DE4028322A1 - Improving channel parameter estimate - separating noise inhibited input signal into target magnitude by additional least-squares estimating device, e.g. kalman filter - Google Patents

Abstract

The process starts with the noise-inhibited input signal (ak), which is separated into a specified target magnitude in an additional estimating device (2). The magnitude is then subjected to filtering in a filter assembly (3-0 to 3-L). The additional estimating device pref. observes the noise-inhibited input signal over a sufficiently long time period. Then temp. estimation.values of the searched magnitude are made available. In the final filtering assembly which may be supplied with extra information over a given channel, the temp. estimation values from the extra estimation device are interpolated. The extra estimation device may be a known least square (LS) type with optimum quadratio error sum. USE/ADVANTAGE - For adaptive filtering, sunc., speech processing, spectral analysis, and in GSM receiver measurements. Shorter aquisition time, reduced error spread.

Description

The invention relates to a method for improving a Channel parameter estimation and an arrangement for its passage guide.

In many areas of technology, as shown in FIG. 1 with the aid of a simplified, schematic block diagram, the parameters of an unknown or partially known system 11 must be estimated, only the input variables I _k and noisy output data z _{k being} known. Here it is understood in the following under a "partially known system" that the current system status is unknown, but there is a knowledge of the statistics of the system. Correspondingly, a known solution principle shown in FIG. 1, an adaptive simulation 12 is created by the unknown or partially known system 11 .

In this way, 12 estimated value _k are obtained as the starting data of the simulation. These estimated values _k are subtracted from observed output signals z _k . Finally, the coefficients of the simulation 12 are changed until an error signal e _k , which is formed in an adder 13 by the difference between the output data z _k and the estimated values _k , in a predetermined manner, for example as a quadratic error u. is minimized. The coefficients of the simulation calculated in this way are the estimates of the original system.

Find examples of such a channel parameter estimate deal in the areas of signal processing and control technology, as well as in system identification, adaptive Equalization, echo cancellation, synchronization (regarding the carrier phase, the clock phase, the frequency,...,) speech processing, spectral analysis, etc.

In the following, the coefficients of a time variant, frequency-selective mobile radio channel are estimated (see see for example J. G. Proakis, Digital Communications, Singapore: McGraw Hill, 2nd edition, 1989).

The system, in this case the channel, is often not completely unknown; rather, there is additional information. In the specific example, this could be, for example, the vehicle _speed v, so that the maximum Doppler shift f _Dmax = v / λ is known, or it could be the maximum echo delay known from network planning, or it could be knowledge from a measurement of that Signal / noise ratio.

Procedure in which knowledge of the statistics of the Ka nals are taken into account as "parametric process ren ". Parametric methods stand out due to the a priori knowledge through a generally high Efficiency compared to non-parametric ver drive out, d. H. the estimation error spread is less. Therefore, it is assumed below that some of the additional information mentioned above is available.

By S. Haykin, Adaptive Filter Theory, Englewood Cliffs, N. J. Prentice-Hall, 1986 are three common adaptive estimates described the process, namely the "Least Mean Squares" - (LMS) procedure (see Chapter 5 in the above cited reference or chapter 6.7.2 in the introduction  published by J.G. Proakis), the "Least Squares "(LS) method (see Chapter 7ff with S. Haykin) and the so-called Kalman method (see Chapter 6 in S. Haykin or B. D. O. Anderson, J.B. Moore, Optimal Fil tering, Englewood Cliffs, N.J .: Prentice-Hall, 1979). Dar there are also various modifications and com combinations of these processes as well as the so-called method correlation method (see here for example G.L. Turin, "Introduction to Spread-Spectrum Antimultipath Techniques and their Application to Urban Digital Radio, " Proc. of the IEEE, volume 68, p. 328-353 of March 1980).

The above-mentioned conventional, non-parametric LMS method is a robust and inexpensive method and is therefore often used. The main disadvantage of this LMS method is its long settling time (= acquisition time), which also depends on the current state (the eigenvalue distribution) of the channel. In addition, the spread of estimation errors in the steady state is larger than, for example, with the so-called Kalman estimators. In addition, the LMS method degrades significantly with non-white input data I _k . The acquisition time can, however, be halved if the recursion step is repeated several times.

