DE4219417A1 - Narrow-band data signal receiver from long-wave transmitter - employs Hilbert transform to produce in=phase and quadrature signal components for coordinate rotation digital computer. - Google Patents

Abstract

The first order Hilbert sampling receiver employs three sample-and-hold circuits, and one digitiser in multiplex operation. Samples are taken at intervals corresp. to one-quarter of the carrier frequency (T) by one sampler for the in-phase and two samplers for the quadrature branch. The digitised signals are weighted and applied to a CORDIC processor which performs immediate amplitude and phase demodulation. Alternatively each of the three samples may have its own digitiser. USE/ADVANTAGE - Suitable for all kinds of modulation. In-phase and quadrature components can be produced for band pass signals in receiver.

Description

The invention relates to a method for receiving narrowband Signals according to the preamble of claim 1.

The method presented is intended for the demodulation of amplitude-, phase- or frequency-modulated signals or a combination of the three modules types of lations are equally suitable.

It is known that for the interference-free reception of long-wave signals particularly well incoherent receivers and especially quadrature are suitable recipients (German Patent No. P 37 33 967.2). As The classic receiver here is the quadrature overlay receiver name (Lüke, signal transmission, Springer textbook 1990, 4th edition, Pages 110-113) (H.W. Schüssler, networks, signals and systems, Textbook 1984, 2nd edition, pages 431-446). Following antenna, ver Strengthening and filtering becomes the input signal of a sine and a cosi nus mixing stage supplied. Inphase (I) and quadrature phase (Q) are created. Filtering then takes place in the so-called intermediate frequency range. The two signal branches become a complex analytical signal composed. This analytical signal only has spectra for positive frequencies tral parts, so that there is no aliasing by undersampling negative frequency components can come.

In (German Patent No. P 37 33 967.2) a digital variant is featured in which the generation of the I and Q phases by a T / 4 sampling shifted to the sampling frequency is made. Here An analytical is also created after intermediate frequency range filtering Time signal.

Demodulation of amplitude-modulated signals can be carried out here Quadrature and rooting can be achieved while for demodulation an arctangent calculation is necessary for phase-modulated signals. For frequency demodulation, phase demodulation still has to be done the time derivative is formed. (Lüke, signal transmission, jumper Textbook 1990, 4th edition, pages 232-237) (J. Wietzke, Darmstadt Promo tion 1988, criteria for the uniform assessment of the principle  Performance of different time signal receivers with inclusion new digital variants, page 10) It is also known that the Hilbert transform is a special filter represents that by means of a special frequency characteristic from the In-phase component generates the quadrature component (H.W. Schüssler, Networks, Signals and Systems, Springer textbook 1984, 2nd edition, pages 475-481) (Kammeyer / Kröschel, digital signal processing, Teubner Study books 1989, pages 119-122). In the digital area this can be done appropriate filters z. B. according to the method of "pulse invariant transforma tion "or the" least squares method ".

Finally, the CORDIC method is known as an iterative procedure (magazine "IRE Transaction on Electronics Computer", Sept. 1959, JE Volder, The CORDIC Trigonometric Computing Technique), which is suitable for the calculation of various trigonometric functions. In particular, when initializing with X-register = x, Y-register = y, phase register = 0 in "rotation mode", a calculation of radius R = (x ² + y ² ) ^0.5 and phase R = arctan (y / x) can be carried out .

However, these known methods have disadvantages. When squaring Superimposition and quadrature scanning is in any case in the intermediate frequency quenzbereich perform a filtering, which is an additional effort represents. The intermediate frequency is usually chosen to be fixed. This leads to, since both in-phase and quadrature phases must occur without aliasing, to considerable restrictions in the choice of the sampling rate of the (sampling) - Mixer.

The sampling above the Nyquistrate in connection with the Hilbert With today's capabilities, transformation as a digital filter is the Processors only possible at low frequencies. Here, on the for Bandpass signals restricted requirements for the Hilbert transforma tion, no consideration.

When demodulating using the in-phase and quadrature components a direct algebraic computation for phase modulation (arctangent) Development over series development very complex.

The invention has for its object a generation of in-phase and Quadrature component for bandpass signals in a universal receiver, d. H. a receiver that is set up for all types of modulation enable.

This task is in a generic method by the kenn Drawing features of claim 1 solved.

