DE4231311C2 - Method for determining the impulse response of a transmission channel with expanded impulses and device for carrying out this method - Google Patents

Description

The invention relates to a method according to the preamble of claim 1 and a device for implementation tion of this procedure.

A particularly advantageous application of such a ver driving and such a facility lies with pulse radar systems.

Radar systems can act as impulse response devices estimate. The radar transmitter is transmitting pulse-shaped signal. This runs through a channel and reaches the radar receiver. From the received signal that from the desired signal and from an additive noise signal exists, the impulse response of the channel should be ge be appreciated. The impulse response is determined by the reflective objects from the emitted signal be hit and who scatter this back to the recipient. By interpreting the estimated impulse response therefore information about the location, size and type of get reflective objects.

Achieving high accuracy in impulse response Estimation requires wide bandwidth and high energy sent impulses. High pulse energy is said to be involved lowest possible peak power of the transmitter output stage  be achieved in order to keep the transmitter effort small. The known promotions can be known to use expanded impulses of large time-bandwidth product fulfill.

DE 38 11 282 A1 and US Pat. No. 5,070,337 Method for determining the impulse response of a Transmission channel with expanded impulses from one Receive signal using knowledge in a transmitter generated periodic or aperiodic test signal known, the received signal to which a correlated or uncorrelated interference signal can be superimposed in one Receiver first one signal-adapted to the test signal Filter is fed.  

The system model from which the invention is based is shown in FIG. 1, wherein 1 denotes a transmitter, 2 a transmission channel, 3 an adder and 4 a receiver. All signal forms limited to a measurement bandwidth B bandbe are assigned a sequence of equidistant, time-discrete samples in the equivalent low-pass range. Complex scalar quantities are identified by underlining. Matrices and vectors are shown in bold. The symbols (.) * And (.) ^T mean conjugate complex or transposed.

The expanded send pulse

a = ( a ₁ , a ₂ ... a _N ) ^T , (1)

the length N at the output of the transmitter 1 according to FIG. 1 passes through the transmission channel 2 with the impulse response

x = ( x ₁ , x ₂ ... x _M ) ^T , (2)

consisting of M distance gates, each of which is assigned a complex reflectivity x _i , i = 1 ... M. With the additive noise

n = ( n ₁ , n ₂ ... n _{M + N-1} ) ^T , (3)

which is fed by the adder 3 , and the Toeplitz matrix

 the received signal is calculated

e = ( e ₁ , e ₂ ... e _{M + N-1} ) ^T = A x + n , (5)

where A x describes the discrete convolution of the expanded impulse a with the impulse response x .

The principle of signal processing in the receiver 4 already described in DE-PS 7 68 068 and used exclusively in today's practice to solve the development problem in determining the impulse response x from the received signal e at a priori known expanded transmission pulse a is based on the Filtering of the received signal e using a filter matched to the expanded transmit pulse a (matched filter). The estimated value is obtained at the output of the signal-matched filter which can be implemented as a digital correlator

_MF = A ^{* T} e = ( A ^{* T} A ) x + A ^{* T} n (6)

the channel impulse response x . To calculate the estimated value _MF , MN complex multiplications are to be carried out. For all real expanded pulses a, the correlation secondary maxima of the autocorrelation function as the elements outside the main diagonals of the matrix A * ^T A in equation (6) falsify the estimate _{MF of} the impulse response x . Such falsifications can lead to the pretense of non-existent targets or to mask the main correlation peaks due to weakly reflecting targets by secondary correlation maxima due to strongly reflecting targets. Therefore, one has to limit the use of expanded impulses that are bred to low correlation secondary maxima. Such a limitation is a hindrance when radar systems with signal form agile are to be realized, in which one wants to choose from the largest possible class of expanded impulses. Even with specifically mismatched filters, the harmful correlation values can only be reduced with a lower signal-to-noise ratio (SNR) at the filter output due to the mismatch loss, thus only alleviating the problems associated with the correlation secondary maxima in channel estimation.

