FR3141024A1 - Method for estimating at least one parameter among a time advance and a frequency offset between first and second communication devices - Google Patents

Abstract

The present invention relates to a method for estimating at least one parameter among a time advance (TA) and a frequency offset (CFO) between a first communication device (TX) and a second communication device (RX) from of a subset (SUB) of samples of a correlation signal (COR), said correlation signal (COR) being based on a signal received (RCD) from the first communication device (TX) and a signal of reference (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 media (MEM_TX). Figure for abstract: FIG. 4

Description

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

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

State of the prior art

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 station). The objectives of uplink synchronization include detecting a preamble (e.g. a PRACH preamble) transmitted by the terminal, and then estimating the timing advance and carrier frequency offset between the terminal and the base station using the detected preamble.

The time advance characterizes the time taken by the signal to propagate from the terminal to the base station. The time advance is estimated by the base station and retransmitted to the terminal for correction. Since 5G networks rely on Orthogonal Frequency Division Multiple Access (OFDMA) to multiplex users, timing advance correction helps integrate subsequent transmissions of the terminal in restricted time-frequency resources with those of other terminals. In contrast, the carrier frequency offset is estimated and compensated within the base station. The carrier frequency shift is due to the difference between the frequencies of the terminal and base station oscillators, as well as the Doppler effect linked to the movement of the terminal.

It is worth emphasizing that proper correction of 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 telecommunications networks mobile. However, existing solutions for estimating time advance and carrier frequency offset are not fully satisfactory for the following reasons.

Following detection of the preamble, the time advance is estimated in the prior art by counting the number of samples between the start of the search window and the position of the largest correlation peak detected. The precision of the estimation of the time advance 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 estimation of the time advance. It follows that existing solutions have low precision in estimating the time advance, which leads to a degradation of communication performance, given that the signals transmitted by the different terminals are not fully orthogonal.

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

There is therefore a need for a precise and low complexity solution making it possible to estimate a time advance and/or a carrier frequency offset between a transmitter and a receiver, for example for uplink synchronization between a terminal and a broadcasting station. base within a mobile communications network.

• une estimation dudit au moins un paramètre à partir d’un sous-ensemble d’échantillons d’un signal de corrélation, ledit signal de corrélation étant basé sur un signal reçu du premier dispositif de communication et un signal de référence,

ledit sous-ensemble comprenant un ou plusieurs groupes disjoints d’échantillons consécutifs du signal de corrélation, un desdits groupes comprenant un échantillon d’amplitude maximale du signal de corrélation, et lesdits groupes comprenant un même nombre prédéfini d’échantillons dont les indices sont fonction de l’indice dudit échantillon d’amplitude maximale. The invention proposes a method for estimating at least one parameter among a time advance and a frequency offset between a first communication device and a second communication device, said method being implemented by the second communication device and including:

• 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 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.

The invention provides a precise and low complexity solution for estimating a time advance and/or a carrier frequency offset between a first and a second communication device.

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

Therefore, the proposed solution, using only the most significant samples of the correlation signal, allows to accurately estimate the time advance and/or frequency offset while providing a low complexity implementation.

It should be emphasized that, compared to the solutions of the prior art, the proposed solution significantly improves the precision of the estimation of the time advance TA and/or the carrier frequency offset CFO. In particular, as discussed previously, the precision of existing solutions for estimating the time advance is limited to a multiple of the sampling period. On the other hand, the precision of the proposed solution is not limited to a multiple of the sampling period and allows a finer estimation of the time advance (i.e. it allows the estimation of a fractional time advance).

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 communications network.

According to one embodiment, the method comprises obtaining the correlation signal from the received signal and the reference signal. To this end, the method comprises for example: a multiplication of the received signal and 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.

According to one embodiment, the reference signal is a Zadoff-Chu sequence. Precisely, the reference signal can be a Zadoff-Chu sequence whose length is a prime number.

Zadoff-Chu sequences exhibit a property of zero autocorrelation and constant amplitude, which is advantageous in terms of orthogonality between users (i.e. between different preambles) and power requirements. More precisely, the autocorrelation between a Zadoff-Chu sequence and a version of itself with a cyclic shift is zero, which allows different users to transmit respectively orthogonal preambles on the same time-frequency resources. Furthermore, the constant amplitude of the Zadoff-Chu sequence allows efficient amplification of the preamble at the transmitter.

According to one embodiment, said at least one parameter comprises the time advance and the frequency offset, and the time advance and the frequency offset are obtained jointly during said estimation.

