FR2759519A1 - DIGITAL SIGNAL TRANSMISSION METHOD, TRANSMITTER AND RECEIVER THEREFOR - Google Patents

Abstract

The invention concerns a method for transmitting a digital signal in the form of blocks, each block comprising at least one bit and corresponding to a symbol to be transmitted, the transmission of each symbol consisting in transmitting at least a frequency constituting a component unequivocally corresponding to this block, the components of different symbols being mutually correlated.

Description

 Method of transmitting digital signals, corresponding transmitter and receiver

 The field of the invention is that of the transmission of digital signals. More specifically, the present invention relates to a method for transmitting digital signals in which the transmission of each block of signals to be transmitted to the attention of a receiver consists of transmitting to this receiver one or more given frequencies characteristic of the data included in this receiver. block.

 The invention also relates to a transmitter and a receiver of such signals and finds a very particular application to the transmission of non-coherent modulation signals in channels having a high dispersion.

In a transmission system where modulation in M-FSK mode (M
Ary Frequency Shift Keying) is used, the digital data to be transmitted (bits) are grouped in blocks, each block comprising a number n of bits, with
M = 2n The transmission of these blocks consists in assigning to each block a given frequency chosen from M and transmitting this frequency to the receiver.

For example, for M = 8, each block comprises 3 bits and each of the blocks that can be transmitted corresponds to one and only one frequency of all the M frequencies. This defines a unique relationship between blocks and frequencies. The transmission takes place at a symbolic period Ts, also called symbol time.

 Figure 1 shows the spectrum of a BFSK signal (n = 1). The amplitude is denoted by A and the frequency f. The central frequencies of the transmitted signals are denoted fg and f1. Each channel has a certain bandwidth due to the time truncation performed for the transmission of each of the frequencies. The difference f1 -f0 is equal to liTs, that is to say that the frequencies fg and f1 are orthogonal (absence of correlation). This ensures that the channels do not overlap and that there is no interference between these channels (crosstalk).

In general, this orthogonality is also respected between the M frequencies of an M-FSK type modulation.

 The disadvantage of this known solution is that the spectral efficiency (ratio of the transmitted bit rate to the total occupied bandwidth) is limited.

More specifically, the maximum rate that can be transmitted is limited to a given value depending on the total allocated bandwidth. An increase in the flow rate results in a limitation of Ts and therefore necessarily in a greater spacing between the frequencies fg and f1.

 The present invention particularly aims to overcome this disadvantage.

 More specifically, one of the objectives of the invention is to provide a method for transmitting digital signals having an improved spectral efficiency compared to the state of the art mentioned above.

 Another object of the invention is to provide a transmitter and a digital signal receiver implementing this method.

 These objectives, as well as others that will appear later, are achieved by a method of transmitting a digital signal in the form of blocks, each of the blocks comprising at least one bit and corresponding to a symbol to be transmitted, transmitting each of the symbols of transmitting at least one frequency constituting a component uniquely corresponding to that block, the different symbol components being correlated with each other.

 There is therefore a non-zero correlation between the components of the transmitted symbols. Bringing together the possible frequencies makes it possible to significantly increase the spectral efficiency.

 Preferably, the method consists in transmitting, for each of the symbols, a number N of components, the components of different symbols being correlated with each other.

 These components can be transmitted by time division and / or frequency diversity.

 The invention also relates to a transmitter of a digital signal in the form of blocks, each of the blocks comprising at least one bit and corresponding to a symbol to be transmitted, the transmitter comprising means uniquely affecting each of the symbols. least one frequency constituting a component of the symbol, the components assigned to different symbols being correlated with each other.

avec Q le nombre de valeurs différentes des composantes, le récepteur comprenant des moyens de calcul maximisant la variable de décision suivante

en se basant, dans le calcul de la variable de vraisemblance relative à un symbole donné, sur les seules sorties des filtres adaptés centrés sur les fréquences où une des composantes serait émise.The invention also relates to a receiver of a digital signal transmitted by such a transmitter, characterized in that it comprises a set of adapted filters each centered on one of the components, the samples of the output signals of these filters constituting the components of a vector Z given by:

with Q the number of different values of the components, the receiver comprising calculation means maximizing the following decision variable

based, in the calculation of the likelihood variable relative to a given symbol, on the only outputs of the adapted filters centered on the frequencies where one of the components would be emitted.

