FR2956938A1 - METHOD AND DEVICE FOR TRANSMISSION, SIGNAL AND CORRESPONDING COMPUTER PROGRAM PRODUCTS. - Google Patents

Abstract

The invention relates to a method for transmitting a signal representative of a source signal, intended to be transmitted via a transmission channel, in a multi-antenna system with nt transmitting antennas and nr receiving antennas. According to the invention, such a method comprises the following steps: spatio-temporal coding by application, to said source signal, of an extended X space-time coding matrix of size nt * (n * nr), n being an integer greater than or equal to 2, delivering an encoded signal; transmission of said coded signal.

Description

Method and device for transmission, signal and corresponding computer program products FIELD OF THE DISCLOSURE The field of the invention is that of spatio-temporal coding for transmission systems with several transmission antennas and several receiving antennas (MIMOs, Multiple-IN Multiple-Out). 2. Prior art 2.1 MIMO techniques There are numerous MIMO techniques in the literature that make it possible to increase either the robustness or the transmission rate compared to 1 SISO system. There are two families of techniques: • Spatial multiplexing techniques make it possible to increase the bit rate of the transmission, but these techniques offer a low degree of diversity and show poor performances with high signal-to-noise ratios (SNR). • Spatiotemporal coding can increase the degree of diversity and improve performance at high SNRs, but this increase is usually accompanied by a deterioration of performance at low SNRs due to the presence of interference between antennas. On the other hand, increasing the degree of diversity generally results in a prohibitive increase in the reception detection complexity. 2.2 Spatio-temporal coding (ST) There are in particular the following spatio-temporal coding types: • Spatio-temporal codes of full yield and maximum diversity: for example Golden codes, described for example in the document "JC Belfiore, G. Rekaya, and E. Viterbo, "The Golden Code: a 2x2 full-rate spacetime code with non vanishing determinants", IEEE Trans. Inform. Theory, vol. 51, No. 4, pp. 1432-1436, April 2005 ". A disadvantage of these codes lies mainly in the complexity of detection. Thus, for a 2x2 Golden code (4 modulation symbols transmitted in 2 time units, yield equal to 2), the degree of diversity is equal to 4 and the detection complexity is proportional to M4, if m is the size of the constellation of modulation. The complexity of the detector is acceptable if M = 4 (QPSK for example), but questionable if M = 16 (16-QAM for example); • Spatio-temporal codes of full efficiency and maximum diversity with reduced detection complexity, described for example in the document "S. Sezginer and H. Sari," Recent results in space-time code design, "Wireless World Research Forum Meeting 20, Ottawa, April 2008 (available at http://www.wreless-world-research.org/index.php?id=350). These codes have the same performance, the same diversity and the same performance as the Golden codes but a detection complexity proportional to M2. This spatio-temporal coding method and the corresponding simplified detection principle are also described in patent document EP 1 978 666 A1, April 2, 2007. In particular, this patent document describes such a spatio-temporal coding, in the case a system with nt = 2 transmit antennas and nr = 2 receive antennas. A group of 4 complex data symbols (sl, s2, s3, s4) is transmitted using the space-time code (ST) following the matrix X given below: X asl + bs3-csz-ds4 cs2 + ds4 csi + ds3 where a, b, c and d are complex quantities to be fixed and where s * denotes the complex conjugate of s. In this matrix representation, the first column represents the combinations of symbols transmitted during the first instant of time and the second column represents the combinations of symbols transmitted during the second instant of time. The first line gives the symbol combinations transmitted on the first antenna and the second line corresponds to the second antenna. If the symbols s1, s2, s3 and s4 are distinct, it is a full-rate ST ("full rate", R = nt = 2) and of maximum diversity (degree of diversity d = nr). x nt = 4). If some of these symbols are equal, the yield is less than 2. For example, if s3 = s4, it is a performance code R = 3/2. The construction of such ST codes is subject to the following constraint: lal = Ibl = Here = Idl. This constraint makes it possible to ensure that the average power transmitted by antenna, by instant of time and by symbol is constant. The main advantage of this particular ST code structure is its low reception decoding complexity. If the symbols belong to constellations of signals of size M (for example, M = 4 for a QPSK modulation, M = 16 for a 16-QAM modulation, ...), it is shown that the optimal receiver has a complexity proportional to M2 whereas in the general case, the decoding complexity of an ST 2x2 code of full efficiency and maximum diversity is proportional to M4, as in the case of Golden codes, which are the reference for performance ST codes full and maximum diversity. On the other hand, it is shown that for a choice of parameters a, b, c and d based on asymptotic performance considerations (justified in the document "JM Paredes, AB Gershman, and M. Gharavi-Alkansari," A new Full-rate full-diversity space-time block with non-vanishing determinants and simplified maximum-likelihood decoding ", IEEE Trans Signal Processing, Vol 56, No. 6, pp. 2461-2469, June 2008"), performance of this ST code are similar to those of the Golden code. 3. OBJECTIVES OF THE INVENTION The object of the invention is notably to overcome these disadvantages of the prior art. More precisely, an objective of the invention, according to at least one embodiment, is to provide a coding technique making it possible to increase the degree of diversity with respect to the state of the art in the field of MIMO transmissions, while keeping a reasonable detection complexity. 4. DISCLOSURE OF THE INVENTION The invention proposes a novel solution detailed by the claims and the following description. 5. List of Figures Other features and advantages of the invention will appear more clearly on reading the following description of a particular embodiment, given as a simple illustrative and nonlimiting example, and the accompanying drawings, among which: FIG. 1 shows error rate curves at the output of the MIMO detector for the diversity scheme 8 proposed in the case of transmission on a Rayleigh type fading channel. 6. Description of an embodiment of the invention 6.1 General Principle The abundant literature on MIMO systems provides diagrams whose degree of diversity is at most equal to nt x nr for nt transmit antennas and nr antennas. reception. The invention proposes, for the same number of transmit and receive antennas, a spatio-temporal coding scheme making it possible to reach a degree of diversity greater than nt x nr.

