Method and device for synchronizing a telecommunications receiving device receiving a very wideband pulse radio signal

Abstract

A synchronization method in a receiver (20) receiving an IR-UWB signal comprising data packets provided with a preamble comprising a first preamble part of at least two occurrences of a first preamble sequence of N pulses spaced by a period T and which are each equal to a reference pulse weighted by a complex coefficient cn, n = 0 to N-1 indicating the rank of the pulse in the first sequence and a second preamble part of at least two occurrences of a second preamble sequence equal to the conjugate of the first sequence, comprising: considering the NP successive samples for n=0 to NP-1, of a slice, of duration NT, of first, respectively second, preamble part of a received packet, determining respectively , with , sampling period; determining the frequency , respectively of the sequence , respectively;calculation of an offset to be applied for synchronization on the received signal according to: Figure for the abstract: Fig. 1;

Description

Title of the invention: Method and device for synchronizing a telecommunications receiving device receiving a very wideband pulse radio signal Technical field

[0001] The invention lies in the field of telecommunications and radiolocation. More particularly, it relates to ultra-wideband impulse radio signals (IR-UWB). Such a signal is emitted by a transmitting device. The receiving device receiving the emitted signal must synchronize in time and frequency with the emitted signal in order to be able to demodulate the transmitted signal and carry out the processing to decode the transmitted message and / or extract information on the physical signal to estimate distance, angle of arrival or location. Prior art

[0002] Synchronization means the alignment, by the receiving device, of its clock on:

[0003] - the same frequency (frequency synchronization), and possibly the same phase ;

[0004] - the same time origin (time synchronization) as that of the transmitter offset by the propagation time of the signal from the transmitter to the receiver.

[0005] In IR-UWB, synchronization is achieved using the preamble that begins the transmitted packet. This preamble is generally made up of symbols formed from a sequence, as in the different IR-UWB physical layers of the IEEE802.15.4 standard (see "IEEE Standard for Low-Rate Wireless Networks," in IEEE Std 802.15.4-2020 (Revision of IEEE Std 802.15.4-2015), vol., no., pp. 1-800, 23 July 2020). These sequences are made up of binary (+1; -1) or ternary (+1; 0; -1) elements that weight the pulses. The symbol is then repeated several times in the preamble.

[0006] Synchronization is achieved in particular by performing a correlation between the received signal and a preamble symbol. The position of the correlation peaks obtained allows for time synchronization. The more one wants to synchronize at low signal-to-noise ratios (SNR) (for example, to have a long range), the longer the sequences to be used in the correlations must be. However, the transmitter and receiver are not perfectly synchronized in frequency either, and this difference limits the duration of the correlation: if the phase rotation on a symbol is too large, the accumulation of pulses ends up being destructive. Non-coherent accumulations can be used to overcome this problem, but then the processing gain is lower than with coherent accumulations.

[0007] There is therefore a need to achieve low SNR synchronization (therefore using long sequences, and giving rise to the accumulation of a large number of pulses) in the presence of conventional central frequency offset (CFO) levels. Summary of the invention

[0008] To this end, according to a first aspect, the present invention describes a method for synchronizing a telecommunications receiving device receiving a very wideband pulsed radio signal comprising data packets, a data packet comprising a preamble, said method comprising a step of synchronizing the receiving device on the received signal as a function of said preamble;

[0009] said method being characterized in that the following steps are implemented by the telecommunication receiving device, the preamble comprising a first preamble part of at least two occurrences of a first preamble sequence of N pulses spaced apart by a period T and which are each equal to a reference pulse weighted by a complex coefficient cn, n = 0 to Nl indicating the rank of the pulse in the first sequence, said preamble further comprising a second preamble part of at least two occurrences of a second preamble sequence equal to the conjugate of the first sequence:

[0010] i / sampling of the preamble with a sampling period Ts, T = PxTs with P an integer greater than or equal to 1;

[0011] ii / considering the successive NP samples for n=0 to NP-1, of a slice, of duration NT, of the first part of the preamble of a received signal packet, determination of the sequence of values, xn = ;

[0012] iii / considering the successive NP samples for n=0 to NP-1, of a slice, of duration NT, of the second part of the preamble of a received signal packet, determination of the sequence of values ​​yn ~ c[#;

[0013] iv / determination of the frequency fd of the sequence xn and of the frequency f of the sequence yn with n=0 to NP-1;

[0014] v / calculation of at least one offset to be applied for synchronization on the received signal among a frequency offset A / and a time offset t$m according to the following equations: [00151

[0016] y ] + + A /

[0017] vi / synchronization step as a function of at least said calculated offset.