Other features and advantages of the invention will appear on reading the following description of a preferred embodiment, given by way of illustration and not limitation, and the accompanying drawings in which - Figure 1 shows the spectrum of a BFSK signal of the known art - Figure 2 shows the time-frequency distribution of the transmitted frequencies
in the invention, the example being taken for Q = 8 - Figure 3 shows the probability of pair error on the Rayleigh channel of
component signals correlated with the signal-to-noise ratio, for
N = 4; FIG. 4 shows the probability of error on the Rayleigh channel of signals to
components correlated according to the signal-to-noise ratio, for N = 4 - Figure 5 shows the probability of error on the Rayleigh channel of signals to
components correlated according to the signal-to-noise ratio, for N = 8 - Figure 6 is a block diagram of an example of a signal transmitter
numerals implementing the method according to the invention, - Figure 7 is a block diagram of an example of a signal receiver
numbers transmitted by the transmitter of Figure 6.

 Figure 1 has been described above with reference to the state of the art.

 The present invention is based on the fact that the Q frequencies that can be transmitted by component have a correlation between them, that is to say that the spacing between these frequencies is less than 1 / Ts. There is therefore a non-zero correlation between the components of the transmitted symbols. The fact of bringing the transmitted frequencies together makes it possible to significantly increase the spectral efficiency.

 FIG. 2 shows the time-frequency distribution of the frequencies transmitted in the invention, the example being taken for Q = 8. The time axis t is subdivided into elementary time boxes of duration Ts and the frequency axis f into 8 channels. spaced two by two from 1 / 4Ts. These frequencies are therefore spaced far less than the distance 1 / Ts guaranteeing the orthogonality. The total band occupied is equal to W = 2ils, identical to that of a conventional BFSK modulation (FIG.

 We will first consider single-dimensional signals, ie the transmission of a symbol occupies only one time slot Ts.

In a given box, at each symbol time Ts, a single frequency is transmitted.

Providing more than two frequencies in the bandwidth W increases the elemental spectral efficiency of the time-frequency plane thus cut. It can be seen that it is possible to transmit 8 different symbols by associating a symbol with a frequency. The number of bits per symbol is 3. This results in a spectral efficiency of 1.5 bitis / Hz. Comparing this example to the case of a BFSK which uses only two frequencies in the same elementary band W, it is found that the gain in spectral efficiency is of a factor 3. In other words, 3 times more bits can be transmitted in the same frequency band.

 The increase in spectral efficiency is accompanied by a minimal degradation of performance due to the nonzero correlation between the different frequencies in an elementary box. However, this degradation is compensated for when high spectral efficiency alphabets are used (multidimensional signals), as described below.

The signals we consider in the following will always use one frequency and only one at a time per time-frequency box. Emitted symbols all have the same energy. A symbol consisting of N components therefore has the following structure

The receiver which will be described later has a filter adapted for each of the possible frequencies. The outputs of the energy detectors of this receiver constitute the vector Z with

Assuming that there is no correlation between the components in the adjacent time-frequency boxes (non-memory transmission channel), the joint probability density of the components of the vector Z is written (relation 1)

The optimal receiver according to the criterion of the maximum at posteriori is the one that chooses the symbol Sj maximizing this joint probability density. It is easily shown that the maximization of the expression of the relation 1 amounts to maximizing the expression

In other words, it is sufficient to base, in the calculation of the likelihood variable relative to a given symbol Sj, only the outputs of the adapted filters connected to the frequencies where a logic state 1 would be transmitted. From this point on, it can be shown that the function of the optimal receiver is to maximize the scalar product (Z, Sj) This maximization consists in calculating the decision variables Aj given by:

 In order to quantify the gain provided by the invention, it is relevant to perform a pairwise error probability calculation in the event of the emission of a symbol S1.

The probability of a bad detection is to decide that the received symbol is S2 # S1. This probability is none other than the probability P (A1 <A2), or also (relation 2):

 In the preceding expression the index ik is omitted and the indices '1' or '2' refer to the symbols S1 and S2 respectively.

