Method for estimating at least one parameter from among a timing advance and a frequency offset between first and second communication devices

Abstract

The present invention relates to a method for estimating at least one from among a timing advance (TA) and a frequency offset (CFO) between a first communication device (TX) and a second communication device (RX) on the basis of a subset (SUB) of samples of a correlation signal (COR), the correlation signal (COR) being based on a signal (RCD) received from the first communication device (TX) and a reference signal (REF). The present invention also relates to a method for training an estimator (EST), a neural network (ENC), a communication device (RX), a communication system (SYS), a computer program (PROG_RX) and a computer-readable medium (MEM_TX).

Description

Description Title of the invention: Method for estimating at least one parameter among a time lead and a frequency offset between first and second communication devices technical field

[0001] The present invention relates generally to the field of telecommunications, and in particular to wireless communications implemented by radio networks such as mobile telecommunications networks (e.g. 3G, 4G, 5G, etc.). Prior art

[0002] In the context of mobile telecommunications networks (e.g., 5G networks), uplink synchronization refers to the process of synchronizing a terminal (e.g., a user terminal) with a base station (e.g., a gNB). The objectives of uplink synchronization include detecting a preamble (e.g., a PRACH preamble) transmitted by the terminal, and then estimating the timing lead and carrier frequency offset between the terminal and the base station using the detected preamble.

[0003] Time lead characterizes the time it takes for a signal to propagate from the terminal to the base station. The time lead is estimated by the base station and relayed to the terminal for correction. Since 5G networks rely on orthogonal frequency division multiple access (OFDMA) to multiplex users, time lead correction allows subsequent transmissions from the terminal to be integrated into limited time-frequency resources with those of other terminals. In contrast, carrier frequency offset is estimated and compensated within the base station. Carrier frequency offset is due to the difference between the oscillator frequencies of the terminal and the base station, as well as the Doppler effect related to the terminal's movement.

[0004] It is important to emphasize that proper correction of the time lead and carrier frequency offset is crucial for communication performance, and therefore, accurate estimation of these critical parameters is a key objective in the development of mobile telecommunications networks. However, existing solutions for estimating the time lead and carrier frequency offset are not entirely satisfactory for the following reasons.

[0005] Following the detection of the preamble, the time lead is estimated in the prior art by counting the number of samples between the start of the search window and the peak position of the strongest correlation detected. The accuracy of the time lead estimation is therefore limited to a multiple of the sampling period. Furthermore, in the prior art, the influence of the carrier frequency offset is not taken into account in the time lead estimation. Consequently, existing solutions exhibit low accuracy in time lead estimation, resulting in degraded communication performance, since the signals transmitted by the different terminals are not fully orthogonal.

[0006] Similarly, existing methods for estimating carrier frequency offset based on a detected preamble demonstrate limited accuracy. For example, in the context of uplink synchronization for 5G networks, Zadoff-Chu sequences are used as the preamble. In this context, Tao et al. ("Enhanced Carrier Frequency Offset Estimation Based on Zadoff-Chu Sequences," IEEE Communications Letters, October 2019) propose a method for estimating carrier frequency offset using the amplitudes of certain correlation peaks. However, the method proposed by Tao et al., i.e., using only the amplitudes of correlation peaks and ignoring phases, results in information loss and limits estimation accuracy. Furthermore, the method of Tao et al.The method estimates the carrier frequency offset without considering the time lead, despite the fact that these two parameters are intrinsically coupled in the received signals. These simplistic assumptions also limit the accuracy of the method by Tao et al. Furthermore, the complexity of this method is not evaluated by Tao et al., although this is essential for real-time implementation in communication systems.

[0007] There is therefore a need for a precise and low-complexity solution to estimate a time lead and / or carrier frequency offset between a transmitter and a receiver, for example for uplink synchronization between a terminal and a base station within a mobile communication network. Description of the invention

[0008] The invention proposes a method for estimating at least one parameter from a time lead and a frequency offset between a first communication device and a second communication device, said method being implemented by the second communication device and comprising: an estimation of said at least one parameter from a subset of samples of a correlation signal, said correlation signal being based on a signal received from the first communication device and a reference signal, said subset comprising one or more disjoint groups of consecutive samples of the correlation signal, one of said groups comprising a sample of maximum amplitude of the signal. general correlation, and said groups comprising the same predefined number of samples whose indices are a function of the index of said sample of maximum amplitude.

[0009] The invention provides an accurate and low-complexity solution for estimating a time lead and / or carrier frequency offset between a first and second communication device.

[0010] To this end, the invention proposes using only a subset of significant samples from the correlation signal to estimate the time lead and / or frequency shift. In one embodiment, it is proposed to use a subset of samples comprising groups of adjacent (i.e., consecutive) samples around the correlation peaks of the correlation signal. Indeed, these samples concentrate most of the energy of the correlation signal (as detailed later), and therefore most of the information. For this reason, the samples in the proposed subset are the most relevant for estimating the time lead and / or frequency shift.

[0011] Therefore, the proposed solution, using only the most significant samples of the correlation signal, allows for accurate estimation of the time lead and / or frequency shift while providing a low-complexity implementation.

[0012] It is worth noting that, compared to prior art solutions, the proposed solution significantly improves the accuracy of the time lead (TA) and / or carrier frequency offset (CFO) estimation. In particular, as discussed previously, the accuracy of existing solutions for time lead estimation is limited to a multiple of the sampling period. In contrast, the accuracy of the proposed solution is not limited to a multiple of the sampling period and allows for a finer estimation of the time lead (i.e., it enables the estimation of a fractional time lead).

[0013] It should be noted that the invention is particularly relevant in the context of uplink synchronization between a terminal and a base station within a mobile communication network.

[0014] In one embodiment, the method comprises obtaining the correlation signal from the received signal and the reference signal. To this end, the method includes, for example: multiplying the received signal by a conjugate of a Fourier transform of the reference signal to obtain an intermediate signal; and applying an inverse Fourier transform to the intermediate signal to obtain the correlation signal.

[0015] In one embodiment, the reference signal is a Zadoff-Chu sequence. Specifically, the reference signal can be a Zadoff-Chu sequence whose length is a prime number.

[0016] Zadoff-Chu sequences exhibit zero autocorrelation and constant amplitude, which is advantageous in terms of orthogonality between users (i.e., between the different (preambles) and power requirements. More specifically, the autocorrelation between a Zadoff-Chu sequence and a version of itself with a cyclic offset is zero, allowing different users to transmit respectively orthogonal preambles over the same time-frequency resources. Furthermore, the constant amplitude of the Zadoff-Chu sequence enables efficient amplification of the preamble at the transmitter.