This embodiment makes it possible to take into account the mutual influence between the time advance and the carrier frequency offset when estimating these parameters. In this way, this embodiment makes it possible to provide a precise estimate of these parameters.

Indeed, as indicated above, existing solutions estimate either the time advance or the frequency offset, independently. However, at the receiver level, these two parameters are intrinsically linked in the correlation signal used for the estimation. In other words, the carrier frequency offset has an impact on the estimation of the time advance and vice versa. On the other hand, the joint estimation of the time advance and the frequency offset, as proposed here, makes it possible to take into account the mutual influence of these parameters and to improve the precision of the estimation.

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

According to this embodiment, the complex values (i.e. both the amplitudes and the phases) of the samples of the subset are used to estimate the time advance and/or the frequency offset. In contrast, the aforementioned solution by Tao et al. only exploits the amplitudes of certain samples to estimate the carrier frequency offset, which results in a loss of information and an inaccurate estimation of this parameter.

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

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

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

This embodiment makes it possible to exploit the multipath propagation components to estimate the time advance and/or the carrier frequency offset. This results in better precision in estimating these parameters for multipath channels.

Precisely, the use of groups of 3 samples makes it possible to take into account the multipath propagation components whose delays vary up to ± one sampling period compared to the average delay. Additionally, groups of 5 samples can be used for delays of up to ± twice the sampling period, and groups of 7 samples can be used for delays of up to ± three times the sampling period. sampling. Note that the timing advance represents the average delay of the multipath propagation components.

According to one embodiment, said subset of samples comprises three disjoint groups of consecutive samples of the correlation signal. More particularly, each of said groups includes one of the three largest correlation peaks (with regard to amplitude).

Indeed, numerical simulations have shown that most of the energy (> 85%) of the correlation signal is concentrated on the three largest correlation peaks. This embodiment therefore provides the most significant samples for estimating the time advance and/or frequency offset and, consequently, allows precise and low complexity estimation of these parameters.

According to one embodiment, said groups respectively comprise a sample whose index verifies:

Or : designates the index of said maximum amplitude sample of the correlation signal; ; denotes the operation modulo - with the length of the reference signal; And is an integer such that . In particular, the parameter is the modular multiplicative inverse of the root of the Zadoff-Chu sequence used as a reference signal.

According to this embodiment, each of said groups respectively 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 largest correlation peak index is obtained during the preamble detection phase.

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.

Firstly, the use of a neural network makes it possible to approximate (i.e. interpolate) an optimal estimation function – in relation to an objective function or a given optimization criterion – of the time advance and/or or carrier frequency offset. As detailed below, it is in particular proposed to use a neural network based on an analytical model of the correlation signal.

Second, the neural network takes as input only the subset of samples of the correlation signal and therefore processes a small amount of samples. Consequently, this embodiment makes it possible to use a neural network of low complexity and low latency which can be advantageously implemented in real time on the deployed communication systems.

For these reasons, this embodiment provides an accurate solution for estimating time advance and/or carrier frequency offset with a low complexity and low latency implementation.

According to one embodiment, the method further comprises a refinement, from said at least one estimated parameter, of an approximate time advance estimated using the index of said maximum amplitude sample.

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

The obtained estimates of time advance 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 carrier frequency offset within a base station.

The precise estimates of the time advance and/or the carrier frequency offset provided by the proposed solution make it possible to improve the equalization of the received signals. This results in improved communication performance (e.g. fewer demodulation errors, higher achievable transmission rates).

According to one embodiment, the first and/or second communication devices comply with 4G and/or 5G standards. Likewise, according to one embodiment, the signals received from the first communication device comply with 4G and/or 5G standards.

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

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, released in March 2013; version 12, released in March 2015; version 13, released 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, released in July 2020; and version 17, released in June 2022.

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.

• une obtention d’au moins un paramètre estimé parmi une avance temporelle et un décalage de fréquence en fournissant audit estimateur un sous-ensemble d’échantillons d’un signal de corrélation d’entraînement ;
• une évaluation d’une fonction objectif à partir du sous-ensemble d’échantillons d’entraînement et dudit au moins un paramètre estimé ; et
• une mise à jour dudit estimateur pour optimiser la fonction objectif.

According to another aspect, the invention proposes a method for training an estimator of at least one parameter among a time advance and a frequency offset between a first communication device and a second communication device, said method comprising:

• obtaining at least one estimated parameter among a time advance and a frequency offset by providing said estimator with a subset of samples of a training correlation signal;
• an evaluation of an objective function from the subset of training samples and said at least one estimated parameter; And
• an update of said estimator to optimize the objective function.