In a further embodiment of the invention, in particular for implementation a universal demodulator, comes according to claim 2 CORDIC processor used, the one phase and amplitude demod performed. Was a subsampling according to claim 10 made by the Hilbert scanner, the rotating carrier needs frequency pointer not to be considered. For frequency modulated Signals is a mathematical differentiation according to claim 8 to carry out over several neighboring values of the phase demodulator. The CORDIC processor can be implemented with little effort speaking claim 5 represents the state machine while for maximum Processing speed before a complete pipeline structure is drawn.

For frequency demodulation can according to claim 9 directly I and Q phases are used. Here is the standardized product rule chatting

(I dQ / dt-Q dI / dt) / (I ² + Q ² )

to calculate.

Touches the Hilbert scanner according to claim 4 at a distance T / 4 Signal frequency, so the further operations to be performed, to generate the I and Q phases, minimal.

Within these pulse groups can according to claim 3 a weighting of the samples for special bandwidth ratios to the center frequency by the Hilbert scanner a good approximation to the Hilbert transformer can be achieved.  

The advantages achieved by the invention are in particular that the effort for the Hilbert transformation using the Hilbert scanner becomes particularly low. The main three advantages are:

• a) In contrast to the quadrature receivers, it is not another Intermediate frequency filtering necessary.
• b) Even with a few weighted samples, see Table 1-3, very good results are achieved. An error of less than 5 _* 10 ^{-5 is} already achieved by the symmetrical Hilbert scanner of the first order, which corresponds to the error in 14-bit quantization. With the quadrature receivers the error is greater by a factor of 1000 with the same ratio of bandwidth to center frequency.
• c) CORDIC demodulation is used primarily for phase demodulation tion a considerable cost advantage compared to direct algebrai calculation reached.

Embodiments of the invention are shown in drawings and are described in more detail below.

Fig. 1 shows the classic implementation of I / Q generation by mixing with the signals of the form cos (2πf _m t) and -j2sin (2πf _m t). With this realization, bandpass filtering must be performed in the IF range f _z = f ₀ -f _m . This is illustrated in Fig. 2 in the spectral range. Fig. 2 (a) shows the bandpass signal at the input of the receiver. After multiplication with the cos signal (spectrum: S _2cos (f)) or the sin signal (spectrum: S _-j2sin (f)), the in-phase component 1 (f) and the quadrature component jQ ( f), see Fig. 2 (d) and (e). These two signals are combined into a complex signal I + jQ, see Fig. 2 (f). Finally, the bandpass filtering mentioned must be carried out. The spectrum from FIG. 2 (g) results. It should be noted that this spectrum has no shares at negative frequencies. This signal is referred to as analytical (HW Schüssler, networks, signals and systems, Springer textbook 1984, page 477) (Lüke, signal transmission, Springer textbook 1990, page 107). The property is typical for all incoherent receivers with I and Q phases and is therefore particularly emphasized here.

If you are looking directly for a filter that forms an analytical signal from a real signal, the Hilbert transformer is a good choice, see Fig. 3 and Fig. 4. The addition of the input signal S (jH (f)) f) and the input signal itself leads to the analytical signal sought.

The associated impulse response and transfer function of the Hilbert-Trans formators result from simple calculation using the definition the Fourier transform to h (t) = 1 / (πt) (H. Marko, methods of Systems Theory, 2nd Edition, Springer Verlag, page 125) The Hilbert transformer can only be realized approximately Lich, because the spectrum has jump points.

For a narrowband bandpass signal there are much lower demands on the Hilbert transformer than for a broadband signal. It only has to be ensured here that the Hilbert transformation condition is valid in the area Df around f ₀ , see FIG. 5.

Hilbert scanning receivers of different approximation and Complexity presented, the order i from the number of use th samples in the Q branch gives:

Order i = <2 ⁱ samples.

The requirement of FIG. 5 is already quite time-line by an analogous run with the duration of T _L = 1 / approximated (4 f _0). This can also be derived from the second name "90 ° phase shifter" for a Hilbert transformer.

The real part in this system becomes identical at f = + / - f ₀ and the imaginary part results at f = + / - f ₀ to Im {H _BP (+/- f ₀ } = - / + j.

This approach can be easily transformed into the digital domain, see Fig. 6 (b).

The delay in the Q branch of the analog Hilbert transformer corresponds to a scan leading by T _L when scanning in the digital range.

