Method for generating a signal, method for constructing a basic sequence, corresponding device and computer program.

Abstract

Method for generating a signal, method for constructing a basic sequence, corresponding computer device and program. The invention relates to a method for generating a signal, implemented in a digital communications system, comprising the following steps: obtaining a basic sequence of complex values, denoted by , such that the autocorrelation function of said basic sequence satisfies , for and otherwise , selection of subsequences of complex values ​​in said basic sequence, use of at least one of said selected subsequences to generate said signal. Figure for the abstract: Figure 4

Description

Title of the invention: Method for generating a signal, method for constructing a basic sequence, corresponding device and computer program. 1. Scope of the invention

[0001] The field of the invention is that of digital communications.

[0002] More specifically, the invention relates to the determination of a sequence of complex values ​​exhibiting particular properties, and its use in communication systems.

[0003] The invention finds applications in particular in the field of wireless communications (for example, by radio waves or unguided optical waves) or wired communications (for example, by optical fiber or electrical cable). In particular, the invention finds applications in the field of IoT (Internet of Things) communications. 2. Prior art

[0004] In order to improve the robustness of communications via a communication channel, it is known to use error-correcting codes. For example, LDPC (Low Density Parity Check) codes, turbo codes, polar codes, or Reed-Salomon codes offer good performance in terms of error correction.

[0005] In the document “Non-Binary Low-Density Parity-Check coded Cyclic Code-Shift Keying” (2013 IEEE Wireless Communications and Networking Conference (WCNC)), E. Boutillon et al. notably proposed the association of a non-binary error-correcting code of the LDPC type with a cyclic code-shift keying modulation CCSK.

[0006] As illustrated in Figure 1, such a coding scheme takes as input a source message. For example, the source message has a size of kxm bits, where each m-tuple of bits corresponds to a symbol of a Galois field of cardinality q = 2m, denoted GF(q). During a first coding step 11, the k symbols of the source message are encoded by a non-binary LDPC (NB-LDPC) code with yield ro = kjn, also called an external code. A codeword output from the NB-LDPC encoder 11 therefore comprises n symbols belonging to GF(q), i.e., n xm bits.

[0007] Each of the GF(q') symbols of the codeword is then encoded during a second modulation step 12 by a CCSK code with a yield of rt = m / q, also called the internal code. Thus, each GF(q) symbol of the codeword (represented by m bits) can be encoded, or modulated, by a sequence of C1 bits.

[0008] A BPSK (“Binary Phase Shift Keying”) modulation can then be implemented during a third step 13 to transmit the n cyclically shifted versions of the sequence of ? bits, each associated with a GF(q) symbol of the codeword.

[0009] More precisely, the CCSK 12 modulation step can implement different steps. In particular, a bijection can be defined between the elements (0, <2°, ..., 6?^-) defined in the Galois field GF(q) and the integers C1 between 0 and q - 1 (0, 1, 2, ..., q - 1). Such a bijection allows the elements of GF(q) and the integers between 0 and q - 1 to be represented indifferently.

[0010] A basic binary sequence of size denoted B, also called a basic sequence, can then be defined: B = (B(i)}, with B(i) E {0,1}. Such The sequence can notably be pseudo-random.

[0011] The CCSK 12 modulation associates in particular with the aleme element of GF(q) the binary sequence Ba defined by a circular rotation (or a cyclic shift) of a positions on the basic binary sequence B :Ba = {BG - a mod q)} £.

[0012] For example, if q = 8 and the basic binary sequence B is defined by B~(1, 0, 0, 1, 1, 1, 0, 0), then the first symbol of GF(8) is associated with the sequence B^ = (0, 0, 1, 1, 1, 0, 0, 1), the second symbol of GF(8) is associated with the sequence IF = (0, 1, 1, 1, 0, 0, 1, 0), and so on. In the given example, this is a circular rotation or a left cyclic shift. It is possible, symmetrically, to define a circular rotation or a right cyclic shift.

[0013] In order to increase the spectral efficiency of the inner code (with an efficiency r■ = m / q in the example above), it was proposed, in particular in the document "Rate-adaptive Inner Code for Non-Binary Decoders", C. Marchand et al. (1st International Symposium on Topics in Coding, 2021), to truncate the CCSK modulation at the first P bits, p ≤ q, to ​​adapt the data rate to the transmission conditions. The efficiency r< of the inner code is then r, = m / p.

[0014] For a truncation of size P, the (Fme element of GF(q) can then be encoded / modulated by a binary sequence B" defined by Bp = (B{a), B{a+1), ..., B(a + p - 1) ) with the index operations performed modulo Q. Hereafter, we call Bp the set of sequences B' of length P, such that # E ( 0, ..., q - 1} •

[0015] In the examples above, the basic sequence considered is a binary sequence. However, it is also possible to use non-binary basic sequences for CCSK modulations. Such non-binary basic sequences are also called NB-CCSK, CCSK ^-ary, or 9-ary CCSK. Just like the binary CCSK sequences, it is possible to truncate 7-ary CCSK sequences.

[0016] By way of example, [Fig.2A] illustrates a transmission scheme combining a Non-Binary code with a Truncated Non-Binary CCSK modulation (NB-TCCSK).

[0017] Such a coding scheme takes as input a source message comprising k information symbols from a Galois field of cardinality q = , denoted GF(q). The source message thus has a size of kxm bits, where each ff7-tuple of bits corresponds to a symbol of GF(q). Initially, the k information symbols of the source message, for example (a₁, a₂, a₃, a₄) with k = 4, are encoded by a non-binary code NB. The resulting codeword comprises n symbols of GF(q), i.e., a codeword of size nxm bits, for example (a₀, a₃, a₇, a₂, a₁, a₄, a₀, a₅, a₂, a₆, a₄) with n = 12. The encoding efficiency of the external code is therefore rg - k, for example r₀ = rg - k.

[0018] In a second step, each symbol of the codeword is encoded by the internal code. The internal code uses a Truncated Non-Binary CCSK (NB-TCCSK) modulation.

[0019] Thus, each symbol GF(q) of the codeword (represented by m bits) can be encoded, or modulated, by a non-binary sequence of 9 elements, or "chips". The non-binary sequence is, for example, constructed from integers from 0 to q - 1, where each integer corresponds to a point on a constellation of size % (constellation 7-airc). For example, if q ≤ 8, the first symbol a0 of the codeword is associated with a first version of the non-binary sequence of 8 chips, for example, the sequence (0,1, 6,7, 4,5, 2,3), according to a (spreading) yield rs = 1 / q = 1 / &. The following symbols (a3, a7, ...) can be associated with other versions of the non-binary sequence, defined by the circular rotation of the non-binary sequence of 7 chips (i.e., 7 versions).

[0020] After encoding a symbol of the codeword, the resulting non-binary sequence of Q chips can be truncated to P chips. For example, the sequence (0,1, 6,7, 4,5, 2,3) of size q - 8 is truncated into a sequence (0,1, 6) of size p - 3, according to a (truncating) yield rt - q!p = 8 / 3.

[0021] Each chip (i.e. each element of the truncated sequence of size P) is then modulated using a modulation of size 7, according to a (modulation) yield of rm — log2(<7), and then transmitted in a communication channel.