An advantageous alternative to signal (mismatched) filtering is that in the article by T. Felhauer, P. Voigt, PW Baier and A. Mämmelä: "The optimal estimate as a beneficial alternative to the correlation in radar systems with expanded pulses" in the magazine "AEÜ"", Vol. 46, 1992, pages 32 to 37 described unbiased optimal estimate. At the output of an optimal estimator for uncorrelated noise n , equation (4) gives the estimated value

_os = ( A * ^T A ) ^-1 A * ^T e = x + ( A ^{* T} A ) ^-1 A ^{* T} n . (7)

According to equation (7), the estimated value _{os can be separated} into the true value of the channel impulse response x and into an additive noise component of minimal variance and is therefore referred to as the optimal, true-to-expect estimate. The price for the complete elimination of the correlation secondary maxima thanks to the expectations is a low SNR degradation compared to the signal-adapted filtering for a large class of expanded pulses.

The algorithm of the optimal estimation according to equation (7), in which the received signal e has an M × (M + N - 1) estimation matrix

M = [ m _ij ] = ( A * ^T A ) ^-1 A * ^T (8)

can be multiplied using a digital correlator according to FIG

L = 2 M + N - 1 (9) time-variant tap coefficients w _i (k), i = 1 ... L, at the input of L multipliers 6 and with L - 1 delay elements 5 and a summing element 7 . The estimated value _os according to equation (7) at the output 8 of the correlator is obtained when the tap coefficients w _i (k) change according to the elements m _ij in the different rows of the estimation matrix M according to equation (8). To calculate the estimated value _os , M. (M + N - 1) complex multiplications are to be carried out. If the number M of the distance gates of the channel impulse response x is very much greater than the length N of the expanded impulse a , which is often the case in pulse radar systems, the expected optimal prediction is associated with a computational effort that is significantly greater compared to the signal-adapted filtering.

The invention has for its object a novel Procedure for high-resolution channel estimation for transmissions systems, especially pulse radar systems, with expan impulses based on the expected expectations To create a painting estimate, the computational effort at approximately the same accuracy of the estimated value of the channel impulse response is significantly lower than that of the expected The best estimate according to equation (7).

This task is carried out in a generic method by the in the characterizing part of claim 1 specified features solved.

Appropriate developments of the inventive method rens and an advantageous device for carrying out of the method are in the further claims specified.

The following is a procedure and a setup for cost-effective high-resolution channel estimation relevant invention explained with reference to figures.

Show it

Fig. 1 is an illustration of the system already described model,

FIG. 2 estimator known way to implement a loyal expected Optimal already described,

Fig. 3, the separation of the unbiased optimum contemptuous in decomp matched filter and Nebenmaxima- reduction filter,

Fig. 4, the low-complexity sub-optimal way according to the invention for implementing the expectation true optimal estimation,

Fig. 4a, the autocorrelation function of FIG. 4,

FIG. 4b shows the correlation function of FIG. 4,

Fig. 5 shows a typical channel impulse response x in pulse radar systems,

Figure 6a, b., C is the estimated values _MF, x _I x _'II'

Fig. 7 post-filtered areas of the estimated value _II

Fig. 8, the resulting estimated as a superposition of the estimate _I and the postfiltered estimated _II,

Fig. 9, the signal-to-noise ratio (SNR) Degradation d (L) dependent on the filter length L for a Frank code of length N = 36,

Fig. 10 is a block diagram of a device for the implementing of the method for high-resolution low-cost channel estimation.

In order to obtain a deeper insight into the optimal estimate that is true to expectations and to enable a clear comparison with the signal-adapted filtering, FIG. 3 shows the optimal estimate 9 that is true to expectations in the two function blocks signal-adapted filter 10 and secondary maximum reduction filter 11 .