The LS method also mentioned above has in usually a much shorter acquisition period; however no channel information is also used with this method uses.

The one used in the Kalman process also mentioned (Minimum variance) Kalman estimator is ultimately based on one by B. D. O. Anderson and J. B. Moore in the cited Literature indicated state model and is consequently parametric. However, the direct application of Kal man estimator at an impractical cost.

The object of the invention is therefore a method for verbs of the channel parameter estimate or a channel identifier cation and an order to implement it in which the estimation error spread and the transient response are equally small. According to the Erfin This is a method for improving the channel parameter estimation by the characteristics in the characteristic Part of claim 1 and in the arrangement for it Carried out by the features in the characterizing part of the Claim 4 reached. Advantageous further developments are Ge subject of the claim to claim 1 directly or indirectly related subclaims.

The invention thus makes a parametric method created to improve channel parameter estimation at which is the replica of the partially known original system deviates as little as possible, so that the estimation errors scatter is low. Furthermore, with the parametric ver drive the replica in a short time according to the invention can be tracked to any initial state. This be indicates a short settling time of the Ver according to the invention driving. Furthermore, both in the inventive method ren as well as the quality in the arrangement for its implementation the estimate adjustable; that means starting from one optimal solution can be inexpensive according to the invention Procedures are derived.

The method according to the invention thus clearly has a improved acquisition duration and in the steady Zu there was an extremely low channel error spread. On top of that is a significantly improved one for non-white input data Performance expected.

The invention based on a preferred Aus management form with reference to the drawing gene explained in detail. It shows  

. Figure 1 shows schematically in the form of a block diagram of a conventional arrangement for parameter estimation;

Fig. 2 also schematically in the form of a block diagram, a preferred embodiment of an arrangement for performing the method according to the invention;

Fig. 3 is a sketch of a time lag of a coefficient of the system and its preliminary simulation and

Fig. 4 in the form of graphs a comparison of estimation error scatter according to the known LMS / Kalman method and the inventive method.

In the present case, the unknown or partially known system to be examined should be a frequency-selective, time-variant channel, which can be represented, for example, by a transversal filter with (L + 1) coefficients f _k ^(l) with 0lL. The output signal of the system is:

where η _{k is} a white, mean-free, Gaussian noise disturbance, and the index k describes changes over time. As already stated in connection with the arrangement according to FIG. 1, the input data I _k and the output data z _{k are} given, while the coefficients f _k ^(l) (0lL) are sought. Here, all sizes are complex.

According to the invention, an arrangement for carrying out the method according to the invention for improving the channel parameter estimate, as can be seen from the schematic illustration in FIG. 2, has an LS estimator 2 and this Kalman filter 3 -0 to 3 -L . By means of the LS estimator 2 , preliminary observations _k ^(l) with 0lL are calculated from the observation of the noisy reception data z _k . The setting criterion is (in terms of time) the minimization of the sum of the quadratic differences | e _k | ² between the received data z _k and the estimated values _k . It can now be shown that the estimated values _k ^(l) are true to expectations under the above conditions; therefore applies

_k ^(l) = f _k ^(l) + η _k ^(l) ; 0lL, (2)

with mean-free noise values η _k ^(l) . The variance of these noise values depends on the speed of the channel changes, the channel noise, the energy distribution of the channel echoes and the effective length of the observation interval.

In FIG. 3, the time course is a coefficient f _k ^(o) of the system and its provisional replica _k ^(o) skiz sheet, eluting with ⚫ Re {f _k ^(o)} and o Re _{k ^(o)} be are drawn.

Various LS solutions are known, as in for example a solution of the deterministic normal equation, a recursive LS procedure (RLS), a lattice procedure, etc. The approaches differ in terms of pre-filtering, stability and effort. To be However, it is important to ensure that the method is achieved by direct dissolution of the system of equations for short known sequence lengths (short training sequences) with the help of a table very effi can be solved efficiently. The different solutions are however not the subject of the above investigations.