In the case where the transmission system has a degree of diversity of constellation n ("signal space diversity") greater than 1, it is possible, within certain constraints, to construct an extended space-time coding matrix of size) and leading to a degree of diversity equal to nx nt x nr. One of the advantages of this type of construction is the increase in diversity while maintaining a level of interference between antennas equivalent to that of a diversity MIMO system nt x nr. In the case of a 2x2 system, the invention makes it possible to construct a spatio-temporal coding matrix with 2 rows and 4 columns, making it possible to obtain a diversity system 8, while limiting the interferences between antennas in order to obtain good performance at low SNR and while keeping detection complexity reasonable. The constellation diversity, of degree n = 2, can be obtained by the application of the turned constellations technique, described in patent document WO 2009/103746, and adopted in DVB-T2. In addition to the construction of the matrix, the invention proposes a method of optimizing the parameters of the extended matrix, making it possible to guarantee good performance at low and average signal-to-noise ratios for different types of transmission channels, which makes this attractive construction when associated with a powerful error correction coding. 6.2 Description of an Embodiment A multi-antenna transmission system (MIMO) with nt transmit antennas and nr receive antennas is considered. The symbols to be transmitted are considered to come from a constellation C of size M and of dimension n. Each modulation symbol s is represented by its n components CI, C2, ..., C ,,. If the components are correlated and each carries all the information of the symbol, the degree of diversity of the constellation is equal to its dimension n. For example, in the classical case where n = 2, CI = I is the in-phase channel, C2 = Q is the quadrature channel, the diversity of 2 can be obtained through the rotation of the constellation as in DVB- T2. The coding method according to this embodiment of the invention makes it possible to construct a space-time code (ST) that takes advantage of the two types of diversity (of the MIMO system and the constellation) in order to reach a maximum degree of diversity. equal to N = nx nt x nr, while maintaining a level of interference between antennas equivalent to that of a diversity MIMO system nt x nr. Increasing the degree of diversity of a MIMO system ensures improved performance with a high signal-to-noise ratio. In a second step, the coding method provides for the use of criteria making it possible to optimize the parameters of the resulting ST code, thus also conferring on it also good performances at low and average signal-to-noise ratios. 6.2.1 Principle of construction of ST codes of diversity N = n x nt x nt. We consider N = n x nt x nr signals if, ..., sN of a constellation C with n dimensions. Each signal consists of n components c ~: = • • •, in, for i = 1 ... N. A first step consists in constructing N new signals s; -.4 from the components c ~ of the N signals s, respecting the following constraint: the set of signals transmitted at the same instant of time by all the antennas must contain at most one component of each signal if, for i = 1 ... N, of the starting constellation C. The set of signals then form a virtual constellation C 'of size Mn. A second step consists in coding the N signals thus obtained using an ST X coding matrix consisting of a set of n elementary matrices, XI ... Xn, of spatio-temporal coding nt x nr, such that: X [X1 Xn] The elements of the matrix X, obtained by linear combination of the signals s ', belong to a third constellation C ", different from this C' If the elementary code used is of maximum diversity nt x nr , the code thus constituted is of diversity N = nx nt x nr If the elementary codes are of full yield ("full-rate" in English, R = nt), the new code is also of full yield (R = nt) The yield of a space-time code R is the average number of modulation symbols transmitted per instant of time.If the code is of full yield, R = nt, to reduce the efficiency of the code, it suffices in the matrix X to force the equality between certain symbols s, in order to effectively transmit a name less than N (this may for example be useful for reducing the complexity of the detector on reception, as described in the example discussed below for n = 2). It should be noted that if there is no constraint on the evolution of the coefficients of the MIMO transmission channel over time, as is the case for example in an Alamouti code where the coefficients are