[0017] According to one embodiment, said at least one parameter includes the time lead and the frequency offset, and the time lead and the frequency offset are obtained jointly during said estimation.

[0018] This embodiment allows for consideration of the mutual influence between the time lead and the carrier frequency shift when estimating these parameters. In this way, this embodiment provides an accurate estimate of these parameters.

[0019] Indeed, as mentioned above, existing solutions estimate either the time lead or the frequency shift independently. However, at the receiver, these two parameters are intrinsically linked in the correlation signal used for estimation. In other words, the carrier frequency shift impacts the time lead estimation, and vice versa. In contrast, the joint estimation of the time lead and frequency shift, as proposed here, allows us to account for the mutual influence of these parameters and improve the accuracy of the estimation.

[0020] According to one embodiment, said at least one parameter is estimated from phases and amplitudes of samples of said subset.

[0021] According to this embodiment, the complex values ​​(i.e., both amplitudes and phases) of the subset samples are used to estimate the time lead and / or frequency shift. In contrast, the aforementioned solution by Tao et al. only uses the amplitudes of certain samples to estimate the carrier frequency shift, resulting in information loss and an inaccurate estimation of this parameter.

[0022] Compared to existing solutions, the use of both amplitudes and phases of correlation samples is advantageous because it does not result in any loss of information and helps to provide accurate estimates of the time lead and / or carrier frequency shift.

[0023] According to one embodiment, the predefined number of consecutive samples respectively included in said groups is equal to 3, 5, or 7.

[0024] In other words, according to this embodiment, each of said groups comprises 3, 5, or 7 adjacent samples, respectively. More specifically, the samples in each group are centered and uniformly distributed around one of the correlation peaks of the correlation signal.

[0025] This embodiment allows the exploitation of multipath propagation components to estimate the time lead and / or carrier frequency shift. This results in improved accuracy in estimating these parameters for multipath channels.

[0026] Specifically, using groups of 3 samples allows us to account for multipath propagation components whose delays vary by up to ± one sampling period relative to the average delay. Furthermore, groups of 5 samples can be used for delays up to ± two times the sampling period, and groups of 7 samples can be used for delays up to ± three times the sampling period. It should be noted that the time lead represents the average delay of the multipath propagation components.

[0027] In one embodiment, said subset of samples comprises three disjoint groups of consecutive samples of the correlation signal. More specifically, each of said groups comprises one of the three largest correlation peaks (with respect to amplitude).

[0028] Indeed, numerical simulations have shown that the majority of the energy (>85%) of the correlation signal is concentrated on the three largest correlation peaks. This implementation therefore provides the most significant samples for estimating the time lead and / or frequency shift and, consequently, allows for an accurate and low-complexity estimation of these parameters.

[0029] According to one embodiment, said groups respectively comprise a sample whose index satisfies: Z = (z p + kü) N ,

[0030] where: l pdenotes the index of said sample of maximum amplitude of the correlation signal; ke TL; (•) denotes the modulo-ZV operation with ZV the length of the reference signal; and ü is an integer such that 0 < ü < ZV. In particular, the parameter ü is the modular multiplicative inverse of u, the root of the Zadoff-Chu sequence used as the reference signal.

[0031] In this embodiment, each of these groups comprises one of the correlation peaks of the correlation signal. According to this embodiment, the indices of the correlation peaks are obtained from the index of the largest correlation peak using a low-complexity calculation. Typically, the index of the largest correlation peak is obtained during the preamble detection phase.

[0032] According to one embodiment, said at least one parameter is estimated using a neural network taking said subset of samples as input and providing said at least one parameter as output.

[0033] First, the use of a neural network allows us to approximate (i.e., interpolate) an optimal estimation function – with respect to an objective function or criterion given optimization – of the time lead and / or carrier frequency shift. As detailed later, it is specifically proposed to use a neural network based on an analytical model of the correlation signal.

[0034] Secondly, the neural network takes as input only the subset of samples from the correlation signal and therefore processes a small number of samples. Consequently, this embodiment allows the use of a low-complexity, low-latency neural network that can be advantageously implemented in real time on deployed communication systems.

[0035] For these reasons, this embodiment provides an accurate solution for estimating the time lead and / or carrier frequency offset with low complexity and low latency implementation.

[0036] According to one embodiment, the process further comprises a refinement, from said at least one estimated parameter, of an approximate time lead estimated using the index of said maximum amplitude sample.

[0037] According to one embodiment, the method further comprises an equalization of signals received from the first communication device from said at least one estimated parameter.

[0038] The estimates obtained for the time lead and / or frequency offset are used in this embodiment by the second communication device (e.g., a base station) to equalize subsequent signals received from the first communication device (e.g., a terminal). For example, the proposed solution can be used to compensate for the carrier frequency offset within a base station.

[0039] The precise estimates of time lead and / or carrier frequency offset provided by the proposed solution allow for improved equalization of received signals. This results in improved communication performance (e.g., fewer demodulation errors, higher achievable transmission rates).

[0040] In one embodiment, the first and / or second communication devices conform to 4G and / or 5G standards. Similarly, in one embodiment, the signals received from the first communication device conform to 4G and / or 5G standards.

[0041] According to these embodiments, the proposed solution applies to 4G and / or 5G networks, i.e., to fourth-generation and / or fifth-generation cellular network technology standards. For example, the first communication device could be a mobile terminal (e.g., a user terminal) and the second communication device could be a base station (e.g., an eNB or a gNB).

[0042] In this disclosure, "4G" means the standard defined by at least one of the following versions of the Third Generation Partnership Project (3GPP): version 8, published in March 2009; version 9, published in March 2010; version 10, published in June 2011; version 11, published in March 2013; version 12, published in March 2015; version 13, published in March 2016; and version 14, published in June 2017. And in this disclosure, "5G" means the standard defined by at least one of the following versions of 3GPP: version 15, published in June 2019; version 16, published in July 2020; and version 17, published in June 2022.

[0043] It is worth mentioning that the proposed solution can also be applied to cellular networks beyond the fifth generation, and more generally to other communication systems.

[0044] According to another aspect, the invention proposes a method for training an estimator of at least one parameter from among a time lead and a frequency shift between a first communication device and a second communication device, said method comprising: obtaining at least one parameter estimated from among a time lead and a frequency shift by providing said estimator with a subset of samples of a training correlation signal; evaluating an objective function from the subset of training samples and said at least one parameter estimated; and updating said estimator to optimize the objective function.

[0045] By "optimization of an objective function," we mean either the minimization of a cost function or the maximization of a payoff function. For example, the estimator can be trained using gradient descent (or gradient ascent) to minimize a cost function (or maximize a payoff function).