By “optimization of an objective function” is meant either the minimization of a cost function or the maximization of a gain function. For example, the estimator can be trained using gradient descent (respectively, gradient ascent) to minimize a cost function (respectively, maximize a gain function).

The method proposed for training an estimator has the advantages described above in relation to the method proposed for estimating a time advance and/or a frequency offset.

In particular, and similarly to the estimation method described above, the subset of training samples 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.

Furthermore, the proposed training method may include multiple iterations of said obtaining, evaluating and updating steps. Training iterations can be performed for subsets of distinct training samples respectively.

According to one embodiment, said estimator is or comprises a neural network.

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

Or : is the subset of training samples; designates the indices of the samples of ; And designate a time advance and a frequency shift estimated by said estimator from ; And denotes a function of , And .

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

The objective function proposed here is a cost function representative of the distance (relative to ) between: the correlation samples provided as input; and the model of noise-free correlation samples, given a time advance and a frequency shift . According to this embodiment, the proposed solution uses an autoencoder, trained to minimize the difference between: an input signal (ie the correlation samples provided as input); and a reconstructed output signal (ie the model of the correlation samples without noise).

Indeed, for Gaussian noise channels, the optimization of this objective function corresponds to the maximization of the likelihood function. The estimator is therefore trained to approximate (i.e. interpolate) the maximum likelihood estimator of the time advance and/or frequency offset. In other words, the estimated time lead and/or frequency shift are obtained such that the observed correlation samples are the most likely.

Consequently, this embodiment makes it possible to provide an estimator trained to output the optimal estimates – with respect to the maximum likelihood criterion – of the time advance and/or the carrier frequency offset.

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 for this reason optimal in terms of precision. Indeed, as detailed below, it can be shown that the obtained estimates of the time advance and the carrier frequency offset are unbiased and reach the lowest achievable variance (i.e. the Cramer-Rao bound).

According to one embodiment, said subset of training samples is generated using simulations of a communications system including the first and second devices. According to one embodiment, said subset of training samples is generated by adding noise to samples expressed by the analytical model , And designating a time advance and a frequency offset.

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

These implementations provide an accurate estimator of timing advance and/or frequency offset for various deployment scenarios. Indeed, the estimator can be trained on data representative of various scenarios, for example different time advance and frequency offset values, different signal/noise ratios, or different propagation conditions.

According to another aspect , the invention proposes an estimator of at least one parameter among a time advance and a frequency offset between a first communication device and a second communication device, said estimator having been trained by a method conforming 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 signal reference.

According to one embodiment, said estimator is or comprises a neural network which has been trained by a method according to the invention. Consequently, the invention extends to a computer-readable information medium on which a program is stored for implementing a neural network according to the invention. Said program comprises instructions which, when the program is executed by at least one processor or a computer, lead said at least one processor or computer to implement a method according to the invention. Furthermore, the invention also provides a computer-readable medium on which data representative of a neural network conforming to the invention are stored, such as hyperparameters and/or weights of the neural network.

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

According to another aspect , the invention proposes a communication device, called a second communication device, comprising at least one processor and a memory on which a program is stored for implementing a method according to the invention.

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.

According to another aspect , the invention proposes a computer program comprising instructions which, when the program is executed by at least one processor or a computer, lead said at least one processor or computer to implement a method conforming to the 'invention.

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

According to another aspect , the invention proposes a computer-readable information medium on which the computer program according to the invention is stored.

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 correspond to a computer integrated circuit in which the program is incorporated and adapted to execute a method as described above or to be used in the execution of such a method.

It should be emphasized that the proposed estimator, communication devices, communication system, program and support have the advantages described above in connection with the proposed method for estimating a time advance and/or a frequency offset. .

There illustrates a communication system according to embodiments of the invention.

There illustrates steps of a method for estimating a time advance and/or a frequency offset according to embodiments of the invention.

There illustrates an architecture of a communication device according to embodiments of the invention.

There illustrates an architecture of a communication device according to embodiments of the invention.

There illustrates steps of a method for estimating a time advance and/or a frequency offset according to embodiments of the invention.

There illustrates an example of a correlation signal used by a method for estimating a time advance and/or a frequency offset according to embodiments of the invention.

There illustrates a method for training an estimator of a time advance and/or a frequency offset according to embodiments of the invention.

There illustrates an objective function used by a method of training an estimator of a time advance and/or a frequency offset according to embodiments of the invention.

There and the illustrate the performance of a method for estimating a time advance and a frequency offset according to embodiments of the invention.