The matched filter 10 first maximizes the signal-to-noise ratio γ _max at its output 12 , while the secondary maximum reduction filter 11 eliminates the disturbing secondary correlation maxima in the estimated value _MF . The price for this elimination of the secondary correlation maxima is a signal-to-noise ratio γ _a reduced at the output 13 of the secondary maximum reduction filter 11 in comparison to the maximized signal-to-noise ratio γ _max by the SNR degradation d. The optimal estimate that is true to expectations thus represents an extension of the theory of conventional signal-adapted filtering. However, since in general all elements v _{ij of} the matrix ( A * ^T A ) ^-1 are different from zero, the implementation of the secondary maximum reduction filter 11 is very large Associated effort. An inexpensive way of implementing the addition to the maxima reduction filter 11 becomes apparent when considering the structure of the matrix ( A * ^T A ) ^-1 which is typical regardless of the expanded impulse and which is structured approximately Toeplitz, ie all elements are in a respective diagonal approximately the same, and for which the amounts | v _ij | of the elements v _ij decrease sharply with increasing distance from the main diagonal.

If the matrix is approximated by an ideally structured Toeplitz matrix, z. B. the elements of the middle row of the matrix ( A * ^T A ) ^{-1 determine} the elements in the respective diagonals of the ideal Toeplitz-structured matrix, and taking into account only the L elements with the largest amounts around the main diagonal of the matrix ( A * ^T A ) ^-1 , the secondary maximum reduction filter 11 can be suboptimally inexpensive with a digital correlator according to FIG. 2, but with L time-invariant tap coefficients

be implemented. Fig. 4 illustrates this example of a Barker code of length N is equal to 13 as the expanded transmitted pulse a. In response to a single expanded pulse a , the autocorrelation function shown in FIG. 4a is obtained at the output of the signal-adapted filter 10 . This autocorrelation function is filtered with a secondary maximum reduction filter 11 , whose L is equal to 50 coefficients according to equation (9) selected from the middle line of the matrix ( A. ^T A ) ^-1 , so that the correlation function shown in FIG Output of this secondary maximum reduction filter 11 results. When calculating the matrix ( A. ^T A ) ^-1 , M was assumed to equal 500 distance gates of the channel impulse response x to be estimated.

In addition to a reduction in the correlation secondary maxima, which also occurs in known similar methods, the correlation function ( FIG. 4b) at the output of a secondary maximum reduction filter 11 specified according to equation (10) has a special feature which is of fundamental importance for the following considerations is. This special feature is the area around the main correlation peak, which always occurs regardless of the selected expanded transmission pulse. The width Δ of this range can be determined in accordance with any expanded pulse of length N solely by the number L of the tap coefficients of the secondary maximum reduction filter 11

Δ = L - (2N - 1) + 1 (11)

can be varied. This secondary maximum-free area always occurs when the entire autocorrection function to be filtered ( FIG. 4a) is at the output of the signal-adapted filter 10 within the secondary maximum reduction filter 11 that can be implemented as a digital correlator.

Due to a complex reflectivity x _{i the} additive uncorrelated noise n is calculated using the covariance matrix

R _n = E ( n n * ^T ) = σ _n ² I (12)

the maximum signal-to-noise ratio at the output of the matched filter 10

Depending on the number L of the tap coefficients w _{i of} the secondary maximum reduction filter 11 , the useful portion is calculated on the basis of the i-th complex reflectivity x _i in the i-th distance gate

Designating the elements of the matrix A * ^T A with b _ij , i, j = 1 ... M, where the elements b _{ij describe} the correlations between the noise values at the output of the signal-matched filter 10 , the variance of the Noise component in the i-th distance gate at the output of the secondary maximum reduction filter 11

to calculate. Equation (14) and equation (15) are used to calculate the signal-to-interference ratio in the i-th distance gate at the output of the secondary maximum reduction filter 11

The SNR degradation is calculated depending on the number L of the tap coefficients w _{i of} the secondary maximum reduction filter 11

 to

The SNR degradation d (L) according to equation (18) is thus the price that must be paid for the suppression of the correlation ne benmaxima by the secondary maximum reduction filter 11 .