In conventional LS implementations, the coefficients _k ^{(l) represent} the end result. However, it can quickly be seen that the result cannot be optimal because no information about the channel has been used until now. In the method according to the invention, the coefficients _k ^(l) are therefore filtered again, the aforementioned a priori knowledge being incorporated. With regard to Fig. 3 be this means that a compensation curve is placed by the coefficients _k ^(o) .

Among the various possible embodiments several options are given below.

The optimal linear post-filtering takes place via (L + 1) (Minimum variance) Kalman filter if the additional information is known. In this way, the Doppler shift, the echo distribution and the signal / noise ratio be taken into account.

The so-called extended Kalman filter offers the possibility ability to estimate the additional information required (see alongside B. D. O. Anderson and J. B. Moore on the above A. Aghamohammadi, H. Meyr, G. Ascheid, "Adaptive Synchronization and Channel Parameters Estimation using an Extended Kalman Filter ", IEEE Trans. On Comm., Volume COM-37, No. 11, stn. 1212 to 1219, November 1989).

It is also conceivable, for example, to only consider the Doppler frequency. This can then be done via a fixed low-pass filter with a cut-off frequency which corresponds to the maximum Doppler frequency f _Dmax or can be carried out via a variable low-pass filter according to the current Doppler frequency.

The so-called LS / Kalman structure shown in FIG. 2 thus corresponds to an "open-loop" structure, the LS estimator 2 acting as an additional device to separate the coefficients and individually the respective Kalman after filter 3 -0 to supply 3 -L. Here, the (L + 1) Kalman post-filters 3 -0 to 3 -L can be set independently or depending on each other; Here, the effort is less in the first case, while in the second case any correlations between the coefficients f _k ^{(l) are} taken into account. Furthermore, the use of second-order filters has proven to be advantageous for the few (on average) high-energy coefficients, while first-order filters are sufficient for the remaining coefficients. The advantage here is that due to the "open-loop" structure, no predication ("time update") has to be carried out during post-filtering, but rather filtering ("measurement update") or even smoothing ("smoothing") can be carried out.

The advantages over the previously known solutions are as follows:
The acquisition duration is largely determined by the LS estimator 2 and is therefore very short and independent of the channel state. As a result, the length of the required training sequence can be shortened, for example, which reduces the redundancy.

The stationary estimation error spread is very low because prior knowledge with be processed. Also dropped in the invention, the mutual influence of one individual coefficients; consequently, a better estimate can be made scatter can be achieved in the steady state. The The consequence of this is that a higher vehicle speed and / carrier frequency leads to the same estimation error spread. It is also expected that non-white input data will be too lead to less severe degradations.

Furthermore, the method works without feedback; ent the risk of incorrect settings of the Kalman Post filter. The process is also time-stable.

In the method according to the invention (L + 1) Kalman filters 3 -0 to 3 -L of lower dimension are used, for example of the order of 1 or 2. However, these filters are much easier to handle than a filter of the order (L +1) or 2 (L + 1).

On top of that, the process works on any one Satisfactory coefficient number.

Compared to the conventional LS process (see example wise J. Haykin, at the point mentioned at the beginning) the effective observation duration due to the post-filtering can be reduced using the LS estimator. Therefore be also channel changes processed faster.

In FIG. 4 Simulation results for various well-te method compared to the present invention are illustrated procedural ren. In this case, a learning curve, which corresponds to a sharply averaged estimation error scatter, is plotted over the discrete time k. A frequency-selective mobile radio channel with echo delays of up to 85 µs was simulated. Such a channel was specified as part of the DAB EUREKA project EU 147 and applies to unfavorable propagation conditions in mountainous areas with conventional network planning using the current broadcasting network. The chosen modulation method was an offset four-phase modulation (Quadrature Phase Shift Keying (QPSK)) with Nyquist filtering (with cosine-shaped rolloff, r = 0.4). The average signal / noise ratio was _s / N _O = 10 dB; the maximum Doppler frequency was f _Dmax = 200 Hz, which corresponds to a driving speed of 240 km / h at a carrier frequency of 900 MHz. The symbol duration (bit duration) was 30 µs (15 µs), ie about 8 bits (L = 7) smear if the pulse shaping is also taken into account.

