DE19616368C1 - Demodulation method for single side band signal - Google Patents

Abstract

The demodulation method involves using a phase method with a Hilbert transformation. This is followed by a calibration which is used to provide correction values for the offset errors of both signal components of the quadrature signal, a correction value for the amplification error of one quadrature signal component and a correction value for the phase error of the other quadrature signal component. A complex quadrature signal with a lower frequency is obtained via analogue quadrature mixing. This is then converted into a digital signal, before compensation via the stored error values, with formation of the sum or difference of the in-phase component and the Hilbert transformation of the quadrature component.

Description

The invention relates to a method and a device for demodulating a SSB signal using the phase method with a Hilbert transformation.

A method for demodulation using the phase method is already known (Report "Generation and demodulation of ESB signals using the phase meter thode "by Dr. Ing Ralph Oppelt in VHF reports 4/86). The report points to the low achievable sideband suppression. This method is preferred used by radio amateurs as it saves the need for a steep filter allowed and it is not a high sideband suppression of z. B. 60 dB arrives.

Digital methods for Hilbert transformation are also known and are e.g. B. in the report "Digital Single Sideband Modulation with Hilbert Transformation" by Christoph Tiefenthaler ("Electronics Industry" 2/87).

Previous purely analog methods lead to offset, amplitude and phase errors of the I and Q signals due to component tolerances, as described in the following signal descriptions by the expressions a _I , b _I and ϕ _I or a _Q , b _Q and ϕ _Q can be represented.

I (t) = a _I + b _I 0.5 U _N cos (ω _N t-ω _T t + ϕ _I ) + b _I 0.5 U _S cos (ω _S t-ω _T t + ϕ _I )

Q (t) = a _Q + b _Q 0.5 U _N sin (ω _N t-ω _T t + ϕ _Q ) + b _Q 0.5 U _S sin (ω _S t-ω _T t + ϕ _Q )

The signals I (t) and Q (t) are generated by an RF signal:

U _HF (t) = U _{N *} sin (ω _N t) + U _{S *} sin (ω _S t)

{Useful signal: U _N sin (ω _N t); Interference signal: U _S sin (ω _S t) with ω _S = ω _N -2ω _T }

is mixed by analog signal processing with the oscillator signal sin (ω _T t) for the I signal or cos (ω _T t) for the Q signal and only the resulting difference frequencies pass a low-pass filter.

In the case of a quadrature mix to a (low) intermediate frequency of an Emp The errors mentioned also have an impact on the quality of the Image rejection.

In the case of a quadrature mix on the baseband of a receiver, take the mentioned errors influence the sideband suppression of an ISB signal or the adjacent channel suppression of an SSB signal.

Attenuation of the image frequency by selective amplifiers is only with great Effort achievable, because the image frequency with a lower subsequent intermediate frequency is not sufficiently far from the frequency of the useful signal.

Another option for suppressing the image frequency lies in the opti of the analog quadrature mixer and the following filters. However, this is especially in the case of series production, only with high adjustment effort and high Costs attainable.  

In US-PS 4,803,700 a method and a demodulator for digital De modulation of an SSB signal described, in which the received SSB signal after bandpass filtering with an analog / digital converter into a digital signal is changed. The actual demodulation, i.e. H. Mixing, filtering and Hilbert transformation then takes place on the digital level.

This is an error due to the largely digital signal processing correction not provided and not required either. A disadvantage of this procedure rens is, however, that it is not readily suitable for SSB signals, that have a high dynamic range. In this case there is a risk that the analog / digital converter is overdriven and the demodulated output signal nal is incorrect or distorted. On the other hand, if this procedure is also for If high signal dynamics are to be suitable, an analog / digital converter must be switched on that meets particularly high requirements in this regard, where due to the effort and costs increase considerably.

The invention was therefore based on the object, a method and a cost-effective Device for demodulating an SSB (single side band) signal (also Called ESB signal) according to the phase method with a Hilbert transformation create with which a reliable demodulation especially of signals is possible with a particularly high dynamic range.

This object is achieved with such a method in that a calibration is carried out first, by means of the two first correction values for offset errors (aK _I , aK _Q ) of the I and Q signals of a quadrature signal, and a second correction value for amplification errors (bK = b _Q / b _I ) of the I signal and two third correction values for phase errors (| sin (ϕ _k ) |, | cos (ϕ _k ) |) of the Q signal can be determined and stored, and that in a first step analog quadrature mixture, a complex quadrature signal (I + jQ) with a low frequency (e.g. intermediate frequency or baseband frequency of a receiver) is generated, which is converted into a digital signal that in a second step an offset error (a _I , a _Q ), in a third step an amplification error (b _I , b _Q ) and in a fourth step a phase error of the I-signal or the Q-signal of the quadrature signal by applying stored correction values is before the sum or difference of the components consisting of the I signal and the Hilbert transformed Q signal is formed in a fifth step.

The object is further achieved by a device for carrying out the method for demodulating an SSB signal using the phase method with a Hilbert transformation solved, which is characterized by digital signal processing processing device with first to third storage devices for first to third cor correction values for the correction of offset, gain and phase errors of a com plex quadrature signal (I + jQ), which consists of a received SSB signal by analog down-mixing to a low frequency (e.g. intermediate frequency or baseband frequency of a receiver) and subsequent digitization was won.