The correlation secondary maxima recognizable in FIG. 4 at the output of the secondary maximum reduction filter 11 arise exclusively during the entry or exit of the autocorrelation function to be filtered ( FIG. 4a) into or out of the secondary maximum reduction filter 11 . In addition to the number L of the tap coefficients of the secondary maximum reduction filter 11, the level of these secondary correlation maxima is also strongly dependent on the choice of the expanded pulse a, in contrast to the width of the region free of secondary maxima.

For the following algorithm for high-resolution channel estimation, the correlation secondary maxima, which arise when the signal to be filtered enters and leaves the secondary maximum reduction filter 11, are of no importance. The algorithm utilizes only the independent of the selected expanded pulse always occurs next maxima devoid region about the correlation main peak and the informa tion due to the interpretable as an intermediate estimated value estimated value _MF at the output of the matched filter Furthermore, characterized in pulse radar systems, to be estimated channel impulse responses x typically by individual groups of closely spaced non-vanishing reflectivities. Fig. 5 shows the amount in a typical pulsed radar systems channel impulse response consisting of M equal to 500 range gates, said non-vanishing only in nine range gates reflectivities occur. These non-vanishing reflectivities are arranged as two groups, each with four reflectivities and a single reflectivity.

If a Frank multi-phase code of length N equal to 36 is used as the expanded pulse a , then with an input-signal-to-noise ratio a _e of 35 dB, the estimated value _MF shown in FIG. 6a at the output of a signal-adapted filter 10 is obtained . Due to the disturbing correlation secondary maxima, the five smallest reflectivities are masked, so that only the four largest reflectivities can be detected. Furthermore, the estimated value _MF can easily be separated into a part _I , in which the disturbing estimation errors are of a purely stochastic nature, see FIG. 6b, and a part _II , in which the disturbing estimation errors are mainly caused by correlation secondary maxima, see FIG. 6c will.

Part _I also includes the detected individual reflectivity, since the correlation secondary maxima are below the noise level at the output of the signal-adapted filter 10 due to this reflectivity below the signal-to-noise ratio a _e and the process gain P _max . Post-filtering _i is therefore not sensible. In contrast, additional reflectivities can be masked by the correlation secondary maxima in Part _II , which makes a post-filtering of _II useful. Part _II can also be separated into two areas, which can be filtered independently of each other. Since these areas are known as a whole for a longer period, the entry and exit of these areas into the secondary maximum reduction filter 11 specified according to equation (10) can be avoided.

If the length L _{x of} the region to be filtered is _II, the number L of the tap coefficients of the secondary maximum reduction filter 11 increases

L = 2 L _x (19)

selected, it can be ensured that the area de _II to be filtered is always moved completely within the secondary maximum reduction filter 11 during the L _x clock steps for calculating the post-filtered estimated value, and thus the secondary correlation maxima are eliminated. Fig. 7 shows _II, after filtering, the individual with the preparation surface according to equation (10) and equation (19) speci fied secondary maxima reduction filter 11. Fig. 8 shows the resulting estimate of the channel impulse response as a superimposition of the unfiltered area and the post-filtered area. It can be seen that all re flectivities can now be clearly detected.

While there is maximum process gain P _max in part _I, the SNR degradation d (L) according to equation (18) occurs in the post-filtered areas of _II depending on the number L of tap coefficients required for post-filtering according to equation (18). In Fig. 9, the SNR degradation d (L) of length N is plotted equal to 36 on the normalized filter length L / N for a Frank code. With the lengths L _x1 equal to 103 and L _x2 equal to 72, the corresponding ranges of _II with equation (19) and FIG. 9 can be the SNR degradations d (L _x1 ) equal to 1.6 dB and d (L _x2 ) equal to 1, 85 dB can be assigned.

The table below shows the number of complex multiplications for the respective estimation algorithms for determining an estimated value.