[0046] The proposed method for training an estimator has the advantages described above in relation to the proposed method for estimating a time lead and / or a frequency shift.

[0047] In particular, and similarly to the estimation method described above, the training sample subset comprises one or more disjoint groups of consecutive samples of the training correlation signal, one of said groups comprising a maximum amplitude sample of the training correlation signal, and said groups comprising the same predefined number of samples whose indices are a function of the index of said maximum amplitude sample.

[0048] Furthermore, the proposed training process may include multiple iterations of the aforementioned acquisition, evaluation, and update steps. The training iterations can be performed for separate subsets of training samples.

[0049] According to one embodiment, said estimator is or includes a neural network.

[0050] According to one embodiment, the objective function is expressed by:

[0051] where: c(l') is the subset of training samples; l' denotes the indices of the samples of c(l'); â and ê denote a time lead and a frequency shift estimated by said estimator from c(l'); and f(l',â,ê) denotes a function of ï , â and ê.

[0052] According to one embodiment, the function is representative of an analytical model expressing a subset of samples of a noise-free correlation signal.

[0053] The objective function proposed here is a cost function representing the distance (with respect to ||-|| 2) between: the provided input correlation samples; and the noise-free correlation sample model, given a time lead â and a frequency shift ê. According to this embodiment, the proposed solution uses an autoencoder, trained to minimize the difference between: an input signal (i.e. the provided input correlation samples); and a reconstructed output signal (i.e. the noise-free correlation sample model).

[0054] Indeed, for Gaussian noise channels, optimizing this objective function corresponds to maximizing the likelihood function. The estimator is therefore trained to approximate (i.e., interpolate) the maximum likelihood estimator of the time lead and / or frequency shift. In other words, the estimated time lead and / or frequency shift are obtained in such a way that the observed correlation samples are as probable as possible.

[0055] Therefore, this embodiment makes it possible to provide an estimator trained to deliver at output the optimal estimates - with respect to the maximum likelihood criterion - of the time lead and / or carrier frequency shift.

[0056] More generally, it is assumed that the proposed estimator (based on the maximum likelihood criterion) is the unbiased estimator with minimum variance, and that it is therefore optimal in terms of accuracy. Indeed, as detailed later, it can be shown that the estimates obtained for the time lead and the carrier frequency shift are unbiased and achieve the lowest feasible variance (i.e., the Cramer-Rao bound).

[0057] In one embodiment, the training sample subset c(Z') is generated using simulations of a communication system comprising the first and second devices. In another embodiment, the training sample subset c(i') is generated by adding noise to samples expressed by the analytical model f(l',a,E), where a and E denote a time lead and a frequency shift, respectively.

[0058] According to these embodiments, the estimator is trained using synthetic (i.e., computer-generated) training data, generated by a communication system simulator, or using an analytical model to which noise is added. For example, the estimator can be trained in the laboratory (i.e. by offline training) using synthetic training data before deployment in a communication system.

[0059] These implementations make it possible to provide an accurate estimator of the timing lead and / or frequency offset for various deployment scenarios. Indeed, the estimator can be trained on data representative of different scenarios, for example, different timing lead and frequency offset values, different signal-to-noise ratios, or different propagation conditions.

[0060] In another aspect, the invention provides an estimator for at least one parameter, including a time lead and a frequency offset, between a first communication device and a second communication device, said estimator having been trained by a method according to the invention. The estimator is further configured to estimate said at least one parameter from a subset of samples of a correlation signal, said correlation signal being based on a signal received from the first communication device and a reference signal.

[0061] According to one embodiment, the estimator is or comprises a neural network trained by a method according to the invention. Consequently, the invention extends to a computer-readable storage medium on which a program is stored to implement a neural network according to the invention. This program comprises instructions which, when executed by at least one processor or computer, cause said processor or computer to implement a method according to the invention. Furthermore, the invention also provides a computer-readable storage medium on which representative data of a neural network according to the invention, such as hyperparameters and / or neural network weights, are stored.

[0062] According to another aspect, the invention proposes a communication device, called the first communication device, comprising at least one processor and a memory on which is stored a program to implement a process comprising the transmission of a preamble generated from a reference signal.

[0063] According to another aspect, the invention proposes a communication device, called a second communication device, comprising at least a processor and a memory on which a program is stored to implement a process according to the invention.

[0064] According to another aspect, the invention proposes a communication system comprising: a first communication device according to the invention; and a second communication device according to the invention.

[0065] According to another aspect, the invention proposes a computer program comprising instructions which, when the program is executed by at least one processor or computer, cause said at least one processor or computer to implement a process according to the invention.

[0066] It should be noted that the computer programs referred to here may use any programming language and may take the form of source code, object code, or an intermediate form between source code and object code, for example in a partially compiled form, or in any other desirable form.

[0067] According to another aspect, the invention provides a computer-readable information medium on which the computer program conforming to the invention is stored.

[0068] The computer-readable medium referred to in this statement may be any entity or device capable of storing the program and readable by any computer equipment comprising a computer. For example, the medium may include a storage medium or a magnetic storage medium, such as a hard drive. Alternatively, the storage medium may be a computer integrated circuit in which the program is incorporated and adapted to perform a process as described above or to be used in performing such a process.

[0069] It should be emphasized that the proposed estimator, communication devices, communication system, program and support offer the advantages described above in relation to the proposed method for estimating a time lead and / or frequency shift. Brief description of the drawings

[0070] FIG. 1 illustrates a communication system according to embodiments of the invention.

[0071] FIG. 2 illustrates steps of a method for estimating a time lead and / or a frequency shift according to embodiments of the invention.

[0072] FIG. 3 illustrates an architecture of a communication device according to embodiments of the invention.

[0073] FIG. 4 illustrates an architecture of a communication device according to embodiments of the invention.

[0074] FIG. 5 illustrates steps of a method for estimating a time lead and / or a frequency shift according to embodiments of the invention.

[0075] FIG. 6 illustrates an example of a correlation signal used by a method for estimating a time lead and / or a frequency shift according to embodiments of the invention.

[0076] FIG. 7 illustrates a method for training a time lead and / or frequency shift estimator according to embodiments of the invention.

[0077] FIG. 8 illustrates an objective function used by a method for training a time lead and / or frequency shift estimator according to embodiments of the invention.

[0078] FIG. 9A and FIG. 9B illustrate the performance of a method for estimating a time lead and a frequency shift according to embodiments of the invention.

[0079] FIG. 10 illustrates an example of the hardware architecture of a communication system according to embodiments of the invention. Description of the implementation methods

[0080] Other features and advantages of the present invention will become apparent from the following description of embodiments of the invention. These embodiments are given by way of illustration and are not intended to be limiting.

