DE19735216A1 - Multicarrier signal transmission method - Google Patents

Abstract

The method involves adding the interference power density spectrum of noise influence and the interference power density spectrum which is formed by exceeding the Guard interval by channel impulse response after a time domain equalisation. The leak effect of the DFT is taken into account for the common interference power density spectrum and the channel capacity is optimised. Preferably, the leak effect is taken into account by multiplying the autocorrelation with a triangular function in the time domain.

Description

The invention relates to a method for transmitting more carrier signals with a coefficient setting of the Zeitbe Reichsentzerrers to shorten the channel impulse response according to the preamble of claim 1.

Systems are in the field of digital signal processing known that a high-rate digital messaging enable. A technique that has recently become more and more popular Gaining importance is the multi-carrier transmission, which is also called "Discrete Multitone (DMT)" or "Orthogonal Frequency Division Multiplex (OFDM) "is known. In the case of multicarrier transmission becomes the data stream to be transmitted in many parallel part streams, which are independent of one another in the frequency division multiplex transferred to another.

In practice, the signal generation is done by an IFFT (Inverse Fast Fourier Transform), where the components of the Vectors in the DFT (Discrete Fourier Transform) range with signal points of a QAM (Quadrature Amplitude Modulation) proves who the. The IFFT creates a signal with a block structure in the Time range. To avoid inter-block interference, with DMT or OFDM a cyclic prefix, the so-called guard Interval. Here the end of the frame is cyclically dem Preceding block in time. The folding with the canal im pulse response then appears as a cyclic convolution, which then in the DFT range by a simple multiplication by complex Coefficients can be described. It simplifies the Equalization, which can now be done in the DFT area and then one simple AGC (Automatic Gain Control) for each wearer speaks.

However, the prerequisite is that the channel impulse response is shorter than the selected guard interval. This can be achieved, on the one hand, by selecting a suitably long guard interval, as is done in the radio range with OFDM (e.g. DAB, digital audio broadcasting). On the other hand, however, there is also the possibility of shortening the impulse response to the length of the guard interval by means of a time area pre-equalization. This leads to a more effective use of the transmission channel, but presupposes that the channel is so slowly ver changeable that an adaptation and tracking of the equalizer coefficients is possible. In cable applications, time domain pre-equalization is the common practice. When setting the equalizer coefficients, not only do you have to pay attention to the brevity of the resulting overall impulse response from the channel and equalizer, but also the resulting signal-to-noise ratio as a further criterion. In "Optimum Finite-Length Equalization for Multicarrier Transceivers", published in IEEE Transactions on Communications, Vol. 44, No. Jan. 1, 1996, N. Al-Dhahir and JM Cioffi describe this issue in more detail. There it is shown that for the optimal setting of the coefficients the following expression must be maximized:

where b _DMT denotes the sum of the partial capacities b _i. Approximately this means that the geometric mean from the individual signal-to-noise ratios of the carriers (SNR _i ) is to be maximized.

The simplest setting method, which only includes the length of the resulting impulse response, would be the approximation of the transmission channel using a fractional-rational expression A (z) / B (z), where the degree A (z) of at most equal to the guard interval -Length should be. A transversal filter with the transfer function B (z) can then serve as a time domain equalizer. Ideally, only A (z) remains as the overall transfer function. The signal-to-noise ratio SNR _i is not taken into account in any way, and the equalization is therefore generally not optimal.

All setting algorithms based on this principle mutually adapt a time domain equalizer W (z) and a replacement system E (z). Here, too, the signal-to-noise ratio SNR _i is not directly included, even if the results are often already quite favorable. Two criteria are mutually observed: the identity between the equivalent system E (z) and the chain connection of channel and equalizer W (z) (minimization of the mean square error) and the length restriction of the overall impulse response. In addition, of course, a length restriction for the equalizer W (z) is generally based on the specification of a maximum number of coefficients.