By transforming the previous expression into a probability of a quadratic Hermitian form, we can define the vector p as follows
P = (T1,1, T2,1, T1,2, T2,2, ..., T1, N, T2, N)
The expression of relation 2 therefore implies
P (S1 S2) = P (f = ptFpg <O) where f = ptFp * is the hermitian form sought with

We know that the characteristic function of such a hermitian form is (relation 3):
= det (I - 1j2R * F) where R = 1E [# t # *] denotes the correlation matrix of the vector p.

avec Afr = fî ,k - f2,k la différence entre les fréquences des deux composantes et = = ,k - é2,k un déphasage tenant compte de l'incohérence des oscillateurs utilisés pour chaque fréquence au récepteur. Nous supposons dans la suite que les corrélations sont toutes différentes.2
The variables rk are none other than the samples at the outputs of the adapted filters. With the symbol S1 being issued, these variables are given by
Tl, k = hk + bl, k
r2, k = pkhk + b2, where k denotes the correlation existing between the two components of order k of the two symbols. If we use rectangular filters of duration Ts, this correlation is expressed as (relation 4):

with Afr = f1, k - f2, k the difference between the frequencies of the two components and = =, k - é2, k a phase shift taking into account the inconsistency of the oscillators used for each frequency at the receiver. We assume in the following that the correlations are all different.

The random variables r1 k follow Gaussian laws centered on variances (relation 5):

For their part, the random variables r2, k also follow Gaussian laws centered but of variances (relation 6):

II résulte de ce qui précède que r1,k et r2,k sont corrélés tel que (relation 8):

On the other hand, it is important to note that noise samples bl, k and b2, k are also correlated. We have indeed (relation 7):

It follows from the above that r1, k and r2, k are correlated such that (relation 8):

où Rk est une matrice 2 x 2 donnée par

Noting that the random variables for two distinct components have zero correlations, the expressions in relations 5 to 8 make it possible to write the correlation matrix of the vector p as

where Rk is a 2 x 2 matrix given by

In these conditions the expression of the characteristic function of the relation 3 becomes

A direct calculation of det (l - j2sRkFk) gives
det (I - j2 # Rk * Fk) = (1 - j2 # uk) (1 + j2 (tk) with:

le rapport signal sur bruit par symbole. In previous expressions we defined

the signal to noise ratio per symbol.

The characteristic function of f is now written

en considérant que ui j pour i W j.By performing a decomposition into simple elements of kJlf (j4), we obtain

considering that ui j for i W j.

The probability of error is equal or even

où r est défini par:
F
&gamma; + 2N
Une expression plus simple de cette probabilité d'erreur, ainsi qu'une expression asymptotique pour les grands rapports signal sur bruit, sont les suivantes

et (relation 9):

where r is defined by:
F
&gamma; + 2N
A simpler expression of this probability of error, as well as an asymptotic expression for large signal-to-noise ratios, are as follows

and (relation 9):

The asymptotic expression of the pair error probability shows that if
| k | is equal to | | whatever k, the degradation of the signal-to-noise ratio per symbol y will be the same whatever the dimension N of the symbols.

For the particular case N = 1, the result is the expression of the error probability of two correlated binary symbols on a Rayleigh channel given by

On the other hand, if all the correlations between the components are identical (k = V k), we know how to compute the probability of error per pair equal to (relation 10):

FIG. 3 shows the probability of error per pair P (S1 -> S2) on the channel of
Rayleigh of component signals correlated as a function of the signal-to-noise ratio y expressed in dB, for a dimension N = 4.

The chosen values of the correlation I p | 2 = 0, I 2 = 0.09, 1 p | 2 = 0.4 and 1 p 1 2 = 0.8 respectively correspond to frequencies spaced apart from 1 / Ts (state of the art, reference 30), 1 / 4Ts (reference 31), 1 / 2Ts (reference 32), and 3 / 4Ts (reference 33). The asymptotic degradation of the performances is in agreement with the expression of the relation 8, which provides for a reduction of the signal-to-noise ratio by a factor 1 - I p | 2
The gain in spectral efficiency obtained using correlated component signals can be illustrated by the following example
Considering first a two-signal alphabet (BFSK) with a diversity of order N = 4, the two symbols of this alphabet are
s1 = (1, 0, 1, 0, 1, 0, 1, 0)
S2 = (0.1, 0.1, 0.1, 0.1)
The performances of this two-symbol alphabet are obtained by using the relation 10 with N = 4 and u = 0. The spectral efficiency is 1/8 bit / s / Hz (the spectral expansion factor with respect to 1 bit / s / Hz is Be = 8). This corresponds to the state of the art.

The invention proposes for its part also to use a diversity of order
N = 4 with correlated component signals, for Q = 8. By numbering the available frequencies in a time-frequency box from 1 to 8, the M = 8 possible symbols are given below by their frequency numbers used in the different components.

