FR2767433A1 - METHOD FOR TRANSMITTING SIGNALS WITH MULTIPLE CARRIERS WITH ADJUSTMENT OF CORRECTIVE COEFFICIENTS IN THE TIME DOMAIN - Google Patents

Abstract

Multi-carrier transmission method in which: a) the parasitic spectral power density of noise influences and the parasitic spectral power density which is formed by exceeding the guard interval by the channel impulse response are combined, b ) the leakage effect of the DFT is taken into account for the common parasitic spectral power density, etc.) the channel capacity is optimized.

Description

MULTI-CARRIER SIGNAL TRANSMISSION METHOD

  WITH ADJUSTMENT OF CORRECTIVE COEFFICIENTS

IN THE TEMPORAL AREA

  The invention relates to a multi-carrier transmission method with adjustment of the corrector coefficients in the time domain in order to reduce the

impulse response of the channel.

  In the field of digital signal processing, systems are known which allow transmission of digital information with a high bit rate. A technique which has become more and more important is the multicarrier transmission which is also called "Discrete Multitone (DMT)" or "Orthogonal Frequency Division Multiplex (OFMD)". During multi-carrier transmission, the data stream to be transmitted is broken down into many parallel partial currents which are transmitted independently

  each other in frequency multiplexing.

  Practically, the generation of the signals is carried out by means of an IFFT (Inverse Fast Fourier Transform), the components of the vector in the field DFT (Discrete Fourier Transform) being occupied by points of

  signals from a QAM (Quadrature Amplitude Modulation).

  The IFFT forms a signal with a block structure in the time domain. To avoid interference between

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  blocks, a cyclic prefix is used during DMT or OFDM transmission, which is called the guard interval. The end of the frame is then placed temporally at the head of the block in a cyclic manner. The convolution with the impulse response of the channel then appears as a cyclic convolution which can be described in the DFT domain by a simple multiplication by complex coefficients. This characteristic simplifies the correction which can now be carried out in the DFT field and then corresponds to a simple AGC

  (Automatic Gain Control) for each carrier.

  However, this assumes that the channel impulse response is shorter than the chosen guard interval. On the one hand, this condition can be guaranteed by choosing a guard interval of appropriate length, which is done in the radio domain for OFDM transmission (for example DAB, Digital Audio Broadcasting). On the other hand, one can also reduce the impulse response to the length of the guard interval by means of a prior correction in the time domain. This solution leads to a more efficient exploitation of the transmission channel but supposes that the channel varies so slowly that an adaptation and a

  adjustment of the correction coefficients are possible.

  When using cables, prior correction in the time domain is the usual procedure. When adjusting the corrector coefficients, attention should be paid not only to the brevity of the resulting overall impulse response of the channel and the corrector, but also, as another criterion, to the resulting signal / noise ratio. In "Optimum Finite-Length Equalization for Multicarrier Transceivers", published in IEEE Transactions on Communications, vol. 44, No. 1, January 1996, N. Al-Dhahir and J.M. Cioffi describe this state of affairs more precisely. They show that, to adjust the coefficients to the optimum, we must maximize the following expression:

N N

  bDMT = bi = log2 (l + SNRi), G1 i = l i = l

  o bDMT designates the sum of the partial capacities bi.

  This roughly means that the geometric mean of the individual signal-to-noise ratios of the

  carriers (SNRi) must be maximized.

  O10 The simplest adjustment method, but which includes only the length of the resulting impulse response, would be the approximation of the transmission channel by a fractional regular expression A (z) / B (z) o A (z) must be at most equal to the length of the guard interval. A transversal filter with the transfer function B (z) can then serve as a corrector in the time domain. Theoretically, there remains only A (z) as a global transfer function. The SNRi signal / noise ratio is not taken into account at all and the correction is therefore generally not optimal. All the adjustment algorithms based on this principle mutually adapt a time domain corrector W (z) and an equivalent system E (z). Here too, the SNRi signal-to-noise ratio is not directly taken into account, even if the results are often quite interesting. Two criteria are considered mutually: the identity between the equivalent system E (z) and the series circuit composed of the channel and of the corrector W (z) (minimization of the mean square error) and the restriction of the length of the impulse response overall. Naturally, we also generally base ourselves on a restriction of the length for the corrector W (z) in

  prescribing a maximum number of coefficients.