There illustrates an example of hardware architecture of a communication system according to embodiments of the invention.

There and the respectively illustrate a communication system and steps of a method for estimating a time advance and/or a frequency offset 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 stages of the proposed method.

As mentioned previously, the invention is particularly relevant in the context of uplink synchronization between a terminal and a base station in a mobile communications network. The following description of the present invention will refer to this particular context, which is given only by way of illustrative example and should not limit the invention.

A SYS communication system comprises, according to an embodiment illustrated by the , a first TX communication device and a second RX communication device. For example, the first TX communication device may be a mobile terminal such as a user terminal and the second RX communication device may be a base station.

The first TX and second RX communication devices communicate with each other using a channel, for example a wireless channel. The communications between the first TX device and the second RX device are thus impacted by a time advance TA and a carrier frequency offset CFO.

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

The TA and CFO parameters must be estimated and compensated in order to obtain better communication performances, 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.

The first TX communication device comprises 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 TX communication device. The transmission of the PR preamble may involve, according to embodiments, different processing operations such as repetition, modulation, amplification, etc.

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

The architecture of the second RX communication device is described below with reference to the steps of the , the second RX communication device can be configured to implement at least one of steps S100 to S400.

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

The correlator XC is configured, according to one embodiment, to obtain, in 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.

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

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

There illustrates an architecture of a communication device according to embodiments of the invention. Exactly there further details the architecture of the first TX communication device previously described with reference to the and the method for generating the preamble PR from a reference signal REF.

In a particular embodiment, the reference signal REF is a Zadoff-Chu sequence which can be expressed by:

Or is the length of the sequence, is the root of the Zadoff-Chu sequence, denotes the modulo-operation , , is a cyclic shift and . Precisely, the reference signal REF is a Zadoff-Chu sequence whose length is a prime number.

According to an embodiment illustrated by the , the generation of the preamble PR comprises at least one of the following steps: an application of a Fourier transform (eg a discrete Fourier transform DFT, or a fast Fourier transform FFT) to the reference signal REF; a frequency modulation (“sub-carrier frequency mapping” in English) of the signal obtained at the output of the Fourier transform; and an application of an inverse Fourier transform (eg an inverse discrete Fourier transform iDFT or an inverse fast Fourier transform iFFT) to the frequency modulated signal. In particular, these steps make it possible to integrate the PR preamble into the frequency resources.

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

There and the respectively illustrate an architecture of a communication device and steps of a method for estimating a time advance and/or a frequency offset according to embodiments of the invention. Exactly there further details the architecture of the second RX communication device and the details steps S100 to S400.

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

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

To obtain the received signal RCD in step S100, the second communication device RX is configured, according to embodiments, to perform at least one of the following steps S110 to S140.

The second RX communication device is configured, according to one embodiment, to acquire, in step S110, a radio signal using the RX_ANT antenna of the second communication device.

The second RX communication device is configured, according to one embodiment, to delete, in step S120, a cyclic prefix and obtain a signal sampled from the radio signal . In particular, step S120 comprises the processing of the radio signal using a radio frequency head (called “radio-frequency front-end RF-FE” in English) of the second communication device to obtain the signal sampled (ie discrete). Furthermore, step S120 may include decimation and filtering of the radio signal , which is typically used for long format preambles to reduce the size of the FFT later.

The second RX communication device is configured, according to one embodiment, to apply, in step S130, a Fourier transform to the signal to get a signal .

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

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

According to this embodiment, the correlator XC is configured to apply, in step S210, a conjugated DFT (ie a DFT then a conjugation) to the samples of the reference signal REF. Therefore, the XC correlator obtains multiple coefficients , which correspond to a complex conjugate representation in the frequency domain of the reference signal REF.

The correlator XC is configured, according to this embodiment, to multiply, in step S220, samples of the received signal RCD by the coefficients obtained and applying, in step S230, an iDFT transform to the multiplication result to obtain the correlation signal COR (a digital signal including multiple samples).

In this way, the XC correlator implements an adapted filter in the frequency domain. Consequently, the correlation signal COR obtained is therefore representative of a cross-correlation between the preamble PR transmitted by the first communication device TX and the reference signal REF. For illustration purposes, an example of a COR correlation signal is shown in Figure and described below.

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

The detector DET is configured, according to one embodiment, to detect, in step S300, the transmission of the preamble PR by the first communication device TX from the correlation signal COR.