 By way of example, the transmission of the symbol S1 consists in transmitting the frequencies 1, 2, 1 and 2 successively (time distribution) or simultaneously (frequency distribution in the total band K * W). A combination of time and frequency transmission is also possible.

The total band K * W necessary for the emission of a symbol remains identical to that of the BFSK (NQ / 4Ts = 8 / Ts) but we now have in this band of
M = 8 symbols and the spectral efficiency goes to 3/8 bit / s / Hz (Be = 2.66).

By way of comparison, conventional BFSK modulation occupies a bandwidth of 2 / Ts. When the transmitted components are no longer spaced apart
Ts / 4, the band gain is a factor of 3 for the transmission of the same bit rate. It is therefore possible, by occupying the same band as that of the conventional BFSK, to provide a total of 4 sub-bands for the transmission of the components. The transmission can therefore operate in frequency diversity.

 It can be seen that any pair of symbols has all four different frequencies. Thus, the diversity of order 4 is obtained. On the other hand, by examining the 8 proposed symbols we deduce that the most correlated symbols (S4 and S7 for example) have two components for which the frequencies are adjacent (at 1 / 4Ts ), a third component with frequencies spaced by 1 / 2Ts and a last one with a spacing of 3/4 Ts. The resulting correlations are I p1 1 2 = 2 12 = 0.8, | p3 | 2 = 0.4 and | 4 | 2 = 0.09 (it is assumed that the filters used are rectangular, and therefore that the correlations are given by the relation 4).

The performance of the correlated component system is increased by the terminal of the union. It indicates that the symbol error probability is less than M-1 times the highest pair error probability. In other words Pe <(M-1) P (S4 or S7)
On the other hand, a lower bound is obtained by noting that the probability of error is greater than the probability of pairwise error of the two most distant symbols (ie the least correlated) but which are the closest neighbors of each other. The two symbols S1 and S2 fulfill this condition. So we have
Pe> P (S1 o S2)
The different error probabilities per pair are obtained using the previously given relation P (S1 o S2). Finally, the probability of a binary error is approximated by Pb = Pe / 2.

 The performance of the two systems is compared in Figure 4 which shows the probability of error on the Rayleigh channel of component-correlated signals as a function of the signal-to-noise ratio expressed in dB, for N = 4. to that of a classical BFSK system (n = 1) for Be = 8 and those in broken lines at the lower and upper bounds mentioned above.

 We note the very good performance of the correlated signals whose location of the lower and upper bounds shows exact performance at least equal to that of the conventional system taken as a reference. Knowing that correlated component symbols bring a gain in spectral efficiency by a factor of 3, it is deduced that they are preferable to conventional FSK signals.

 The same remark can be made for a diversity of order 8 (see Fig.5).

Si N = 1, une corrélation | 2 = 0,95 sur la composante unique du symbole implique une dégradation de -13 dB du rapport signal sur bruit. Par contre pour N = 8, la contribution à la dégradation totale d'une composante k ayant la même corrélation 2 1 2 = 0,95 se réduit à -1,6 dB, alors qu'elle n'est plus que de -0,4 dB pour N = 32. Increasing the N dimension makes it easier to absorb more and more correlated components. Indeed, the degradation of the signal-to-noise ratio is given by the factor

If N = 1, a correlation | 2 = 0.95 on the single component of the symbol implies a degradation of -13 dB of the signal-to-noise ratio. On the other hand, for N = 8, the contribution to the total degradation of a component k having the same correlation 2 1 2 = 0.95 is reduced to -1.6 dB, whereas it is only -0 , 4 dB for N = 32.

When we know that this value of the correlation corresponds to frequencies spaced by i / 8Ts, we understand well the constructive effect of large dimensions combined with the highest densities of emission frequencies.

 The performances obtained can be further improved by using an optimal diversity alphabet in terms of distance between the components and spectral occupancy.

 FIG. 6 is a block diagram of an example of a digital signal transmitter embodying the method according to the invention.