[0022] Figure 2B illustrates in particular the truncated sequence obtained (0,1, 6), where each chip corresponds to a point on the 8-PSK constellation.

[0023] It is known that the quality of a modulation scheme depends on the distance between the constellation points. In the examples above, based on modulation Whether binary or non-binary, truncated or untruncated CCSK, the quality of the modulation scheme depends in particular on the minimum Euclidean distance between two sequences.

[0024] We are interested below in determining the minimum Euclidean distance between two binary or non-binary sequences, obtained by applying a circular rotation of a positions, respectively b positions, to a basic sequence. If the basic sequence is untruncated, then P = Q; if the basic sequence is truncated, then p < q; and if the basic sequence is extended, then p >

[0025] The square of the distance between the two sequences Bp and is defined as: 100261 < / ( C «A = |sÿ +- 2R ( ( c < >j

[0027] with R^^, B1^ 'a real part of the expression of the scalar product between the two sequences B« ct BPr and ct 'CS squared norms of the vectors B„ and respec tively. In the case where the points corresponding to the graphical representations of the complex values ​​of the sequences Bp and B^ are placed on the unit circle, then 100281 f / (^X) 2 = 2p-2R((Bi;X))

[0029] The minimum distance associated with this Bp family of P-sized sequences (i.e., associated with the base sequence and its different versions obtained by right or left circular rotation) can thus be expressed in the following form:

[0030] D(bp) = with a, be GF(q) and** b

[0031] As previously stated, CCSK modulation defines in particular a bijection between the ? elements (0, ab, ..., 6A2) defined in the Galois field GF(q) and *7 integers between 0 and q - 1 (0, 1, 2, ..., q - 1). Therefore, a, b belong indifferently to GF(q) or to {0, ..., q - 1}.

[0032] This minimum distance can be normalized to obtain an average minimum distance per chip (per element / symbol): [00331

[0034] We can thus deduce, in the case where the points corresponding to the graphical representations of the complex values ​​of the sequences B« and B^s are located on the unit circle:

[0035] = 2 - |xmax{R(^x^})} with

[0036] When the sequence is not truncated, i.e. P ~ ¢, it is possible to maximize D^B1} using a CAZAC sequence (in English, "Constant Amplitude Zero Autocorrelation"), for example a Zadoff-Chu sequence. For this type of sequence, the Out-of-phase cyclic autocorrelations are equal to zero, i.e., (- 0 for « * b. Consequently, the normalized minimum distance is optimal, with D^B1'] — 2-

[0037] However, these properties are no longer verified when the sequence is truncated, i.e. P <Q.

[0038] By way of example, Figure 3 illustrates the evolution of the normalized minimum distance D(BP^) as a function of the size P of the sequence after truncation. If p = g = 64, the normalized minimum distance is optimal with D^B1^ = 2. If PS ≥ 9, the normalized minimum distance decreases and collapses rapidly as P decreases.

[0039] There is therefore a need for a new type of sequence which can in particular be used for the implementation of a non-binary CCSK modulation, exhibiting good properties in terms of minimum distance, before or after truncation. 3. Description of the invention

[0040] The proposed solution is based on a signal generation method, implemented in a digital communications system, comprising the following steps: • obtaining a basis sequence of complex values, denoted B, such that the autocorrelation function Rbb of said basis sequence B, defined by Rbb(t) = L^(n)B(n + r mod qf, with B((n + r) mod q)^ complex conjugate of 5( (n + r) mod ^), and r = 0, 1, ..., q-1, satisfies:

[0041] RB^T = iqlc} = e^^ c_l)

[0042] with ? a multiple of c, c > 1, h and c are coprime integers, and y2 = - 1,

[0043] and:

[0044] RBB( t ) = 0 otherwise, • selection of A subsequences of P (consecutive) complex values ​​in said basic sequence B, such that said subsequence 2, denoted BÀ = with 2 e { 0, A -1}, 1 A is equal to:

[0045] 5^ = (5(^(2)), 5(5'(2) + 1 mod q), ..., B(s(À) + p-lmod q)}

[0046] with s(X) an integer belonging to ( 0, ., q - 1} corresponding to a position in said base 5 sequence, and B(s(À ) ) the complex value associated with said position 5(2) in said base 5 sequence, • use of at least one of said selected sub-sequences to generate said signal.

[0047] According to the invention, a basic sequence with particular properties is used to generate subsequences also with particular properties, notably in terms of orthogonality or minimum distance. In particular, The generation of the basic sequence can be carried out in advance, and the basic sequence(s) can be stored, for example, in a database internal to the entity implementing the process below, or accessible by such an entity.

[0048] For example, if C = 4, the representation of the autocorrelation function Rrb in the complex plane exhibits symmetry of order 4. The family comprising the base sequence and at least one cyclically shifted version of the base sequence has a normalized minimum distance D(B) equal to 2, and the family comprising the selected subsequences also has a normalized minimum distance D(BP) equal to 2 for certain values ​​of P, notably p → q / 4, p → q / 2, p = 3q / A

[0049] Thus, the basic sequence and its cyclically shifted versions are orthogonal (as with Zadoff-Chu sequences). Moreover, the selected subsequences have a minimum distance of 2p (which is not the case for truncated Zadoff-Chu sequences).

[0050] It is thus possible to adapt the length P of the subsequence used to generate the signal according to the needs of the communication system.

[0051] It is recalled in particular that the basic sequence B has a size and the subsequence a size P. In one particular embodiment, p < q. In this case, a subsequence is considered to be a truncation or a portion of the basic sequence, or of a cyclically shifted version of the basic sequence. In another embodiment, P < q. In this case, a subsequence is the basic sequence or a cyclically shifted version of the basic sequence. In yet another embodiment, p > q. In this case, since an overall sequence is formed from the basic sequence and at least one partial repetition of the basic sequence, a subsequence is a truncation or portion of the overall sequence.

[0052] In a particular embodiment, the cardinality of A is greater than or equal to 2, i.e. A>2.

[0053] In a first application example, the subsequences are spreading sequences intended to be used by terminals, or groups of terminals, distinct from said communications system, for example when implementing an access protocol.

[0054] For example, the method according to one embodiment implements a step of allocating one of said selected sub-sequences to a terminal of said communications system, and of transmitting said signal using said sub-sequence.

[0055] For example, a base station can generate a number of subsequences and allocate a distinct subsequence, or subsequence identifier, to the terminals within its coverage area. Alternatively, a terminal of the system communications can allocate itself a subsequence from a set of subsequences obtained from the basic sequence.

[0056] A terminal can then use the subsequence allocated to it for its communications with the base station, which makes it possible to resolve, or at least limit, collision problems when several terminals wish to establish a radio communication with the base station simultaneously.

[0057] Thus, a first user can use a first set of subsequences to modulate a first data signal, and a second user can use a second set of subsequences to modulate a second data signal. Even if the terminals of both users were to transmit the first and second data signals simultaneously, a decoder would be able to decode the different data signals thanks to the significant distance between the subsequences.