Since only one sample value is used here to implement the Hilbert transformer, this system is to be referred to as "zero-order Hilbert scanner". Since Hilbert zero-order scanners and quadrature scanning receivers according to (German Patent No. P 37 33 967.2) appear very similar, these two scanning principles are compared in FIG. 7 for clarification. The parameter M describes the factor of undersampling compared to a sampling with Nyquistrate, ie sampling rate with twice the highest signal frequency component. M = 1 thus describes a sampling with Nyquistrate. M = 2 describes an undersampling by a factor of 2, etc. In the zero order Hilbert sampling, a sampling shifted by 90 ° to the signal period (T _L = 1 / (4 f ₀ )) is carried out, while in the quadrature sampling one by the sampling period 90 ° shifted scanning is carried out (T _L = 1 / (4 f _A )).

The Hilbert zero-order scanner delivers for very narrow-band signals pretty good results by adding more samples (and possible weighting) can still be improved. Are principally two different strategies possible:

• a) If terms with a longer transit time, which are favorably odd multiples of the delay T _L, are added, see FIG. 8 (a), a kind of Fourier series development of the Hilbert spectral function is carried out in the bandpass range under consideration. This approximation should be called asymmetrical. If one considers the I-scan as the zero point of the pulse group, then there is a purely acausal pulse group.
• b) The fact is used that an odd real time function has a purely imaginary odd spectrum. Since the real part is zero, the corresponding error also becomes zero. The scan sequence realized by Fig. 8 (b) is said to be symmetrical (strictly speaking, it is skew-symmetrical) since each pulse group is also symmetrical.

A modified method was used to optimize the coefficients Gradient descent method used, as z. B. in (Engeln-Müllges / Reuter,  Numerical Mathematics for Engineers, BI Wissenschaftsverlag, 5th edition, Page 170).

Now the results of the optimization are briefly explained. The optimism tion was carried out for three signals, the error measure as follows was chosen:

Minimum of the maximum error: | H _{BP, n} (f) - / + j |
+/- f ₀ -Δf / 2 <f <+/- f ₀ + Δf / 2.

Tables 1 to 3 show the results of the optimization. The use The signals were:

• a) DCF77 signal with f ₀ = 77.5 kHz and Δf = 20 Hz
• b) DCF77 signal with f ₀ = 77.5 kHz and Δf = 1 kHz
• c) FAX IF signal with f ₀ = 455 kHz and Δf = 6 kHz

It can be seen in the upper part of Table 2 that the symmetrical Hilbert scanner of the first order <(ie an I sample with a weight of 1 and two Q samples with a weight of +/- 0.5), for all the example signals for one 14-bit quantization is perfectly sufficient. This corresponds to a maximum error of 2 ^-14 = 6.1 10 ⁵ = 6,110 ^-3 %.

While Tables 1 and 2 show the results of a computer-specific optimization, Table 3 shows the result of a simplification for a technically favorable implementation. A coefficient 0.5 can thus be realized in the binary number system by a simple shift operation. A coefficient 1.5 only requires a shift operation and an addition. Table 3 also contains the maximum bandwidth Δf in Hz: for DCF77 signals and the ratio Δf / f ₀ for any bandpass signals for various resolution requirements in bits. If an n-bit resolution is required, there is a tolerable deviation from the ideal Hilbert transformer of E = 2 ^-n = 10 ^{-n * 6/20} .

As shown in the last section, a Hilbert sample receiver for bandpass signals can be implemented with relatively little error and little effort. If we now use the Hilbert scanner as in Fig. 9, the result is a complex analytical signal. This signal can now be reduced without an "integer band" violation occurring, since there is an analytical signal, see FIG. 10. Since the Hilbert transformation is carried out with a pure scanning receiver (with weighted coefficients) , the sampling rate reduction M _{1 can be included} directly in the sampling. In detail, FIG. 10 (a) is the (band-pass filtered) signal at the input of the receiver. In Fig. 10 (b) the sum of Hilbert transforms and the input signal itself represents Darge, as it arises due to the special position of the sampling times of the Hilbert scanner. Since A / D conversion and sampling rate reduction by M ₁ due to subsampling result in a periodic continuation of the analytical spectrum from FIG. 10 (b), convolution with D ₁ (f) must be carried out in the spectral range, which is shown in FIG. 10 ( d) shows. The digital signal now present (time function: s _dI [n] + js _dQ [n] = s _d [n]; spectrum: S _d (e ^{j ω} ) can now be decimated by M ₂ in a second decimation stage until the 10 (e) border repetition spectra, thus reducing the total by M = M ₁ M _2. The digitally decimated signal s _dd [n] with associated spectrum S _dd (e ^{j ω} ) is thus produced at the output of the receiver. .

