ of steering vectors:^^ = ^ ^^^^^and then by ,the opposite of theHermitian inner product mentioned above:^ where |z| is Hermitian innerproduct (also called Frobenius inner product) between matrices P and Q, and ||M|| isthe norm of matrix M. Angle values ^^^ , ^^^ are thus determined using a first maximum likelihoodestimation. The determined angle values ^^^ , ^^^ thus define the direction of the userequipment 6 with respect to the configurable surface 4 and minimize a value calculatedbased on a Hermitian inner product between a first matrix ^^comprising the pilotsignals as received at an antenna (here antenna 1) of the first communication device(here the base station 2) and a second matrix (here ^^ calculatedbased on the estimated angle values ^^ ^, ^^^ and on any values for^^ , ^^. The method of Figure 2 then comprises a step S8 of determining a first delay ^^̂associated with the path between the base station 2 and the configurable surface 4,and a second delay ^^̂ associated with the path between the user equipment 6 andthe configurable surface 4, that minimize a distance calculated based on at least onedifference (here based on a plurality of differences respectively relating to distinctantennas, precisely a pair of differences respectively relating to a pair of antennas) between a first vector ^^of complex gains computed based on possible respectivevalues of the first delay and the second delay and a second vector ^^ of complex gainsestimated based on the estimated angle values ^^^, ^^^, the determined angle values^^^ , ^^^ and pilot signals received at the concerned antenna a.This step S8 is for instance performed by first computing, for each antenna a ofa pair of antennas A = {^, ^} where ^, ^ ∈ [1.. ^] such that the Euclidian distancebetween these antennas i and j is maximized, and for each subcarrier k, the amplitude^^^,^and phase ^^,^of the estimated overall gain (for the channel between basestation 2 and user equipment 6 via configurable surface 4) as follows:^ where ^^,^ product betweenvectors u and v, ||v|| is the norm of vector v and arg z is the argument of (complexnumber) z, and steering vectors ^^(^, ^) are defined above,and then by determining the first delay ^^̂ and the second delay ^^̂ that minimizethe quadratic sum of the differences (for the pair of antennas ^ = {^, ^}) between thefirst vector ^^of complex gains computed based on possible respective values of thefirst delay ^^ and the second delay ^^ and the second vector ^^ of complex gainsdetermined based on values ^^^,^, ^^,^determined for the same antenna:^ ^^ where ^^^= ^^ is the inner radius of the far-field region (where ^^ is thewavelength of the carrier frequency), D being the biggest dimensionof the reconfigurable surface 4 , ^^^ is the cell radius, ^^ ^ ^^dependent betweenantennas and ^^ = [^^^,^^^^^,^ , … , ^^^,^^^^^,^]^. For instance, the sought delay can correspond to the delay at antenna i (^^,^=^^ ) and the delay ^^,^ at antenna j can then be determined based on ^^ (i.e. ^^,^depends upon ^ ^ ^,^ ^ ) taking into consideration the geometricalbetween antennas i and j. Delay values ^^̂, ^^̂ are thus determined using a second maximum likelihoodestimation. The first maximum likelihood estimation and the second maximum likelihoodestimation can for instance be performed using a genetic algorithm. Reference can bemade for instance to the article “Genetic Algorithm Optimisation for MaximumLikelihood Joint Channel and Data Estimation”, by Chen, S, and Y. Wu in Proceedingsof 1998 IEEE International Conference on Acoustics, Speech and Signal Processing. pp.1157-1160. As a possible variation however, one at least of the first and second maximum likelihood estimation may be performed by grid search or using a neural network interpolator. Estimated parameters ^^^, ^^^, ^^̂, ^^^ , ^^^ , ^^̂ characterising the communicationchannel between the base station 2 and the user equipment 6 via the configurablesurface 4 have thus been produced.As the estimated parameters ^^^, ^^^, ^^̂ relating to the communication channelbetween the base station 2 and the configurable surface 4 remain relatively steady, itis possible to perform (at least some) further channel estimations by estimating characteristics of the communication channel between the configurable surface 4 andthe user equipment 6 