[0058] The proposed solution notably allows for an increase in the number of users in the communications system. Indeed, it should be noted, as an example, that according to the prior art, if we consider a Zadoff-Chu sequence of length q = 16, it is possible to generate 16 orthogonal sequences of length q - 16.

[0059] According to the invention, if we consider a basic sequence of length q = 64, it is possible to generate 64 distinct sub-sequences of length p — 16.

[0060] Now the higher the number of distinct sequences, the higher the number of users who can communicate simultaneously in the communications system can be.

[0061] In a second application example, said sub-sequences are code words from a dictionary intended to be used by a coder of said communications system.

[0062] For example, the method implements the association of at least one coded symbol, obtained at the end of a coding step of at least one source symbol, to one of said selected sub-sequences.

[0063] Such sub-sequences can in particular be used in a communications system implementing a coding scheme with a binary or non-binary encoder with non-binary CCSK modulation, truncated or untruncated.

[0064] The length P of the subsequences can in particular be chosen taking into account the conditions of the transmission channel.

[0065] In particular, if the transmission channel has little noise or interference, the length of the subsequences can be reduced by choosing p < q, thereby increasing the transmission rate. Conversely, if the transmission channel has a lot of noise and / or interference, the length of the subsequences can be increased to obtain better immunity to noise and / or interference. with, in return, a decrease in transmission rate. The rate is therefore adaptive ("rate-adaptive").

[0066] In a particular embodiment, the basic sequence B is constructed from the following steps: • obtaining an initial vector ® comprising q / c real elements, • for each real element (Xk) of said initial vector 0, transformation of said real element 0(Æ) into a complex element A (7c), according to the expression: [°067] a(£) = (c#)1 / 2^ - 1} and J2= -1, • determination of a Krönecker product between the vector A formed from said complex elements A( £) and a binary vector A of size ∑ i ~ c, such that A(i — h) — 1 and A( i # h ) = 0, with i {0, c - 1}, etc. being coprime integers, yielding a basis vector X of size ¢, • transformation from the frequency domain to the time domain (for example implementing a Fast Inverse Fourier Transform of size 7) of said basis vector X, delivering said basis sequence B of 7 complex values.

[0068] It is noted in particular that the multiplicative coefficient used in determining the vector A makes it possible to obtain a basis sequence B having, on average, components whose energy (i.e., the square of their modulus) is equal to 1. We then obtain directly by construction |^|2 _

[0069] Such steps make it possible in particular to construct in a deterministic way, in the frequency domain, a basic sequence and sub-sequences exhibiting good properties in terms of orthogonality or minimum distance.

[0070] Recall that the Kronecker product between the vector A of size -ql C and the binary vector A of size nA ~ gives the vector X = Kronecketi A , A) of size nx - nAx nA - <1, with ^nA + a given by X(k) - A (0) x A(a), with ôe {0, nA-1) etae {0,

[0071] According to a first example, the q / c real elements of said initial vector © are chosen randomly.

[0072] According to a second example, the qj c real elements of said initial vector O are chosen so that the points corresponding to the graphical representations of the 7 complex values ​​of the basic sequence B belong to at least one circle, for example to the unit circle (7-PSK modulation, for "Phase Shift Keying") or to concentric circles (7-APSK modulation, for "Amplitude Phase Shift Keying").

[0073] In this way, it is easier to modulate the subsequence, or the signal obtained from the subsequence.

[0074] In this way, the basic sequence, or a subsequence obtained from the basic sequence, can have support on a ^-APSK modulation (for example 16 APSK or 32 APSK).

[0075] According to a particular embodiment, with c = 4, a modified initial vector 0' is obtained by adding a vector V of size qj c, called the added vector, and the initial vector 0 of q / c real elements, said added vector V being equal to vx N, with ve [1, q - 1] and N a vector of size q]c constructed by choosing its first q / (2c) elements in the set ] - 1,0, 1}, then copying the first q / (2c) elements so that N(i) — N(i + q / (2 c)), i — 0,L .... q! (2c) - 1.

[0076] It is thus possible to generate a basic sequence maximizing the normalized minimum distance.

[0077] According to a particular embodiment, the selection step selects a subset of subsequences, denoted BÀ, of cardinality A, from the set Bp of subsequences of size P, such that said subset BÀ has the largest normalized minimum distance [)[B'}: 100781 + {r((b^

[0079] with R^ B; , B; ) ) 'a P^ie real of the expression of the scalar product between the subsequence BA. and the subsequence B x2 e {0 A - 1} 2-In a particular embodiment, c is equal to 3, 4 or 5.

[0080] For example, if c = 3, then A =

[010] or A =

[001] . If c = 4, then A =

[0100] or A =

[0001] . If c = 5, then A =

[01000] , A =

[00100] , A =

[00010] or A =

[00001] .

[0081] In particular, when c is equal to 3 or equal to 4, the minimum normalized distance for the basic sequence is optimal and is equal to 2, for the values ​​of p — qf 3 and p = 2q / 3, or p = q / 4, p = q / 2 and p = 3q / 4, respectively.

[0082] The representation in the complex plane of the autocorrelation function Rbb exhibits respectively a symmetry of order 3, 4 or 5.

[0083] The invention also relates to a method for constructing a basic sequence of complex values, denoted B, intended for use in a digital communications system, implemented by a processor, characterized in that the autocorrelation function Rbb of said basic sequence B, defined by RwP) = ï^n)B((n + r) nmlq) \ with mod q)'^ “■"P1^ the conjugate of B( (n + r ) mod q), and r = 0, 1, ..., q - 1, satisfies:

[0084] RB^y = iq / cj = for zg {0, c -1}

[0085] with a multiple of c, O ï, h and c of the relatively prime integers, and y2 — - [,

[0086] and:

[0087] Rbb(t) = 0 otherwise.

[0088] In particular, such a basic sequence can be constructed in different ways, notably in the time domain or in the frequency domain.

[0089] In another embodiment, the invention relates to a device for generating a corresponding signal.

[0090] Such a device includes at least one processor configured to implement the steps described above.

[0091] Such a device is particularly suitable for implementing the signal generation or basic sequence construction process described above. For example, it is integrated into a base station or a communications system monitoring device (allowing, for example, each user to be assigned a spreading sequence), or into a communication system terminal.

[0092] This device may, of course, include the various features relating to the methods according to the invention, which may be combined or taken individually. Thus, the features and advantages of this device are the same as those of the method described above. Consequently, they are not detailed further.

[0093] The invention further relates to one or more computer programs comprising instructions for implementing a process as described above when this or these programs are executed by at least one processor.