Two publications are described here as representative of the bene approach mentioned: van Bladel, M., Moeneclaey, M .: "Time-domain Equalization for Multicarrier Communication", he appeared in Proc. Communication Theory Mini-Conference (Globecom '95), Singapore, 13-17 Nov. 1995, pp. 167-171. and Farhang-Boroujeny, B .: "Channel Memory Truncation for Maximum Likelihood Sequence Estimation ", also published in Proc. Communication Theory Mini-Conference (Globecom '95), Singapore, Nov 13-17, 1995, pp. 172-176. Also in the above publication by N. Al-Dhahir and J.M. Cioffi makes this approach unnecessary wise in the practical implementation of the equalizer adjustment used again. In these these procedures, however, will not the total disturbance performance included.

The object of the invention is therefore to provide a method for transmission to make available multicarrier signals, the one op optimal equalizer adjustment with the greatest possible processing amount speed allows.

This task is made possible by the distinctive features of the An Claim 1 solved.

In the method according to the invention, an equalizer adjustment is carried out carried out, which focuses on the optimization of only one criteri ums, which was already given in the above equation G1, be restricts. This means it becomes the geometric mean of the Signal-to-noise ratio maximized. However, the Total disturbance power included, both of which originate from disturbances can, but also from exceeding the guard Interval (inter-block interference) due to too long a total time pulse response can result.

The interference power density spectra obtained from Rau apparent flows, such as crosstalk interference, as well as those caused by exceeding the guard interval by the channel impulse response after time domain equalization ent stand together to form a common interference power density spectrum men.

A common optimum is found, which means that does not necessarily affect the overall impulse response to the length of the guard interval is limited. It is important to him inventive method also that the so-called Leckef effect of the DFT is included. When transforming into the DFT area, which is part of the DMT receiver, becomes a rectangular signal window for taking the time signal used. This has no meaning for the useful signal component, because this has a cyclic prefix. For noise signals and also the signal components that exceed the guard interval However, this does not apply. There is no cyclical one for this Prefix, and it must be the influence of the rectangular window for the Calculation of the signal-to-noise ratio per carrier must be included.

The method according to the invention therefore offers advantages Restriction to only one optimization criterion and through cor Direct calculation of the signal-to-noise ratio including the leak effect.

Another advantage is the range of the transmission is increased. The uniform conversion is also advantageous genz, d. H. there are fewer fluctuations in the results for different lengths.

The invention is described below on the basis of exemplary embodiments explained in more detail in connection with the accompanying drawings.

Show:

Fig. 1 is the block diagram of a conventional transmission system,

Fig. 2 for example, four channel impulse responses elicited by the respective nearest samples,

Fig. 3 shows the flowchart of the method according to the invention,

Fig. 4, the signal-to-noise ratio at the various support positions, and

Fig. 5, the normalized impulse response function of the samples.

A common approach is to consider a replacement system that has the desired impulse response length. In Fig. 1 the underlying block diagram is shown. In the block diagram, n _k 2 denotes the sampled values of a noise interference, e _k ^{6 denotes the sampled} values of the error between the output of the true system and the equivalent system E (z) 5, and z -Δ 4 is used to model a dead time. H (z) represents the channel transfer function 1 and W (z) the equalizer 3 .

In the method according to the invention, the substitute system 5 can be dispensed with, since the system is optimized by setting only one criterion of the equalizer 3 .

The steps to be repeated iteratively according to the method according to the invention are shown below. In Fig. 3, the corresponding steps are presented as a flow chart Darge.

N _Tr is the maximum possible number of carriers. Assuming a baseband signal in which the two halves of the DFT frame are to be assigned complex conjugate to one another, the DFT length is then N _DFT = 2.N _Tr . However, the method according to the invention uses oversampling in the frequency domain, as a result of which the DFT length N _{DFT 2} actually used becomes N _{DFT 2} = 4.N _Tr .