 The transmitter of FIG. 6 comprises a mapping unit 60 ensuring the blocking of a bit stream applied to it. The blocks each contain n bits. These blocks are applied to a transformation unit 61 which provides for each of the blocks treated N voltage levels. Each voltage level corresponds to a component of a block. These voltage levels are then applied to an interleaving unit 62 followed by a voltage controlled oscillator (VCO) 63 having on its output the interleaved frequencies corresponding to the components of the blocks to be transmitted. These frequencies are in series with an optional serial-parallel converter 64, provided in the case where the transmission was to be carried out in several subbands. This subband concept is shown in FIG. 2 where two subbands SB1 and SB2 are provided. The transmission of the components in sub-bands makes it possible to transmit simultaneously (in the same time interval Ts) several components (frequency diversity).

 The different components are then applied to a set of K mixers 651 to 65K, with K the number of sub-bands provided. Mixers 651 to 65K provide the subband distribution of the transmitted components. The frequency shifted components are then summed by an adder 66. A mixer 67 receiving a signal from a local oscillator 68 transposes the sum signal to a carrier frequency. The modulated signal is then applied to a transmitting antenna 69.

 The purpose of interleaving unit 62 is to combat selective fading of the transmission channel. Thus, the transmission channel acts independently on the different components.

 If the transmission is done by time distribution only, the different components of the symbols to be transmitted are transmitted in different time / frequency boxes and the transmission of a 4-component symbol (example given above) lasts 4Ts.

 Of course, the embodiment of this transmitter is given for information only, and many other possibilities exist.

 FIG. 7 is a block diagram of an example of a receiver of digital signals transmitted by the transmitter of FIG. 6.

The signal received by an antenna 70 is applied to a mixer 71 receiving a frequency transposition signal from a local oscillator 72. The output signal of the mixer is applied to K subband filters 731 to 73K These filters are filters bandpass centered on the central frequencies of the subbands. The filtered signals are then applied to a set of matched filters 741 to 74K * Qt with Q the number of components provided per subband. The frequencies f1 to fQ correspond to the components and the frequencies F1 to FK to the central frequencies of the subbands. The output signals of these filters are sampled at the symbol frequency 1 / Ts to provide samples Zi, j, with i the index corresponding to the subband considered and j the index corresponding to the detected component. These samples are applied to a calculation unit 75 intended to form the vector Z given previously

It will be noted in this expression of the vector Z that the number of components
N of the transmitted symbols is not necessarily equal to K. This is due to the fact that a temporal transmission of the components can be combined with a frequency diversity, in the subband sense.

 The calculation unit 75 preferably operates according to the prior a priori criterion given above, that is, it considers that the transmitted block is the one that maximizes the joint probability density of the components of this vector Z.

The calculation unit 75 thus provides an estimate S equal to the symbol Sj which maximizes Aj given by:

 The estimate S is then applied to a demapping unit 76 transforming the estimated symbol into bits.

 The invention therefore makes it possible to use correlated components and therefore a greater usable frequency density. As a result, there is greater spectral efficiency.

 The performances obtained with the correlated signals are good and make it possible to obtain in the given example a gain in spectral efficiency by a factor of 3 compared with a conventional system occupying the same band and using the same order of diversity. The performance in binary error probability remains comparable, if not better, than that of the known M-FSK systems.

 The invention applies in particular to non-coherent modulation. The transmission medium used is any.

Claims (6)

A method of transmitting a digital signal in the form of blocks, each of said blocks comprising at least one bit and corresponding to a symbol to be transmitted, the transmission of each of said symbols of transmitting at least one frequency constituting a corresponding component. unequivocally to this block, characterized in that the components of different symbols are correlated with each other. 2. Method according to claim 1, characterized in that it consists in transmitting, for each of said symbols, a number N of components, the components of different symbols being correlated with each other. 3. Method according to claim 2, characterized in that said components are transmitted by time division. 4. Method according to one of claims 2 and 3, characterized in that said components are transmitted by frequency diversity. 5. Emitter of a digital signal in the form of blocks, each of said blocks comprising at least one bit and corresponding to a symbol to be transmitted, said transmitter comprising means (61, 63) uniquely affecting each of said symbols at the least one frequency constituting a component of said symbol, characterized in that the components assigned to different symbols are correlated with each other. 6. Receiver of a digital signal transmitted by a transmitter according to claim 5, characterized in that it comprises a set of adapted filters (741 to 74K * Q) each centered on one of said components, the samples of the signals of output of said filters constituting the components of a vector Z given by:

 with Q the number of different values of said components, said receiver comprising calculation means (75) maximizing the following decision variable

 based, in calculating the likelihood variable relative to a given symbol, on the outputs of said matched filters (741 to 74K * Q) centered on the frequencies where one of said components would be transmitted.