[0018]

[0019]

[0020] Such a method makes it possible to achieve low SNR synchronization (therefore using long sequences, and giving rise to the accumulation of a large number of pulses) even in the presence of frequency offset. In embodiments, such a method will further comprise at least one of the following features: - the receiving device implements the following steps: - perform a Discrete Fourier Transform, called DFT, of the xn for n = 0 to NP-1 determined for a slice indexed kd, then determine nd = argmax ( max | X1^ | ) 'where X^f0 = T FD( ' n0 G Œ 0, P - 1 ]] and then determine the index md G [ 0; N - 1 ]] of the maximum of the modulus of xkdr'd ■> ie. m — ar°max ' - determine an estimate, / , of the value of the frequency f. with J d f Ms • .N . nT^^^T J d md I NT 7- if md > f perform a Discrete Fourier Transform, called, DFT of 1¾, for n = 0 to NP-1, determined for a kg indexed slice, then given yk» nâ - TFD(\^ ) ' rt0 e IQ - 1 J and then determine the index m y'nP+n^l mg G [ 0; N - 1 J of the maximum of the modulus of ■> ie- m» = argmax I ; determine an estimate, j- , of the value of the frequency f „ with a. NT T ' m?

[0021]

[0022]

[0023] - the receiving device determines an estimate ^f of the frequency offset Af using the following formula: fd+fg; if md and do not have the same parity, the value of that of md and whose second largest Fourier transform value is closest to the maximum is then modified, the value of the modified index being set equal to the index of this second value; the receiving device implements the following steps: calculation of = ) - let md2 be the neighboring index of !nd such that | yVtq and I are spaced by less than a predefined value, the value of ^(p is determined by applying: if Aç?() < 0 and md - md2 < 0 then Aç? = Aç?() + 2tt

[0024] if A^o > 0 and md - md2 > 0 then Aç? = A^{) - 2æ

[0025] otherwise A^> = Aç>0 - determination of an estimate ^-of the frequency shift A / using the following formula fd+fs . “ T~ + 2^NT

[0026] According to another aspect, the invention describes a computer program intended to be stored in the memory of a telecommunications receiving device further comprising a microcomputer, said computer program comprising instructions which, when executed on the microcomputer, implement steps i, ii, iii and iv of a method according to the first aspect of the invention.

[0027] The invention also describes a non-transitory computer-readable medium storing such a computer program.

[0028] According to another aspect, the invention describes a telecommunications receiver device, adapted to receive a very wideband pulsed radio signal comprising data packets, a data packet comprising a preamble, said receiver device being adapted to carry out a synchronization operation on the received signal as a function of said preamble;

[0029] said device being characterized in that, the preamble comprising a first preamble part of at least two occurrences of a first preamble sequence of N pulses spaced apart by a period T and which are each equal to a reference pulse weighted by a complex coefficient cn, n = 0 to Nl indicating the rank of the pulse in the first sequence, said preamble further comprising a second preamble part of at least two occurrences of a second preamble sequence equal to the conjugate of the first sequence, the device is adapted to sample the preamble with a sampling period Tx, T — PX Ts with P an integer greater than or equal to 1;

[0030] the device is further adapted to, considering the successive NP samples s» for n=0 to NP-1, of a slice, of duration NT, of the first part of the preamble of a received signal packet, determine the sequence of values, xn = cF»; l / - J

[0031] the device is further adapted to, considering the successive NP samples for n=0 to NP-1, of a slice, of duration NT, of the second part of the preamble of a received signal packet, determine the sequence of values ​​y» = c[p]^«;

[0032] the device is further adapted to determine the frequency fd of the sequence xn and the frequency / ? of the sequence with n=0 to NP-1;

[0033] the device is further adapted to calculate at least one offset to be applied for synchronization on the received signal from among a frequency offset A / and a time offset t$m according to the following equations: 100341

[0035] j+ e)

[0036] the device being further adapted to carry out synchronization as a function of at least said calculated offset.

