A METHOD AND AN APPARATUS FOR DETERMINING PHASE AND FREQUENCY DEVIATION

Abstract: In a method of determining a phase difference between two sine-shaped electrical signals, where the phase difference is known to be small and the signals are represented in a complex form, the complex conjugate value of the one signal is multiplied by the other signal, and the imaginary value of the result is used as an estimate of the phase difference between the two signals. An apparatus for the same purpose has signal paths for the two signals and comprises means which are capable of multiplying the complex conjugated value of one of the signals by the other signal, and which are capable of representing the imaginary value of the multiplication result on an output and using it as an estimate of the phase difference between the two signals.

Description: A method and an apparatus for determining phase and frequency deviation The invention concerns a method and an apparatus for determining a phase difference between two sine-shaped electrical signals. Digital communications systems, such as e.g. the common European radiotelephone system, which is also called GSM, often employ coherent data receivers. For these to func¬ tion correctly, it is essential that the data receiver is either in phase and time synchronism with the signal re¬ ceived, or somehow knows the correct phase and time syn¬ chronism. However, in communications systems based on transmission of packets of data which have a finite length, it is not necessary that the data receiver is constantly in phase and time lock with the signal received, as long as it is ensured that the phase and time errors between the data receiver and the received signal are of a modest size. In e.g. the GSM system, which is based on this type of transmission, each packet of data contains information for determining phase and time synchronism. Accordingly, if frequency synchronization is performed, and the phase is obtained from the transmitted information, it is not ne¬ cessary that the data receiver constantly attempts to be in phase lock with the signal received. A central function in a receiver for e.g. the GSM system is therefore determination of the frequency error between the received signal and the own reference of the receiver. Phase modulation is employed in e.g. the GSM system. This means that in principle the transmitted bits are repre¬ sented as phase shifts in the signal. The said information for determining frequency synchronism may consist of a long row of uniform bits, which means e.g. that the phase increases evenly, or in other words, that a pure sine wave having a slightly higher frequency than the carrier wave is transmitted. The European Patent Application EP 389 974 discloses a method and an apparatus for correction of frequency errors in e.g. such a communications system. Here, the received signal is mixed with a reference signal, generated in the receiver, to produce the so-called baseband signal. This signal appears in a complex form with both a real portion and an imaginary portion. Digital signal processing of this signal produces a control signal which can be used for controlling the reference signal of the receiver. However, the digital signal processing is relatively com- plex, since e.g. the phase is determined by means of an inverse tangent function, which necessitates either a series expansion requiring a large amount of computation, or a preperformed tabulation of the inverse tangent func¬ tion, which likewise requires an extremely large amount of computation. The invention provides a method enabling a phase diffe¬ rence between two signals and thereby a frequency devia¬ tion to be determined in a much simpler manner, so that "the method can be performed in analog mode or in digital mode, as desired, there being just employed simple multi¬ plications of the incoming signals. This is achieved according to the invention in that the complex conjugated value of the one signal is multiplied by the other signal, and then using the imaginary portion of the result as an estimate of the phase difference be¬ tween the two signals, it having been found that this gives a very accurate estimate in case of small phase differences. When, as stated in claim 2, the one signal is generated from the other, the method provides an extremely good approximation for the frequency deviation between the in¬ put signal and a known reference frequency. When moreover, as stated in claim 3, the signal is passed through an automatically adjusted amplifier circuit giving the signal a constant amplitude, then the method can be employed even if the amplitude of the signal varies. In a special embodiment of the invention the signal is transmitted through an analog-digital converter, as men¬ tioned in claim 4, following which the signal processing takes place digitally. Claim 5 defines an apparatus for performing the method for determining a phase difference, and claim 6 corresponding¬ ly concerns an apparatus in which the frequency deviation with respect to a reference frequency can be determined. Claims 7 and 8 define embodiments which moreover comprise an automatically adjusted amplifier circuit and an ana¬ log/digital converter, respectively. The invention will be explained more fully below with reference to the drawing, in which fig. 1 shows a block d:..gram for transmitter/receiver in which the invention can be utilized, fig. 2 shows a unit for determining the phase difference between two signals, fig. 3 shows a unit which is capable of determining the frequency deviation of a signal from a reference fre¬ quency, fig. 4 shows the unit of fig. 3 supplemented with an auto¬ matically adjusted amplifier circuit, and fig. 5 shows the unit of fig. 4 supplemented with an ana¬ log/digital converter. Fig. 1 shows a block diagram for a