The advantages of this method and the device are u. a. in that the sturgeon frequencies can be suppressed sufficiently without being in the RF frequency position must be attenuated by a filter or selective amplifier.

With a relative gain error of b _I / b _Q = 3% and a phase error of ϕ = 2 °, the interference signal is attenuated in the LF level of only 32.7 dB without applying a correction. By correcting the errors according to the invention, the attenuation can be improved to 60 dB.

The subclaims have advantageous developments of the inventive concept Go to content.  

According to the method, a calibration is preferably carried out before the first step, using the two first correction values for offset errors (aK _I , aK _Q ) of the I and Q signals, and a second correction value for gain errors (bK = b _Q / b _I ) of the I Signal and two third correction values for phase errors (| sin (ϕ _k ) |, | cos (ϕ _k ) |) of the Q signal are determined and stored.

The calibration can be carried out automatically at predetermined time intervals or if necessary, to be influenced by aging of analog components compensate.

For calibration, a sinusoidal test signal must be applied instead of the RF signal switches and demodulated, whose frequency from the carrier frequency of the De modulator deviates by a quarter of the digital sampling frequency, with the calculation Arithmeti correction values in successive calibration steps mean and rms values of the I and Q signals from four successive serve the samples.

In a first calibration step, the first correction values ak _I = -a _I and ak _Q = - a _Q for offset errors are preferably first calculated and stored from the arithmetic mean values of the I and Q signals of the quadrature signal.

In a second calibration step, the second correction value b _k = b _Q / b _I for the gain error is then calculated from the effective values of the offset error-corrected I and Q signals of the quadrature signal and stored.

Finally, the third correction values can be carried out in a third calibration step for the correction of phase errors of the offset error corrected and Hilbert-transformed Q signals based on the mathematical relationships

| sin (ϕ _k ) | = 2 _* Useff _* Udeff and

| cos (ϕ _k ) | = Udeff²-Useff²

are formed and saved, whereby

and Useff is the effective value of the sum I (t) + HT (Q (t)) and Udeff the effective value of the difference I (t) -HT (Q (t)) and HT (Q (t)) represents the Hilbert transformed Q signal Q (t).

In the actual error correction, the second step is preferred the offset errors of the I and Q signals by adding the stored first cor correction values for the I or Q signal corrected.

With the third step, the gain error of the offset corrected I-signal (I'-signal) compared to the offset-corrected Q-signal (Q'-signal) by Mul tiplication of the I'-signal balanced with the second correction value.

Finally, phase errors are corrected in the fourth step, the Q'-signal being Hilbert transformed (Q _HT signal), the gain-corrected I'-signal (I '' signal) and the Q'-signal around the Hilbert group delay -Transformation is delayed (I _dT - or Q _dT signals), the Q _HT - and the Q _dT signal is multiplied by the third correction values (Q _HT '- or Q _dT ' signals), the I _dT T -Signal is added to the Q _dT 'signal (S₁ signal) and the Q _HT ' signal is added to the S₁ signal (S₂ signal).

The Q _HT 'signal is preferably inverted and added to the S₁ signal (D₁ signal), and the signals S₂ and D₁ are converted into analog signals and output.

Furthermore, the Q _HT 'signal can be subtracted from or added to the I signal depending on the frequency position of the HF signal and the phase correction can be carried out with a positive or negative correction angle depending on the HF frequency position of the signal, with a signal whose frequency is greater is than that of the carrier, e.g. B. an upper side band, with the expression U _USB = I _dT -Re {(Q _HT + jQ _dT ) _* e⁻ ^{d k} } and a signal whose frequency is lower than that of the carrier, for. B. a lower sideband, with the expression U _LSB = I _dT + Re {(Q _HT + jQ _dT ) _* e ^{j ϕ k} } is calculated.

Finally, the algebraic sign for the third correction value sin (ϕ _k ) is preferably changed if the effective value of the difference signal is increased by the sole action of the amounts of the correction values sin (ϕ _k ) and cos (ϕ _k ).

The device is preferably characterized by a calibration device for loading calculation of the first to third correction values using one instead of the received test signal fed into the HF signal.

It also preferably assigns a Hilbert transformer Hilbert transformation of the offset-corrected Q signal (Q′-signal).

Finally, there are also a first and a second delay stage for delay of the I '' signal or the Q 'signal by the group delay of Hilbert transformer provided.

An embodiment of the invention results from the following description based on the drawing nung. It shows:

Fig. 1 is a schematic diagram of an embodiment of the invention and

FIG. 2 shows a detailed circuit diagram of the structure according to FIG. 1.

Fig. 1 shows a basic structure of a circuit according to the invention. An RF signal is present at its input, which is initially processed in an analog manner: a quadrature mixer 3 i, 3 q mixes with carrier signals sin (ω _T t) and cos (ω _T t), the sum frequency components of the I- and Q signals with downstream low-pass filters 4 i, 4 q are suppressed. The difference frequency signals of the mixed products are digitized in A / D converters 5 i, 5 q and then fed to a digital signal processing device 100 , in which the correction takes place. Then the corrected signal is converted into an analog LF signal with a D / A converter 200 .