[0037] In embodiments, such a device will further comprise at least one of the following features:

[0038] - said device is adapted to perform a Discrete Fourier Transform, named, TFD, of the xn for n = 0 to NP-1 determined for a slice indexed kd, then determine _ argmax max | X^'l° | ' or - TFD A^+„o ) ' «9 G [ Q, P - 1 J and then determine the index GJ (XN - 1 I of the maximum of the module of , iæ. md = argmax|4f'

[0039] said device being adapted to determine an estimate, £, of the value of the J d frequency 4 with a; i 1 « ™ A NT M “ 2

[0040] said device being adapted to carry out a Discrete Fourier Transform, called, TFD, of the , for n = 0 to NP-1, determined for a slice indexed kg, then given na — TFI)( VI 0, ? " 1 II and then determine the index mg GI 0; N - 1 ]] of the maximum of the module of Y^'! ■> iæ. / ng = argmax q '

[0041] said device being adapted to determine an estimate, f , of the value of the J a ô frequency f „ with f AA if mg < y ; f 0— j mx 1 „ ,v [ NT ” ~ S1 “ T

[0042] - said device is adapted to determine an estimate ^f of the offset in frequency Af using the following formula: _ fd+fg ;

[0043] - said device is adapted to, if md and do not have the same parity, modify the value of that of md and whose second largest Fourier transform value is closest to the maximum, the value of the modified index being set equal to the index of this second value. Brief description of the drawings

[0044] The invention will be better understood and other characteristics, details and advantages will appear more clearly on reading the following description, given without limitation, and thanks to the appended figures, given by way of example.

[0045] [Fig-1] [Fig.l] represents steps of a synchronization method in a embodiment of the invention;

[0046] [Fig.2] [Fig.2] schematically represents a transmitter device and a receiver device in one embodiment of the invention;

[0047] [Fig.3] [Fig.3] represents the structure of a data packet in one embodiment of the invention;

[0048] [Fig.4] [Fig.4] schematizes the pulses of a preamble of a packet in an embodiment of the invention;

[0049] [Fig.5] [Fig.5] represents a 500 MHz Gaussian pulse used in one embodiment of the invention;

[0050] [Fig.6] Figure 6 represents the Fourier transforms of the sequences x^>+n in one embodiment of the invention;

[0051] [Fig.7] [Fig.7] represents the empirical complementary distribution function of the frequency deviation estimation error in one embodiment of the invention;

[0052] [Fig.8] [Fig.8] shows the time synchronization error in one embodiment of the invention.

[0053] Identical references may be used in different figures when they designate identical or comparable elements. Description of the embodiments

[0054] In [Fig.2], a transmitter device 10 and a receiver device 20 adapted to implement IR-UWB telecommunications in an embodiment of the invention are shown.

[0055] The transmitter device 10, hereinafter referred to as transmitter 10, comprises an electronic processing module 11 and a radio frequency (RF) module 12. The electronic processing module 11 comprises a memory and a microcontroller (not shown). Typically, the processing module 11 of the transmitter is adapted to carry out in particular the following processing operations: application of error-correcting codes, interleaving of data, transformation of bit sequences into symbols, framing, application of pulse-shaping filters. The RF module 12 of the transmitter 10 is adapted to carry out the following processing operations: transposing the signal from the baseband to the carrier frequency, amplifying and filtering the signal and transmitting an IR-UWB radio signal via an RF antenna. The memory stores instructions, which, when executed on the microcontroller, implement those (or some) of the steps relating to the processing module 11 of the transmitter 10 and set out below.

[0056] Similarly, the receiver device 20, hereinafter called receiver 20, comprises an electronic processing module 21 and a radiofrequency module 22. The electronic processing module 21 comprises a memory 210 and a microcontroller 211. Typically, the RF module 22 of the receiver 20 is adapted to carry out the processing of transposition into baseband of the received signal, filtering and amplification of the received signal. The processing module 21 of the receiver 20 is in particular adapted to carry out the following processing such as sampling at the period T, filtering, slicing, multiplication of the slices by a predefined sequence, a frequency estimator, correction of the carrier frequency deviation and of the time offset, transformation of the received symbols into an input metric for error correction decoding (typically the LLR for Log Likelihood Ratio), deinterlacing, decoding.The memory 210 stores instructions which, when executed on the microcontroller 211, implement in particular those (or some) of the steps relating to the processing module 21 of the receiver 20 and set out below.

[0057] The IR-UWB telecommunications implemented between the transmitter 10 and the receiver 20 are for example in accordance with the definition generally adopted, namely: a UWB signal (signal whose either the bandwidth / carrier frequency ratio is greater than 20%, or the bandwidth is greater than 500 MHz) made of short-duration pulses (these pulses have a duration which corresponds to the bandwidth of the signal: of the order of 2 ns for 500 MHz, 1 ns for 1 GHz etc.).

[0058] [Fig. 3] represents the general structure, at the physical layer level, of a data packet 40 transmitted in an IR-UWB signal transmitted by the transmitter 10 and received by the receiver 20 in one embodiment of the invention.