In conclusion, there are two concrete versions of a Hilbert scan of the first order:

Fig. 11 shows the Hilbert scanner first order with a plurality of samplers, and an A / D converter in multiplex mode, in accordance with the claims 1-7. The signal at the receiver input is filtered and amplified by a pre-circuit. This is followed by an I scanner and two scanners for the Q branch. The samples are taken from the input signal at a distance T / 4 of the carrier frequency and stored in the capacitors. A voltage value is then fed to the A / D converter via an analog selection circuit (multiplexer). The digital signals are weighted digitally and then fed to the CORDIC processor, which immediately performs AM and PM demodulation.

Fig. 12 shows the Hilbert scanner of the first order with several A / D converters, according to claims 1-6. The signal at the receiver input is filtered by a pre-circuit and amplified separately in the individual branches. The gain can already include the coefficient weighting. This is followed by an IA / D converter and two A / D converters for the Q branch. The samples of the transducers are taken from the input signal at a distance T / 4 of the carrier frequency. The present digital signals are then read in by a CORDIC processor, which immediately performs AM and PM demodulation.

The advantages of the Hilbert scanning receiver are as follows sum up:

By generating an I and Q phase, a complex analyti is obtained signal.

Scan receivers are more suitable than the (analog) quadrature overlay receiver for the generation of the I and Q phase, since the multiplication by simple sampling is replaced.

"Integer band" scanning and quadrature scanning require careful selection of the parameters M, k and f _A for undersampling so that there is no "integer band" violation.

The Hilbert transformer is very easy to use with a Hilbert scanner approach.

The Hilbert scanning receiver is more suitable than quadrature scanning with subsampling, since no further filtering to generate I- and Q- Phase are necessary and there is also no Hilbert scan "Integer band" violation can come.

Of particular interest for the use of the CORDIC algorithm as a demodulator is the binary number representation), which is the direct result of the A / D conversion. The option of using the CORDIC principle to transform right-angled to polar coordinates (X, Y to R, R) is also used, since this directly represents AM or PM demodulation. A classic calculation of the polar coordinates with R = (X ² + Y ² ) ^0.5 and R = arctan (Y / X) requires extensive calculation and is significantly simplified by the CORDIC algorithm.

The CORDIC algorithm is an iterative procedure in which a pointer in the X, Y plane is rotated by a certain angle +/- α _i in each step. A distinction is made between vectorization (X, Y to R, R), which corresponds to demodulation, and rotation (R, R to X, Y), which corresponds to modulation.

In the following we want to restrict ourselves to vectorization, since a calculation of (R, R) has to be realized. The basic procedure is explained using the example from FIG. 13. The starting point is the vector "1", which is given as the X and Y coordinate value. This vector is now rotated by an angle +/- α _i in each iteration step so that it ultimately comes to lie on the X axis. The accumulated angle Σ _{i = 1} ^{i = n} α _i represents the phase sought, while the value of X _n corresponds to the radius sought. It can be shown (magazine "IRE Transaction on Electronics Computer" Sept. 1959, JEVolder, The CORDIC Trigonometric Computing Technology) that the vector rotation can be traced back to simple arithmetic shift and add operations:

X _{i + 1} = X _i- / + Y _i 2 ^{- (i-2)}
Y _{i + 1} = Y _i +/- X _i 2 ^{- (i-2)}

It can be seen that the calculations of X _{i + 1} and Y _{i + 1 are} very simple in terms of circuit technology (shift operation and addition).

The CORDIC algorithm can be used in a state machine as well also realize in a complete pipeline structure.

Both architectures can be advantageously implemented with a programmable gate array. FIG. 14 is a state machine with register arithmetic work is presented, which is preferred when possible space will be consumed in the PGA component.