transmitter/receiver known per se for a digital radiotelephone system, such as e.g. the common European digital radiotelephone system, which is also called GSM, in which the invention can be utilized. A signal is received on an antenna 1 and passes a duplexer 2, and then it arrives at the radio frequency receiver 3. The output signal from this is passed to mixing points 6 and 7. The frequency synthetizing unit 4 generates an oscillator signal which should desirably have the same frequency as the carrier wave frequency in the signal re¬ ceived on the antenna 1. The oscillator signal is trans¬ mitted to the mixing point 6 and via the phase shifter unit 5 to the mixing point 7. The mixing points 6 and 7 provides the so-called baseband signal in a complex form, which is transmitted to the equalizer 8 and further on to the decoder 9, which represents the received information on its output. Also included are a control unit 13 as well as the transmitter circuits 10, 11 and 12. As mentioned, the oscillator signal from the frequency synthetizing unit 4 should desirably have the same fre¬ quency as the carrier wave for the received signal. However, to ensure correct reception it is necessary to synchronize the oscillator signal to the received fre- quency at the beginning of each packet of data. A fre¬ quency error estimator 14 is provided for this purpose, and it is in this unit that the invention described here can be employed. In e.g. the GSM system phase modulation is used for coding the transmitted information. This means that the trans¬ mitted bits are represented as phase shifts in the trans¬ mitted signal. Precisely owing to the synchronization data packets are regularly transmitted with a frequency correc¬ tion sequence consisting of a long row of uniform bits, e.g. a series of l's. This means that the phase of the transmitted high frequency signal increases evenly. This in turn means that a pure sine wave having a frequency slightly higher than the carrier wave frequency is trans¬ mitted in reality. If the carrier wave frequency (measured in radians/sec) is designated ω and the baseband signal frequency ω , the transmitted signal will thus have a fre¬ quency of ω + ω in this case. The oscillator frequency from the frequency synthetizing unit 4 can then be repre¬ sented by ωc + Δω, Δω corresponding to a small frequency error. It is well-known from the literature that the out¬ put signal from the mixing points 6 and 7 will then con¬ tain a term having the frequency + Δ. as well as some high frequency terms, which, however, may be filtered off by means of lowpass filters. The frequency error estimator 14 serves to detect the fre¬ quency error Δω, following which its output signal may be used e.g. for adjusting the oscillator frequency from the frequency synthetizing unit 4, so that the frequency error proceeds toward zero. If the complex output signal from the mixing points 6 and 7 is designated r(t), its fre¬ quency, which is thus + Δω here, may be designated ω (t) and its phase correspondingly * (t). The instantaneous frequency can then be derived by diffe¬ rentiating the phase, which means that d* r (t) ω r (t) = dt If, however, the frequency error can be assumed to be con¬ stant over a time interval Δt, the instantaneous frequency can more easily be found by means of the following expres¬ sion: * r (t)-« r (t-Δt) « r (t) = Δ The frequency can thus be found by calculating a phase difference. Fig. 2 shows a unit 20 for calculating the phase diffe¬ rence between two signals r 1 (t) and r 2 (t), which are both supplied to the unit, and which are both in a complex form. The following formula, wherein a * denotes the complex conjugated figure: Im{z 2 .z* } = Im{|z 2 |.e- J .|z 1 |.e~- 1 } = |z 2 | . |z 1 | .sine(<* 2 -ø 1 ) generally applies to two complex figures z. and z 2 (z χ = Iz- .e 3 ; z 2 = |z 2 |.e J ) When the phase difference between the two figures is small, then hence lm{z 2 . z * } for small phase differences between the two complex fi¬ gures. This expression shows that for small phase differences be¬ tween two complex figures an approximation for the phase difference between the two complex figures can be found using multiplication. Further Im{(Re{z 2 }+j.Im{z 2 })(Re{z 1 }-j.Im{z 1 })} Φ -Φ φ 2 φ l \ * 2 \ - \ *_ \ Re{z-}.Im{z 2 }-Re{z 2 ).Im{z 1 ) | z 2 l • l z ι l if this expression is used for the phase difference be¬ tween two complex figures on the unit 20 from fig. 2, it will thus be seen that for the unit 20 to calculate the phase difference between the two signals r..(t) and r 2 (t), it must contain an electronic circuit capable of calculat¬ ing the following expression: lm{r 2 (t).r 1 *(t)} Δ*(t)=ø 2 (t)-* 1 (t) = |r 2 (t)|.|r 1 (t)| Re{r 1 (t)}.lm{r 2 (t)}-Re{r 2 (t)}.lm-Cr 1 (t)} |r 2 (t)|.|r 1 (t)| As mentioned before, the instantaneous frequency of the complex r(t) on the output of the mixing points 6 and 7 in fig. 1 can be found * by means of the expression * r (t)-* r (t- Δt) Δt Where the unit from fig. 2 can calculate the phase dif¬ ference between two different signals r.(t) and r 2 (t), we thus here need a unit capable of calculating the phase difference between the same signal at two different points of time; but this can be obtained merely by letting the one signal be a delayed version of the other. ' However, for the expression to apply, the phase difference must be quite small, as mentioned, and thus also the time diffe- rence Δt must be quite small. As mentioned, the frequency « (t) = " (t) + Δo(t). If we now select Δt to be a quarter wavelength for a ( ), we would, if Δω was zero, obtain a phase difference of 90°. Now we thus obtain a phase difference of 90° plus an error contribution because of Δω. If the delayed signal is then phase shifted +90°, we thus obtain two signals whose phase difference is partly so small that the unit from fig. 2 can be used, and is also precisely an expression of the frequency error Δω(t) in which we are interested. Thus, when Δt is equal to a quater wavelength of ω i r (t)-0 r (t-Δt) Δt * r (t)-[* r (t-Δt)+90' Δω(t) = Δt Fig. 3 shows the unit 20 known from fig. 2 as well as a delay unit 21 and a phase shifter unit 22, which are so incorporated that the signal r.