[0081] Figures 1 and 2 illustrate, respectively, a communication system and steps in a method for estimating a time lead and / or a frequency shift according to embodiments of the invention. In particular, these figures are described here to briefly introduce the context of the invention, the communication devices involved, and the main steps of the proposed method.

[0082] As mentioned previously, the invention is particularly relevant in the context of uplink synchronization between a terminal and a base station in a mobile communication network. The following description of the present invention will refer to this particular context, which is given only by way of illustration and is not intended to limit the invention.

[0083] A communication system SYS comprises, according to an embodiment illustrated in FIG. 1, a first communication device TX and a second communication device RX. For example, the first communication device TX can be a mobile terminal such as a user terminal and the second communication device RX can be a base station.

[0084] The first TX and second RX communication devices communicate with each other using a channel, for example, a wireless channel. Communications between the first TX device and the second RX device are thus affected by a time lead (TA) and a carrier frequency offset (CFO).

[0085] The time lead TA characterizes the time taken by the signal to propagate from the first TX communication device to the second RX communication device, while the carrier frequency offset CFO is due to the difference between the oscillator frequencies of the first TX and second RX communication devices, as well as the Doppler effect related to the movement of one device relative to the other.

[0086] The TA and CFO parameters must be estimated and compensated to achieve better communication performance, e.g., in terms of achievable data rates and reliability. To this end, the first TX communication device transmits a preamble (i.e., a synchronization signal known to both devices) which is used by the second RX communication device to estimate the TA and CFO parameters.

[0087] The first communication device TX includes a preamble generator PG configured to generate a preamble PR from a reference signal REF (known to both devices), said preamble PR being transmitted by the first communication device TX. The transmission of the preamble PR may involve, depending on embodiments, various processing operations such as repetition, modulation, amplification, etc.

[0088] The second RX communication device comprises, according to an embodiment illustrated by FIG. 1, at least one of the following elements: a correlator XC; a detector DET; and an estimator EST.

[0089] The architecture of the second RX communication device is described below with reference to the steps in FIG. 2; the second RX communication device can be configured to implement at least one of the steps S100 to S400.

[0090] The second communication device, RX, is configured, according to one embodiment, to obtain a received RCD signal at step S100. Receiving the RCD signal may involve various processing operations such as amplification, filtering, demodulation, etc. In particular, the RCD signal is received from the first communication device, TX, for example, via a wireless channel. Consequently, the received RCD signal may be representative of the transmitted PR preamble, impacted by channel effects such as noise, multipath propagation, attenuation, etc.

[0091] The correlator XC is configured, according to one embodiment, to obtain, at step S200, a correlation signal COR from the received signal RCD and the reference signal REF. Typically, the correlation signal COR is representative of a cross-correlation between the transmitted preamble PR and the reference signal REF.

[0092] The DET detector is configured, according to one embodiment, to detect, at step S300, the transmission of a PR preamble by the first TX communication device from the COR correlation signal. As previously stated, a first task of uplink synchronization is to detect the transmission of a preamble.

[0093] The EST estimator is configured, according to one embodiment, to estimate, at step S400, the TA time lead and / or the CFO carrier frequency offset between the first TX and second RX communication devices from the COR correlation signal. More precisely, the EST estimator performs the S400 estimation step if, and only if, the PR preamble is detected in the received RCD signal during step S300.

[0094] Figure 3 illustrates the architecture of a communication device according to embodiments of the invention. Specifically, Figure 3 further details the architecture of the first communication device TX previously described with reference to Figure 1 and the method for generating the preamble PR from a reference signal REF.

[0095] In a particular embodiment, the reference signal REF is a Zadoff-Chu sequence which can be expressed as:

[0096] where N is the length of the sequence, u is the root of the Zadoff-Chu sequence, (•)« denotes the modulo-N operation, C v = v ■ N cs , N cs is a cyclic shift and ve [0,63]. Specifically, the reference signal REF is a Zadoff-Chu sequence whose length N is a prime number.

[0097] According to an embodiment illustrated in FIG. 3, the generation of the PR preamble comprises at least one of the following steps: applying a Fourier transform (e.g., a discrete Fourier transform (DFT) or a fast Fourier transform (FFT)) to the reference signal REF; frequency mapping (sub-carrier frequency mapping) of the output signal from the Fourier transform; and applying an inverse Fourier transform (e.g., an inverse discrete Fourier transform (iDFT) or an inverse fast Fourier transform (iFFT) to the frequency-modulated signal. In particular, these steps enable the PR preamble to be integrated into the frequency resources.

[0098] The signal obtained from the inverse Fourier transform can be repeated, and a cyclic prefix can be added. It is worth noting that in the context of 5G networks, prefixes are generated from Zadoff-Chu sequences in various formats, e.g., different lengths, different frequency ranges, etc. The PR preamble generated by the first TX communication device is transmitted, for example, using the TX_ANT antenna of the first TX communication device.

[0099] Figures 4 and 5 illustrate, respectively, the architecture of a communication device and the steps of a method for estimating a time lead and / or a frequency shift according to embodiments of the invention. Specifically, Figure 4 provides further details of the architecture of the second RX communication device, and Figure 5 details steps S100 to S400.

[0100] According to an embodiment illustrated by FIG. 4 and 5, the proposed method for estimating a time lead TA and / or a frequency offset CFO is implemented by the second communication device RX and includes at least one of the steps S100 to S500 described below.

[0101] According to one embodiment, the second RX communication device comprises: a radio unit RX_RU configured to obtain the received RCD signal; and a digital unit RX_DU configured to estimate the TA time lead and / or a CFO frequency offset using the received RCD signal.

[0102] To obtain the received RCD signal at step S100, the second communication device RX is configured, according to embodiments, to perform at least one of the following steps SI 10 to S 140.

[0103] The second RX communication device is configured, according to one embodiment, to acquire, at step S110, a radio signal r(t) using the RX_ANT antenna of the second communication device.

[0104] The second communication device RX is configured, according to one embodiment, to remove a cyclic prefix at step S120 and obtain a sampled y(nTs) signal from the radio signal r(t). Specifically, step S120 includes processing the radio signal r(t) using a radio-frequency front-end (RF-FE) of the second communication device to obtain the sampled (i.e., discrete) y(nTs) signal. Furthermore, step S120 may include decimation and filtering of the radio signal r(t), which is typically used for long-format prefixes to reduce the size of the subsequent FFT.

[0105] The second RX communication device is configured, according to one embodiment, to apply, at step S130, a Fourier transform to the signal y(nTs) to obtain a signal Y(m).