[0094] The invention also relates to a computer-readable information carrier containing instructions for a computer program as mentioned above. 4. List of figures

[0095] Other features and advantages of the invention will become more apparent upon reading the following description of a particular embodiment, given by way of simple illustrative and non-limiting example, and the accompanying drawings, among which: - [Fig. 1] illustrates a coding scheme combining a non-binary error-correcting code of the LDPC type with a cyclic code-shifting modulation CCSK according to the prior art, - Figure [2A] illustrates a transmission scheme combining a non-binary error-correcting code with a prior art Non-Binary Truncated CCSK (NB-TCCSK) modulation, - [Fig.2B] illustrates an example of a truncated sequence obtained in the transmission scheme of [Fig.2A], - Figure 3 shows the evolution of the normalized minimum distance in depending on the size P of the sequence after truncation, according to the prior art, - Figure 4 shows the main steps implemented by a signal generation method according to one embodiment of the invention, - Figure 5 illustrates the main steps for constructing a basic sequence in the frequency domain, - Figure 6A illustrates an example of the representation of a basic sequence with q = 75 and Figure 6B shows the evolution of the normalized minimum distance as a function of the size P of the subsequences, - Figure 7A illustrates another example of the representation of a basic sequence with q = 75, Figure 7B the evolution of the normalized minimum distance D^BP^ as a function of the size P of the subsequences, and [Fig.7C] illustrates the representation in the complex plane of the associated autocorrelation function, - Figure 8 illustrates the representation in the complex plane of an example of a C4 sequence, - Figure 9A and Figure 9B illustrate examples of C4 sequence representation with q = 64, - Figure 10A and Figure 10B illustrate other examples of C4 sequence representation with q = 64, - Figure 11 illustrates yet another example of C4 sequence representation, - Figure 12 presents the simplified structure of an entity in a communication system communications implementing a signal generation technique according to an embodiment of the invention.

[0096] 5. Description of an embodiment of the invention

[0097] 5.1 General Principle

[0098] The general principle of the invention is based on the construction of a basic sequence of length ? exhibiting particular properties, and the use of this basic sequence, or of a subsequence of length P obtained from this basic sequence, in a digital communications system.

[0099] Figure 4 shows the main steps implemented by a signal generation method according to an embodiment of the invention.

[0100] In a first step 41, a basic sequence of 9 complex values, denoted B, is obtained as input to the process. In particular, the autocorrelation function Rbb of said basic sequence B is defined by RBB(t) - + t) mod q) =, t = 0.1, ..., q-1' venfie '

[0101] RB]iT = iqlc) = e^RB^ For i cl}

[0102] with # a multiple of c, O \ h and c are coprime integers, and y2 = -1,

[0103] and:

[0104] Rbs(t) = 0 otherwise.

[0105] Various techniques, presented below, can be implemented for the construction of such a basic sequence.

[0106] By way of example, the basic sequence is equal to B — (5(0), 5(1), ..., 5(15)), with q — 16.

[0107] In a second step 42, A subsequences of P complex values ​​are selected from the base 5 sequence, such that said subsequence 2, denoted B, = Bp(s(at)\ with 2 G { 0, .. A - 1}, 1 A, is equal to:

[0108] Bà-Bp(s(à))-{B(s(2)), B(s(2) + 1 mod q), ..., 5(5(2) + p-1 mod ^))

[0109] with 5( 2 ) an integer belonging to {0, -, q - 1} corresponding to a position in said base 5 sequence, and B( s( À ) ) the complex value associated with said position s(2) in said base 5 sequence,

[0110] For example, we select A = 3 subsequences of p — 8 complex values ​​in the base 5 sequence. [YES] 5^ = ^(5(0) ) = (5(5(0) ), 5(5(0) +1 mod q), ..., 5(5(0) +p-1 mod q) ]

[0112] 5^ = 5^(5(1)) ~ {#(5( 1) ), B(s( 1) + 1 mod q), ..., B(s( 1) + p~ 1 mod q)}

[0113] B; 2 = BP(^2)) = {5(5(2) ), 5(5(2) + 1 mod q), ..., B(s(2) + p-1 mod q)]

[0114] with 5(0) = 3, 5(1) = 7, 5(2) =12.

[0115] Thus, a first subsequence 5^ corresponds to the 8 consecutive complexes starting from B(3), a second subsequence B^ corresponds to the 8 consecutive complexes starting from B(7), and a third subsequence 5^ corresponds to the 8 consecutive complexes starting from B(14), modulo

[0116] During a third step 43, at least one of the selected sub-sequences B}=i> BA=l and 5^ is used to generate said signal.

[0117] For example, each of the selected subsequences can be allocated to a separate terminal of the communications system and used by the terminal to generate a useful signal, for example by encoding, spreading, or modulating the useful data with the selected subsequence. In this way, it is possible for a receiver to decouple the received signals.

[0118] The different sub-sequences can also form the code words of a dictionary intended to be used for encoding user data.

[0119] 5.2 Construction of the basic sequence

[0120] Different techniques can be implemented for the construction of a basic sequence.

[0121] 5.2.1 Construction in the frequency domain, with c arbitrary

[0122] Figure 5 illustrates the main steps for constructing a basic sequence in the frequency domain. The basic sequence obtained using this technique can be represented in the complex domain by non-unit points, i.e., by points not all located on the unit circle.

[0123] In a first step 51, an initial vector ® is obtained comprising <7 / c real elements. Recall that ci is a multiple of c, c > F

[0124] For each real element 0(^) of the initial vector O, the real element 0( / :) is transformed into a complex element A (k) in a second step 52, according to the expression:

[0125] =

[0126] In a third step 53, a Krônecker product is determined between the vector A formed of the complex elements A(k) and a binary vector A of size nA ~ c, such that A(i = h) = 1 and A(ih) = 0, with ie {0, c -1}, h etc are coprime integers, delivering a basis vector X of size <7.

[0127] Finally, in a fourth step 54, a transformation from the frequency domain to the time domain of the basis vector X is applied (for example, an inverse Fast Fourier Transform), delivering the basis sequence B of ? complex values.

[0128] An example of an algorithm for implementing such a construction method is proposed below:

[0129] for k = 0 at q / c -1 [0B0]

[0131] end for;

[0132] A = zerosÇk c) (construction of a zero vector of size c)

[0133] A(h) = 1 (with h such that h and c are coprime numbers)

[0134]

[0135] B =

[0136] According to a first example, for c = 3 and q — 75, the initial vector 0 of size 25 (75 / 3) can be chosen by randomly taking numbers between 0 and q - 1 = 74;

[0137] 0 = (8 49 37 58 53 67 66 25 52 14 2 55 37 35 67 45 46 64 60 43 13 17 66 2 36 )•

[0138] Figure 6A illustrates the points corresponding to the graphical representations of the q — 75 complex values ​​of the basic sequence B obtained with such an initial vector 0 and h = 1.

[0139] The representation in the complex plane of the autocorrelation function Rbb of the basis sequence B exhibits a symmetry of order 3.

[0140] Figure 6B illustrates the evolution of the normalized minimum distance in function of the size P of the subsequences. If p = q 13 = 25, if p = 2q / 3 = 50, or if p = q = 75, the normalized minimum distance is optimal with [)( p1]

[0141] According to a second example, for c = 5 and q — 75, the initial vector 0 of size 15 (75 / 5) can be chosen by randomly taking numbers between 0 and q - 1 = 74;

[0142] 0 = (8 49 37 58 53 67 66 25 52 14 2 55 37 35 67)

[0143] Figure 7A illustrates the points corresponding to the graphical representations of the ^ = 75 complex values ​​of the basic sequence B obtained with such an initial vector 0 and h — 3.

[0144] The representation in the complex plane of the autocorrelation function Rbb of the basis sequence B exhibits a symmetry of order 5.