only, i.e. by only updating the parameters ^^^ , ^^^ , ^^̂.In this goal, it is possible (at step S10) to first select L configurations amongstthe N distinct configurations of the configurable surface 4 used during step S2.The (restricted) codebook containing this L selected configurations is denoted:^^. Said differently, the restricted codebook ^^ contains (as columns) L vectors ^^extracted from the codebook ^ mentioned above.The number L of vectors (corresponding to configurations of the configurablesurface 3) in the restricted codebook ^^is here equal or greater than 3 and / or much smaller than the number N of vectors (corresponding to configurations of theconfigurable surface 3) in the codebook ^. The number L of vectors in the restrictedcodebook ^^is for instance smaller than a tenth of the number N of vectors in the codebook ^. Said differently, the number L of selected configurations is here smaller than atenth of the number of distinct configurations of the configurable surface 4 used duringstep S2. The selected configurations correspond for instance to the L strongest (pilot)signals received by the base station 2 (e.g. on a particular antenna a) during step S2.If we denote (^^)^the signals received for the nth time-symbol (i.e. the vector ofthe nthcolumn of the matrix ^^), which has thus been received at step S2 while theconfigurable surface 4 had a configuration defined by the vector ^^, the L selectedconfigurations ^^ corresponds to the L indices n for which the signal strength ‖(^^)^‖is maximum. Then, at step S12, pilot signals (defined in a matrix XS comprising K rows and L columns, all elements being here equal to “1”) are sent from the user equipment 6 tothe base station 2 via the configurable surface 4 over the L time-symbols, theconfigurable surface 4 being configured in accordance with vector ^^of the codebook ^th^at the ntime-symbol, i.e. when a pilot signal defined by the nth column of matrixXSis transmitted. We denote ^^the matrix containing signals received by the particular antenna a(mentioned above) of base station 2 over the L time-symbols (^^ thus also having Krows and L columns).The method then comprises a step S14 of determining updated values of angles^^^ , ^^^ which minimize a further value calculated based on a Hermitian inner productbetween matrix ^^ and another matrix calculated based on previously estimatedangles ^^^, ^^^, on these updated values ^^^ , ^^^ and on the (restricted) codebook ^^.Precisely, in the present case, updated values of angles are determined by a further maximum likelihood estimation as follows:^ ^ ^^ ^ ^^^^ ^ The method value of the delay ^^̂ on the path between the configurable surface 4 and the user equipment 6. It is proposed here to determine this updated value based on the previouslyestimated angles ^^^, ^^^, on the previously estimated delay ^^, on the updated anglevalues ^^^ , ^^^ and on the restricted codebook ^^ as follows:for each subcarrier k, the amplitude of the overall gain ^^^is computed as ^^^^^ and the where ^^is the kth row of to the kthsubcarrier) (these estimations being made in connection with a particular antenna a of the base station 2 as indicated above). An average value of the computed delays ^^,^ may be used as the updated valueof ^^̂: ^ Thus, updated values have for estimated parameters ^^^ , ^^^ , ^^̂.The method can loop to step S12 to obtain a new updated estimation of theseparameters ^^^ , ^^^ , ^^̂, possibly after a predetermined (idle) time.Over a longer period of time, the method of Figure 2 can be implemented againstarting at step S2 in order to also adapt parameters ^^^, ^^^, ^^̂ to possible changes inthe environment. Several possibilities will now be presented for estimation of angles ^^, ^^ at stepS4. According to a first embodiment, which is now described with reference to Figures 3 to 5, step S4 comprises:- for each of at least some possible configurations of the configurable surface(defined for instance in the codebook ^), transmitting, from the base station 2 to theuser equipment 6 via the configurable surface 4, a plurality of test signals respectivelyproduced using distinct precoding matrices; -measuring, by the user equipment 6, values respectively representative of aquality of transmission of the test signals; -sending, from the user equipment to the base