(t) is partly delayed cor¬ responding to a quarter wavelength for the frequency and is partly phase shifted 90° before being used as the signal r~(t). The overall function of the circuit in fig. 3 will thus be Im{r(t).[j.r(t-Δt]*} Δω(t) = Δt. |r(t)|. |r(t-Δt)| -Re{r(t).r*(t-Δt)} Δt.|r(t)|.|r(t-Δt)| -Re{r(t)}.Re{r(t-Δt)}-Im{r(t)}.Im{r(t-Δt)} Δt. |r(t)| . |r(t-Δt)| If we assume that the numerical value of r(t) is constant, then, because also Δt is constant, the denominator of the fraction is constant, which means that by computing the numerator of the fraction we obtain an expression of the frequency error multiplied by a constant. Thus, the elec¬ tronic circuit does not have to take the denominator of the fraction into consideration. If the condition that the numerical value of r(t) is con¬ stant is not satisfied, the circuit can be supplemented with an automatically adjusted amplifier circuit 23, as shown in fig. 4, ensuring that the signal has a constant amplitude on its output. The circuit described here can function either in analog mode or in digital mode. The analog mode of operation is described above; however, it will frequently be an advan¬ tage to have the signal processing take place digitally. In that case the circuit is moreover provided with an analog/digital converter 24, as shown in fig. 5. It will be appreciated that the automatically adjusted amplifier circuit can also be positioned before the ana¬ log/digital converter and thus work in analog mode, while the rest of the signal processing takes place digitally. The described method can thus be used for calculating the phase difference between two signals, as shown in fig. 2, or it may be used for calculating how much the frequency of a signal differs from a known reference frequency, as shown in the subsequent figures. In addition to the use described here in a receiver in a digital communications system, the invention can also be used in all other fields where it is desired to determine a phase or frequency de¬ viation, provided that the conditions described above are satisfied. An example is two radio transmitters transmitting on two different frequencies which are close to each other, it being desired to determine whether the frequency of the one transmitter drifts with respect to the other.

Claims: P a t e n t C l a i m s : 1. A method of determining a phase difference between two sine-shaped electrical signals, said phase difference be¬ ing known to be small, said signals being represented in a complex form, c h a r a c t e r i z e d by multiplying the complex conjugated value of the one signal by the other signal, and using the imaginary value of the result as an estimate of the phase difference between the two signals. 2. A method according to claim 1, wherein the frequency of the one signal has a frequency deviation from a known reference frequency, c h a r a c t e r i z e d by gene¬ rating the other signal by passing the first signal through a delay unit delaying the signal k of the period time of the known reference frequency, and then phase shifting the signal 90°, and additionally using the re- suit of the multiplication as an estimate of said fre¬ quency deviation. 3. A method according to claim 2, c h a r a c t e r ¬ i z e d by passing the first signal prior to the signal processing through an automatically adjusted amplifier circuit which gives the signal a constant amplitude. 4. A method according to claim 2 or 3, c h a r a c ¬ t e r i z e d by passing the first signal prior to the signal processing through an analog/digital converter, said signal processing then taking place digitally. 5. An apparatus for determining a phase difference be¬ tween two sine-shaped electrical signals, said phase dif- ference being known to be small, said signals being repre¬ sented in a complex form, c h a r a c t e r i z e d in that it has signal paths for the two signals and comprises means which are capable of multiplying the complex conju¬ gated value of one of the signals by the other signal, and which are capable of representing the imaginary value of the multiplication result on an output and using it as an estimate of the phase difference between the two signals. 6. An apparatus according to claim 5, wherein the fre¬ quency of the one signal has a frequency deviation from a known reference frequency, c h a r a c t e r i z e d in that a connection path from the signal path for the one signal to the signal path of the other signal incorporates a delay unit with a delay time of of the period time of the known reference frequency and a phase shifter unit capable of providing a phase shift of 90°, so that the other signal can be generated from the first signal, and that the signal on the output can be used as an estimate of said frequency deviation. 7. An apparatus according to claim 6, c h a r a c t e r ¬ i z e d in that it comprises an automatically adjusted amplifier circuit in the signal path for the first signal, said amplifier circuit being capable of giving the signal a constant amplitude before the signal processing. 8. An apparatus according to claim 6 or 7, c h a r a c ¬ t e r i z e d in that it comprises an analog/digital converter, and that the signal processing circuits are adapted to perform the signal processing digitally.

Inventors: MADSEN BENNY, MADSEN, BENNY
Applicants: CETELCO AS, DANCALL RADIO AS, CETELCO A/S, DANCALL RADIO A/S
Application year: 1992
Main classification: H03D3
IPC codes: H04B1