[0145] Figure 7B illustrates the evolution of the normalized minimum distance in function of the size P of the subsequences. If p = q! 5 = 15, if p = 2q / 5 = 30, if p - 3ql 5 = 45, if p = 4ç / 5 = 60, or if p = q - 75, the normalized minimum distance is optimal with D^B?} - 1.38-

[0146] We note that the minimum distance £)^BP^ is not equal to 2 in this case, but slightly less than 1.38. This corresponds to the minimum distance between two points of a pentagon located on the unit circle, as illustrated in [Fig.7C].

[0147] 5.2.2 Special case c — 4

[0148] We are interested below in the particular case c — 4. A basic sequence constructed with c = 4 is also called a C4 sequence.

[0149] As stated previously, the autocorrelation function Rbb of a basic sequence B satisfies:

[0150] Rb^t = / 4) = £^RBi^ For 1 G 1 °' 1 '2' 31

[0151] with $ a multiple of 4, h and 4 being coprime, h takes its values ​​in the set {1,3}.

[0152] and:

[0153] Rbb(t) = 0 otherwise.

[0154] A basic sequence B of size P of type C4 (i.e. with c = 4) can therefore be characterized by its circular autocorrelation function Rbb(t) which satisfies the following property:

[0155] Rbb(t = iq14) = q* Jlh with ie {0, 1, 2, 3} and j2= -1 Rbb(t)=Q otherwise

[0156] The parameter h allows us to define two types of C4 sequence: h — 1 corresponds to a C4 sequence whose points of the autocorrelation function for r — iqj 4 with i.e. {0, 1, 2, 3} are connected in a clockwise direction (C4 sequence "clockwise"), while h - 3 corresponds to a C4 sequence whose autocorrelation function points for r - iq / 4 with / e {0, 1, 2, 3] are connected in a counterclockwise direction (C4 "anti-clockwise" sequence). The value of / 1 = 3 corresponds to h = -1 because (-1 mod 4) = (3 mod 4).

[0157] The graphical representation of the autocorrelation function of the C4 type basis sequence in the complex plane, also called the C4 constellation, draws a cross centered at 0 which connects the zero point with the points jq, - jq, and therefore has a symmetry of order 4. The C4 sequence thus derives its name from the words "Constellation", "Cross", "Circular", "auto-Correlation" (in French constellation, croix, auto-corrélation circulaire).

[0158] Such a C4 sequence makes it possible to obtain a normalized distance equal to 2 for different values ​​of P, notably p = q / 4, p = q / 2, p = 3q / 4 and P ~

[0159] A generic algorithm for constructing basic sequences in the frequency domain, with arbitrary c, has been detailed above. Various techniques for constructing C4 basic sequences are presented below.

[0160] 5.2.3 Construction of the basic sequence by operations research, with c — 4

[0161] According to a first technique, we define a priori the constellation C of the start as an ordered set of q points of the complex plane, C = (C(O), C(l), ..., Ciq - 1)) and the basic sequence B by a permutation P of size P which associates to the i-th element B(i) of the basic sequence B the complex point C(p ( i ) ), i.e. B ( i ) = C(p ( i ) ), for z = 0, L ..., q -1.

[0162] The constellation C can be constructed as C-(C(i) =e2JmK / = 0.1, ..., q- 1) for example.

[0163] The aim is then to solve a known optimization problem: for a set P of given values ​​of P (P = {q / 4} or P = { 1, 2, 3, ..., q - 1} for example), find the Popt permutation that maximizes the sum of the distances f)(BP^ peP -

[0164] Pop = argmax^pD^)),

[0165] This first technique makes it possible to find C4 sequences for small sequences (q 16). For larger sequences (typically q > 16), this solution is difficult to implement due to the exponential increase in the size of the search space for solutions (the number of permutations of a set of 4 elements in a set of 4 elements varies as a factorial of ¢).

[0166] 5.2.4 Construction of the basic sequence by recursion, with c = 4

[0167] According to a second technique, it is possible to construct C4 sequences such that the points corresponding to the graphical representations of the 4 complex values ​​of the C4 sequence (constellation) are uniformly distributed on the circle unit, using a recursion algorithm to determine the phase P of the points:

[0168] Initialization:

[0169] ¢)(0)=0

[0170] Recursion: for i = 1 to q -1

[0171] (p{i+ 1) =(p(J) x (1 + 1) + a mod q

[0172] with a = 1 or a = - Iet / = 4.

[0173] From this, we deduce sequence C4:

[0174] = / = 0.1, q-1

[0175] By way of example, Figure 8 illustrates the representation in the complex plane of the C4 sequence thus constructed for a = 1, l = 4 and q = 64. Two successive points of the sequence are linked by a line, forming a 4-cup epicycloid.

[0176] Other sets of recursion are known, for example, the astroid defined by the recursion ¢) ( / +1 ) = ( ~(p(i) X ( / - 1) + «) mod q or by the recursion ¢)( / +1) = ^( / ) +4x / + 1 mod q.

[0177] It is also possible to modify this recursion to decrease the number of points in the constellation while maintaining a C4 constellation. For example, to go from a 64-PSK constellation (regular constellation with 64 points) to a 32-point constellation (half the number of points) or a 16-point constellation (a quarter of the number of points), simply transform the sequence using the following function:

[0178] ^'(i) = a[^ J

[0179] with respectively a = 2 and a = 4.

[0180] 5.2.5 Construction of the basic sequence in the time domain, with c = 4

[0181] According to a third technique, it is possible to construct C4 sequences in the time domain.

[0182] An example of an algorithm that can be implemented to generate a class of C4 sequences of length with # multiple of 4 is presented below, such that the points corresponding to the graphical representations of the C1 complex values ​​of a C4 sequence are on the unit circle.

[0183] We thus consider as input an offset vector O of size 4 taking its values ​​between 0 and q - 1 (this condition is sufficient to obtain a C4 sequence having points located on the constellation <?-PSK définie par l’ensemble k = 0, 1, q - 1} ; ce n’est toutefois pas une condition nécessaire : cette contrainte est indiquée à titre d’exemple uniquement), P une permutation de l’ensemble (1, 2, 3, 4) et d une variable prenant soit la valeur + 1, soit - 1.

