DE19735216C2 - Method for transmitting multicarrier signals with a coefficient setting of the time domain equalizer - Google Patents

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 the preamble of claim 1.

There are systems in the field of digital signal processing known to have a high-rate digital message transmission enable. A technique that has been increasing in recent times Gaining importance is multicarrier transmission, which is also called "Discrete Multitone (DMT)" or "Orthogonal Frequency Division Multiplex (OFDM) "is known. In multi-carrier transmission the data stream to be transmitted is divided into many parallel parts streams which are independent of one another in frequency division multiplexing be transferred to others.

In practice, the signal is generated by an IFFT (Inver Fast Fourier Transform), taking the components of the vector in the DFT (Discrete Fourier Transform) area with signal points a QAM (Quadrature Amplitude Modulation). The IFFT creates a signal with a block structure in the time domain rich. To avoid inter-block interference, DMT or OFDM a cyclic prefix, the so-called guard Interval. Here the frame end is cyclical Block preceded by a block. Folding with the canal The pulse response then appears as a cyclic convolution, which then in the DFT area by simple multiplication with complex Coefficients can be described. It simplifies the Equalization, which can now be done in the DFT range and then one simple AGC (Automatic Gain Control) for every wearer speaks.  

However, the prerequisite is that the channel impulse response is shorter than the selected guard interval. You can do this on the one hand by choosing a correspondingly long guard interval range, as is the case with OFDM (e.g. DAB, digital Audio broadcasting) happens. On the other hand, it offers also the possibility of impulse response through a time realign pre-equalization to the length of the guard interval shorten. This leads to a more effective use of the transfer supply channel, but requires that the channel ver so slowly is changeable that an adaptation and tracking of the equalizer coefficient is possible. For cable applications, the time is empire pre-equalization is the usual procedure. At the one Positioning the equalizer coefficients is not just for brevity the resulting total impulse response from channel and equalizer to pay attention, but as a further criterion occurs the result signal-to-noise ratio. In "Optimum Finite- Length Equalization for Multicarrier Transceivers " in IEEE Transactions on Communications, Vol. 44, No. Jan 1 1996, N. Al-Dhahir and J.M. Ciofft describe this subject stop more precisely. There it is shown that for the optimal setting to maximize the coefficient of the following expression is.

where b _DMT denotes the sum of the partial capacities b _i . Approximately, this means that the geometric mean of 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 by a fractionally rational expression A (z) / B (z), the degree A (z) being equal to or less than the guard interval -Length should be. A transversal filter with the transfer function B (z) can then serve as a time domain equalizer. Ideally, the only remaining transfer function is A (z). The signal-to-noise ratio SNR _i is not taken into account here in any way, and the equalization is therefore generally not optimal.

Other setting algorithms 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 taken into account, even if the results are often quite favorable. Two criteria are mutually observed: the identity between equivalent system E (z) and derailleur circuit consisting of channel and equalizer W (z) (minimization of the mean square error) and the length restriction of the total impulse response. In addition, a length restriction for the equalizer W (z) is of course generally also taken as a basis by specifying a maximum number of coefficients.

Two publications are representative of the described bene procedure called: von Bladel, M., Moeneclaey, M .: "Time-domain equalization for multicarrier communication", he appeared in proc. Communication Theory Mini-Conference (Globe com '95), Singapore, Nov. 13-17, 1995, pp. 167-171. and Farhang Boroujeny, B .: "Channel Memory Truncation for Maximum Likeli hood Sequence Estimation ", also published in Proc. Commu nication Theory Mini-Conference (Globecom '95), Singapore, 13- 17 Nov. 1995, pp. 172-176. Also in the above release of N. Al-Dhahir and J.M. Ciofft make this approach unnecessary in the practical execution of the equalizer adjustment again used. However, these procedures do not Total interference power included.

The object of the invention is therefore to provide a method for transmission to make available multicarrier signals that an op  Maximum equalizer adjustment with the largest possible processing area allows speed.

This task is characterized by the characteristics of the contractor spell 1 solved.

In the method according to the invention, an equalizer adjustment is carried out performed on the optimization of only one criterion um, which has already been given in equation G1 above, be limits. This means it becomes the geometric mean of the Signal-to-noise ratio maximized. However, the Total interference power included, both from interference can, but also from exceeding the Guard Intervals (inter-block interference) due to a too long total timpulse response can result.

So one summarizes the interference power density spectra that from Rau apparent flows, such as crosstalk disorders, as well as those that exceed the guard interval by the channel impulse response after time domain equalization stand together to a common interference power density spectrum men.

A common optimum is found, which means that not necessarily the total impulse response to length of the guard interval is limited. What is important with him inventive method also that the so-called Lec effect of the DFT is included. When transforming into the DFT area, which is part of the DMT receiver a rectangular signal window for the extraction of the time signal used. This has no meaning for the useful signal component, because it 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 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 through Restriction to only one optimization criterion and by cor correct calculation of the signal-to-noise ratio including the leak effect.

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

The invention is described below using exemplary embodiments explained in connection with the accompanying drawings.

Show:

Fig. 1 is a block diagram of a conventional stems Übertragungssy,

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 shows the signal-to-noise ratio in the different carrier 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. The basic block diagram is shown in FIG. 1. In the block diagram, n _k 2 characterize the samples of a noise disturbance, e _k 6 the samples of the error between the output of the true system and the replacement 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 replacement system 5 can be dispensed with, since the optimization of the system takes place via the setting of only one criterion of the equalizer 3 .