assumed to remain constant over two successive transmission times, the order of the columns of X can be changed without this having any effect on the properties of the resulting ST code. 6.2.2 Casn = nt = n,. = 2 In the particular case where n = nt = nr = 2, the previously presented method makes it possible to construct a diversity ST code 8 for a 2x2 MIMO system. We consider 8 modulation symbols s, derived from a constellation of size M for which the channels in phase I and quadrature Q are correlated, that is to say that I and Q both carry the whole of the symbol information. This is the case, for example, of DVB-T2 rotated constellations, described in more detail below. The representation of such a symbol in the complex plane is given by: s, = I. + jQ, i = 1 ... 8. The first step consists of distributing the 16 I and Q components of these 8 signals in 8 signals s ~, j = 1 ... 8. To respect the constraint indicated above, the four signals s; ... s4 '• • s4 can be constituted by the combination of the components I,, Iz, I3, I4 and Q5, Q6, Q7, Qs and ss • • • s8 by the combination of the complementary components I5, I6, I ,, I8 and Q,, QZ, Q3, Q4. In a manner similar to the rotated constellation signals transmitted in the DVB-T2 system, the signals s belong to an extended virtual constellation C 'at 2 poles M nts. The second step is to transmit the 8 s signals; • • • s8 following the space-time coding matrix X defined by: as '+ bs3 X = cs' + ds4u cs '* ds4 * as' + bs 'cs6 * ds' * cs6 * cs , * + ds3 * cs6 + ds8 css * + ds, * where a, b, c, and d are the parameters of the ST code, that is, complex quantities whose modules are constrained by transmitted power considerations . Their optimization is essentially to determine their angle. It is possible to change the order of the columns of X without this having any effect on the properties of the resulting ST code. In the particular case of this matrix structure, to benefit from a detection complexity limited in reception, the following association constraint must be respected: the set of components I and Q used for the construction of s; and sz must be complementary to all the components I and Q used for the construction of ss and s6 For example, if s; = 1 + jQ5 and sz = 12 + jQ6, the signals ss and s6 must be constructed on the basis of 15, 16, Q, and Qz, for example ss = 15 + jQ2 and s6 = 16 + jQ, (the other combinations are also possible). The same constraint applies for the construction of s3 and s4 on the one hand and s; and s8 on the other hand. This constraint being respected, it can be shown that, for a full performance code (R = 2), the detection complexity of the 8 symbols is proportional to M4, a complexity equivalent to that of a 2x2 Golden code for the detection of 4 symbols. For lower yields, the detection complexity is reduced. For a yield code R = 7/4, for example if s3 = s4 and s; ~ s8 (or vice versa), the complexity is proportional to M3. For a yield code R = 3/2, for example if s3 = s4 and s; = s8, the complexity is proportional to M2. For a yield code R = 5/4, for example if s3 = s4 = s; = s8, the complexity is proportional to M. 6.2.3 Principle of the constellations turned on the emission, this technique consists in replacing the traditional modulator by a modulator whose constellation of points has undergone a rotation of an angle a and, d on the other hand, to introduce an interlace between the I and Q channels before carrying out the transmission so that the two components I and Q of the same constellation symbol are not transmitted on the same OFDM sub-carrier. In practice, the interleaving may be a simple shift or delay of one or more symbol times between channels I and Q. The value of the angle of rotation a depends on the constellation considered. This has been determined for each digital modulation according to distance criteria which allow to improve the system performances for transmissions on classical models of fading channels (Rayleigh channel) but also on fading channels presenting events. erasures. 6.2.4 Optimization of the Resultant ST Code Parameters Conventionally, the parameters of the ST codes are optimized to minimize the probability of error at the output of the optimal detector with a very high signal-to-noise ratio (probability of asymptotic error), which amounts to maximize the diversity gain and coding gain of the ST code. The corresponding criteria are called "rank criterion" and "determinant criterion". These two criteria lead to obtaining a range of acceptable parameter values. However, these criteria do not guarantee the minimization of the probability of error for low and medium signal-to-noise ratios (SNR).