[0184] From these inputs, the following algorithm generates a unitary C4 sequence B of size:

[0185] M(Q) = 0; M(l) =|; M(2) M(3) = $;

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208] for & = 0 to g / 4 l for z = 0: 3 ¢(4x k+i)- O(i) + kx (4 + 8d + M(p(i) ) ) end for end for (p = (p mod q for i = 0 to q -1 B(i) = That's it. 5.2.6 Construction of the basic sequence in the frequency domain, with c = 4 According to a fourth technique, it is possible to construct C4 sequences in the frequency domain, as presented in the general case with any 6. We present below an example of an algorithm that can be implemented to generate a class of C4 sequences of length ci, with # multiple of 4, such that the points corresponding to the graphical representations of the complex values ​​of a C4 sequence are located or not on the unit circle. We consider as input a size Q, an initial vector © comprising 2 real elements, and h a variable taking either the value + 1 to generate a C4 “clockwise” sequence, or - 1 to generate a C4 “anti-clockwise” sequence. From these inputs, the following algorithm generates a unitary or non-unitary C4 sequence B of size ¢, denoted X in the frequency domain: for k = 0 to q / 4 -1 A Ç ifa . ' endfor;A=[0 0 y] X - Kronecker( A, A ) B — ifft(X). For c = 4, the binary vector A is either equal to [ 0 1 0 0] if h ~ + 1, or equal to [ 0 0 0 1] if / z = - 1. As already indicated, ( - 1 mod 4) = (3 mod 4). This technique makes it possible, in particular, to construct non-unitary constellations. As an example, Figures 9A and 9B illustrate the graphical representations of the C4 sequences obtained for ^=64, an initial vector 0 = f Q = j2. î = 0, 1, ..., 15) and ~ + For figure 9A, or h = - 1 for the [Fig.9B]. A C4 sequence constructed with a random initial vector ® is not necessarily unitary, i.e. the points associated with its graphical representation in the form of a constellation are not necessarily located on a circle.

[0209] However, it is possible to constrain the choice of real values ​​of the initial vector 0 so that the sequence C4 is unitary by construction.

[0210] Conversely, all unit sequences already found can be constructed from a specific initial vector 0.

[0211] In order to obtain a unitary C4 sequence, according to a first example, if q — with t > 1, the q / 4 real elements of the initial vector 0 can be chosen such that:

[0212] + r) = d(r) + u^r^2t+l

[0213] with: - d a real vector of size 2^1. Note that there are no constraints on the construction of the vector d. It can be chosen randomly or optimized according to a criterion specific to the application. For example, we can consider the optimization of the normalized distance [)( B') for particular values ​​of p. As an illustration, p = 1 will generate a C4 sequence associated with a constellation whose minimum distance between two points of the constellation will be maximized; - Y a permutation of the set _ 2t l - 1), 0 < r < 2M and 0 < m < 2M.

[0214] According to a second example, if q — 22f+i = 25, with t = 2, the q / 4 real elements of the initial vector 0 can be chosen such that:

[0215] ©(p(O)W(p(O))

[0216] 0( / ,(1))=^(1))

[0217] 0(2 + p(O)) = j( / >(O)) + 2^+ieo

[0218] 0(2 + ^(1))=^(1)+2^(1-6^

[0219] 0(4 + / ,(0)) =d(p(0))

[0220] 0(4 + ^(1))=67( / 7(1))+2^2)

[0221] 0(6 + / ,(0))=^(0)) + 2^0

[0222] 0(6 + / 9(1))=^(1))+2^1+6^

[0223] with:

[0224] d a real vector of size 2M- Again, there is no constraint on the construction of the vector d. It can be chosen randomly or optimized according to a criterion specific to the application. For example, one can consider the optimization of the normalized distance Ï)(BP} for particular values ​​of p. As an illustration, p = 1 will generate a C4 sequence associated with a constellation whose minimum distance between two points of the constellation will be maximized;

[0225] P a permutation of the set (0,1) (p— (0,1) or / +=(1,0)). [°226] Qo^H-1,1}2-

[0227] According to a third example, if q — 22r+i = 27, with t = 2, the q / 4 real elements of the initial vector 0 can be chosen such that:

[0228] 0(z&28 + p(O)) =tZ(p(O))+32eoz2

[0229] 0(z&28 + p(l)) = d(p(1))+64(

[0230] 0(z& 28 + p(2) )= J( / >(2) ) +16(3 + 26?)ï2+96( / z3) — 4 - [°231] 0(z&28+p(3)) = d(X3)) + 16(5 + 263)z2 + 32(^

[0232] with:

[0233] i & 28 = i - (i mod 4),

[0234]

[0235] d a real vector of size 2 / -i- Again, there is no constraint on the construction of the vector d,

[0236] P a permutation of the set (0,1, 2, 3)

[0237] (e) ef-lli4-

[0238] 5.2.7 Construction of the basic sequence in the minimizing frequency domain with c = 4

[0239] A modified initial vector 0' can notably be obtained from an initial vector 0, allowing for the generation of a unitary C4 sequence, such that the points corresponding to the graphical representations of the complex values ​​of a basis sequence obtained from the modified initial vector correspond to the points of a constellation diagram of a q-APSK modulation. In particular, it is possible to apply the frequency-domain method to generate a q-APSK constellation and an associated C4 sequence maximizing the distance L^B^, i.e., the minimum distance between two points of the constellation.

[0240] The modified initial vector 0 can in particular be obtained by adding an added vector V of size q / c and the initial vector 0 of qj c real elements, such that the added vector V is equal to v XN, with ve [L q - 1] and N a vector of size q / c constructed by choosing its first q / (2c) coordinates in the set {-1,0, 1}, then copying the first q / (2c) coordinates such that N(i) — N(i + q / (2c)), i = 0,1, ..., q / (2c)-l.

[0241] An example of an algorithm for obtaining a basis sequence that minimizes the distance D^B^ from a unitary basis sequence is presented below. As an example, c = 4 and q = 64. It should be noted, however, that the algorithm The proposed method can be generalized to different values ​​of c or of length 9 of the sequence.

[0242] We therefore consider as input a unitary C4 sequence of size q — 64, denoted B.

[0243] In a first step, the vector representing the unitary C4 sequence B is transformed from the time domain to the frequency domain:

[0244] X = fft( B).

[0245] We then seek to extract, from the basis vector X thus obtained, the initial vector 0 comprising 1 = 15 real elements (used to construct the sequence B), by de ending the phases of the 16 non-nuisance coefficients (coefficients located at indices equal to h mod 4, with h = + 1 for a "clockwise" sequence and h = - 1 for an "anti-clockwise" sequence).

[0246] In a subsequent step, the initial vector 0 is modified by adding to it a vector V (added vector) of size 16 defined as follows:

[0247] ^ = ^^^(^(0),^(1),^(2),^(3).,^(4).^(5),^(6),^(7),^(0),^(1).^(2),^(3),^(4),^(5),^(6),^^

[0248] with ve [L q - 1] a real number which can take for example integer values ​​in the interval [1, 63] and the coefficients 7V (?) taking their value among -1, 0 or and 1.

[0249] This allows us to obtain a modified initial vector 0=0 + V, and consequently to construct a new sequence B using the technique of constructing C4 sequences in the frequency domain presented previously, from the modified initial vector 0'.

[0250] It is then possible to determine the value of the sequence thus created. It then suffices to generate different sequences B' to keep only the one maximizing D^)-

[0251] As an example, we consider as input a unitary C4 sequence of size q = 64, denoted B, obtained by the frequency method from an initial vector O = (0,61,52,44,0, 45,20,60,0, 29,52,12,0, 13,20,28) and h = + 1, which gives the unitary C4 sequence illustrated in [Fig.1OA].

[0252] With v = 18 and N = (-1, +1, 0, +1, 0, -1, +1, -1), the added vector V is equal to:

[0253] V = (-18, +18, 0, +18, 0, -18, +18, -18, -18, +18, 0, +18, 0, -18, +18, -18)

[0254] The addition of the added vector and the initial vector gives:

[0255] 0' = O+V = (-18,79,52,62,0, 27, 38, 42, -18,47,52,30,0, -5,38,10).