[0059] The packet 40, whose format is for example compliant with the IEEE802.15.4 standard as cited above, begins with a preamble (Preamble 41) which is used by the receiver 20 for packet detection, time synchronization and frequency synchronization. The SFD field 42, for “Start of Frame Delimiter”, makes it possible to determine the end of the preamble. The PHR field 43, for “PHY Header”, contains data on the packet such as the size of the data present in the PHY payload field 44. The PHY payload field 44 contains the useful data from the point of view of the physical layer.

[0060] The preamble according to the invention comprises a first preamble part comprising (in the present case, formed of) the repetition of a symbol and a second preamble part comprising (in the present case, formed of) the repetition petition of another symbol. Each of these symbols comprises (here is formed of) a respective sequence of pulses, each pulse in the sequence being equal to a reference pulse weighted by a complex coefficient.

[0061] The general principles of a synchronization method according to the invention are now explained.

[0062] For the (n+l)th pulse in the symbol considered in the first part of the preamble, the complex weighting coefficient has the value Cn — cxp( -2^ ), for ne ¢0, N - 1 I with N the size of the sequence of pulses constituting the symbol.

[0063] Figure 4 represents pulses of the first preamble part, each weighted by their associated complex coefficient, in an embodiment considered for illustration purposes (in the diagram, the coefficients are only + / -1 to simplify the representation).

[0064] Let p(t) be the waveform used for the reference pulse, T the distance between two consecutive pulses called PRP (for Pulse Repetition Period in English). A symbol of the first part of the preamble is then written:

[0065] u(t) = 'L^Cn.pÇt- nT)

[0066] The first part v(t) of preamble 44 emitted by transmitter 10 contains M repetitions of this symbol, with M greater than or equal to 2: 100671 = ^U(t-kNT) +

[0068] The signal received by the receiver 20 has undergone the propagation channel h(t) and the noise of the receiver n(t), so the first part of the preamble received is:

[0069] +n(t)

[0070] where (if) is the convolution of the waveform with the channel: p (t} —

[0071] Furthermore, the receiver 20 is not perfectly aligned in frequency with the transmitter 10, a frequency offset term A / is taken into account, as well as a phase term 0 and a time origin fo:

[0072] s(t) - r (t - tQ) exp(lûrAft + z^)

[0073] Finally the signal is sampled by the receiver 20, with a period Ts;

[0074] sn = s(nTs)

[0075] We assume that Ts is a submultiple of T; T — PX Ts (P is the number of samples per PRP)

[0076] The signal is further divided into slices of duration NT (the duration of a symbol), by the receiver 20:

[0077] = sn+kNP

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] where k is the slice number and n is the index inside the slice ( ne [ ttAT5-!] ). Let the vector d be of size N x P whose components dn are the cn repeated P times: d — [ Cq, tQ, Cj, . ... CJ, .. ., 0y_|. C N-[ ] The result of the term-by-term product of each slice wk by the conjugate of d is: xk — wk-d = [cQSkNP, CQSi+kNP, .... C / v-Avp-i+^vp] Or, expressed more simply, the n+1 th component of this vector is written: x» ~ C j Sn+kNp Using the previous expressions: ( n + kNP ) Ts -t0-(lN+m)T) + n(\n + kNP ) T.. ) ) exp ( 2ot Af ( n + kNP ) T s + ) = fjïj ((nT* + (k-1)NT-tü-mT) + n( (n + kNP)Ts) )exp(2mAf (n + kNP) Ts + i$) If we assume that the support of pf(t) is shorter than the PRP (otherwise we can assimilate the residual interference to noise and integrate it into n( t) ), that is to say that its support is in [ QT[, only one term (at most) of the double sum is non-zero, it is the one which verifies: 0 < nTs + ( k - / ) NT - r0 - mT < T Which amounts to: m=[(> + (t- / )V)-^| with / such that | j il _ Iç j (if the solution for l is not in [0, Ml], we are not in the preamble). So we have: -d = cp, jx ( ^ph(nTs+ (kl)NT-t0-mT) +«( (n+kNP)Ts) ) xexp(2mAf (n + kNP)Tf+i^) Generally speaking, the sequence has a phase increment of AA, even in considering a modulo N for the edge effects if N is even (i.e. when n - A < 0 or n -&>N-1), which corresponds to a frequency of -A-. A / y Applying this to our case, by subsampling by a factor P, a = [ | > - % ] (avcc =?o [^vr]). we then have: A = [^] +e Or : ' fl ci n I n IS l°m II e _ U S1P ' LPJ “ T " LTJ 1 otherwise

[0101] Taking into account the frequency offset, the frequency fd of the sequence (for a fixed value of k, and n varying from 0 to NP-1) is:

[0102] = ] + e) ​​+ A /

[0103] The estimation of fd allows us to have a relationship between ?o and A / .