[0106] The second communication device RX is configured, according to one embodiment, to extract, at step S140, the received RCD signal from the Ym signal. In other words, step S140 consists of performing frequency demodulation ("frequency demapping"). Furthermore, when the reference signal REF is repeated within the PR preamble, step S140 may include a combination of sequence repetitions in the frequency domain.

[0107] The XC correlator is configured, according to one embodiment, to perform the following steps S210 to S230 to obtain the correlation signal COR. As shown in FIG. 4, the XC correlator takes as input samples of the received signal RCD and samples of the reference signal REF.

[0108] According to this embodiment, the XC correlator is configured to apply, at step S210, a conjugate DFT (i.e., a DFT followed by conjugation) to the samples of the reference signal REF. Consequently, the XC correlator obtains multiple coefficients a m * , which correspond to a complex conjugate representation in the frequency domain of the reference signal REF.

[0109] The XC correlator is configured, according to this embodiment, to multiply, at step S220, samples of the received RCD signal by the coefficients obtained a,', t and apply, at step S230, an iDFT transform to the result of the multiplication to obtain the COR correlation signal (a digital signal comprising multiple samples).

[0110] Thus, the correlator XC implements a suitable filter in the frequency domain. Consequently, the resulting COR correlation signal represents a cross-correlation between the PR preamble transmitted by the first communication device TX and the reference signal REF. An example of a COR correlation signal is shown in FIG. 6 and described below.

[0111] It is important to note, however, that within the framework of the invention, other implementations of the XC correlator can be envisaged, such as the use of cross correlation in the time domain.

[0112] The PET detector is configured, according to one embodiment, to detect, at step S300, the transmission of the preamble PR by the first communication device TX from the correlation signal COR.

[0113] For example, the DET detector can implement a detection decision criterion based on a power delay profile of the COR correlation signal. Specifically, according to this particular embodiment, the DET detector detects the PR preamble if the root mean square (RMS) amplitude of a sample of the COR correlation signal exceeds a predefined threshold. Other implementations of the DET detector could be considered within the scope of this invention.

[0114] According to one embodiment, the DET detector is configured to obtain and deliver at output the LP index of the detected main correlation peak CPK1, i.e. the index of the sample with maximum amplitude of the COR correlation signal.

[0115] In particular, the DET detector is configured to obtain, at step S310, an approximate estimate of the TA time lead from the LP index of the detected CPK1 main correlation peak. Consequently, the accuracy of the approximate TA time lead estimate is limited to a multiple of the sampling period.

[0116] The EST estimator is configured, according to one embodiment, to estimate, in step S400, the time lead TA and / or the carrier frequency shift CFO from the correlation signal COR. In particular, the estimator is configured to implement the subsequent steps S410 and S420.

[0117] The EST estimator is configured, according to this embodiment, to select, at step S410, a subset of samples SUB from the correlation signal COR. As detailed below, the EST estimator performs, at step S410, a feature extraction and selects the most significant samples of the correlation signal for estimation.

[0118] Consequently, the EST estimator is configured to estimate the TA time lead and / or the CFO frequency offset from the SUB sample subset. In particular, the EST estimator is configured to provide the SUB sample subset as input to a ENC encoder, which delivers at output the estimate â of the time lead and / or the estimate ê of the frequency offset.

[0119] The description above provides an overview of the proposed solution (i.e., the architecture of the proposed communication devices and the steps of the proposed process). Based on this overview, the implementation of the EST estimator is detailed below with reference to Figure 6. More generally, Figure 6 is used to describe the principle of the proposed solution and its advantages.

[0120] Figure 6 illustrates an example of a correlation signal used to estimate a time lead and / or a frequency shift according to embodiments of the invention. More specifically, Figure 6 illustrates a graph of the quadratic amplitude |c(Z)| 2 (y axis) of a COR correlation signal as a function of the sample index l (x axis).

[0121] An analytical model of the COR correlation signal is detailed below. We consider a noise-free single-path channel between the first TX and second RX communication devices with a time lead TA r and a frequency offset CFO 5f. Furthermore, we consider the reference signal REF to be a Zadoff-Chu sequence as defined by Eq. 1. It can be shown theoretically that the proposed model based on a single-path channel also allows for the modeling of multipath channels, given that the duration of the reference signal (typically 1 ms) is large compared to the spread of the delays in these channels (typically 50 to 500 ns).

[0122] It can be shown that the COR correlation signal obtained by the XC correlator, according to the above embodiments, can be expressed as:

[0123] where Z e [0,ZV - 1] is the sample index, N is the length of the reference signal REF, ü is the modular multiplicative inverse of u, the root of the reference signal REF, i.e., üu = KN + 1. The parameters a represent the time lead and the offset, respectively. of standardized frequencies. T s is the sampling period and at RA is the spacing between subcarriers used by the SYS communication system so that T s = — - — , L designating the RA' size of the iDFT of the first TX communication device.

[0124] Terms and functions A", <p, S L and S in Eq. 2 are defined as follows:

[0125] where h is the complex channel gain, 0 is the amplitude factor for the signal transmitted by the first TX communication device, N CPis the length of the cyclic prefix and K is defined by üu = KN + 1 as stated previously.

[0126] Numerical simulations have shown that most of the energy (>85%) of the COR correlation signal is concentrated in the terms with {-1, 0, 1} in the sum of Eq. 2. Therefore, the COR correlation signal c(Z) can be accurately approximated by a simplified model ê(Z) expressed by:

[0127] The simplified model ê(Z) in Eq. 3 involves a sum of three terms, which correspond to the three largest correlation peaks CPK1-CPK3 in the COR correlation signal. With regard to Fig. 6, the first term for d = 0 corresponds to the main correlation peak CPK1 and the other two terms d = -1, 1 correspond to the secondary correlation peaks CPK2, CPK3.

[0128] The LP index (also designated as Z) pThe CPK1 main correlation peak is obtained by the DET detector and is provided as input to the EST estimator. The indices l p+ and p _ the two other correlation peaks CPK2 and CPK3 can be obtained on the basis (i.e. are a function of) the index l p of the main CPK1 correlation peak using the following expressions: l p+ = (l p + ü) ; and

[0129] The implementation of the EST estimator relies on the analytical model and simulation results above to accurately estimate the time lead TA a and / or the frequency shift CFO s. In particular, the selection, in step S410, of the subset of samples SUB used for the estimation is based on the results above.

[0130] The SUB sample subset of the COR correlation signal can be defined as follows with reference to FIG. 6.

[0131] As discussed previously, most of the COR correlation signal energy is concentrated on the three largest correlation peaks CPK1-CPK3 with respective indices l p , L p+ and p Therefore, the SUB sample subset comprises, according to one embodiment, three groups Gl, G2, G3 of COR correlation signal samples, each group comprising one of the CPK1, CPK2, CPK3 correlation peaks.