For example, the DET detector can implement a detection decision criterion from a power delay profile of the COR correlation signal. Precisely, the detector DET, according to this particular embodiment, detects the preamble PR if the quadratic amplitude of a sample of the correlation signal COR is greater than a predefined threshold. In the context of the invention, other implementations of the DET detector could be considered.

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

In particular, the detector DET is configured to obtain, in step S310, an approximate estimate of the time advance TA from the index LP of the main correlation peak CPK1 detected. Consequently, the precision of the approximate estimate of the time advance TA is limited to a multiple of the sampling period.

The EST estimator is configured, according to one embodiment, to estimate, in step S400, the time advance TA and/or the carrier frequency offset CFO from the correlation signal COR. In particular, the estimator is configured to implement the following steps S410 and S420.

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

Accordingly, the estimator EST is configured to estimate the time advance TA and/or the frequency offset CFO from the subset of samples SUB. In particular, the EST estimator is configured to provide the subset of SUB samples as input to an ENC encoder, which outputs the estimate time advance and/or estimation of the frequency shift.

The description above gives an overview of the proposed solution (ie the architecture of the proposed communication devices, the steps of the proposed method). From this overview, the implementation of the EST estimator is detailed below with reference to the . More generally, the is used to describe the principle of the proposed solution and its advantages.

FIG . 6 illustrates an example of a correlation signal used to estimate a time advance and/or a frequency offset according to embodiments of the invention. More precisely, FIG. 6 illustrates a graph of the quadratic amplitude (y axis) of a COR correlation signal as a function of the sample index (x axis).

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 timing advance TA and a CFO frequency offset . Furthermore, we consider that the reference signal REF is 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 modeling of multi-path channels, since the duration of the reference signal (typically, 1 ms) is large compared to the spreading of the delays of these channels (typically, 50 to 500 ns).

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

Or is the sample index, is the length of the reference signal REF, is the modular multiplicative inverse of the root of the reference signal REF, ie . The settings And represent the normalized time advance and frequency offset respectively. is the sampling period and is the spacing between subcarriers used by the SYS communication system so that , designating the size of the iDFT of the first TX communication device.

Terms and functions , , , And in Eq. 2 are defined as follows:

Or is the channel complex gain, the amplitude factor for the signal transmitted by the first TX communication device, is the length of the cyclic prefix and is defined by as indicated previously.

Numerical simulations showed that most of the energy (> 85%) of the COR correlation signal is concentrated on the terms with in the sum of Eq. 2. Therefore, the COR correlation signal can be accurately approximated by a simplified model expressed by:

The simplified model in Eq. 3 implies a sum of three terms, which correspond to the three largest CPK1-CPK3 correlation peaks in the COR correlation signal. Regarding FIG. 6, the first term for corresponds to the main correlation peak CPK1 and the other two terms correspond to the secondary correlation peaks CPK2, CPK3.

The LP index (also referred to as ) of the main correlation peak CPK1 is obtained by the DET detector and is provided as input to the EST estimator. The clues And of the two other correlation peaks CPK2 and CPK3 can be obtained on the basis (ie are a function) of the index of the main correlation peak CPK1 using the following expressions: ; And .

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

The subset of SUB samples of the COR correlation signal can be defined as follows with reference to the .

As discussed previously, most of the energy of the COR correlation signal is concentrated on the three largest correlation peaks CPK1-CPK3 of respective index , And . Consequently, the subset of samples SUB comprises, according to one embodiment, three groups G1, G2, G3 of samples of the correlation signal COR, each group comprising one of the correlation peaks CPK1, CPK2, CPK3.

However, in the context of the invention, it could also be envisaged embodiments in which the subset of SUB samples comprises more than three groups, each group comprising an index correlation peak with .

According to one embodiment, each of the G1-G3 groups of the SUB subset comprises samples around each CPK1-CPK3 correlation peak. In other words, each group G1-G3 respectively comprises multiple consecutive samples comprising one of the CPK1-CPK3 correlation peaks.

The use of multiple samples around the CPK1-CPK3 correlation peaks allows the TA time advance to be accurately estimated for multipath channels, i.e. in the presence of multiple propagation paths with different normalized delays . Therefore, the number of samples in each group G1-G3 of the SUB subset can be set according to the channel delay spread between the first TX and second RX communication devices. It should be noted that the time advance (respectively ) represents the average normalized delay (respectively the average delay) of the multiple propagation paths of the channel.

For example, the selection of 3 samples in each group G1-G3 (ie a correlation peak and a sample on each side of it) makes it possible to exploit the multipath propagation components including the delays go up to ± one sampling period , ie . Similarly, groups of 5 samples (as shown in FIG. 6) can be used for delays up to ± twice the sampling period , ie ; and groups of 7 samples for delays up to ± three times the sampling period , ie .