[0104] According to the invention, the second preamble part emitted following the first preamble part comprises a repeated symbol equal to the conjugate, "*( / ■), of the symbol t) and by considering this conjugate symbol in place of the previous one, the yk are obtained, similarly to what was described with reference to the first preamble part, by multiplying by d instead of

[0105] = x (kl)NT-t0-mT) +n( (n+kNP^Ts) jx expi2àrAf (n+kNP)Ts+i^)

[0106] As a function of the yk the equivalent of fd, which we call f „ , is obtained, i.e. the frequency of y* = _ „2™ Q ] + € j + A /

[0107] Knowledge of fd and / makes it possible to go back to the value of / q and / or the value of A / (more precisely / q»ï: for time synchronization on the preamble, this is what we are looking for), to implement time synchronization (as a function of %„) and / or frequency synchronization (as a function of A / ).

[0108] To avoid ambiguities in the estimation of A / , it is necessary to have a phase rotation between two pulses less than 77 in absolute value, which corresponds to j A / | <

[0109] [Fig.l] represents the steps of a synchronization method in one embodiment of the invention, exploiting the general principles set out above.

[0110] In a step 101, the transmitter 10 constructs and transmits an IR-UWB signal in which the data packets each comprise a preamble, comprising a first preamble part v(f) repeating M times, with M greater than or equal to 2, the symbol ll( t ) ) and comprising, following the first preamble part, a second preamble part repeating M' times, with M' greater than or equal to 2) the symbol t ) • When M is taken equal to M', the second preamble part is equal to y*( t) ■

[0111] In a step 102, the RF module 22 of the receiver 20 receives the packets from this transmission and transposes them into baseband. Using the same names as those used in the description of the general principles of the invention above, the processing module 21 after sampling (Ts) obtains the values ​​sn as a function of the first part of the preamble of a packet considered.

[0112] In a step 103, a division into slices of these successive values ​​of s» is carried out by the processing module 21, which then determines, for at least one slice of size NP, the values ​​M = sn+kNP where k is the number of the slice considered and11 the index inside the slice (ne JQ NP - 1 ] ).

[0113]

[0114]

[0115]

[0116] In a step 104, the processing module 21 calculates xk = w* • d and thus determines the X^, for at least one slice (the slice indexed k) and for n = 0 to NP-1. The processing indicated above in steps 102-104 relating to the first part of the preamble are also carried out relating to the second part of the preamble: the processing module 21 thus determines the y^, for at least one slice (indexed k') and for n = 0 to NP-1 (k' can be chosen equal or not to k). In a step 105, the processing module 21 determines the frequency fd of the sequence x^ The frequency jd is, depending on the embodiments, determined as a function of a single slice of the X% or of several of the slices (for example by averaging the different frequency values ​​obtained on different slices), which improves the accuracy of the determined estimate. The same applies to the frequency / relative to the yk. There are various methods for determining these frequencies: uti

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] use of the Discrete Fourier transform described below or calculation of the average phase variation between two PRPs (by argument of the average of the complex conjugate products of the samples spaced by one PRP) and division by T etc. In a step 106, the processing module 21 then calculates at least one of the parameters A. / and as a function of the values ​​of the frequencies fd and f obtained in step 105 and the following system of equations: = + +^^g= ^7^((^1 + 6) +A / e as defined above (in the case described below, it is the estimate of n which will give e, the n coming from the FFT which will have the strongest signal. In practice, the n which interests us is on the impulse. The support of p(t) begins before the impulse, the is relative to the start of the support so necessarily the fractional part of / q / T will be smaller than that of n / P and therefore we will always have € = 0). Then the processing module 21 performs at least one synchronization step 107 with respect to the packet considered, among a frequency synchronization according to the value obtained for A / and a time synchronization according to the value obtained for Frequency synchronization can be achieved by applying a correction to the phase of samples received sn for example by multiplying them by exp Tx there time synchronization by shifting the received samples in time. Further processing is then carried out in one embodiment, once the synchronization performed on the received packet, depending on this processing on its preamble: decoding of data in Payload field 44, measurement of arrival time (for location purposes) based on predefined symbols present in the packet...

[0123] The present invention makes it possible to achieve low SNR synchronization (therefore using long sequences, and giving rise to the accumulation of a large number of pulses) in the presence of conventional frequency offset (CFO) levels, typically of the order of 20 or 40 ppm.

[0124] As an example in the context of a digital application, N = 1024, T — 8 ns, Ts — 500 ps and the Gaussian pulse has a bandwidth of 500 MHz at -10 dB, as shown in [Fig.5]:

[0125] / ?(r) = Aexp^-(|)"^

[0126] where A is the amplitude and t = 1.37 ns (to have a 500 MHz band).