  We mention here two publications representative of the described procedure: M. van Bladel, M. Moeneclaey: "Time-domain Equalization for Multicarrier Communication", published in Proc. Communication Theory Mini-Conference (Globecom 1995), Singapore, November 13 to 17, 1995, pages 167 to 171 and B. Farhang- Boroujeny: "Channel Memory Truncation for Maximum Likelihood Sequence Estimation", also published in Proc. Communication Theory Mini-Conference (Globecom 1995), Singapore, November 13 to 17, 1995, pages 172 to 176. In the aforementioned publication by N. Al-Dhahir and O10 JM Cioffi, this provision is unnecessarily reused in the practical implementation of equalizer corrector. However, in all of these processes, the

  overall stray power is not taken into account.

  The invention therefore relates to a method of transmitting signals with multiple carriers which allows optimal equalization with a maximum processing speed. This problem is solved by a method of the type mentioned in the introduction and in which: a) the parasitic spectral power density of noise influences and the parasitic spectral power density which is formed by exceeding the interval are combined by addition guard by the channel impulse response after correction in the time domain to give a common parasitic spectral power density, b) the leakage effect of the DFT is taken into account for the common parasitic spectral power density, and c) optimizes the channel capacity R = l1og2 (l + SNRi), U being the set of carrier positions of ieU for which the optimization must be carried out.

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  In the method according to the invention, an equalization is carried out limited to the optimization of a single criterion which has already been given in the expression Gl mentioned above. In fact, the geometric mean of the signal / noise ratio is maximized. In doing so, however, we include the global parasitic power which can as well come from parasites as result from exceeding the guard interval (interference between blocks) by a global impulse response too

long.

  The densities of parasitic spectral powers, which come from influences of noise, for example from crosstalk parasites, are therefore grouped together with those which are formed when the guard interval is exceeded by the channel impulse response after the correction in the domain. temporal to give a

  common parasitic spectral power density.

  We thus find a common optimum, which means that the overall impulse response is not necessarily limited to the length of the guard interval. Another important aspect of the method according to the invention is that the leakage effect of the DFT is taken into account. During the transformation in the DFT domain, which is part of the DMT receiver, a rectangular signal window is used for the sampling of the time signal. This has no

  importance for the useful signal component because this

  ci has a cyclic prefix. This is not the case, however, for noise signals and also for signal components which exceed the guard interval. For these signals, there is no cyclic prefix and the influence of rectangular windowing must be taken into account for the

  calculation of the signal / noise ratio for each carrier.

  The method according to the invention therefore offers advantages by limiting it to a single criterion

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  optimization and by correct calculation of the ratio

  signal / noise including leakage effect.

  Another advantage is that the range of the transmission is increased. Furthermore, regular convergence is also advantageous, that is to say that there appears less variation in the results for

different lengths.

  Preferably: a) the leakage effect is taken into account by multiplying the autocorrelated element (inverse transform of the noise power density function) by a triangular function in the time domain, and b) the position of the detection frame on the reception side by determining the maximum energy within a domain of length equal to the length of the guard interval plus one, the detection frame whose position is characterized by the content

  maximum energy, starting after this domain.

  Other characteristics and advantages of the invention will emerge more clearly on reading

  the description below, made with reference to the figures

  appended, in which: FIG. 1 is the diagram of a usual transmission system, FIG. 2 represents examples of four impulse responses of channels, deduced from the closest sampled values, FIG. 3 is the flow diagram of the method according to the invention, FIG. 4 represents the signal / noise ratio for the different carrier positions and FIG. 5 represents the normalized impulse response as a function of the sampled values. A usual way of proceeding is to consider an equivalent system which has the desired impulse response length. Figure 1 shows the basic diagram. In this diagram, nk 2 characterizes the sampled values of a parasitic noise and ek 6 the sampled values of the error between the output of the real O10 system and the equivalent system E (z) 5, zA 4 is used to model a dead time . H (z) represents the function of

  channel 1 transfer and W (z) corrector 3.

  In the method according to the invention, it is possible to dispense with the equivalent system 5 because the optimization of the system is effected by the adjustment of a single criterion of the corrector 3. The steps to be repeated by iteration according to the method according to the invention are described below. Figure 3 shows the corresponding steps in the form

organization chart.