• 1. Normalize the ratios of H _i / N _i such that Σ _i | H _i | ² / Σ _i | N _i | ^{2 shows} the actual signal-to-noise ratio SNR _v upstream of the equalizer when all possible carriers are occupied with constant power
  
• 2. Product S _{i of} the channel transfer function H _i times the equalizer transfer function W _i in the DFT domain
  S _i = H _i .W _i G3.
• 3. IFFT to determine the associated impulse response
  s = IFFT (S) G4.
• 4. Determination of the mean signal power density component | N _i ^s | ^{2 of} the part of the impulse response that extends beyond the guard interval into the next frame.
• 5. Determine the DFT transform N _{i of} the impulse response of the disturbance, taking into account all spectral properties of the disturbance. N _i ² is then the noise power density function. The product of N _i and the equalizer transfer function W _{i is} formed.
  N _i ^s = N _i .W _i G5.
• 6. Addition of the interference power components from equations G4 and G5.
  | N _i | ² = | N _i ^s | ² + | W _i ⁿ | ² G6.
• 7. Calculation of the interference power density | N _i | ² associated auto-correlated n _i
  n _i = IFFT (| N _i | ² ) G7.
• 8. Incorporating the leakage effect of the DFT by multiplying n _i by a triangle function t _i
  The multiplication of the time domain equivalent (auto correlation sequence) of the noise power density with a triangle function describes, according to Kammeyer, KD, Kroschel, K .: "Digitale Signalverarbeitung", Teubner, Stuttgart, 1996, p. 231, the influence of a rectangular window that occurs in the formation on the receiving side the DFT is given due to the principle. In order to be able to represent this triangular function approximately in the time-discrete time domain vector, oversampling was selected in the frequency domain, here by a factor of 2. As already mentioned, this means that the method according to the invention is based on a frequency raster which has at least half the carrier spacing.
• 9. Transformation of λ into the DFT domain
  Λ = FFT (λ) G9.
• 10. Determine the signal-to-noise ratio SNR _i for each carrier used. Here, no frequencies are taken into account that have arisen from oversampling, but only those actually used in the original carrier spacing.
  SNR _i = S _i / Λ _i , i ∈ U G10.
  U denotes the amount of actually occupied carrier positions.
• 11. Summation of all channel capacity components of the individual carriers, which corresponds approximately to the geometric mean of all SNR _i , i ∈ U.
  R is the target variable and is determined by a multidimensional optimization algorithm, for example AMOEBA (Downhill Simplex Method) in Press, WH, Flannery, BP, Teukolsky, SA, Vetterling, WT: "Numerical Recipes", Cambridge University Press, Cambridge, 1989, p. 289 ff., Maximized by modifying the time domain equalizer coefficients. The change in R between two successive iterations can serve as a criterion for terminating the algorithm. I. E. the value of R is always temporarily stored for the next iteration so that a comparison can then be carried out. If the change falls below a certain threshold, the iteration can be terminated.

Step 4 must be described in somewhat more detail with reference to FIG.

A DMT receiver will usually time the detection frame 7 in such a way that the inter-block interference is minimized. A compromise is found in which post-oscillations 11 a and 11 b of components of the previous frame 9 a and pre-oscillators 12 a and 12 b of components of the following frame 9 b must be included as a disturbance. Fig. 2 shows an example of four channel impulse responses 10 a to 10 d (for the sake of clarity continuously represents Darge), caused by the respective closest samples from. Depending on the length of the channel impulse response after the time domain equalization, one thinks of further impulse responses based on the respective following sample values (indicated by dots in FIG. 2). For each possible position, the cut of the impulse response, which falls within the evaluation frame 14 , must be taken through rectangular windowing and the resulting Störlei stung density can be calculated by FFT and subsequent squared amount. All these contributions from components of the neighboring frames 9 a and 9 b are to be added up in order to obtain an average interference power density caused by exceeding the guard interval 8 . Since the same rectangular window is also used for the pulse response sections as for signal-independent noise, the leakage effect of the DFT must also be taken into account here. Therefore, both interference components are combined in step 6 before the Lec keffekt is included.

The length of the guard interval 8 is n _G. It is possible to estimate the position of the detection frame 7 by finding that for different positions of a subframe 13 of length n _G +1 in which the maximum energy in the subframe 13 is contained. After this subframe 13 , the detection frame 7 begins.