station, at least one report REPcontaining at least some of these measured values; -estimating the angles ^^, ^^ based on the measured values (here based on themeasured values received at the base station 2 in a report REP).For each configuration of the configurable surface used in this step, the number of the transmitted test signals is for instance equal to the number M of antennas in thebase station 2. Said differently, in the present example, for each configuration of theconfigurable surface, M distinct test signals are sent at M respective distinct times(each test signal involving the transmission by the M antennas of electromagneticsignals produced using a precoding matrix associated with the specific transmissiontime). In practice, each test signal is for instance a Channel Status Information – Reference Signal (CSI-RS) and / or the report REP is for instance a Channel Status Information (CSI) report. The measured values are each for instance a measured power of the test signal received by the user equipment 6, such as the Received Signal Received Power (RSRP) contained in the CSI report. As a possible variation, the measured values may be a signal-to-noise ratio, for instance the Signal-to-Noise and Interference Ratio (SINR) contained in the CSI report. The estimated angles ^^^, ^^^ may then be the angles associated with theprecoding matrix of the base station antenna used when transmitting a test signalresulting in the maximum measure value among the values measured throughout the transmission of the various test signals. According to a first possibility shown in Figure 3, the configurable surface 4 issuccessively configured in the N configurations defined in the codebook ^ and, whilethe configuration surface 4 is in a given configuration (defined by the vector vector ^^,i.e. the N configurable elements of the configurable surface 4 are respectively configured to apply a phase shift given by the corresponding element of the vector^^), M test signals are transmitted from the base station 2 to the user equipment 6 viathe configurable surface 4. The user equipment 6 measures the received power (e.g. RSRP) and / or thesignal-to-noise ratio (e.g. SINR) of each test signal and, once the MxN test signalshave been received, transmit to the base station 2 a report REP (here a CSI report)indicating the test signal (associated with a given configuration and a given precoding matrix) for which the measured value (here the received power or the signal-to-noise ratio) is maximum. As explained above, the base station 2 can deduce the estimated angles ^^^, ^^^from the given precoding matrix for which the measured value of the test signal was maximum. This first possibility makes it possible to obtain an accurate estimation of angles, but necessitates a rather large number (NxM) of test signals in practice. According to a second possibility shown in Figure 4, the configurable surface 4 is successively configured in only N1 configurations defined in the codebook ^, N1 being greater or equal to 1 and / or much smaller than the number of configurable elements N (N1 being for instance smaller than a tenth of the number of configurable elements N). As in the first possibility, while the configuration surface 4 is in a givenconfiguration (defined by the vector ^^ , i.e. the N configurable elements of theconfigurable surface 4 are respectively configured to apply a phase shift given by the corresponding element of the vector ^^), M test signals are transmitted from the base station 2 to the user equipment 6 via the configurable surface 4. The user equipment 6 measures the received power (e.g. RSRP) and / or thesignal-to-noise ratio (e.g. SINR) of each test signal and, once the MxN1 test signalshave been received, transmit to the base station 2 a report REP (here a CSI report)indicating the test signal (associated with a given configuration and a given precoding matrix) for which the measured value (here the received power or the signal-to-noise ratio) is maximum. As for the first possibility, the base station 2 can deduce the estimated angles^^^, ^^^ from the given precoding matrix for which the measured value of the test signalwas maximum. This second possibility involves less test signals as only MxN1 test signals areused (i.e. here less than a tenth of the MxN