[0132] However, within the scope of the invention, embodiments could also be envisaged in which the sample subset SUB comprises more than three groups, each group comprising a correlation peak with index Z = (l p + kü) N with ke Z.

[0133] In one embodiment, each of the G1-G3 groups of the SUB subset comprises samples around each CPK1-CPK3 correlation peak. In other words, each G1-G3 group comprises multiple consecutive samples, each containing one of the CPK1-CPK3 correlation peaks.

[0134] Using multiple samples around the CPK1-CPK3 correlation peaks allows for the accurate estimation of the time lead TA for multipath channels, i.e., in the presence of multiple propagation paths with different normalized delays a'. Therefore, the number of samples in each group G1-G3 of the SUB subset can be determined based on the channel delay spread between the first TX and second RX communication devices. It should be noted that the time lead a (respectively T) represents the mean normalized delay (respectively the average delay) of the multiple propagation paths of the channel.

[0135] For example, selecting 3 samples in each group G1-G3 (i.e., a correlation peak and a sample on each side of it) allows us to exploit the multipath propagation components whose delays a' extend up to ± one sampling period T s , i.e., -1 < a' < 1. Similarly, groups of 5 samples (as shown in FIG. 6) can be used for delays a' up to ± twice the sampling period T s , i.e. - 2 < a' < 2; and groups of 7 samples for delays a' up to ± three times the sampling period T s , i.e. - 3 < a' < 3.

[0136] Therefore, the number of samples in each group G1-G3 of the SUB subset is fixed at 3, 5, or 7 samples depending on the embodiment. Thus, the number of samples in the SUB subset is respectively equal to 9 (i.e., 3 groups of 3 samples), 15 (i.e., 3x5), and 21 (i.e., 3x7).

[0137] The ENC encoder is, according to one embodiment, a neural network taking as input the subset of samples SUB and delivering an estimate α of the time lead TA and / or ε of the frequency shift CFO.

[0138] For example, the ENC neural network is fully connected and comprises: an input layer of 42 neurons (i.e., 3 of the groups of 7 complex samples); three hidden layers of 42, 22, and 8 neurons respectively; and an output layer of 2 neurons (i.e., the estimates α and ε). Furthermore, sigmoid activation functions can be used for the input and hidden layers, and linear activation functions can be used for the output layer. It is worth noting that the ENC neural network comprises a limited number of neurons and therefore exhibits low implementation complexity.

[0139] It should be noted that, according to one embodiment, the ENC encoder uses the complex values ​​(i.e. the amplitudes and phases) of the samples in the SUB subset to jointly estimate the TA time lead and the CFO frequency offset.

[0140] The proposed solution allows for the accurate estimation of these critical parameters while maintaining a low-complexity implementation. It can advantageously be implemented in real time on communication systems. Indeed, the proposed solution enables the joint estimation of the time lead (TA) and the frequency offset (CFO) using a low-complexity neural network (ENC) that takes as input only a subset (SUB) of a few significant samples of the correlation signal (COR).

[0141] Within the scope of the invention, it could also be envisaged to use means other than a neural network to implement the ENC encoder, and thus estimate the TA time lead and / or the CFO frequency shift. For example, other machine learning algorithms could be used.

[0142] The proposed method for training the EST estimator is presented below with reference to FIG. 7 and 8. In addition, the performance of the EST estimator is discussed with reference to FIG. 9A and 9B.

[0143] The use by the SYS communication system of the estimated TA time lead and CFO frequency offset is exemplified below.

[0144] In particular, the estimated TA time lead is, according to one embodiment, used during an S500 step to refine or replace the approximate time lead estimated by the DET detector.

[0145] In one embodiment, the time lead estimate α of TA is transmitted to the first communication device TX for correction. This allows subsequent transmissions from the first communication device TX to be integrated into time-frequency constraints with other communication devices.

[0146] It could also be considered to equalize subsequent signals received from the first TX communication device (i.e., subsequent received data) using the estimated TA time lead and CFO frequency offset. For example, the estimated CFO carrier frequency can be provided to a higher layer for frequency offset compensation for subsequent received data.

[0147] FIG. 7 and FIG. 8 respectively illustrate a method for training a time lead and / or frequency shift estimator and an objective function used to train the estimator according to embodiments of the invention.

[0148] Specifically, FIG. 7 illustrates the training of the proposed ENC encoder, which estimates the TA time lead and / or the CFO frequency offset from the SUB sample subset of the COR correlation signal.

[0149] As mentioned previously, the ENC encoder can be a neural network. The following description of the proposed training method will refer to this particular embodiment, which is given only as an illustrative example and is not intended to limit the invention.

[0150] The method for training the EST estimator, according to embodiments, includes at least one of the following steps illustrated in FIG. 7.

[0151] The method for training the estimator comprises, in one embodiment, supplying the ENC encoder with a subset of training samples TR_SUB of a correlation signal TR_COR. In this way, an estimated time lead TA â and / or an estimated frequency shift CFO ê are obtained at the output of the ENC encoder.

[0152] The method for training the estimator includes, in one embodiment, evaluating an objective LOS function from the training sample subset TR_SUB and the resulting <2 and / or ê estimates. The objective LOS function used for training is discussed in more detail below.

[0153] The method for training the estimator includes, in one embodiment, updating the ENC encoder to optimize the objective LOS function. For example, the ENC encoder update includes updating the weights of the ENC neural network to optimize the objective LOS function using a backpropagation gradient algorithm.

[0154] According to one embodiment, the training process may include several iterations of the previous steps for distinct training subsets TR_SUB.

[0155] The objective function LOS used for training, and more generally the proposed training method, are directly based on the analytical model of the COR correlation signal presented previously with reference to FIG. 3.

[0156] Specifically, the objective function LOS used for training is derived from the maximum likelihood estimator of the time lead (TA) and carrier frequency offset (CFO) within the simplified analytical model described above. It is worth recalling that the objective of maximum likelihood estimation is to find the parameters that make the observed data most probable within the assumed model.

[0157] We use the following notation below. Let a represent the normalized time lead and s the normalized frequency offset. The estimated normalized time lead and frequency offset obtained at the output of the encoder (ENC) are denoted â and ê. We denote c(I') the training sample subset TR_SUB, with V being the indices of the samples in the training subset c(Z'). Symbols in bold are used for vectors.

[0158] Considering a Gaussian noise channel and the simplified analytical model, it follows that the maximum likelihood estimator of the time lead a and the frequency shift Σ is expressed by: (â,s) = arg min ||c(I') — ê(Z')|| 2 . (Eq. 4) a, s, A"

[0159] In the equation above, c(I') represents the analytical model of the noise-free correlation signal in the presence of a time lead a and a frequency shift E for the indices V as defined in Eq. 3.