The procedure is formally described again below. First of all, for the sake of simplicity, we assume that the zero time point of the total impulse response s _{i is placed} in such a way that the energy of the pre-( 12 a, 12 b) and post-oscillations ( 11 a, 11 b) of the impulse response is the same, ie the Zero time lies in the "energy focus" of the impulse response. Such a time axis shift has no effect on the results. The impulse response is thus for i = -n _ν,. . ., 0,. . . n _n different from zero (in practice the amount is smaller than a certain threshold). Let n _n be the number of post-oscillation samples and n _v the number of pre-oscillation samples. The mean signal power ^{density component} | _{N i s2 |} the part of the impulse response that extends beyond the guard interval into the next frame can now be calculated as follows:

Pre-oscillator

For all σ _v = 0,. . . n _n -a (possible positions of the impulse response, originating from the different sample values; a see Fig. 2)

The frame length of the evaluation frame was chosen _{again to be 4N Tr} in accordance with the oversampling in the frequency range.

Nachschwinger

For all σ _n = 0,. . ., n _n - n _G + a - 2:
s _i ^{(σ _n )} = s _{n G} , i = 0,. . ., n _n - n _G + a - 2 - σ _n
s _i ^{(σ _n )} = 0, i = n _n - n _G + a - 1 - σ _n,. . ., 4N _Tr - 1
S ^{(σ _n )} = FFT (s ^{(σ _n )} ).

The power density of the inter-block interference then results in

By way of example in FIGS. 4 and 5 comparative profits or losses with an equalizer according to the inventive method (curve 10 in Fig. 4 and 30 in Fig. 5) and an equalizer, resulting from the above fractional-rational Ka nalapproximation ( Curves 20 in Fig. 4 and curve 40 in Fig. 5). Are shown in Fig. 4 th the Kanalkapazitä log ₂ (1 + SNR _i) corresponding to the signal-to-noise ratios and in Fig. 5, the overall impulse response of the channel and Entzer shown rer, wherein the selected guard interval of length 32 with vertical , dashed lines is indicated. The canal used as a basis was a symmetrical twin vein 0.4 mm in diameter and 3.5 km in length. A so-called AslMx (connection line multiplexer) within the same star quad was assumed to be the source of interference as a near-end crosstalk interferer. In simulations of ADSL (Asymmetric Digital Subscriber Line), using the method according to the invention resulted in a range increase of approx. 200 m compared to the equalizer setting by fractional-rational channel approximation. Another advantage of the method is the uniform convergence, ie there are fewer fluctuations in the results for different lengths. This is not the case with the fractional-rational approximation. It is also important that the method according to the invention only includes those carrier positions in the optimization which are specified for later use. Frequency ranges can thus be saved as required.

Claims (4)

1. Process for the transmission of multicarrier signals with a coefficient setting of the time domain equalizer, characterized by the following process steps:

• a) additive consolidation of the interference power density spectrum of noise influences and the interference power density spectrum that arises when the guard interval is exceeded by the channel impulse response after time domain equalization into a common interference power density spectrum,
• b) Consideration of the leakage effect of the DFT for the common interference power density spectrum, and
• c) Optimizing the channel capacity size
  where U is the set of carrier positions for which the optimization is to be carried out.

2. The method according to claim 1, characterized in that

• a) the leakage effect is taken into account by multiplying the autocorrelated (inverse transform of the noise power density function) with a triangle function in the time domain, and
• b) the location of the receiving-side detection frame is estimated by determining the maximum energy within a range of the length of the guard interval increased by one, the detection frame, the position of which is characterized by the maximum energy content, begins after this range.

3. The method according to claim 2, characterized in that that to realize the multiplication with a triangle function in the time domain oversampling in the DFT (Frequency) range and thus a corresponding extension tion of the time domain vector is provided. 4. The method according to claim 3, characterized in that that oversampling in the DFT (frequency) range by the Factor 2 is chosen.