For the example according to FIGS. 6 to 8, the number of complex multiplications for calculating a quasi-secondary maxima-free estimated value could be reduced to 33793 or 12.6% with the inventive method for high-resolution channel estimation from 267500 with optimal expectations. Compared to the signal-adapted filtering, a significantly improved dynamic is achieved through a little additional effort. Since the side maxima free area in the output signal of the side maxima reduction filter 11 occurs independently of the selected expanded pulse, the system designer is no longer restricted to a small class of specially bred expanded pulses with good correlation properties when using the method according to the invention for high-resolution channel estimation. The resulting variety of signal shapes is particularly interesting if a signal-formable pulse radar system is to be implemented.

An advantageous device for implementing the method for cost-effective high-resolution channel estimation according to the invention is described below with reference to FIG. 10.

The received signal e first reaches a signal-matched filter 10 already present in conventional radar receivers. The estimated value _MF at the output 12 of the signal-adapted filter 10 is separated by a threshold circuit 14 controlled by a control logic 18 into a part _I at the output 16 which is not to be further filtered and into a part _II at the output 15 which is distorted by disturbing correlation maxima. The process gain P _max of the signal-adapted filter 10 determined by the length N of the expanded pulse and the signal-to-noise ratio γ _{e on} the input side determine the noise level at the output 12 of the signal-adapted filter 10 which is necessary for the separation. Parts _I and _II are first temporarily stored in digital memories 19 and 17, respectively. The individual areas of x _II are now sequentially filtered. If a region of _{II has} the length L _x , then the first 2.L _x tap coefficients w _{i of} the secondary maximum reduction filter 11 which can be implemented as a digital correlator are activated in accordance with equation (9). The area of length L _x of _II to be filtered is loaded into the first L memory cells of a shift register 22 . During the following L _x clock steps, the area to be filtered is correlated by _II with the tap coefficients w _i , i = 1 ... 2L _x previously activated by the control logic 18 . At the output 20 of a summing element 7 , the area of the post-filtered part _II which is free from interfering correlation secondary maxima is obtained. The digital correlator used for post-filtering (secondary maximum reduction filter 11 ) consists of a shift register 22 with 2M memory cells, 2M multipliers 6 for feeding in the maximum 2M activated tap coefficients w _i and the summing element 7 . However, the maximum number of 2M tap coefficients is only activated if the entire estimated value at the output 12 of the filter 10 matched by the signal is falsified by disturbing correlation secondary maxima, ie if _MF is _II . After all areas of _{II have been} re-filtered, the resulting estimate is determined in digital memory 19 by overlaying _I with the part _II that has been re-filtered and output at output 21 .

The maximum 2M tap coefficients required for post-filtering can be calculated a-priori off-line for the expanded transmission pulse used and stored in one of the digital memories 17 or 19 . Since the accuracy of the estimated value at the output 21 of the device according to FIG. 10 depends only to a small extent on the correlation properties of the expanded transmission pulse, the method according to the invention can be used particularly advantageously in signal-formable radar systems, since the system designer chooses the expanded pulses is no longer limited to a class of specially bred waveforms. In a signal-formable radar system, the corresponding 2M tap coefficients must be calculated off-line according to equation (10) for all the expanded pulses used and stored in a digital memory in the receiver. In contrast, if the optimal estimate according to equation (7) is used, a complete estimation matrix M with M. (M + N - 1) elements would have to be stored in the receiver for each expanded pulse used. The method according to the invention is thus not only significantly less expensive (see the table already explained above), but also can be implemented much more memory-efficiently than the optimal estimate that is true to expectations.

By a slight modification of the control logic 18 can also be achieved with the device according to FIG. 10 who the that only reflectivities of particular interest render distance gates without systematic errors due to correlation secondary maxima and thus be estimated with the greatest accuracy. Such a modification would be of particular importance in a target tracking radar, where the distance of objects by the tracking algorithm is known a priori in a certain area.