The invention makes it possible to supplement the known criteria of rank and of the determinant by distance criteria that make it possible to minimize the probability of error at low and medium SNRs. These criteria apply to the virtual constellation C "formed by the different elements of the matrix X. They are based on the determination of the one-dimensional distances dlD of the virtual constellation C". To do this, we project this constellation on one of its n dimensions and measure the distances between neighbors on the projected axis. The criterion applied depends on the transmission channel considered: • for a transmission channel having a high erasure rate, the set of parameters that maximizes the minimum value of the distances d1D between two neighbors is retained; • For a fading transmission channel with little or no erasure, we look for the sets of parameters for which the distribution of distances dlD is closest to a Gaussian distribution. It is indeed known in the field of numerical modulations that constellations whose distribution of points follows a Gaussian distribution have better performances than constellations with uniform distribution. The corresponding gain is called shaping gain ("shaping gain"). This optimization criterion is therefore a constellation shaping criterion. A pragmatic method of applying this criterion is to search for the sets of parameters leading to the greatest possible differences between the minimum value and the maximum value of dlD and to retain those for which the distribution of the distances is closest to a maximum. Gaussian distribution. We now present an example of optimization of the parameters in the case n = nt = n ,, = 2. The parameters a and c are taken equal to 1 /, 17 to simplify the detector (this constraint is in fact not limiting and avoid complex division in the receiver). For the determination of the parameters b and d, the criteria of rank and determinant are used: • application of the rank and determinant criteria to the extended code to determine a first range of allowable values for b and d. For instance, in the case of a QPSK type constellation C: = 1/2 angle (b) E [57.3 °, 214.86 °] and d = e '2b; • application of a criterion of the minimization / maximization of the unidimensional distance to the parameters belonging to the interval determined using the preceding criterion. The results obtained depend on the channel:

^ erase channel: the values of b and d lead to the maximization of the minimum value of the distance dlD in the case of a constellation C of type: o QPSK: Ibi =, angle (b) = 118 ° andd = e b, 1/2 o 16-QAM: Ib 1 = angle (b) = 67 ° or angle (b) = 168.25 ° and d = e 2b;

fade channel: The first step is to look for a range of angles that corresponds to small values of the 1D distance between neighbors. The second step is to look for a range of angles that corresponds to strong values of the 1D distance between neighbors. The intersection of these two ranges of angles leads to lb '=, angle (b) E [114.6 °, 154.7 °] and d = e 2 b, that the starting constellation C is of type QPSK or 16-QAM. All of these angles are permissible for the proposed ST code. In this interval, a particular value of b and d allows both to lead to the extreme values of the distance 1D, it is: Ibi =, angle (b) = 135 ° and d = e '2b. This angle is the same in the case of a constellation C of type QPSK or 16-QAM. This characteristic is also verified for all QAM modulations. In a third step, the analysis of the 1D distance distribution for these parameter values confirm a distribution close to a Gaussian distribution.

Compromised for the two types of channels: it turns out that the optimal angle for the fading channels has a minimum distance of 1D low and that the corresponding detector does not show good performance on the channels with a high rate of erasures . In the case where the presence or absence of erasures is not known, it is preferable to adopt a compromise angle: the values of b corresponding to the highest values of dlD are identified and the one with the larger gap with the maximum value of d1D. 136.25 ° d 3 zb o QPSK: Ibi =, angle (b) = and = e, 16-QAM = 131.25 ° = 138.5 °: Ibi = o d = e 2b. , angle (b) or angle (b) and It should be noted that the values of the parameters obtained a, b, c, and d are independent of the efficiency of the space-time code R.

6.3 Results Figure 1 shows error rate curves at the output of the MIMO detector for the diversity scheme 8 proposed in the case of transmission on a Rayleigh fading channel. The curves were plotted with the following parameter values: a = c = 1, Ibi = 1, angle (b) = 135 ° and d = e 3 2 b. , E -NE

For the full yield code, the scheme proposed according to the invention is better in performance than the Golden code 2x2, whatever the SNR considered. For example, this gain is greater than 1 dB at an SNR of 0 dB and several dBs at high SNR. It should be noted that the error rate curves are nevertheless crossed when compared with a low spatial diversity multiplexing system, but this crossover occurs at much lower SNR values than with the Golden Code.

On the other hand, when we consider the lower yields, in particular R = 3/2, the scheme proposed by the invention represents the best compromise between performance / spectral efficiency / complexity.

Claims (8)

REVENDICATIONS1. A method of transmitting a signal representative of a source signal, intended to be transmitted via a transmission channel, in a multi-antenna system with nt transmitting antennas and nr receiving antennas, characterized in that it comprises the following steps: - spatio-temporal coding by application, to said source signal, of an extended X space-time coding matrix of size nt x (n nr), n being an integer greater than or equal to 2, delivering an encoded signal; transmission of said coded signal. 2. Transmission method according to claim 1, characterized in that said coding matrix X consists of a set of n elementary spatio-temporal coding matrices and in that said method comprises, prior to said coding step, a step of rotating the modulation constellation C of said source signal. 3. Method for transmitting a signal representative of a source signal, intended to be transmitted via a transmission channel, in a multi-antenna system with nt transmitting antennas and nr receiving antennas, characterized in that nt = nr = 2 and in that said method comprises the following steps: spatio-temporal coding by application, to said source signal, of an extended X space-time coding matrix of size nt x (n nr), n being equal to 2, delivering a coded signal, said matrix X being such that as; + bs3 û cs' * û ds' * as' + bs' X cs' + ds' csi * + ds' * cs' + ds' 2 4 6 8s6 with si, j = 1 ... 8 - ds8 css * + ds7 * belonging to a rotated virtual modulation constellation C 'and a, b, c and d parameters of said spatio-temporal coding; transmission of said coded signal. 4. Transmission method according to claim 3, characterized in that said parameter of said spatio-temporal coding are such that: 1 - a = c = 1 / f and PI =, angle (b) = 118 ° and d = e 2 b, when the modulation is of the QPSK type and said transmission channel is of the erase type; 1 -A - a = c = 1 / and =, angle (b) = 136.25 ° and d = e 2b, when the modulation is of QPSK type and said transmission channel is of fading type with variable rates of erasures; a = c = 1 / and =, angle (b) = 67 ° or angle (b) = 168.25 ° and d = the modulation is of 16-QAM type and said transmission channel is of erase type; a = c = 1 / and =, angle (b) = 131.25 ° or angle (b) = 138.5 ° and d = when the modulation is of 16-QAM type and said transmission channel is of fading type with rates erasure variables; - a = c = 1 / 1E and lb '=, angle (b) = 135 ° and d = e 3b, when said 1/2 transmission channel is of fading type. 5. Signal representative of a source signal to be transmitted according to the transmission method of claims 1 to 4. 6. 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 the implementation of the transmission method according to at least one of claims 1 to 4. 7. Apparatus for transmitting a signal representative of a source signal, intended to be transmitted via a transmission channel, in a multi-antenna system with nt transmitting antennas and nr receiving antennas, characterized in that it comprises: spatio-temporal coding means by applying, to said source signal, an extended space-time coding matrix X of size nt x (n nr), n being an integer greater than or equal to 2, delivering a coded signal; means for transmitting said coded signal. 10. Method for receiving a signal according to claim 5. 11. 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 the reception method according to the claim 8. .yr 2b, when