Consequently, the number of samples in each group G1-G3 of the SUB subset is fixed at 3, 5, or 7 samples depending on embodiments. Thus, the number of samples in the SUB subset respectively is equal to 9 (i.e. 3 of groups of 3 samples), 15 (i.e. 3×5), and 21 (i.e. 3×7).

The ENC encoder is , according to one embodiment, a neural network taking as input the subset of samples SUB and delivering an estimate of the time advance TA and/or of the CFO frequency offset.

For example, the ENC neural network is fully connected and includes: an input layer of 42 neurons (ie 3 groups of 7 complex samples); three hidden layers of respectively 42, 22, and 8 neurons; and a 2-neuron output layer (ie estimates And ). Additionally, sigmoid-like 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 mentioning that the ENC neural network includes a limited number of neurons and therefore has low implementation complexity.

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 of the SUB subset to jointly estimate the time advance TA and the frequency offset CFO.

The proposed solution makes it possible to accurately estimate these critical parameters while maintaining a low complexity implementation. The proposed solution can advantageously be implemented in real time on communication systems. Indeed, the proposed solution makes it possible to jointly estimate the time advance TA and the frequency offset CFO using a low complexity ENC neural network taking as input only a subset SUB of a few significant samples of the signal of COR correlation.

The proposed method for training the EST estimator is presented below with reference to the and 8. Furthermore, the performance of the EST estimator is discussed with reference to the and 9B.

L ' use via the SYS communication system of the ' time advance TA And of frequency shift CFO estimatedis exemplified below.

In particular, the estimated time advance TA is, according to one embodiment, used, during a step S500, to refine or replace the approximate time advance estimated by the detector DET.

According to one embodiment, the estimation of the time advance TA is transmitted to the first communication device TX for correction. This allows subsequent transmissions of the first TX communication device to be integrated into restricted time-frequency resources with other communication devices.

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

L has and the respectively illustrate a method for training an estimator of a time advance and/or a frequency offset and an objective function used to train the estimator according to embodiments of the invention.

Exactly there illustrates the training of the proposed ENC encoder, which estimates the time advance TA and/or the frequency offset CFO from the subset of samples SUB of the correlation signal COR.

As mentioned earlier, 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 by way of illustrative example and should not limit the invention.

The method for training the EST estimator , according to embodiments, comprises at least one of the following steps illustrated by the .

The method for training the estimator comprises, according to one embodiment, supplying as input to the ENC encoder a subset of training samples TR_SUB of a correlation signal TR_COR. In this way, an estimated time advance TA and/or an estimated CFO frequency offset are obtained at the output of the ENC encoder.

The method for training the estimator comprises, according to one embodiment, an evaluation of an objective function LOS from the subset of training samples TR_SUB and estimates and or obtained. The LOS objective function used for training is discussed in more detail below.

The method for training the estimator comprises, according to one embodiment, an update of the ENC encoder to optimize the LOS objective function. For example, the ENC encoder update includes an update of the ENC neural network weights to optimize the LOS objective function using a gradient backpropagation algorithm.

According to one embodiment, the training method may comprise several iterations of the previous steps for distinct TR_SUB training subsets.

The LOS objective function 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 the .

Precisely, the LOS objective function used for training is derived from the maximum likelihood estimator of the time advance TA and the carrier frequency offset CFO under the above simplified analytical model. It is worth remembering that the goal of maximum likelihood estimation is to find the parameters that make the observed data most likely under the assumed model.

We use the following notations below. Either representing the normalized time advance and representing the normalized frequency offset. The normalized estimated time advance and frequency offset obtained at the output of the ENC encoder are noted And . We notice the subset of training samples TR_SUB, being the indices of the samples of the training subset . Bold symbols are used for vectors.

Considering a Gaussian noise channel and the simplified analytical model, it follows that the maximum likelihood estimator of the temporal advance and frequency shift is expressed by:

In the equation above, represents the analytical model of the correlation signal without noise in the presence of a time advance and a frequency shift for clues as defined in Eq. 3.

Maximum likelihood estimates , are defined as the values which minimize the distance (compared to the Euclidean norm ) between input correlation samples and correlation samples without noise . In other words, the estimates , are selected so that the observed correlation samples are the most likely within the framework of the assumed model.