Claims (10)

1. A method for determining the impulse response x (t) of a transmission channel with expanded impulses from a received signal e (t) using the knowledge of the periodic or aperiodic test signal a (t) generated in a transmitter on the basis of the known, so-called expected, optimal estimate The received signal e (t), to which a correlated or uncorrelated interference signal n (t) can be superimposed, is first fed in a receiver to a filter adapted to the test signal a (t) and then to a further filter for reducing the correlation secondary maximum, characterized in that the output signal of the signal-matched filter ( 10 ) by a threshold value-forming decision algorithm into a part to be filtered, in which the disturbing estimation errors are mainly caused by correlation secondary maxima, and a part not to be filtered, in which the disturbing estimation errors are of a purely stochastic nature, we separated d, whereby only the part to be filtered is fed to the further filter ( 11 ), the transmission behavior of which is determined by the test signal a (t) and the length of the part to be filtered, and which thereby eliminates the disturbing correlation secondary maxima regardless of the type of test signal a (t) that it determines an accurate estimate of the transmission channel within the time range assigned to the part to be filtered. 2. The method according to claim 1, characterized, that by means of the filter matched to the signal Filters the disturbing secondary correlation maxima suboptimally only be suppressed to the extent that they are in the output side Noises disappear. 3. The method according to claim 1 or 2, characterized, that the signal-to-noise ratio of the signal before and / or  after the matched filter, first by coherent and / or incoherent integration is increased by the post to be able to carry out the following separation more easily. 4. The method according to any one of claims 1 to 3 characterized, that the received signal in the receiver before further processing processing is digitized first. 5. The method according to any one of the preceding claims, marked by use in a pulse radar receiver. 6. Device for performing the method according to one of the preceding claims, characterized in that the output ( 12 ) of the signal-adapted filter ( 10 ) with a signal separation device ( 14 ) influenced by the decision algorithm is connected, that the output for the output signal portion of the signal separation device to be filtered ( 14 ) is connected to a secondary maximum reduction filter ( 11 ), and that the output for the signal portion not to be refiltered and the signal passed through the secondary maximum reduction filter ( 11 ) are combined to form a common output signal. 7. Device according to claim 6, characterized in that the signal separation device is realized by a controllable threshold circuit ( 14 ) in connection with a control logic ( 18 ). 8. Device according to one of claims 6 and 7, characterized in that all filters ( 10 , 11 ) are implemented in analog technology, in particular in the form of electroacoustic tapped delay lines or electroacoustic convolvers. 9. Device according to one of claims 6 and 7, characterized in that all filters ( 10 , 11 ) are implemented by correlators with time variants and / or time invariant evaluation coefficients in digital technology and to control the process sequence one or more digital processors or other digital Control units are provided. 10. The device according to claim 9, characterized in that the output ( 12 ) of the matched filter ( 10 ) to the input of a threshold circuit ( 14 ), the Schwle le is controlled by a control logic ( 18 ), that the threshold circuit is two Outputs ( 16 , 15 ), one of which ( 16 ) outputs the signal part ( _I ) which is not to be further filtered to a first input of a first digital memory ( 19 ) which is also controlled by the control logic ( 18 ), and of which the another ( 15 ) passes the signal part ( _II ) to be filtered to an input of a second digital memory ( 17 ) which is also controlled by the control logic ( 18 ), that the output of the second digital memory ( 17 ) has a secondary maximum reduction filter ( 11 ) forming digital correlator is connected, which previously activate from a shift register ( 22 ) with 2M memory cells, 2M multipliers ( 6 ) for feeding a maximum of 2M by the control logic ( 18 ) tap coefficients (w _i ; i = 1 ... 2M) and a summing element ( 7 ) is composed that the output ( 20 ) of the summing element is connected to a second input of the first digital memory ( 19 ) and that in the first digital memory ( 19 ) it is not post-filtered ( _I ) and the post-filtered part ( _TE ) of the signal, ie the signal parts fed to its two inputs, are superimposed and result in a resulting estimate (), which is taken from the output ( 21 ) of the first digital memory ( 19 ).