test signals used in the first possibility).According to a third possibility shown in Figure 5, the configurable surface 4 is successively configured in distinct configurations amongst the N configurationsdefined in the codebook ^ and, while the configuration surface 4 is in a givenconfiguration (defined by the vector vector ^^, i.e. the N configurable elements of theconfigurable surface 4 are respectively configured to apply a phase shift given by the corresponding element of the vector ^^), M test signals are transmitted from the base station 2 to the user equipment 6 via the configurable surface 4. For the M test signals transmitted while the configurable surface 4 is in a givenconfiguration, the user equipment 6 measures the received power (e.g. RSRP) and / orthe signal-to-noise ratio (e.g. SINR) of each of the M test signals and transmit to thebase station 2 a report REP1, REP2, REPN2 (here a CSI report) indicating the maximum measured value (i.e. here the maximum received power or signal-to-noise ratio) and the test signal (associated with a given precoding matrix) for which the measured value (here the received power or the signal-to-noise ratio) is maximum. The base station 2 compares (by performing a test T1, TN2) the received maximum measured value to a predefined threshold, and further proceeds depending on the result of the test (comparison): -if the maximum measured value is below the predefined threshold (as in testT1 in Figure 5), the method continues by changing the configuration of the configurable surface 4 and sending M test signals while the configuration is in the new configuration, as explained above; -if the maximum measured value is above (or equal to) the predefined threshold(as in test TN2), no further test signals are transmitted and the base station 2 candeduce the estimated angles ^^^, ^^^ from the precoding matrix for which the measuredvalue of the test signal was maximum as reported in the last received report REPN2.The third possibility makes it possible to reduce the number of test signals (as MxN2 test signals are used, N2 being generally inferior to N) compared to the first possibility, while still scanning a reasonable number of configurations if necessary (thanks to the use of the predefined threshold). According to a second embodiment, the estimation of angles ^^, ^^ at step S4 isperformed by:- for each antenna (except a particular antenna), determining estimations of thepilot signal received at the concerned antenna based on the pilot signal received atthe particular antenna and for various possible values of angles ^^, ^^;- estimating angles ^^^, ^^^ as the possible value for each angle ^^, ^^ for which adistance based on differences, for the various antennas (except the particularantenna), between the pilot signal received at the concerned antenna and the determined estimation of the pilot signal received at the concerned antenna is minimum. The pilot signals just mentioned may be the same as the pilot signals used instep S2 (in which case step S4 should be performed after step S2 as described above),or may be specific pilot signals used only for estimation of the angles ^^, ^^.As explained in the appendix below, the pilot signal received at an antenna b(distinct from the particular antenna, here for instance antenna 1) can be written basedon the pilot signal received at the particular antenna (here antenna 1) as follows: ^^ = ^^ + ^^(⊘ being the Hadamard an Additive White GaussianNoise) and can thus be estimated using: ^^ = ^^ ^^ + ^^ where ^^is a phase ^(^^ ^ ^ ^,^^^^,^) ^^^^^(^^,^^^^, ) ^^ = … ^ ^ where each on the angles^^, ^^ (and on the the antenna a in the base station 2, which is fixed for agiven situation). The angles ^^^, ^^^ can then be estimated as follows:^^^ ^ ^^ APPENDIX The matrix form expression (already given above for any antenna a) of the signal received by the particular antenna (antenna 1) is: ^ ^ ^= ^^ ⊙ ^^^ ⊙ ^ℎ^ ^ + ^^Knowing that ^^^^ = ^^ , this formula can be rewritten as:^^ ^ ^^ ^^ ^^^ ^ Thus, ^^can be ^= ^^^^^^ ⊘ ^ ^ ⊘ ^ − ^^^^^^ ⊘ ^^^ ^^ ^ ^^ ^^ ^^ ⊘ ^^Considering the second term as an Additional White Gaussian Noise gives:^ ^^^^^ ^ ^^ ^Introducing this of the signal receivedat antenna b results in: ^^^ ^ ^ ^ ^^ ^ such that, be estimated as: ^^ = ^^ + ^^ where ^^is also Noise.