Furthermore, we can see in Eq. 3 that with a function expressed by:

In practice, the coefficient is unknown. For this reason, it is interesting to reformulate the maximum likelihood estimator in Eq. 4 (so that it no longer involves the coefficient ) as following :

The expression of Eq. 6 provides maximum likelihood estimates And . However, the calculation of estimates And Using this expression in communication systems is difficult. For example, an exhaustive grid search may be too complex to implement in real time.

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 And . Using the ENC neural network allows for a low latency and low complexity implementation.

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

According to this embodiment, the LOS objective function to be optimized during training is a cost function to be minimized. In fact, the optimization of this LOS objective function corresponds to the maximization of the likelihood function.

For information purposes, the graph in FIG. 8 provides an illustration of the LOS objective function from Eq. 7 based on the estimates obtained And . We can conclude from the graph of the , and more generally from the results of numerical simulations, that the objective function LOS L is a well-posed convex function with a single global minimum.

According to an embodiment illustrated by FIG. 7, the objective LOS function can be evaluated using a decoder from the simplified analytical model. The decoder is configured to evaluate from estimates And using the expression from Eq. 5.

It should be emphasized that optimizing the LOS objective function from Eq. 7 corresponds to the minimization of the distance between : the subset of samples of the correlation signal (ie an input signal); And the analytical model of the correlation signal without noise for a temporal advance and a frequency shift (ie a reconstructed output signal). Thus, this embodiment of the proposed solution exploits an auto-encoder neural network.

However, in the context of the invention, it could also be envisaged to use other methods to drive the ENC encoder, for example by using a cost function representative of the error between the time advance and carrier frequency offset and estimates And obtained.

The training sample subset TR_SUB can be computer generated. Thus, the method for training the EST estimator may comprise a generation of at least a subset of training samples TR_SUB. In particular, multiple TR_SUB training subsets of correlation samples can be generated with different timing advance values and frequency shift , and signal-to-noise ratios (SNR), and then used for multiple training iterations.

According to a particular embodiment, the generation of the subset of training samples TR_SUB includes an evaluation of the analytical model and adding noise to it in order to obtain the subset of training samples TR_SUB . It should be remembered that the function designates an analytical model expressing a correlation signal without noise.

An example of implementation of the proposed training method is now given. For example, the ENC neural network was trained using an Adam optimizer and 5000 training subsets of simulation-generated samples. The training subsets of samples were generated with different values of And evenly distributed across the range And , and with different SNR values ranging from -10 dB to 20 dB. Then, the proposed solution achieves, for a test correlation signal, an accuracy of 97% for the estimation of the temporal advance and 92% for the estimation of the frequency shift

There and the illustrate the performance of a method for estimating a time advance and/or a frequency offset according to embodiments of the invention. The graphics of and 9B show the relationship between channel quality (x-axis) and the accuracy of the estimated time advance TA and carrier frequency offset CFO (y-axis).

Precisely, the graph in FIG. 9A illustrates the root mean square error (RMSE) of the time advance TA estimated 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 CFO carrier frequency offset estimated obtained with the proposed solution as a function of the SNR in dB.

In order to evaluate the performance of the proposed solution, the root mean square error of the estimates And are compared to the root of their respective Cramer-Rao bound (CRLB). It should be remembered that the Cramer-Rao bound provides the lower bound of the variance of an unbiased estimator, ie the minimum achievable mean squared error.

We consider the analytical model previously exposed and a complex Gaussian noise with circular symmetry , the SNR being expressed by . It can be shown by deriving the Cramer-Rao bound that the minimum achievable errors (ie ) And (ie for time advance estimates and frequency shift are given by:

As illustrated in FIGS. 9A and 9B, the roots of the mean square errors of the estimates And obtained with the proposed solution for the time advance TA and the frequency offset CFO approach their respective minimum achievable error.

As discussed previously, the accuracy of existing solutions for time advance estimation is limited to a multiple of the sampling period. On the other hand, the precision of the proposed solution is not limited to a multiple of the sampling period and allows a finer estimation of the time advance (i.e. it allows the estimation of a fractional time advance). It should be emphasized that, compared to the prior art, the proposed solution significantly improves the precision of the estimation for the time advance TA and the carrier frequency offset CFO.

More generally, it is assumed that the proposed estimator (from the maximum likelihood criterion) is the unbiased estimator with minimum variance and that it is, for this reason, optimal in terms of precision. Indeed, the estimates of the time advance TA and the carrier frequency offset 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 present the smallest achievable variance).

There illustrates an example of hardware architecture of a communication system according to embodiments of the invention.