If maximum processing speed is important, each calculation level of the algorithm is implemented in hardware, which leads to a complete pipeline structure. With the complete pipeline structure, it is possible that the phase register is initialized in such a way that the rotating carrier frequency pointer does not have to be taken into account in the further calculation by taking into account the reverse presentation. Is z. B. If a Nyquist scan is carried out, the phase register must be alternately initialized with 0 and 180 °. Such a complete pipeline structure, as successfully implemented in a programmable gate array, is shown in FIG. 15.

Captions for pictures and tables

Fig. 1 Analog implementation for generating the I and Q phase (quadrature superimposed receiver)
Fig. 2 Spectral representation of the analog I / Q generation
Fig. 3 The Hilbert transformer
Fig. 4 Formation of an analytical signal using a Hilbert transformer
Fig. 5 requirements for the Hilbert transformer with bandpass signals
Fig. 6 Analog Hilbert transformer with delay line and Hil bert scanner zero order
Fig. 7 Comparison of the scanning sequences of Hilbert scanner zero order and quadrature scanning with subsampling
Fig. 8 scanning sequence of the Hilbert scanner for the (a) asymmetrical and (b) symmetrical scanner
Fig. 9 Hilbert scanning receiver with subsampling
Fig. 10 Spectral diagram for Hilbert scanning receiver with subsampling by a factor of M ₁ = 2
Fig. 11 Hilbert first order receiver with A / D converter in multiplex mode
Fig. 12 Hilbert first order receiver with 3 A / D converters and coefficient weighting by amplifier setting
Fig. 13 Transformation from rectangular to polar coordinates using the CORDIC algorithm
Fig. 14 CORDIC processor implemented as a state machine
Fig. 15 CORDIC processor as a complete pipeline structure

Table 1: Coefficients of the unbalanced Hilbert sample receiver Table 2: Coefficients of the symmetrical Hilbert scanning receiver Table 3: Coefficients of a technically favorable realization of the Hil bert scanning receiver  

Table 1

Table 2

Table 3

Claims (12)

1.Procedure for the reception of narrow-band signals from special long-wave transmitters for data transmission (e.g. DCF77, DCF37, DCFS4, etc.) with the aid of a receiver which contains an antenna, amplifier, filter, scanner and digital circuits for signal evaluation, and in which the signal is first filtered and sampled in two signal paths (I and Q phases), characterized in that a Hilbert transformation is carried out approximately by suitable selection of the sampling times and with suitable coefficients during the sampling. 2. The method according to claim 1, characterized in that the Hilbert Trans formation of the resulting two phases are fed to a CORDIC processor, which performs AM and PM demodulation. 3. The method according to claim 1 + 2, characterized in that spe for the scanning ziale optimized coefficients according to Tables 1, 2 and 3 are used. 4. The method according to claim 1 or 3, characterized in that the (weighted) Samples offset from each other by a quarter period of the carrier frequency be taken. 5. Arrangement according to claim 1, 2 or 3, characterized in that the CORDIC Processor in the form of a complete pipeline structure or in the form of a state machine is realized. 6. Arrangement according to one or more of claims 1, 2, 3 and 4, characterized records that the sampling and coefficient weighting by different A / D Converter with associated input amplifiers takes place. 7. Arrangement according to one or more of claims 1, 2, 3 and 4, characterized records that the analog / digital conversion contains several samplers by one A / D converters are followed in the MULTIPLEX, taking the coefficient weighting done digitally.   8. Arrangement according to one or more of claims 1 to 5, characterized in net that for FM demodulation a mathematical differentiation of several neighbors real PM values (in the simplest case, a difference between two neighboring barter PM values). 9. Arrangement according to claim 1, characterized in that after the Hilbert Trans formation of FM demodulation through differentiation, addition and division according to the standardized product rule. 10. Arrangement according to one or more of claims 1, 2, 3, 6, 7 and 8, characterized ge indicates that subsampling (i.e. in violation of the known scan theorems) is carried out in which the respective scanning sequences are an integer Multiples of the period of the carrier frequency are apart (i.e. on such Kind that the rotating carrier frequency pointer to be the same with each scan is coming). 11. The arrangement according to one or more of claims 1, 2, 3, 6, 7 and 8, characterized ge indicates that oversampling is being performed on the phase register of the CORDIC processor is initialized negatively according to the carrier phase. 12. The arrangement according to one or more of claims 1 to 11, characterized net that the realization of a universal long-wave data receiver Scanners optionally have different Ab tuned to the different transmitters keying frequencies are supplied.