The method and the device serve, in particular, to influence the influences of the amplitude error (offset error: a _I , a _Q and amplification error: b _I , b _Q ) of the I signal or of the Q signal and of the phase error ϕ = ϕ (I) - ϕ (Q) -90 ° of the quadrature signal, which consists of the complex signal I + jQ, to compensate.

The following explanations are given with reference to FIG. 2. Before the interference suppression can be improved, a calibration is necessary. The calibration is carried out by first carrying a test signal U _c sin (ω _c t) from an oscillator via a switch 2 to the first and second analog ring mixers 3 i, 3 q. The frequency of the test signal should deviate by fa / 4 (fa = sampling frequency of the analog-digital converter) from the oscillator frequency of the ring mixer in order to enable precise calculations of the signal levels. The first ring mixer 3 i also has the signal sin (ω _T ) and the second ring mixer 3 q the signal cos (ω _T ) for mixing. The case ω _c <ω _{T is} assumed for this description.

Only the differential frequency signals of the mixed products in the I and Q branches pass through the first and second low-pass filters 4 i, 4 q and are each forwarded to the digital signal processing 100 via the first and second A / D converters 5 i, 5 q.

The following signals are thus available:

I (t) = a _I + b _I 0.5 U _c cos (ω _c t-ω _T t + ϕ _I ) = a _I + b _I 0.5 U _c cos (ω _T t-ω _c t-ϕ _I )

Q (t) = a _Q Q + b _Q 0.5 U _c sin (ω _c t-ω _T t + ϕ _Q ) = a _Q -b _Q 0.5 U _c sin (ω _T t-ω _c t-ϕ _Q )

a _I and a _Q : offset error of the analog pre-stage.

b _I and b _Q : gain error of the analog preamplifier.

ϕ _I and ϕ _Q phase error of the analog preamplifier.

A calibration device 6 calculates the arithmetic mean values of the signals and from these the correction values for the offset errors ak _I = -a _I and ak _Q = -a _Q. These correction values are then written into a first or second memory 7 i, 7 q and from now on act via a first or second adder 8 i, 8 q to correct the offset errors of the signals I and Q.

The offset error-corrected signals I 'and Q' are then detected by the calibration device 6 in order to calculate the relative gain error b _I / b _Q. For this purpose, the effective values of the I'- and Q'-signals are calculated and the quotient b _I / b _Q = Ueff (I) / Ueff (Q) is formed. The RMS values are calculated by adding four successive samples in quadratic fashion. The correction factor b _k = b _Q / b _{I is then} calculated and written to a third memory 9 . From now on, the correction factor b _k acts on the I 'signal via a first multiplier 10 . Now that the amplitude errors of the signals have been corrected, the signals are:

I ′ ′ (t) = b _Q 0.5 U _c cos (ω _T t-ω _c t-ϕ _I ) and

Q ′ (t) = -b _Q 0.5 U _c sin (ω _T t-ω _c t-ϕ _Q )

to disposal. Now the value 1 is written into a fourth memory 11 a for the value cos (ϕ _k ) and the value 0 for the correction factor sin (ϕ _k ) into a fifth memory 11 b. These values form the complex value cos (ϕ _k ) + j sin (ϕ _k ) and, in principle, have a phase-shifting effect (initially with ϕ _k = 0 °) on the signal Q _HT + JQ _dT , which is now in a complex form digital Hilbert transformer 14 and a first delay element 15 is formed.

Since only the real part of the phase-shifted signal (Q _HT + jQ _dT ) _* e ^{j ϕ k} z. B. to generate the signal U _LSB = I _dt + Re {(Q _HT + jQ _dT ) _* e ^{j ϕ k} , only this is calculated as follows:
a first multiplier 12 forms the signal Q _HT ′ = Q _{HT *} cos (ϕ _k ),
a second multiplier 13 forms the signal Q _dT '= Q _{dT *} sin (ϕ _k ).

The I '' signal is delayed by a second delay element 16 by the group delay of the Hilbert transformer 14 and thus forms the signal I _dT . The group term of the Hilbert transformer T _H corresponds to n / 2 _* T _a ; n is the order of the Hilbert transformer and T _{a is} the sampling period of the digital part. By a third adder 17 , the sum signal S₁ = I _dT + Q _dT 'and by a fourth adder 18, the sum signal S₂ = S₁ + Q _HT ' is formed. With a fifth adder 19 and an inverter 20 , the difference D₁ = S₁-Q _HT 'is formed.