[0127] In one embodiment, the processing module 21 estimates the values ​​of fd and f using a discrete Fourier transform (a step of detecting the presence of the preamble can be included by comparing the Fourier transform values ​​obtained as explained below to a threshold). For a given k, the sequence x^ has a length, therefore the subsampled sequences x^P+n have a length N ( «oe ([ 0-,^-11 >-

[0128] Let TFD be the Fourier transform function:

[0129] X^=TFD(^+J

[0130] m E [ 0; N - 1 U (Discrete Fourier Transform of a sequence of length N)

[0131] where kd corresponds to a slice.

[0132] Let nd be the value of no such that the maximum of s°it 'c maximum on the no of the maxima on the m:

[0133] n _ argmaxf max| )

[0134] This amounts to choosing the subsampling offset that samples the pulses at their maximum.

[0135] Figure 6 represents, with the frequencies on the abscissa and the amplitude on the ordinate, the Fourier transforms of the sequences x^+n (here n 3 = 17 and f ( = - 25 4 MHz).

[0136] Let md EJ 0; N - 1 ] be the index of the maximum of the module of X^'11:

[0137] _ argmax | X^11

[0138] mE J 0; 7V-1J In one embodiment, the value of the maximum can serve as detection of the preamble as mentioned above, by comparing it to a threshold.

[0139] The processing module 21 determines an estimate of fd:

[0140] a I

[0141] The processing module 21 does the same on the second part (corresponding to the conjugated symbol) of the preamble. The estimate of nd is still valid so we calculate directly:

[0142] TFF)( ykg j

[0143] where kg corresponds to a slice where we are in the presence of the conjugate sequence. The fact of being in the presence of the conjugate sequence can be done by comparing the value of the maximum of the module of the Fourier transform to a threshold.

[0144] Let G [[ O, N - 1 J , the index of the maximum of the module of:

[0145] mg _ argmax |

[0146] The processing module 21 then determines an estimate of / „:

[0147] af —A. < A. / p — [ nu iw [ ÿÿ " K S1 ~

[0148] From these estimates, we deduce the estimate of the frequency offset:

[0149] ~ T~

[0150] The estimations of J d and f are carried out modulo 1 / T (Fourier Transform of a sampled signal with the period PTS = T), so the estimation of is modulo 1 / 27", so to avoid ambiguity: it is necessary that | A / | < 1 / 4T-

[0151] In the example above, P TFDs are carried out (one for each number from 0 to Pl). In other embodiments, any number of TFDs, greater than or equal to 1 and strictly less than P is only carried out and taken into account for the estimations, knowing that the closer this number is to P, the better the precision of the estimation will be.

[0152] With T = 8 ns, it is obtained | A / | <31 MHz. For a center frequency around 10 GHz (case of the highest channel of "IEEE Standard for Low-Rate Wireless Networks," in IEEE Std 802.15.4-2020 (Revision of IEEE Std 802.15.4-2015), vol., no., pp. 1-800, 23 July 2020), the relative offset is 3100 ppm (the oscillators conventionally used are better than a few tens of ppm). The supported frequency offset depends only on T and not on N. This allows the use of long sequences to support low SNR. Conversely, if we want to be able to support 40 ppm, this allows distances between pulses of up to 625 ns.

[0153] To improve accuracy, several techniques may be used in conjunction in embodiments:

[0154] First of all, the indices md and ms must theoretically have the same parity. Indeed, if lom is zero, we would have f} and / equal. When increases by T, then md increases by 1 and decreases by 1 and therefore they keep the same parity.

[0155] So if md and ms do not have the same parity, the value of the one whose second value the largest Fourier transform (i.e. the second largest value among the for md and the second largest value among the | for is the closest to the maximum is then modified. The value of the index retained (i.e. the value of the one retained among md and m") will be that of the index of this second value. For example, if md — 2 and mg = 7, it is calculated fj) _ | - | X^1^ | • P31 I r\ _ | yA^oI ! ludd~ I - !a3 I M _ I | I ! U8g “ 11 7 r 116 I rv _ III v^s>"o I l ugd - K 7 r 11 s I example, Ddd is the smallest of the four differences, md will be corrected to give it the value 3 instead of 2, will remain at 7. Similarly, if Dgg is the smallest, ms will be corrected to give it the value 6 instead of 7 and md will remain unchanged. Beware of side effects: the left neighbor of 0 is N - 1, the right neighbor of N -1 is 0.