  NTr is the maximum number of carriers. If a baseband signal is assumed in which the two halves of the DFT frame can be occupied by complex conjugate elements, then the DFT length is NDFT = 2 NTr. The method according to the invention however uses oversampling in the frequency domain, which means that the length DFT actually

used is NDFT2 = 4 NTr.

  1. Normalization of the Hi / Ni ratios so that ZiiHiI2 / EilNiI2 reproduces the signal / noise ratio SNRv before the corrector in the case of the occupation of all the carriers

  possible with constant power.

  Hi = Hi SNRv ii G2 Zi IHiI2 v 2. Product Si of the channel transfer function Hi by the corrector transfer function Wi in the DFT domain Si = Hi Wi G3 3. IFFT to determine the associated impulse response s = IFFT (S) G4 4. Determination of the mean signal power density component N of the part of the impulse response s which goes beyond

  the guard interval in the next frame.

  5. The DFT Ni transforms of the impulse response of the parasites are determined, all the spectral characteristics of the parasites being included. is then the noise power density function. We form the product of Ni

  by the Wi corrector transfer function.

  Ni = Ni Wi GS 6. Addition of the parasitic power components

from expressions G4 and G5.

  Nil2 Ni + wi G6 7. Calculation of the autocorrelated element neither associated with the

  parasitic power density INiI2.

  ni = IFFT (INil2) G7 8. Inclusion of the leakage effect of the DFT by multiplying neither by a triangular function ti Xi = ni ti, i = 0, ..., 4NTr-1 G8 2NTr - ii = 0, ., 2NTr i 0, = ... 2NTr

1 iN = r NTr + l, ..., 4NTr -

  2NTr ti 2NTr The multiplication of the time domain equivalent (autocorrelation result) of the noise power density by a triangular function described, according to KD Kammeyer, K. Kroschel: "Digitale Signalverarbeitung", Teubner, Stuttgart, 1996 , page 231, the influence of a rectangular windowing which exists in principle during the formation of the DFT on the reception side. In order to be able to represent this triangular function approximately in the time domain vector discrete in time, we have chosen an oversampling in the frequency domain, here by a factor 2. Consequently, as already mentioned, the method according to l invention is based on a frequency grid which has at least

  half the gap between carriers.

  9. Transformation of X in the DFT domain

A = FFT (X) G9

  10. Determination of the SNRi signal / noise ratio for each carrier used. Frequencies which result from oversampling are not taken into account here, but only those actually used in the difference between

initial carriers.

  SNRi = Si / Ai, i e U G10 U denotes the set of carrier positions

actually occupied.

  11. Addition of all the channel capacity components of the individual carriers, which corresponds approximately to the geometric mean of all the SNRi, ie U. R = log2 (l + SNRi) Gll iU R is the quantity sought and is maximized by a multi-dimensional optimization algorithm, for example AMOEBA (Downhill Simplex Method) in WH Press, BP Flannery, SA Teukolsky, WT Vetterling: "Numerical Recipes", Cambridge University Press, Cambridge, 1989, pages 289 et seq., by l 'through the modification of the corrector coefficients in the time domain. As a criterion for stopping the algorithm, one can use the variation of R between two successive iterations, that is to say that one always temporarily stores the value of R for the next iteration so that a comparison can then be made. . If the variation becomes below a certain threshold,

iteration can be stopped.

  We still describe step 4 with a little more

details using Figure 2.

  A DMT receiver will normally place the detection frame 7 in time so as to minimize interference between blocks. We then find a compromise position for which both post-pulse oscillations 11a and llb of components of II 2767433 the previous frame 9a as well as pre-pulse oscillations 12a and 12b of components of the next frame 9b must be taken into account as parasites. FIG. 2 shows for example four impulse responses of channels 10a to 10d (represented in continuous form for reasons of clarity) deduced from the closest sampled values. Depending on the length of the channel impulse response after correction in the time domain, one can imagine other impulse responses from the following sampled values (indicated by dots in Figure 2). In each possible position, the section of the impulse response which falls into the evaluation frame 14 must be sampled by a rectangular windowing and the resulting parasitic power density must be calculated by an FFT and then by a formation of the square of the value absolute. All these contributions of components of neighboring frames 9a and 9b are to be added to obtain an average power density

  interference due to exceeding the guard interval 8.

  As the same rectangular window is used for the impulse response sections as for signal independent noise, the leakage effect of the DFT is also to be taken into account here. The two parasitic components are therefore grouped together in step 6 before

to include the leakage effect.