[0256] The initial vector thus modified and the variable h — + 1 can then be used to generate a new sequence B ' such as the non-unitary C4 sequence illustrated in [Fig.1OB].

[0257] For example, the sequence B' thus constructed has a minimum distance D(B') = 6.12x 10'2-

[0258] 5.3 Application Examples

[0259] 5.3.1 Construction of orthogonal basic sequences

[0260] As previously indicated, the basic sequences thus constructed can in particular be spreading sequences intended to be used by terminals, or groups of terminals, distinct from a communications system.

[0261] Indeed, in a multi-user context, it is advantageous to associate specific sequences with users (or groups of users) in order to help the multi-user detection task.

[0262] In particular, it is possible to choose a C4 “clockwise” sequence (with h = +1), denoted x, and a C4 “counterclockwise” sequence (with h = -1), denoted X. Indeed, these two types of sequences are, by construction, orthogonal to each other. In fact, calculating the cross-correlation between the sequences x and x in the frequency domain gives: 102631 x).fft(y) •)=0

[0264] Since X — fft(x) has non-zero frequencies at indices k — 1 mod 4, while E — fft(y) has non-zero frequencies at indices k — 3 mod 4, we therefore deduce that 7?xv(r) = 0, for any value of r.

[0265] 5.3.2 Identification by p-size subsequences

[0266] In a multi-user context, it can also be advantageous to associate subsequences of size P with users (or groups of users) to aid the multi-user detection task. For example, a basic sequence of size 5 can be truncated into at least one subsequence of size P.

[0267] By way of example, consider a communication system with q = 4p users (or user groups), in which we wish to associate each user with a sequence of size P that allows them to identify themselves in a multi-user protocol. It is notably possible to construct a sequence C4 x of size μ and to associate the th'th user (or user group) with the sequence of size p defined by x^. Indeed, it is possible to show that: if (k -l) ≤ 0 mod p, then xf) q, - if l = k + 2p mod q then (x^, xf) = - p, and therefore, according to the equation d \ x k^ x k+lq) “FJ + RFC + 2 z J + if l = k + p mod q, then (x£, xf} = ±j P- and therefore, according to the equation: 102691 d( xl x^ ) 2 = 2q - 2R ( ( x^

[0270] This amounts to showing that p — q! 4 and for all k, = yP — ph P xk “ J Xk+3p

[0271] with h indicating the direction of rotation of the C4 sequence (thus, jh = j and j~h = - j if h = 1, and jh = - j and fih ~ j if h — -1).

[0272] This subsampling technique can of course be extended to other sequence lengths (in particular, p = q / 2 or p = 3^ / 4, or other values ​​of P). Moreover, the number of sequences allocated can be less than P.

[0273] For example, such a system is advantageous for initiating communication in a cellular network between a mobile and a base station.

[0274] 5.3.3 Identification by subsequences and orthogonal sequences

[0275] In particular, it is possible to increase the number of users, or groups of users, in a communications system, by combining the use of subsequences of size P and basic sequences or orthogonal subsequences (i.e., where the distance between each sequence is significant), so as to increase the number of users easily separable from one another.

[0276] Various examples are presented below.

[0277] According to a first example, for *7 “ P, it is possible to generate 2q sequences of size P~P from two C4 sequences x and 3' of size ¢, with h → +1 for sequence x, and h = -1 for sequence y. The 2ç spreading identifiers / sequences of size P~P can then be defined by the union of the ? sequences a = 0,L^<7-l} and b _ o,l,q-\}.

[0278] In particular, it is possible to choose the C4 x and 2' sequences so that the distance between the disjoint sequences is equal to 2q, thus allowing an efficient separation of users from each other.

[0279] As an example, for q — 64, it is possible to define a sequence x called epi-cycloid with ci — + 1 and a sequence k epi-cycloid with a = - 1. This makes it possible to create a set of 128 sequences of size 64 with a normalized distance between two distinct sequences equal to 2.

[0280] According to a second example, for q — 2p, it is possible to generate — 2q sequences of size p - 2 from two C4 sequences x and of size Q, with for the sequence x, h = 4-1, and for the sequence y, h — - 1. The 2q identifiers / spreading sequences of size p — qj2 can then be defined by the union of the 2 sequences {C a = 0,1, _ q-1} and (yP b = q1, q-1). I b J

[0281] In particular, it is possible to choose the C4 x and y sequences so that the distance between two disjoint sequences is equal to thus allowing an effective separation of users from each other.

[0282] By way of example, for q = 64, it is possible to define the sequence x from the initial vector 0 = (46, 62, 0, 38, 14, 62, 0, 6, 46, 62, 0, 38, 14, 62, 0, 6) and / t = +1, and the sequence y from the initial vector O = (42, 44, 0, 38, 10, 44, 0, 6, 42, 44, 0, 38, 10, 44, 0, 6) and -1, to obtain this property. This allows the creation of a set of 128 sequences of size 32, with a normalized distance between two distinct sequences equal to 2.

[0283] According to a third example, for q = 4p, it is possible to generate 4p = q p-size sequences £ from two C4 sequences x and y of size Q, with h — + 1 for sequence x, and h — - 1 for sequence 3'. The 2q identifiers / sequences of spreading size p = ~ can then be defined by the union of the ? sequences {< a = 0,1,q-1} and (vp b = 0 i ~ q_ drb 2 J

[0284] For this case, it is notably possible to choose the C4 sequences x and 3' allowing the minimum distance between two sequences to be maximized. For example, for q = 64, it is possible to define the sequence x from the initial vector 0 = (1, 2,3, 4,1, 18,35,52,1, 34,67,100,1, 50,99,14) and h = -1.

[0285] The sequence obtained is notably illustrated in [Fig. 11].

[0286] To generate the sequence in reverse, it is possible to define x ( i ) = x ( q - i ), i = 0,1, ..., q - 1 with the operations on the indices performed modulo ¢.

[0287] The minimum (non-normalized) distance between two subsequences from the base sequence x and the base sequence 2 is 14.5, in other words, whatever

[0288] It is of course possible to use two sequences constructed with a random initial vector and h = +1, and h = -1. The minimum distance remains of the same order.

[0289] 5.3.4 Coding Scheme

[0290] As previously stated, the basic sequences thus constructed can also define codewords in a dictionary intended for use by an encoder of said communications system.

[0291] In particular, such basic sequences can be used in a coding scheme combining a binary or non-binary error-correcting code with CCSK cyclic code-shift modulation, as illustrated in [Fig. 1], or in a coding scheme combining a binary or non-binary code with binary or truncated non-binary CCSK modulation, as illustrated in [Fig. 2A].

[0292] 5.3.5 Other Application Examples

[0293] Although motivated by the design of an efficient NB-TCCSK coding scheme, the proposed basic sequences, in particular the C4 sequences, can also be used in other application areas.In particular, such sequences can be used in place of Zadoff-Chu sequences, for example in 5G protocols.

[0294] 5.4 Corresponding Device

[0295] Finally, in relation to [Fig. 12], the simplified structure of an entity of a communications system implementing a signal generation technique according to one of the particular embodiments described above is presented.