The signals S₂ and D₁ are calculated as follows:

S₂ = I _dt + Re {(Q _HT + jQ _dT ) _* e ^{j ϕ k} } = I _dT + Q _HT + Q _dT ′

D₁ = I _dT -Re {(Q _HT + jQ _dT ) _* e ^{-j ϕ k} } = I _dT - (Q _HT ′ -Q _dT ′)

With t ′ = t- (n / 2) _* T _a :

I _dT (t ′) = b _Q 0.5 U _c cos (ω _T t′-ω _c t′-ϕ _I ) and

Q _HT (t ′) = b _Q 0.5 U _c cos (ω _T t′-ω _c t′-ϕ _Q )

Q _dT (t ′) = -b _Q 0.5 U _c sin (ω _T t′-ω _c t′-ϕ _Q )

The calibration device 6 detects the level of the sum signal S₂ = I _dT (t ′) + Q _dT ′ (t ′) + Q _HT ′ (t ′) by forming the effective value. The following mathematical transformations should show that the level of the sum signal depends on the phase error of the quadrature signal:

I _dT (t ′) = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I )

Q _HT ′ (t ′) = Q _HT (t ′) _* cos (ϕ _k ) = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q ) _* 1

Q _HT ′ (t ′) = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q )

Q _dT ′ (t ′) = Q _dT (t ′) _* sin (ϕ _k ) = -b _Q 0.5 U _c sin ((ω _T -ω _c ) t′-ϕ _Q ) _* 0

Q _dT ′ (t ′) = 0

S₂ = I _dT (t ′) + Q _HT ′ (t ′)

S₂ = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I ) + b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q )

with: cos (α) + cos (β) = 2 _* cos ((α + β) / 2) _* cos ((α-β) / 2)

S₂ = b _Q U _c cos ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q ) / 2) _* cos ((- ϕ _I + ϕ _Q ) / 2)

The effective value is calculated in the device from four successive ones Samples by calculating the root of the sum of the squares of the samples becomes and corresponds to the effective value of S₂:

The calibration device 6 detects the level of the difference signal D 1 = I _dT (t ') + Q _dT ' (t ') - Q _HT ' (t ') by forming the effective value. The following mathematical transformations are intended to show how the level of the difference signal depends on the phase error of the quadrature signal:

D₁ = I _dT (t ′) + Q _dT ′ (t ′) - Q _HT ′ (t ′)

D₁ = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I ) -b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q )

with: cos (α) -cos (β) = -2 _* sin ((α + β) / 2) _* sin ((α-β) / 2

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q ) / 2) _* sin ((- ϕ _I + ϕ _Q ) / 2)

D₁ = b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q ) / 2) _* sin ((ϕ _I -ϕ _Q ) / 2).

The effective value is calculated in the device from four successive ones Samples by calculating the root of the sum of the squares of the samples becomes and corresponds to the effective value of D₁:

The quotient d _s = Useff / Udeff can be used to calculate the interference suppression d _s .

The interference signal suppression is optimal if the Q signal is rotated around the phase ϕ _Q -ϕ _I , since this means that the expression sin ((ϕ _I -ϕ _Q ′) / 2) = sin ((ϕ _I -ϕ _Q + (ϕ _Q -ϕ _I )) / 2) becomes zero. In order to calculate the correction factors sin (ϕ _k ) = sin (ϕ _Q -ϕ _I ) and cos (ϕ _k ) = cos (ϕ _Q -ϕ _I ), the values Useff and Udeff are formed by using the effective values Useff and Udeff with the factor

be multiplied.

Hence: Useff = | sin ((ϕ _Q -ϕ _I ) / 2 and Udeff = | cos ((ϕ _Q -ϕ _I ) / 2 |.

The amounts of the correction factors are then calculated as follows:

| sin (ϕ _k ) | = sin (2 _* (ϕ _Q -ϕ _I ) / 2) = 2 _* sin ((ϕ _Q -ϕ _I ) / 2) _* cos ((ϕ _Q -ϕ _I ) / 2) = 2 _* Useff _* Udeff ′

| cos (ϕ _k ) | = cos² ((ϕ _Q -ϕ _I ) / 2) -sin² ((ϕ _Q -ϕ _I ) / 2) = Udeff²-Useff².

After the values | sin ((ϕ _k ) | and | cos (ϕ _k ) | have been calculated, they are written into the fourth and fifth memories 11 a, 11 b and are thus effective. The following signals are now available:

I _dT (t ′) = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I )

Q _HT ′ (t ′) = Q _HT (t ′) _* cos (| ϕ _k |) = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q ) _* cos (| ϕ _k | )

Q _dT ′ (t ′) = Q _dT (t ′) _* sin (| ϕ _k |) = -b _Q 0.5 U _c sin ((ω _T -ω _c ) t′-ϕ _Q ) _* sin (| ϕ _k |)

Q _HT ′ (t ′) = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q ) _* cos (| ϕ _k |)

with: cos (α) _* cos (β) = 0.5 cos (α-β) + 0.5 cos (α + β)

Q _HT ′ (t ′) = b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |) + cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |))

Q _dT ′ (t ′) = -b _Q 0.5 U _c sin ((ω _T -ω _c ) t′-ϕ _Q ) _* sin (| ϕ _k |)

with: sin (α) _* sin (β) = 0.5 cos (α-β) -0.5 cos (α + β)

Q _dT ′ (t ′) = -b _Q 0.25 U _c (cos ((ω _T ω _c ) t′-ϕ _Q - | ϕ _k |) -cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |))