[0160] The maximum likelihood estimates α, ε are defined as the values ​​that minimize the distance (with respect to the Euclidean norm ||-||) between the input correlation samples c(I') and the noise-free correlation samples c(I'). In other words, the estimates α, ε are selected such that the observed correlation samples c(I') are the most probable within the assumed model.

[0161] Furthermore, we can see in Eq. 3 that c(I') = A" ■ fl' , a, £) with f(l', â, £) a function expressed by:

[0162] In practice, the coefficient A” is unknown. For this reason, it is useful to reformulate the maximum likelihood estimator in Eq. 4 (so that it no longer involves the coefficient 4") as follows:

[0163] The expression in Eq. 6 provides the maximum likelihood estimates â and ê. However, calculating the estimates â and s using this expression in communication systems is difficult. For example, an exhaustive grid search might be too complex to implement in real time.

[0164] Therefore, it is proposed to use an ENC neural network to efficiently approximate the maximum likelihood estimator of Eq. 6 and, thus, obtain the estimates â and E. The use of the ENC neural network allows for a low latency and low complexity implementation.

[0165] According to this embodiment, the training of the ENC neural network is based on the expression of Eq. 6 using the following objective function LOS:

[0166] According to this embodiment, the objective LOS function to be optimized during training is a cost function to be minimized. In fact, optimizing this objective LOS function corresponds to maximizing the likelihood function.

[0167] As an example, the graph in FIG. 8 provides an illustration of the objective function LOS L of Eq. 7 as a function of the estimates obtained â and ê. We can conclude from the graph in FIG. 8, and more generally from the results of the numerical simulations, that the objective function LOS L is a well-posed convex function with a single global minimum.

[0168] According to an embodiment illustrated in FIG. 7, the objective function LOS L can be evaluated using a decoder from the simplified analytical model. The decoder is configured to evaluate f(l',â,E) from the estimates â and ê using the expression from Eq. 5.

[0169] It should be emphasized that the optimization of the objective function LOS L of Eq. 7 corresponds to the minimization of the distance ||c(Z') - c(I')|| 2 between: c(I') the subset of samples of the correlation signal (i.e., an input signal); and c(I') the noise-free analytical model of the correlation signal for a time lead α and a frequency shift ε (i.e., a reconstructed output signal). Thus, this implementation of the proposed solution uses a self-encoding neural network.

[0170] However, within the scope of the invention, it could also be envisaged to use other methods to train the ENC encoder, for example by using a cost function representative of the error between the time lead a and the carrier frequency offset E and the estimates â and ê obtained.

[0171] The TR_SUB training sample subset can be computer-generated. Thus, the method for training the EST estimator may include generating at least one TR_SUB training sample subset. In particular, multiple TR_SUB training subsets of correlation samples can be generated with different values ​​of time lead a and frequency offset E, and signal-to-noise ratios (SNRs), and then used for multiple training iterations.

[0172] According to a particular embodiment, the generation of the training sample subset TR_SUB c(I') includes evaluating the analytical model f(l', a, E) and adding noise to it to obtain the training sample subset TR_SUB c(I'). It should be noted that the function f(l', a, s) denotes an analytical model expressing a noise-free correlation signal.

[0173] An example of the implementation of the proposed training method is now given. For example, the ENC neural network was trained using an Adam optimizer and 5000 simulation-generated training subsets. The training subsets were generated with different values ​​of a and E uniformly distributed in the range |a| < 3 and |E| < 1, and with different SNR values ​​ranging from -10 dB to 20 dB. The proposed solution then achieves, for a test correlation signal, an accuracy of 97% for the estimation of the time lead a and 92% for the estimation of the frequency shift ε

[0174] FIG. 9A and FIG. 9B illustrate the performance of a method for estimating a time lead and / or a frequency shift according to embodiments of the invention. The graphs in FIG. 9A and 9B show the relationship between channel quality (x-axis) and the accuracy of the estimated TA time lead and CFO carrier frequency offset (y-axis).

[0175] Specifically, the graph in FIG. 9A illustrates the root mean square error (RMSE) of the estimated time lead TA â obtained with the proposed solution as a function of the SNR in dB. The graph in FIG. 9B illustrates the root mean square error of the estimated carrier frequency offset CFO ê obtained with the proposed solution as a function of the SNR in dB.

[0176] To evaluate the performance of the proposed solution, the root mean square error of the estimates â and ê is compared to the root of their respective Cramer-Rao lower bound (CRLB). It is worth recalling that the Cramer-Rao lower bound provides the lower limit of the variance of an unbiased estimator, i.e., the minimum attainable root mean square error.

[0177] We consider the analytical model previously presented and a complex Gaussian noise i^|2 with circular symmetry C / V(0, CT 2 ), the SNR being expressed by p = . It can be shown by differentiating the Cramer-Rao bound that the minimum attainable errors AT min (ie Aa min • T s ) and A5 min (i.e. AE) min • HAS M The estimates for the time lead T and frequency shift Sf are given by:

[0178] As illustrated by FIG. 9A and 9B, the roots of the mean squared errors of the estimates â and ê obtained with the proposed solution for the time lead TA and the frequency shift CFO approach their respective minimum attainable errors.

[0179] As discussed previously, the accuracy of existing solutions for time lead estimation is limited to a multiple of the sampling period. In contrast, the accuracy of the proposed solution is not limited to a multiple of the sampling period and allows for a finer estimation of the time lead (i.e., it allows for the estimation of a fractional time lead). It is worth noting that, compared to prior art, the proposed solution significantly improves the estimation accuracy for both the time lead (TA) and the carrier frequency offset (CFO).

[0180] More generally, it is assumed that the proposed estimator (based on the maximum likelihood criterion) is the unbiased estimator with minimum variance and is therefore optimal in terms of accuracy. Indeed, the estimates of the time lead (TA) and the carrier frequency shift (CFO) are unbiased (i.e., the values ​​of the estimates are on average the true values ​​of these parameters) and reach their CRLB at a high SNR (i.e., they exhibit the smallest achievable variance).

[0181] FIG. 10 illustrates an example of the hardware architecture of a communication system according to embodiments of the invention.

[0182] The first TX communication device exhibits, in one embodiment, the hardware architecture of a computer. As shown in FIG. 10, the first TX communication device includes at least one PROC_TX processor. Typically, the PROC_TX processor executes instructions to perform the operations of the first TX communication device and any algorithm, method, function, process, stream, and procedure described in this disclosure.