[0156] Then the resolution of the estimator of fd and f (here the step of the transform) is 1 / NTS. To improve this and therefore improve the resolution of by looking for the fractional part of the index of the maximum of the Fourier transform, the phase rotation between two successive Fourier transforms (M must then be greater than or equal to 3) is calculated for the index md:

[0157] - argx^^conj (XÏl'dd))

[0158] The fractional part sought is &(p / 2tt

[0159] To take this fractional part into account, one must pay attention to the case where the frequency fd falls in the middle of two Fourier transform frequencies. This can be detected in two ways: either |A(pJ is close to Æ, or is close to +î| or || ■ The sign of must be consistent with the index of the second maximum. Otherwise, the processing module 21 adds or subtracts 2zr to Aç>0. Let md2 be the neighboring index ^di, which is either md -1 or md + 1, paying attention to the side effects (we are modulo N) of md such that ct are close (their difference is less than a fixed threshold, for example less than 0.3 in relative terms), the processing module applies the following rules (while paying attention to the side effects: if ,nd is Nl and md2 is 0, we consider that the difference is -1 and not Nl (0 and Nl are distant from 1)):

[0160] If A^o < 0 and md - md2 < 0 then A <p = Aç?0 + 2tt

[0161] If A<p() > 0 and md - md2 > O then Aç? = Aç>0 - 2 / r

[0162] Otherwise Atp = A^Q

[0163] The final frequency offset estimate made by the processing module is then:

[0164] r U ~ T" + ^NT

[0165] The performances are illustrated in Figure 7. They are obtained from a simulation on 10,000 draws with frequency deviations inducing phase rotations up to HEt on a sequence (i.e. 610 kHz) distributed uniformly. The SNR is -10dB at the level of a pulse (Gaussian additive white noise channel). The other numerical values ​​are those indicated at the beginning of the part. Thus it emerges from [Fig.7] that the estimation error is less than 6400 Hz in 99% of cases.

[0166] The estimation of the time synchronization is deduced from the estimation of frequency = £f)NPT,- 6

[0167] We can consider e always zero (see above). The fractional part of tonJT is given by nd. Thus the estimate of t^n is given by: 101681

[0169] The performances, resulting from the same simulation as above, are given in [Fig.8]. The synchronization error is at most 500 ps (1 sample), largely acceptable in view of the shape of the pulse represented in [Fig.5].

[0170] The method may be implemented by executing software instructions on a processor. Alternatively, it may be implemented by dedicated hardware, typically a digital integrated circuit, either specific (ASIC) or based on programmable logic (e.g. FPGA / Field Programmable Gate Array).

Claims

Claims

1. A method of synchronizing a telecommunications receiving device (20) receiving a very wideband pulse radio signal comprising data packets, a data packet comprising a preamble, said method comprising a step of synchronizing the receiving device (20) to the received signal as a function of said preamble; said method being characterized in that the following steps are implemented by the telecommunication receiving device (20), the preamble comprising a first preamble part of at least two occurrences of a first preamble sequence of N pulses spaced apart by a period T and which are each equal to a reference pulse weighted by a complex coefficient cn, n = 0 to Nl indicating the rank of the pulse in the first sequence, said preamble further comprising a second preamble part of at least two occurrences of a second preamble sequence equal to the conjugate of the first sequence: i / sampling of the preamble with a sampling period Ts, T — PX Ts with P an integer greater than or equal to 1; ii / considering the NP successive samples sn for n=0 to NP-1, of a slice, of duration NT, of the first part of the preamble of a received signal packet, determination of the sequence of values, xn - |5„; iii / considering the successive NP samples zn for n=0 to NP-1, of a slice, of duration NT, of the second part of the preamble of a received signal packet, determination of the sequence of values ​​— c[#]^n; iv / determination of the frequency fd of the sequence xn and the frequency of the sequence yn with n=0 to NP-1; v / calculation of at least one offset to be applied for synchronization on the received signal among a frequency offset A / and a time offset according to the following equations: vi / synchronization step based on at least said calculated offset.