I _dT (t ′) = b _Q 0.5 U _c cos (ω _T t′-ω _c t′-ϕ _I ) and

Q _dT ′ (t ′) = -b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |) -cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |))

Q _HT ′ (t ′) = b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |) + cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |))

The calibration device 6 detects the level of the sum signal by forming the effective value:

S₂ = I _dT (t ′) + Q _dT ′ (t ′) + Q _HT ′ (t ′):
S₂ = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I ) -b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | Iϕ _k |) - cos ((ω _T -ω _c ) t ′
-ϕ _Q + | ϕ _k |)) + b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |) + cos ((ω _T -ω _c ) t′- ϕ _Q + | ϕ _k |))

S₂ = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I ) + b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |)

with: cos (α) + cos (β) = 2 _* cos ((α + β) / 2) _* cos ((α-β) / 2)

S₂ = b _Q U _c cos ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q + | ϕ _k | / 2) _* cos ((- ϕ _I + ϕ _Q - | ϕ _k |) / 2)

and the level of the differential signal:

D₁ = I _dT (t ′) + Q _dT ′ (t ′) - Q _HT ′ (t ′)

D₁ = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I ) -b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |) - cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |)) - b _Q 0.25 U _c (cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |) + cos ((ω _T -ω _c ) t′-ϕ _Q + | ϕ _k |))

D₁ = b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _I ) -b _Q 0.5 U _c cos ((ω _T -ω _c ) t′-ϕ _Q - | ϕ _k |)

with: cos (α) -cos (β) = -2 _* sin ((α + β) / 2) _* sin (α-β) / 2)

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q - | ϕ _k |) / 2) _* sin ((- ϕ _I + ϕ _Q + / | ϕ _k |) / 2)

D₁ = b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q - | ϕ _k |) / 2) _* sin ((ϕ _I -ϕ _Q - | ϕ _k |) / 2)

The difference signal only becomes zero if: (ϕ _I -ϕ _Q - | ϕ _k |) = 0. In this case, | ϕ _k | = ϕ _I -ϕ _Q. However, if we first assume that the angle ϕ _I -ϕ _{Q is} actually negative, the following applies:

| ϕ _k | = - (ϕ _I -ϕ _Q ) = ϕ _Q -ϕ _I.

| ϕ _k | in this case it must be replaced by ϕ _Q -ϕ _I. Will | ϕ _k | by (ϕ _Q -ϕ _I ) he results in:

S₂ = b _Q U _c cos ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q + | ϕ _k |) / 2) _* cos ((- ϕ _I + ϕ _Q - | ϕ _k |) 2)

S₂ = b _Q U _c cos ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q + ϕ _Q -ϕ _I ) / 2) _* cos ((- ϕ _I + ϕ _Q -ϕ _Q + ϕ _I ) / 2)

S₂ = b _Q U _c cos ((ω _T -ω _c ) t′- ϕ _I ) _* cos (0)

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q - | ϕ _k |) / 2) _* sin ((- ϕ _I + ϕ _Q + | ϕ _k | ) / 2)

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q -ϕ _Q + ϕ _I ) / 2) _* sin ((- ϕ _I + ϕ _Q + ϕ _Q - ϕ _I ) / 2) D₁ = -b _Q U _c sin ((ω _T -ω _c ) t′-ϕ _Q ) _* sin (ϕ _Q -ϕ _I )

Assuming that the angle ϕ _I -ϕ _{Q is} positive, we have: | ϕ _k | = ϕ _I -ϕ _Q. Will | ϕ _k | replaced by (ϕ _I -ϕ _Q ), we get:

S₂ = b _Q U _c cos ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q + | ϕ _k |) / 2) _* cos ((- ϕ _I + ϕ _Q - | ϕ _k |) / 2)

S₂ = b _Q U _c cos ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q + ϕ _I -ϕ _Q ) / 2) _* cos ((- ϕ _I + ϕ _Q --ϕ _I + ϕ _Q ) / 2)

S₂ = b _Q U _c cos ((ω _T -ω _c ) t′-ϕ _Q ) _* cos ((ϕ _Q -ϕ _I ))

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q - | ϕ _k |) / 2) _* sin ((- ϕ _I + ϕ _Q + | ϕ _k | ) / 2)

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t ′ + (-ϕ _I -ϕ _Q -ϕ _I + ϕ _Q ) / 2) _* sin ((- ϕ _I + ϕ _Q + ϕ _I - ϕ _Q ) / 2)

D₁ = -b _Q U _c sin ((ω _T -ω _c ) t′-ϕ _I ) _* sin (0)

Since both variants can be given, the effective value of the difference signal is recalculated after the phase amount has been applied for correction. If the level is greater than before, the sign of the correction factor sin (ϕ _k ) is changed.

After this last step, the calibration is complete. All correction values remain effective, and instead of the test signal, the RF signal is applied via switch 2 .

The demodulation of an RF signal, consisting of two useful signals, is now described after the calibration has been completed and the phase correction values for ϕ _k = ϕ _I - ϕ _{Q have been} set.

The following signals form the RF signal:

U _HF = U _{I *} sin (ω₁t) + U₂ _* sin (ω₂t) with z. B. f₁ = 63,000 MHz and f₂ = 62,940 MHz.