The first TX communication device presents, according to one embodiment, the hardware architecture of a computer. As shown in the , the first TX communication device comprises at least one PROC_TX processor. Generally, the PROC_TX processor executes instructions to carry out the operations of the first TX communication device and any algorithms, methods, functions, processes, flows and procedures described in the present disclosure.

The first TX communication device also comprises, according to 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 limitation is attached to the nature of the communication interfaces between the TX and RX communication devices, which can be wired or non-wired, and implement any protocol known to those skilled in the art (Ethernet, Wi-Fi® , Bluetooth®, 3G, 4G, 5G, 6G, etc.).

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 can be read by the processor PROC_TX and stores a computer program PROG_TX in accordance with the invention, containing instructions for carrying out the steps implemented by the first communication device TX of a method in accordance with the invention.

The second RX communication device presents, according to one embodiment, the hardware architecture of a computer. As shown in the , the second RX communication device comprises at least one PROC_RX processor. Generally, the PROC_RX processor executes instructions to carry out the operations of the second RX communication device and any algorithms, methods, functions, processes, flows and procedures described in the present disclosure.

The second RX communication device also comprises, 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.

According to one embodiment, the second RX communication device comprises a MEM_RX memory which constitutes a storage medium according to the invention. The memory MEM_RX can be read by the processor PROC_RX and stores a computer program PROG_RX in accordance with the invention, containing instructions for carrying out the steps, implemented by the second communication device RX, of a method in accordance with the invention.

Claims (19)

Method for estimating at least one parameter among 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 at least one parameter (TA, CFO) from a subset (SUB) of samples of a correlation signal (COR), said correlation signal (COR) being based on a signal received (RCD) from the first communication device (TX) and a reference signal (REF),

in which said subset (SUB) comprises one or more disjoint groups (G1-G3) of consecutive samples of the correlation signal (COR), one of said groups (G1) comprising a maximum amplitude sample (CPK1) of the signal correlation (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 sample (CPK1). Method according to claim 1, wherein said at least one parameter comprises the time advance (TA) and the frequency offset (CFO), and wherein the time advance (TA) and the frequency offset (CFO) are obtained jointly during said estimation (S422). Method according to claim 1 or 2, in which said at least one parameter (TA, CFO) is estimated (S422) from phases and amplitudes of the samples of said subset (SUB). Method according to any one of claims 1 to 3, 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 4, in which 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 5, in which said groups (G1-G3) respectively comprise a sample (CPK1-CPK3) whose index verifies:
Or : designates the index (LP) of said maximum amplitude sample (CPK1) of the correlation signal (COR); ; denotes the modulo-operation with the length of the reference signal (REF); And is an integer such that . Method according to any one of claims 1 to 6, in which said at least one parameter (TA, CFO) is estimated (S422) using a neural network (ENC) taking as input said subset (SUB) of samples and providing output of said at least one parameter (TA, CFO). Method according to any one of claims 1 to 7, comprising a refinement (S430), from said at least one estimated parameter (TA), of an approximate temporal advance estimated using the index (LP) of said sample of maximum amplitude (CPK1). Method according to any one of claims 1 to 8, comprising equalization of signals received from the first communication device (TX) based on said at least one parameter (TA, CFO) estimated. Method according to any one of claims 1 to 9, in which the first communication device (TX) and/or the second communication device (RX) comply with 4G and/or 5G standards. Method according to any one of claims 1 to 10, wherein the signals received from the first communication device (TX) comply with 4G and/or 5G standards. Method for training an estimator (EST) of at least one parameter among 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 at least one estimated parameter from 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);
• an evaluation of an objective function (LOS) from the subset of training samples (TR_SUB) and said at least one parameter (TA, CFO) estimated; And
• an update of said estimator (ENC) to optimize the objective function (LOS).

Method according to claim 12, in which the objective function (LOS) is expressed by:
Or : is the subset of training samples (TR_SUB); designates the indices of the samples of ; And designate a time advance (TA) and a frequency offset (CFO) estimated by said estimator (EST) from ; And denotes a function of , And . Method according to claim 13, in which the function is representative of an analytical model expressing a subset of samples of a noise-free correlation signal. A method according to claim 14, wherein said subset of training samples (TR_SUB) is generated: 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 , And designating a time advance (TA) and a frequency offset (CFO). 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 15. Communication system (SYS), including:

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

Computer program (PROG_RX) comprising instructions which, when the program (PROG_RX) is executed by at least one processor (PROC_RX), lead said at least one processor (PROC_RX) to implement the method according to any one of the claims 1 to 15. Computer-readable information carrier (MEM_RX) on which the computer program (PROG_RX) according to claim 18 is stored.