Claims

CLAIMS1. A method for estimating characteristics of a communication channel between a firstcommunication device (2) and a second communication device (6) and via a configurablesurface (4) having a plurality of configurable elements, comprising the following steps:- receiving pilot signals from the second communication device (6) at the firstcommunication device (2) and via the configurable surface (4);- estimating at least one first angle defining a direction of the first communicationdevice (2) with respect to thesurface (4);- determining at least one second angle (^^ , ^^ ) defining a direction of the secondcommunication device (6) with respect to the configurable surface (4) and whichminimizes a value calculated based on a Hermitian inner product between a first matrixcomprising the pilot signals as received at the first communication device (2) and asecond matrix calculated based on the at least one first angle and on the at least onesecond angle;- determining a first delay associated with the path between the first communicationdevice (2) and thesurface (4), and a second delay (^^) associated with thepath between the second communication device (6) and the configurable surface (4), thatminimize a distance calculated based on at least one difference between a first vector of complex gains computed based on possible respective values of the first delay and thesecond delay, and a second vector of complex gains estimated based on the at least onefirst angle and the at least one second angle.

2. A method according to claim 1, wherein the second matrix is calculated based on aHadamard product between a matrix comprising steering vectors from the firstcommunication device (2) to the configurable surface (4) that are estimated based on theat least one first angle, and a matrix comprising steering vectors from the configurablesurface (4) to the second communication device (6) that are estimated based on the atleast one second angle.

3. A method according to claim 2, wherein the second matrix is a product of the transposeof said Hadamard product by a configuration matrix representative of respectiveconfigurations of the configurable surface (4) during the transmission of pilot signals, andwherein said value is equal to the opposite of the square of the module of said Hermitianinner product divided by the square of a norm of the second matrix.

4. A method according to any of claims 1-3, wherein the first matrix comprises K x Nelements representing respectively pilot signals received on an antenna of the firstcommunication device (2) on K subcarriers at N times.

5. A method according to any of claims 1-4, wherein the first communication device (2)comprises a plurality of antennas, and wherein the step of estimating the at least one first angle comprises:- for each of a plurality of configurations of the configurable surface (4), transmitting, fromthe first communication device (2) to the second communication device (6) via theconfigurable surface (4), a plurality of test signals respectively produced using distinctprecoding matrices;- measuring, by the second communication device (6), values respectively representativeof a quality of transmission of the test signals;- estimating the at least one first angle based on the measured values.

6. A method according to any of claims 1-4, wherein the first communication device (2)comprises a first antenna and other antennas, and wherein the step of estimating the atleast one first angle comprises:- for each one of the other antennas, determining estimations of the pilot signal receivedat the concerned other antenna based on the pilot signal received at the first antenna andfor various possible values of the angle defining the direction of the first communicationdevice (2) with respect to the configurable surface (4);- estimating the at least one first angle as the possible value for which a distance basedon differences, for the various other antennas, between the pilot signal received at theconcerned antenna and the determined estimation of the pilot signal received at the concerned antenna is minimum.

7. A method according to any of claims 1-6, comprising the following steps:- selecting a plurality of configurations;- transmitting further pilot signals at a plurality of times respectively associated with theselected configurations, the configurable surface (4) being configured at each time in theselected configuration associated with the concerned time;- determining an updated value of the at least one second angle which minimizes a furthervalue calculated based on a Hermitian inner product between a third matrix comprisingsaid further pilot signals received at the first communication device (2) and a fourth matrixcalculated based on the at least one first angle and on the updated value of the at leastone second angle.

8. A method according to any of claims 1-7, wherein transmitting the pilot signals comprises transmitting a pilot signal at each of a plurality of times, and wherein theconfigurable surface (4) is respectively configured in a plurality of distinct configurationsat said plurality of times.

9. A method according to any of claims 1-8, wherein the first communication device is abase station (2) and wherein the second communication device is a user equipment (6).

10. A method according to any of claims 1-9, wherein the second angle ^^^is determined as ^^where ^^is said a on said at leastone first angle, ^^(^^ , ^^) is a matrix of steering vectors depending on possible valuesfor the second angle, ^ is a matrix which columns respectively define variousconfigurations taken by the configurable surface (4) during the receiving step and ^^^ isanother angle defining the direction of the second communication device (6) with respectto the configurable surface (4) and concurrently determined.

11. A method according to any of claims 1-10, wherein the first delay and the seconddelay are determined aswhere ^^is the first the first communicationdevice (2), ^^ is the second vector of complex gains for an antenna a of the firstcommunication device (2), A is a subset of antennas among antennas of the firstcommunication device (2), c is the celerity of light in vacuum, ^^^ is an inner radius of thefar-field region and ^^^ is a cell radius.

12. Computer program comprising instructions executable by a processor and suitable to implement a method according to any of claims 1-11 when these instructions are executed by the processor.

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