If the noise were zero, the channel could be measured exactly in (2L +1) = 15 bit clocks; initially L = 7 bits are required to bring the memory allocation into a defined initial state; after additional (L + 1) = 8 bit clocks, an equation system with (L + 1) equations is available for the (L + 1) unknowns. This theoretical limit is drawn in Fig. 4 as a vertical line.

The top curve applies to the case of a combined LMS / Kalman estimator with (L + 1) = 8 first order sub-filters, whereby only a simple recursion is carried out. It should be noted that this case already has a small spread of estimation errors than the conventional nonparametric LMS method treated at the beginning with reference to FIG. 1.

The other curves apply in the event that the LMS-Re course back and forth twice back and forth, as well is carried out back and forth as often as required. The one The oscillation period is then reduced from approx. 40 bit cycles approx. 20 bars. In addition, however, there is the duration of L = 7 Clocking until the memory allocation has settled; this is taken into account that the abscissa around this value is moved.

The bottom curve finally shows the simulation results for the method according to the invention with the same parameters, the method being carried out with the arrangement shown in FIG. 2 consisting of an LS estimator 2 and downstream Kalman filters 3 -l to 3 -L. In this embodiment, the LS estimator 2 is executed in the direct embodiment (see S. Haykin in the place mentioned at the beginning). The (L + 1) = 8 post-filters were 1st order filters; this corresponds to the case of partial filters 1 . Order in the LMS / Kalman procedure mentioned above. As can be seen, the acquisition time is reduced again, to about 5 bit clocks (plus the (2L + 1) = 15 clocks until enough equations are available).

Transferred to future pan-European mobile communications system GSM (Group Sp´ciale Mobile) with a maximum  Echo delay of 20 µs in a bit duration of 3.7 µs be this result indicates that the GSM channel in about 13 clocks can be measured. So far, a correlation ver drive (see G.L. Turin at the point mentioned above) used and 26 bit clocks are required for this. Furthermore is a smaller spread of error estimates in the steady Zu stood recognizable because influencing the coefficients not applicable.

By choosing downstream higher-order filters the steady spread of estimation errors can be further increased be reduced. Furthermore, the acquisition period can still thereby further reduced when the input data windowed and weighted.

Furthermore, the method according to the invention can also be applied to the area already mentioned, namely at the System identification, for example a channel parameter estimation, adaptive equalization, echo cancellation, synchronization (with regard to the carrier phase, frequency, the clock phase. . .), speech processing, spectralana lysis etc. apply. Another very important thing The application is channel measurement during training phase in the so-called GSM receiver.

Claims (4)

1. A method for improving a channel parameter estimate, characterized in that the noisy input signal (z _k ) is separated by means of an additional device ( 2 ) into the target variable (f _k ^(l) , 0lL), and then in a filter arrangement ( 3 -0 to 3 -L) is subjected to post-filtering. 2. The method according to claim 1, characterized in that the noisy input signal (z _k ) is observed in the additional device ( 2 ) over a sufficiently long period of time and then provisional estimates (f _k ^(l) ) of the size sought are provided. 3. Process according to claims 1 and 2, characterized in that in the arrangement provided for post-filtering ( 3 -0 to 3 -L), into which additional information about the channel is introduced, generated by the additional device ( 2 ) , preliminary estimates ( _k ^(l) ) are interpolated. 4. Arrangement for performing the method according to claims 1 and 2, characterized in that the additional device in terms of the minimum, quadratic error sum optimal, known per se LS (least squares) estimator ( 2 ), which is one An arrangement of parallel-fed Kalman filters ( 3 -0 to 3-1 ) is arranged downstream of optimal, linear time-variant post-filtering to minimize variance.