[0183] The first TX communication device also includes, in one embodiment, COM_TX communication means which are used by the first TX communication device to communicate, in particular, with the second RX communication device. No limitations are attached to the nature of the communication interfaces between the TX and RX communication devices, which may be wired or wireless, and implement any protocol known to those skilled in the art (Ethernet, Wi-Fi®, Bluetooth®, 3G, 4G, 5G, 6G, etc.).

[0184] According to one embodiment, the first TX communication device comprises a MEM_TX memory which constitutes a storage medium according to the invention. The MEM_TX memory is readable by the PROC_TX processor and stores a computer program PROG_TX according to the invention, containing instructions to perform the steps implemented by the first TX communication device of a process according to the invention.

[0185] The second RX communication device, in one embodiment, exhibits the hardware architecture of a computer. As shown in FIG. 10, the second RX communication device includes at least one PROC_RX processor. Typically, the PROC_RX processor executes instructions to perform the operations of the second RX communication device and any algorithm, method, function, process, stream, and procedure described in this disclosure.

[0186] The second RX communication device also includes, according to one embodiment, COM_RX communication means which are used by the second RX communication device to communicate in particular with the first TX communication device.

[0187] According to one embodiment, the second RX communication device includes a MEM_RX memory which constitutes a storage medium according to the invention. The MEM_RX memory is readable by the PROC_RX processor and stores a PROG_RX computer program according to the invention, containing instructions to perform the steps, implemented by the second RX communication device, of a process according to the invention.

Claims

Claims Method for estimating parameters comprising a time advance (TA) and a frequency offset (CFO) between a first communication device (TX) and a second communication device (RX), said method being implemented by the second communication device (RX) and comprising: an estimation (S422) of said parameters (TA, CFO) from a subset (SUB) of samples of a correlation signal (COR), said correlation signal (COR) being based on a received signal (RCD) from the first communication device (TX) and a reference signal (REF), the time advance (TA) and the frequency offset (CFO) being obtained jointly during said estimation (S422), and wherein said subset (SUB) comprises one or more disjoint groups (G1-G3) respectively comprising: multiple consecutive samples of the correlation signal (COR) including a correlation peak (CPK1-CPK3),one of said groups (G1) comprising a maximum amplitude correlation peak (CPK1) of the correlation signal (COR), and said groups (G1-G3) comprising a same predefined number of samples whose indices are a function of the index (LP) of said maximum amplitude correlation peak (CPK1). Method according to claim 1, wherein said parameters (TA, CFO) are estimated (S422) from phases and amplitudes of the samples of said subset (SUB). Method according to any one of claims 1 to 2, wherein said subset (SUB) of samples comprises three disjoint groups (G1-G3) of consecutive samples of the correlation signal (COR). Method according to any one of claims 1 to 3, wherein said predefined number of consecutive samples respectively included in said groups (G1-G3) is equal to 3, 5, or 7. Method according to any one of claims 1 to 4,in which said groups (G1-G3) respectively comprise a said correlation peak (CPK1-CPK3) whose index verifies:, Z = (z p + kü) N , where: l p denotes the index (LP) of said maximum amplitude correlation peak (CPK1) of the correlation signal (COR); ke TL; (-) N denotes the modulo-ZV operation with ZV the length of the reference signal (REF); and û is an integer such that 0 < ü < N.

6. Method according to any one of claims 1 to 5, wherein said parameters (TA, CFO) are estimated (S422) using a neural network (ENC) taking as input said subset (SUB) of samples and providing as output said parameters (TA, CFO).

7. Method according to any one of claims 1 to 6, comprising a refinement (S430), from a said estimated parameter (TA), of an approximate time advance estimated using the index (LP) of said maximum amplitude correlation peak (CPK1).

8. Method according to any one of claims 1 to 7, comprising an equalization of signals received from the first communication device (TX) from at least one said estimated parameter (TA, CFO).

9. Method according to any one of claims 1 to 8, wherein the first communication device (TX) and / or the second communication device (RX) comply with the 4G and / or 5G standards.

10. Method according to any one of claims 1 to 9, wherein the signals received from the first communication device (TX) comply with the 4G and / or 5G standards.

11. A method for training an estimator (EST) of parameters comprising a time advance (TA) and a frequency offset (CFO) between a first communication device (TX) and a second communication device (RX), said estimator (EST) comprising a neural network (ENC), said method comprising: obtaining estimated parameters comprising a time advance (TA) and a frequency offset (CFO) by providing said estimator (EST) with a subset of samples (TR_SUB) of a training correlation signal (TR_COR), the estimated time advance (TA) and frequency offset (CFO) being obtained jointly; evaluating an objective function (LOS) from the subset of training samples (TR_SUB) and said estimated parameters (TA, CFO);and an update of said estimator (ENC) to optimize the objective function (LOS), and wherein said training subset (TR_SUB) comprises one or more disjoint groups (GIGS) respectively comprising: multiple consecutive samples of the correlation signal (COR) including a correlation peak (CPK1-CPK3), one of said groups (Gl) comprising a maximum amplitude correlation peak (CPK1) of the training correlation signal (TR_COR), and said groups (G1-G3) comprising the same predefined number of samples whose indices are a function of the index (LP) of said maximum amplitude correlation peak (CPK1).; 12. Method according to claim 11, in which the objective function (LOS) is expressed by: where: c(l') is the subset of training samples (TR_SUB); l' denotes the indices of the samples of c(l'); â and ê denote a time advance (TA) and a frequency offset (CFO) estimated by said estimator (EST) from c(i'); and f(l', â, £) denotes a function of l', a. and ê.

13. The method of claim 12, wherein the function f(l',â,E) is representative of an analytical model expressing a subset of samples of a noise-free correlation signal.

14. The method of claim 13, wherein said subset of training samples (TR_SUB) c(l') is generated: by using simulations of a communication system (SYS) comprising the first device (TX) and the second device (RX); or by adding noise to samples expressed by the analytical model f l', a, £), a and E denoting a time advance (TA) and a frequency offset (CFO).

15. Communication device (RX), comprising at least one processor (PROC_RX) and a memory (MEM_RX) on which a program (PROG_RX) is stored for implementing the method according to any one of claims 1 to 14.

16. Communication system (SYS), comprising: a first communication device (TX), comprising at least one processor (PROC_TX) and a memory (MEM_TX) on which is stored a program (PROG_TX) for implementing a method comprising a transmission of a preamble (PR) generated from a reference signal (REF); and a second communication device (RX) according to claim 15.

17. Computer program (PROG_RX) comprising instructions which, when the program (PROG_RX) is executed by at least one processor (PROC_RX), cause said at least one processor (PROC_RX) to implement the method according to any one of claims 1 to 14.

18. Computer-readable information medium (MEM_RX) on which the computer program (PROG_RX) according to claim 17 is stored.

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