The RF signal is passed through the switch 2 and mixed down by the carrier signals sin (ω _T t) and coS (ω _T t) at the first and second mixer 3 i, 3 q (f _T = 62.97 MHz).

The sum frequency signals are suppressed by the first and second low-pass filters 4 i, 4 q. The differential frequency signals of the mixed products are supplied to the digital signal processing unit 100 via the first and second A / D converters 5 i, 5 q. The signals are initially:

I (t) = (U₁ _* sin (ω₁t) + U₂ _* sin (ω₂t)) _* sin (ω _T t) = 0.5 U₁ cos ((ω₁-ω _T ) t) + 0.5 U₂cos ((ω₂-ω _T ) t)

Q (t) = (U₁ _* sin (ω₁t) + U₂ _* sin (ω₂t)) _* cos (ω _T t) = 0.5 U₁ sin ((ω₁-ω _T ) t) + 0.5 U₂ sin ((ω₂-ω _T ) t)

The errors a _I , a _Q , b _I , b _Q , ϕ _I and ϕ _Q , which result from the analog signal processing, are taken into account as follows:

I (t) = a _I + b _I 0.5 U₁ cos ((ω₁-ω _T ) t + I) + b _I 0.5 U₂ cos ((ω₂-ω _T ) t + ϕ _I )

Q (t) = a _Q + b _Q 0.5 U₁ sin ((ω₁-ω _T ) t + Q) + b _Q 0.5 U₂ sin ((ω₂-ω _T ) t + ϕ _Q )

First, the offset errors are corrected by the first and second adders 8 i, 8 q. Then:

I ′ (t) = b _I 0.5 U₁ cos ((ω₁-ω _T ) t + ϕ _I ) + b _I 0.5 U₂ cos ((ω₂-ω _T ) t + ϕ _I )

Q ′ (t) = b _Q 0.5 U₁ sin ((ω₁-ω _T ) t + ϕ _Q ) + b _Q 0.5 U₂ sin ((ω₂-ω _T ) t + ϕ _Q )

The gain error of the I branch is matched to that of the Q branch by the first multiplier 10 . Therefore:

I ′ ′ (t) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t + ϕ _I ) + b _Q 0.5 U₂ cos ((ω₂-ω _T ) t + ϕ _I )

Q ′ (t) = b _Q 0.5 U₁ sin ((ω₁-ω _T ) t + ϕ _Q ) + b _Q 0.5 U₂ sin ((ω₂-ω _T ) t + ϕ _Q )

The following applies to even functions: cos ((ω₂-ω _T ) t + ϕ _I ) = cos ((ω _T -ω₂) t-ϕ _I ) and for odd functions: sin ((ω₂-ωbt + ϕ _Q ) = - sin ((ω _T -ω₂) t-ϕ _Q )

I ′ ′ (t) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t-ϕ _I )

Q ′ (t) = b _Q 0.5 U₁ sin ((ω₁-ω _T ) t + ϕ _Q ) -b _Q 0.5 U₂ sin ((ω _T -ω₂) t-ϕ _Q )

I '' (t) is delayed by a first delay stage 16 by the group delay T _{H of} the Hilbert transformer 14 :

I _dT (t ′) = 1 ′ ′ (tT _H )

I _dT (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I )

Q ′ (t) is transformed by the Hilbert transformer 14 :

Q _HT (t ′) = HT (Q ′ (t ′))

Q _HT (t ′) = b _Q 0.5 U₁ -cos ((ω₁-ω _T ) t ′ + ϕ _Q ) + b _Q 0.5 U₂ cos ((ω _T t-ω₂) t′-ϕ _Q )

and multiplied by cos (ϕ _k ) by the second multiplier 12 :

Q _HT ′ (t ′) = Q _HT (t ′) _* cos (ϕ _k )

Q _HT ′ (t ′) = (b _Q 0.5 U₁ -cos ((ω₁-ω _T ) t ′ + ϕ _Q ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _Q )) _* cos (ϕ _k )

Q _HT ′ (t ′) = b _Q 0.25 U₁ (-cos ((ω₁-ω _T ) t ′ + ϕ _Q + ϕk)) + b _Q 0.25 U₁ (-cos ((ω₁-ω _T ) t ′ + ϕ _Q -ϕ _k ))
+ b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕk) + b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q -ϕ _k )

Q '(t) is delayed by a second delay stage 15 by the group delay T _{H of} the Hilbert transformer 14 :

Q _dT (t ′) = Q ′ (tT _H )

Q _dT (t ′) = b _Q 0.5 U₁ sin ((ω₁-ω _T ) t ′ + ϕ _Q ) -b _Q 0.5 U₂ sin ((ω _T -ω₂) t′-ϕ _Q )

and multiplied by the third multiplier 13 by sin (ϕ _k ):

Q _dT ′ (t ′) = Q _dT (t ′) _* sin (ϕ _k )

Q _dT ′ (t ′) = (b _Q 0.5 U₁ sin ((ω₁-ω _T ) t ′ + ϕ _Q ) - b _Q 0.5 U₂ sin ((ω _T -ω₂) t′-ϕ _Q )) _* sin ( ϕ _k )