2. A method of synchronizing a telecommunications receiving device (20) according to claim 1, wherein the device receiver (20) implements the following steps: - perform a Discrete Fourier Transform, called DFT, of the xn for n = 0 to NP-1 determined for a slice indexed kd, then determine = argmax( max|X*f°l ) ' where _ DFTÇx^ w0G II and then determine the index md E [ 0; N - 1 ]] of the maximum of the module of , ie. m _ argmaxjX^I ; - determine an estimate, / , of the value of the frequency fd J d with f — if m ,< — ' J.: ^N [ NT Ts ' ~ 2 - perform a Discrete Fourier Transform, called TFD, of the , for n = 0 to NP-1, determined for a slice indexed kg, then given nd = TFdI ' n0 E [JQ P-1 ]] and then determine the index rn^ E | 0; N - 1 U of the maximum of the module of ■> ''c' aremax\Y" ' - determine an estimate, f , of the value of the frequency J a with if m < A m, 1 • N

3. A method of synchronizing a telecommunications receiving device (20) according to claim 2, wherein the receiving device (20) determines an estimate ^^of the frequency offset A / using the following formula: f,+ / ,.A / =

4. A method of synchronizing a telecommunications receiving device (20) according to claim 2, wherein if md and do not have the same parity, the value of that of md and ms whose second largest Fourier transform value is closest to the maximum is then modified, the value of the modified index being set equal to the index of this second value.

5. A method of synchronizing a telecommunications receiving device (20) according to any one of claims 2 and 4, according to which the receiving device (20) implements the following steps: calculation of arg(x^conj^X^ ) - let md2 be the neighboring index of md such that I and 1 are spaced by less than a predefined value, the value of Aç> is determined by applying: if A <p() < 0 et md - md2 < 0 alors A^ = A^() + 2 / r si A^o >0 and md - md2 > 0 then = A^() - 2tf otherwise A^ = A^ - determination of an estimate ^^'of the frequency shift A / using the following formula / ',+ / „ a«> •.

6. A computer program, intended to be stored in the memory of a telecommunications receiving device (20) further comprising a microcomputer (211), said computer program comprising instructions which, when executed on the microcomputer (211), implement steps i, ii, iii and iv of a method according to one of the preceding claims.

7. Telecommunications receiving device (20), adapted to receive a very wideband pulse radio signal comprising data packets, a data packet comprising a preamble, said receiving device (20) being adapted to perform a synchronization operation on the received signal as a function of said preamble;said device being characterized in that, the preamble comprising a first preamble part of at least two occurrences of a first preamble sequence of N pulses spaced apart by a period T and which are each equal to a reference pulse weighted by a complex coefficient cn, n = 0 to Nl indicating the rank of the pulse in the first sequence, said preamble further comprising a second preamble part of at least two occurrences of a second preamble sequence equal to the conjugate of the first sequence, the device is adapted to sample the preamble with a sampling period Ts, T = PXT x with P; integer greater than or equal to 1; the device (20) is further adapted for, considering the NP successive samples sn for n=0 to NP-1, of a slice, of duration NT, of first part of preamble of a received signal packet, determining the sequence of values, xn = cf"; the device (20) is further adapted for, considering the NP successive samples for n=0 to NP-1, of a slice, of duration NT, of second part of preamble of a received signal packet, determining the sequence of values ​​yn ~; the device (20) is further adapted for determining the frequency fd of the sequence and the frequency f of the sequence yn with n=0 to NP-1;the device (20) is further adapted to calculate at least one offset to be applied for synchronization on the received signal from among a frequency offset A / and a time offset according to the following equations: fd=Nh\([t'f\ + €)+^ fg “ ' npts ( [ “ ] + + the device (20) being further adapted to carry out synchronization according to at least said calculated offset.;

8. Telecommunications receiver device (20) according to claim 7, adapted to perform a Discrete Fourier Transform, called DFT, of the xn for n = 0 to NP-1 determined for a slice indexed kd, then determine „ = argmax( max 1 X^f° 1 ) ' where ~ DFT^Xk'ÿ II Q 1 and then determine the index md E [ 0; N - 1 U of the maximum of the modulus of ■> '-c- md = argm^|X^'rf| ; said device (20) being adapted to determine an estimate, f , of 7 d the value of the frequency fd with f < A. ; ( NT Ts Sl md 2 said device (20) being adapted to perform a Discrete Fourier Transform, called DFT, of the , for n = 0 to NP-1, de- y np+nci r terminated for a indexed slice kg, then given ykg, nd_ TrrJ r I ttP-1 .J and then determine im -11 ^yynp+„dj the index [J 0; N - 1 ]] of the maximum of the modulus of y^'J, ie- mg = argmaxj' said device (20) being adapted to determine an estimate, f , of J g the value of the frequency / g with < A. fe ~ me 1 . v ci 1 r,-. S* 15 NT ' Ts s - 2

9. A telecommunications receiving device (20) according to claim 8, adapted to determine an estimate ^y of the frequency offset Af using the following formula: o. ?,+ / „.

10. Telecommunications receiving device (20) according to claim 8, adapted to, if md and do not have the same parity, modify the value of that of md and whose second largest Fourier transform value is closest to the maximum, the value of the modified index being set equal to the index of this second value.

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