The steps to be repeated iteratively in accordance with the method according to the invention are shown below. In Fig. 3, the corresponding steps are shown 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 conjugate complex to be occupied, 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 actually used N _DFT2 to N _DFT2 = 4. N _Tr becomes.

• 1. Normalize the ratios of H _i / N _i so that Σ _i | H _i | ² / Σ _i | N _i | ^{2 shows} the actual signal-to-noise ratio SNR _v before the equalizer when occupying all possible carriers with constant power
  
• 2. Product S _{i of} the channel transfer function H _i times equalizer transfer function W _i in the DFT range
  S _i = H _i . W _i G3
• 3. IFFT to determine the associated impulse response
  s = IFFT (S) G4
• 4. Determine the average signal power density component | N _i ^s | ^{2 of} the part of the impulse response s 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 ⁿ = N _i . W _i G5
• 6. Add the interference power components from steps 4 and 5 .
  | N _i | ² = | N _i ^s | ² + | N _i ⁿ | ² G6
• 7. Calculation of the interference power density | N _i | ² associated autocorrelated n _i
  n _i = IFFT (| N _i | ² ) G7
• 8. Include the leak effect of the DFT by multiplying n _i by a triangular function t _i
  

The multiplication of the time domain equivalent (Auto correlation sequence) of the noise power density with a three corner function describes according to Kammeyer, K.D., Kroschel, K .: "Digital signal processing", Teubner, Stuttgart, 1996, P. 231, the influence of a rectangular window, which in the the formation of the DFT at the receiving end is given in principle. About this triangular function approximately in time-discrete To be able to represent time domain vector was in frequency range oversampling, chosen here by a factor of 2. As already mentioned, this means that the fiction method is based on a frequency grid that is at least has at least half the support spacing.

• 1. Transformation of λ in the DFT area
  Λ = FFT (λ) G9
• 2. Determine the signal-to-noise ratio SNR _i for each carrier used. Here, no frequencies are taken into account, which resulted from the oversampling, but only those actually used in the original carrier distance.
  U denotes the amount of the actually occupied carrier positions.
• 3. 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 the termination criterion of the algorithm. That is, the value of R is always buffered 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. 2.

A DMT receiver will usually place the detection frame 7 so that the inter-block interference is minimized. A compromise situation is found in which post-oscillators 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 nearest sample values. Depending on the length of the channel impulse response after the time domain equalization, one thinks of further impulse responses based on the respectively following samples (indicated by dots in FIG. 2). For every possible location, the cut-out of the impulse response, which falls into the evaluation frame 14 , must be removed through rectangular fenestration and the resulting Störlei density calculated by FFT and subsequent amount square formation. All of these contributions from components of the neighboring frames 9 a and 9 b are to be added together in order to obtain an average interference power density caused by the exceeding of the guard interval 8 . Since the same rectangular window as for signal-independent noise is also used for the pulse response sections, the leakage effect of the DFT must also be taken into account here. Therefore, both interference components are summarized in step 6 before the Lec effect 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 the one in which the maximum energy is contained in the subframe 13 for different positions of a subframe 13 of length n _G + 1. After this subframe 13 , the detection frame 7 begins.

The procedure is formally described below. We first assume the simplicity that the zero point in time of the total impulse response s _{i is set} so that the energy of the pre ( 12 a, 12 b) and post oscillators ( 11 a, 11 b) is the same as the impulse response, ie The zero point lies in the "energy focus" of the impulse response. Such a timeline shift has no effect on the results. The impulse response is therefore different from zero for i = -n _v , ..., 0, ... n _n (in practice 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 average signal power ^{density component} | N _i ^s2 | the part of the impulse response s that extends beyond the guard interval into the next frame can now be enriched as follows:

Vorschwinger

For all σ _v = 0, ... n _n - a (possible positions of the impulse response, based on the different samples; a see Fig. 2)

The frame length of the evaluation frame was chosen to be 4N _Tr in accordance with the oversampling in the frequency range.

Resonator

For all σ _n = 0, ..., n _n - n _G + a - 2:

S _i ^(σn) = S _{n G -a + 1 + i + σn} , i = 0, ..., n _n - n _G + a - 2 - σ _n

S _i ^(σn) = 0, i = n _n - n _G + a - 1 - σ _n , ..., 4N _Tr - 1

S ^(σn) = FFT (S ^(σn) )

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

Examples in FIGS . 4 and 5 are comparative results with an equalizer according to the method according to the invention (curves 10 in FIGS. 4 and 30 in FIG. 5) and an equalizer that results from the fractional-rational channel approximation described above ( 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 underlying channel was a symmetrical twin wire with a diameter of 0.4 mm and a length of 3.5 km. A so-called AslMx (connecting line multiplexer) within the same star quad was assumed to be the source of the interference as a near crosstalk. In the case of simulations of ADSL (Asymmetric Digital Subscriber Line), using the method according to the invention, the range was increased by approximately 200 m compared to the equalizer setting by fractionally 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 fractional-rational approximation. It is also important that the method according to the invention only includes those carrier positions in the optimization that are specified for later use. Frequency ranges can thus be left out as desired.

Claims (4)

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

• a) additive combining the interference power density spectrum of noise influences and the interference power density spectrum, which arises when the guard interval is exceeded by the channel impulse response after time domain equalization, to form a common interference power density spectrum,
• b) taking into account 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 (back-transformed of the noise power density function) by a triangular function in the time domain, and
• b) the position of the reception-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, starting after this range.

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