Q _dT ′ (t ′) = b _Q 0.25 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _Q -ϕ _k ) -b _Q 0.25 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _Q + ϕ _k )
-b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q -ϕ _k ) + b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕ _k )

S₂ (t ′) = I _dT T (t ′) + Q _dT ′ (t ′) + Q _HT ′ (t ′)

S₂ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω2) t′-ϕ _I ) + b _Q 0.25 U₁ cos ( (ω₁-ω _T ) t ′ + ϕ _Q -ϕk) -b _Q 0.25 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _Q + ϕ _k ) - b _Q 0.25 U₂ cos ((ω _T -ω₂) t ′ -Φ _Q -ϕk) + b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕ _k ) + b _Q 0.25 U₁ (-cos ((ω₁-ωbt ′ + ϕ _Q + ϕ _k ) ) + b _Q 0.25 U₁ (-cos ((ω₁-ω _T ) t ′ + ϕ _Q -ϕ _k )) + b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕ _k ) + b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q -ϕ _k )

S₂ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) -b _Q 0.5 U₁ cos ( (ω₁-ω _T ) t ′
+ ϕ _Q + ϕk) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕ _k )

If ϕ _{k is} replaced by (ϕ _I -ϕ _Q ), we get:

S₂ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) -b _Q 0.5 U₁ cos ( (ω₁-ω _T ) t ′
+ ϕ _Q + ϕ _I -ϕ _Q ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕ _I -ϕ _Q )

S₂ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) -b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I )
+ b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-2 ϕ _Q + ϕ _I )

S₂ (t ′) = b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-2 ϕ _Q + ϕ _I )

with cos (α) + cos (β) = 2 _* cos (α + β) / 2) _* cos ((α-β) / 2)

S₂ (t ′) = b _Q 0.5 U₂ 2 cos [(2 (ω _T -ω₂) t′-2 ϕ _Q ) / 2] _* cos [(2 ϕ _Q -2 ϕ _I ) / 2]

S₂ (t ′) = b _Q U₂ cos ((ω _T -ω₂) t′-ϕ _{Q *} cos (ϕ _Q -ϕ _I )

D₁ (t ′) = I _dT (t ′) + Q _dT ′ (t ′) - Q _HT ′ (t ′)

D₁ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) + b _Q 0.25 U₁ cos ( (ω₁-ω _T ) t ′ + ϕ _Q -ϕk) -b _Q 0.25 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _Q + ϕ _k ) - b _Q 0.25 U₂ cos ((ω _T -ω₂) t ′ -Φ _Q -ϕ _k ) + b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q + ϕ _k ) - b _Q 0.25 U₁ (-cos ((ω₁-ω _T ) t ′ + ϕ _Q + ϕk)) - b _Q 0.25 U₁ (-cos ((ω₁-ω _T ) t ′ + ϕ _Q -ϕ _k )) - b _Q 0.25 U₂ cos ((ω _T -ω₂) t ′ - (ϕ _Q + ϕ _k ) -b _Q 0.25 U₂ cos ((ω _T -ω₂) t′-ϕ _Q -ϕ _k )

D₁ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) + b _Q 0.5 U₁ cos ( (ω₁-ω _T ) t ′ + ϕ _Q -ϕ _k ) -b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _Q -ϕ _k )

If ϕ _{k is} replaced by (ϕ _I -ϕ _Q ), we get:

D₁ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) + b _Q 0.5 U₁ cos ( (ω₁-ω _T ) t ′ + ϕ _Q -ϕ _I + ϕ _Q ) -b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _Q -ϕ _I + ϕ _Q )

D₁ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I ) + b _Q 0.5 U₁ cos ( (ω₁-ω _T ) t ′ + 2 ϕ _Q -ϕ _I ) -b _Q 0.5 U₂ cos ((ω _T -ω₂) t′-ϕ _I )

D₁ (t ′) = b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + ϕ _I ) + b _Q 0.5 U₁ cos ((ω₁-ω _T ) t ′ + 2 ϕ _Q -ϕ _I )

with cos (α) + cos (β) = 2 _* cos ((α + α) / 2) _* cos ((α-β) / 2)

D₁ (t ′) = b _Q 0.5 U₁ 2 cos [(2 (ω₁-ω _T ) t ′ + 2 ϕ _Q ) / 2] _* cos [(2 ϕ₁-2 ϕ _Q ) / 2]

D₁ (t ′) = b _Q U₁cos ((ϕ₁-ϕ _T ) t ′ + ϕ _{Q *} cos (ϕ _I -ϕ _Q )

The signals are separated from one another (S₂ (t ′) = f (U₂), D₁ (t ′) = f (U₁)) and can be read out after a further digital signal processing unit 21 via D / A converters 22 , 23 .