  Let nG be the length of the guard interval 8. It is possible to estimate the position of the detection frame 7 by finding among different positions of a frame sector 13 of length nG + l that for which the frame sector 13 contains the maximum energy. The detection frame 7 begins after this frame sector 13. The procedure is further described below in a formal manner. It is first assumed for simplicity that We still describe below, formally, how to proceed. To simplify, we first assume that the zero of the time of the global impulse response if is placed so that the energy of oscillations before pulse (12a, 12b) and that of oscillations after pulse (lia, 1lb) of the impulse response are equal, that is, the zero of time is at the "center of gravity" of the energy of the impulse response. Such a shift in the time axis has no influence on the results. For i = -nv, ..., 0, ..., nn, the impulse response is therefore different from 0 (in practice, absolute value below a certain threshold), nn being the number of sampled values of oscillations after pulse and nv the number of sampled values of oscillations before pulse. The average signal power density component N of the part of the impulse response s which exceeds the guard interval to go to the next frame can then be calculated as follows Oscillations before pulse For all 0v = 0, ..., nn-a (possible positions of the impulse response, deduced from the different sampled values; 'a' Cf. figure 2) 4NTrl_ = Saiav, i = 0, ..., nv - a- Cv

(crv) 0 i = nv - a - av +, ..., 4NTr-

  4NTr -1-1i S (av) = FFT (S ('yv)) Here we have again chosen 4NTr cdmme length of the evaluation frame to remain consistent with the

  oversampling in the frequency domain.

  Oscillations after impulse For all on = 0, ..., nn-nG + a-2: S an) =, = SnG i = .., nn - nG + a - 2 - an S (an) = 0, i = nn nG + a - 1 On, .. 4NTr 1 S (an) = FFT (S (an)) The power density of the interference between blocks is therefore | NSi -úS (av)} + Si) av a Figures 4 and 5 show as examples of the results to be compared for a corrector according to the method according to the invention (curves 10 in Figure 4 and 30 in Figure 5) and for a corrector which results from the fractional rational channel approximation described above (curves 20 in Figure 4 and 40 in Figure 5). FIG. 4 shows the log2 channel capacities (l + SNRi) as a function of the signal / noise ratios and in FIG. 5 the overall impulse response of the channel and of the corrector, the chosen guard interval of length 32 being indicated. by vertical dashed lines. The channel chosen was a symmetrical two-conductor wire 0.4 mm in diameter and 3.5 km in length. For the noise source, a so-called AslMx (connection line multiplexer) element inside the same star-quadrant cable has been assumed as near-end noise. During simulations of ADSL lines (Asymmetric Digital Suscriber Line), we then obtained using the method according to the invention an increase in range of about 200 m compared to the corrector setting with the channel approximation.

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  rational fractional. Another advantage of the method is regular convergence, that is to say that there appear fewer variations in the results for different lengths. This is not the case with the fractional rational approximation5. Another important aspect is that the method according to the invention does not include during

  optimization as the carrier positions that are prescribed for further operation. We can thus leave aside at will certain frequency domains.

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Claims (4)

  1. A multi-carrier transmission method with an adjustment of coefficients of the corrector in the time domain, characterized by the following steps: a) the parasitic spectral power density of noise influences and the parasitic spectral power density are added together which is formed by exceeding the guard interval by the impulse response of o10 channel after correction in the time domain to give a common parasitic spectral power density, b) the leakage effect of the DFT is taken into account for the common parasitic spectral power density, and c) the channel capacity R = 1 g2 (1 + SNRi) is optimized, U being the set of positions of i e1 carriers for which the optimization must be performed.   2. Method according to claim 1, characterized in that a) the leakage effect is taken into account by multiplying the autocorrelated element (inverse transform of the noise power density function) by a triangular function in the domain temporal, and 16 2767433   B) the position of the detection frame on the reception side is estimated by determining the maximum energy within a domain of length equal to the length of the guard interval plus one, the detection frame, of which position is characterized by 'content   maximum energy, starting after this domain.   3. Method according to claim 2, characterized in that one provides for the implementation of the multiplication by a triangular function in the time domain 0 oversampling in the (frequency) domain DFT and therefore a corresponding extension   of the vector in the time domain.   4. Method according to claim 3, characterized in that one chooses an oversampling in   the DFT (frequency) domain by a factor of 2.