[0296] Such an entity comprises a memory 121 including a buffer memory, a processing unit 122, equipped, for example, with a processor P, and driven by the computer program 123, implementing the signal generation process according to one embodiment.

[0297] At initialization, the code instructions of the computer program 123 are, for example, loaded into RAM before being executed by the processor of the processing unit 122.The processor of the processing unit 122 implements the steps of the process described above, according to the instructions of the computer program 123, to: • obtain a basic sequence of 4 complex values, denoted 5, such that the autocorrelation function Rbb of said basic sequence B, defined by Rbb(t) = mod qf with B^n+r) mod qfle complex conjugate of B((n + f) mod q) and T = 0,1, ...,q- 1, satisfies:

[0298] Rb / t = iq I cj = for ie {0, .., c - 1}

[0299] with 4 a multiple of c, c > 1, h and c are coprime integers, and j2 — _ 1, .

[0300] and:

[0301] Rbb(t) ~ 0 otherwise, • select A subsequences of P complex values ​​in said basic sequence B, such that said subsequence 2, denoted p, = ^(5(2))' ​​with 2 G {0, A - 1}, 1 A, is equal to:

[0302] B2 = {B(s(2)), B(s(à) + ïmodqY ..., B(s(A) +p-1 mod q)}

[0303] with 5(2) an integer belonging to {0, q - 1} corresponding to a position in said basic sequence B, and B(5(2)) the complex value associated with said position 5(2) in said basic sequence B, • use at least one of the said selected sub-sequences to generate said signal.

[0304] Such an entity, or a separate entity, may also implement a technique for constructing such a basic sequence.

Claims

1.

2.

3. Claims A method of generating a signal, implemented in a digital communications system, comprising the following steps: • obtaining a basic sequence of ? complex values, denoted B, such that the autocorrelation function Rbb of said basic sequence B, defined by bbiM = (n)B(n + r mod q^' with B((n + t) mod qf the complex conjugate of B((n + t) mod q) and t = 0,1, .... q - 1, verifies: RBiT = id / c) = e-^ {0, ol} with *7 a multiple of c, c > 1, h etc. coprime integers, and f=-l. And : Rbb(t) = 0 otherwise' • selection of A subsequences of P complex values ​​in said basic sequence B, such that said subsequence 2, noted with 2 e {0, A - 1}, 1 A, is equal has : BÀ = {B(s(À)), B(s(à) + 1 mod q), ..., B(s( A} + p-1 mod q)} with 5 ( 2 ) an integer belonging to { 0, ». q - 1} corresponding to a position in said base sequence B, and B(s(À) ) the complex value associated with said position ^(2) in said base sequence B, • use of at least one of said selected sub-sequences to generate said signal. Method according to claim 1, characterized in that said sub-sequences are spreading sequences intended to be used by terminals, or groups of terminals, distinct from said communications system. Method according to any one of claims 1 and 2, characterized in that it comprises a step of allocating one of said selected sub-sequences to a terminal of said communications system, and of transmitting said signal using said sub-sequence.

4. Method according to claim 1, characterized in that said subsequences are code words of a dictionary intended to be used by an encoder of said communications system.

5. Method according to claim 4, characterized in that it implements the association of at least one coded symbol, obtained at the end of a step of coding at least one source symbol, with one of said selected sub-sequences.

6. Method according to any one of claims 1 to 5, characterized in that said basic sequence B is obtained from the following steps: • obtaining an initial vector 0 comprising q / c real elements, • for each real element Q(k) of said initial vector 0, transformation of said real element ÇXk) into a complex element A (k), according to the expression: a • determination of a Krônecker product between the vector A formed of said complex elements A (k) and a binary vector A of size nA — c. such that A(i — h)=l and A(i^h) =0, with ie {0, c - 1}, etc. prime integers, delivering a basic vector X of size q, • transformation of the frequency domain into the time domain of said basic vector X, delivering said basic sequence B of Q complex values.

7. Method according to claim 6, characterized in that said q / c real elements of said initial vector 0 are chosen randomly.

8. Method according to claim 6, characterized in that said q)c real elements of said initial vector 0 are chosen so that the points corresponding to the graphical representations of the 9 complex values ​​of said basic sequence B belong to at least one circle.

9. Method according to claim 6, characterized in that said q / c real elements of said initial vector O are chosen so that the points corresponding to the graphical representations of the 4 complex values ​​of said basic sequence B correspond to the points of a constellation diagram of a q-PSK or q-APSK modulation.

10. Method according to claim 6, characterized in that c — 4 and in that a modified initial vector © is obtained by adding a vector V of size q ! c, called added vector, and said initial vector 0 of qj c real elements, said added vector V being equal to v XN, with ve[lq - 1] and N a vector of size q / c constructed by choosing its qlQc) first elements in the set { - 1.0, 1}, then by copying the q / (2c) first elements so that N(i) = N(i + q / (2c)), i = 0,1, q / (2c)-l.

11. Method according to any one of claims 1 to 10, characterized in that said selection step selects a subset of subsequences, denoted b\ of cardinality A, from the set Bp of subsequences of size P, such that said subset BÀ has the largest normalized minimum distance O ( B'' j : {B.,, B^) )) with R( the real part of the expression of the scalar product between the subsequence Bj} and the subsequence B^, 4 22e {0, Al}2-

12. Method according to any one of claims 1 to 11, characterized in that c is equal to 3, 4 or 5.

13. Method for constructing a basic sequence of $ complex values, denoted B, intended to be used in a digital communications system, said method being implemented by a processor, characterized in that the autocorrelation function Rqb of said basic sequence B, defined by rbb(t)= ^n=qB(n)B( (n + t) mod q), with B ( (n+ t) mod q) *the complex conjugate of B ( (n + t) mod q), and T = 0,1, .,., q - 1, verifies: = (0, , c-1) with a multiple of e, c > 1, h and 6 of the integers prime to each other, and f=-l. And : Rbb(t) ~ + mod qj = 0 s^non-

14. Device for generating a signal, implemented in a digital communications system, comprising at least one processor configured to: • obtain a basic sequence of complex values, denoted B, such that the autocorrelation function R bu of said basic sequence B, defined by ( T ) = ELo5 (11 ) B^n + r) m°d ' aVeC B((n + t) mod q^the complex conjugate of B((n + r) mod q) and T = 0,1, ..., q - 1, verifies: RB!It = iq / c) = for / e {0. c -1} with # a multiple of c, O 1, h etc. of the coprime integers, and / = -1. And : Rbb(t) - 0 otherwise, • select A subsequences of P complex values ​​in said basic sequence B, such that said subsequence z. noted p} - B^s^^ with G {0, A - 1}, 1 A < is equal to: BÀ = {B(s(À)), B(s(À.) + lmod q), B(s(À) + p-lmod q)} with 5 ( A ) an integer belonging to 10, q - 1} corresponding to a position in said base sequence B, and ) the value complex associated with said position sQ) in said base sequence B, • use at least one of said selected sub-sequences to generate said signal.

15. Computer program product downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor, characterized in that it comprises program code instructions for implementing a method according to at least one of claims 1 to 13.

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