Claims (16)

1. A method for demodulating an SSB signal according to the phase method with a Hilbert transformation, characterized in that first a calibration is carried out by the first two correction values for offset errors (aK _I , aK _Q ) of the I and Q signals Quadrature signals, a second correction value for gain errors (bK = b _Q / b _I ) of the I signal and two third correction values for phase errors (| sin (ϕ _k ) |, | cos (ϕ _k |) of the Q signal) are determined and stored be, and that then in a first step by analog quadrature mixing a complex quadrature signal (I + jQ) with a low frequency (z. B. intermediate frequency or baseband frequency of a receiver) is generated, which is converted into a digital signal that in a two th step an offset error (a _I , a _Q ), in a third step an amplification error (b _I , b _Q ) and in a fourth step a phase error of the I signal and the Q signal of the quadrature signal, respectively s is compensated by applying stored correction values before the sum or difference of the components consisting of the I signal and the Hilbert-transformed Q signal is formed in a fifth step. 2. The method according to claim 1, characterized in that the calibration automatically with predetermined time intervals. 3. The method according to claim 1 or 2, characterized in that a sinusoidal test signal is applied for calibration is switched and demodulated, the frequency of a carrier frequency of a De modulator deviates by a quarter of the digital sampling frequency, with the calculation Arithmeti correction values in successive calibration steps mean and rms values of the I and Q signals from four successive serve the samples.   4. The method according to claim 3, characterized in that in a first calibration step, the first correction values ak _I = -a _I and ak _Q = -a _Q for offset errors from the arithmetic mean values of the I and Q signals of the quadrature signal are calculated and can be saved. 5. The method according to claim 3 or 4, characterized in that in a second calibration step, the second correction value b _k = b _Q / b _I for the gain error from the effective values of the offset error-corrected I and Q signals of the quadrature signal is calculated and saved becomes. 6. The method according to claim 3, 4 or 5, characterized in that in a third calibration step, the third correction values for correcting phase errors of the Hilbert-transformed Q signal on the basis of the mathematical relationships | sin (ϕ _k ) | = 2 _* Useff ′ _* Udeff ′ and | cos (ϕ _k ) | = Udeff²-Useff² are formed and saved, whereby and Useff is the effective value of the sum I (t) + HT (Q (t)) and Udeff the effective value of the difference I (t) -HT (Q (t)) and HT (Q (t)) the Hilbert-transformed Q Signal Q (t). 7. The method according to any one of the preceding claims, characterized in that with the second step, the offset errors of the I and Q signals are corrected by adding the stored first correction values ak _I , ak _Q to the I and Q signals. 8. The method according to any one of the preceding claims, characterized in that with the third step of the gain error of the offset-corrected I-signal (I'-signal) compared to the offset-corrected Q-signal (Q'-signal) by multiplying the I'-signal is compensated with the second correction value b _k . 9. The method according to any one of the preceding claims, characterized by a fourth step for correcting phase errors with which the Q'-signal is Hilbert transformed (Q _HT signal), the gain-corrected I'-signal (I '' - signal) and the Q′-signal is delayed by the group delay of the Hilbert transformation (I _dT or Q _HT signals), the Q _HT and the Q _dt signal are multiplied by the third correction values (Q _HT ′ or Q _dT signals), the I _dT signal is added to the Q _dT signal (S₁ signal) and the Q _HT signal is added to the S₁ signal (S₂ signal). 10. The method according to claim 9, characterized in that the Q _HT 'signal is inverted and added to the S₁ signal (D₁ signal) and that the signals S₂ and D₁ are converted into analog signals and output. 11. The method according to claim 9 or 10, characterized in that the I signal, the Q _HT 'signal is subtracted depending on the frequency position of the RF signal or added to this and the phase correction depending on the RF frequency position of the signal with positive or negative correction angle it follows, with a signal whose frequency is greater than that of the carrier, for. B. a res res sideband, with the expression U _USB = I _dT -Re {(Q _HT + jQ _dT ) _* e ^{-j ϕ k} } and a signal whose frequency is lower than that of the carrier, for. B. a lower sideband, with the expression U _LSB = I _dT + Re {(Q _HT + jQ _dT ) _* e ^{j ϕ k} } is calculated. 12. The method according to any one of the preceding claims, characterized in that the sign for the third correction value sin (ϕ _k ) is changed if the effective value of the difference signal by the sole effect of the amounts of the correction values sin (ϕ _k ) and cos (ϕ _k ) gets bigger. 13. Device for carrying out the method for demodulating an SSB signal using the phase method with a Hilbert transformation, characterized by a digital signal processing device ( 100 ) with first to third memory devices ( 7 i, 7 g; 9 ; 11 a, 11 b) for first to third correction values for the correction of offset, gain and phase errors of a complex quadrature signal (I + jQ), which is obtained from a received SSB signal by analog downmixing to a low frequency (e.g. intermediate frequency or baseband frequency of a receiver ) and subsequent digitization. 14. The apparatus according to claim 13, characterized by a calibration device ( 6 ) for calculating the first to third correction values on the basis of a test signal fed in instead of the received SSB signal. 15. The apparatus according to claim 13 or 14, characterized by a Hilbert transformer ( 14 ) for Hilbert transformation of the offset-corrected Q signal (Q'-signal). 16. The device according to one of claims 13 to 15, characterized by a first and a second delay stage ( 16 , 15 ) for delaying the I '' signal or the Q'-signal by the group delay of the Hilbert transformer ( 14 ) .