JPH0424903B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a demodulator for phase modulated signals and the like. Although synchronous detection with excellent characteristics is exclusively used for demodulating phase modulated signals, a reference carrier wave that is the same as the transmission carrier wave is required during detection. For this reason, it is common for the transmitting side to transmit only the transmission carrier wave for a certain period of time before transmitting information so that the same reference carrier wave can be reproduced on the receiving side. Then, after a reference carrier wave is prepared on the receiving side, the phase modulation signal is transmitted for the first time. The time it takes for the transmitting side to send out a transmission carrier wave is completely wasted time from the perspective of information transmission, so the shorter it is, the better. Therefore, the reference carrier generator (carrier regeneration circuit) on the receiving side prepares a synchronization system with a fairly wide band and completes carrier synchronization in a relatively short acquisition time. The result is that the engine is strongly affected by this, resulting in frequent cycle slips.

The purpose of the present invention is to mainly demodulate phase modulated signals using a narrowband phase synchronization system that is not susceptible to input noise and without receiving a carrier wave signal from the transmitting side, which can be called useless information. It is something to do.

This invention includes a sampling circuit that samples a k-phase phase modulated wave after quasi-synchronous detection at a symbol rate and obtains N sample values from X ₁ to X _N from time t ₁ to t _N ; j(ωoti+θo)} and output ωo
and θo are variable, an error detector that obtains a value k times the phase difference between the output of the reference signal oscillator and the output of the sample circuit, and an output of the error detector.
Ai and an adder for obtaining a cumulative value A from i=1 to N; a product-sum circuit for obtaining a sum B from the product of A _i and t _i for i=1 to N; Initial phase error estimate θ~o for reference signal oscillator output
and a phase difference estimating circuit that calculates the phase rotation speed estimated value Δ~ω by a linear combination of the constant coefficients of A and B, and the ωo and θo of the reference signal oscillator are calculated as ωo+Δ~ω and θo+θ~o, respectively. and a multiplier that multiplies the sample value Xi by the complex conjugate value of the oscillator output, and obtains a demodulated signal with carrier phase synchronization from the multiplier output. .

Next, the present invention will be explained in detail with reference to the drawings. FIG. 1 shows a demodulated signal when product detection is performed on a two-phase modulated wave with an O-π phase using a receiving side reference carrier wave different from the transmitting carrier wave by Δω rad/s. It is assumed that the reference carrier wave has a phase difference of θo from the transmission carrier wave. In order to correctly demodulate this two-phase modulated wave, it is necessary to accurately estimate Δω and θo, and perform a phase correction of −(Δωt+θo) on the demodulated signal shown in the figure. Since 1 to 6 in FIG. 1 are demodulated signals sampled at symbol transmission intervals T (seconds), the phase difference θ _D between 1 and 2 in FIG. 1 is directly ΔωT. Therefore, Δω is obtained as θ _D /T. If the O-π modulation is not applied, the phase difference between 2 and 3 would be equal to θ _D , but
In this case, it is (θ _D +π). Similarly 3
and 4, 4 and 5, and 5 and 6 are also superimposed with phase changes due to modulation. The phase change due to modulation between each sample is always exactly ±π. Therefore, by subtracting the ±π change among the phase changes between successive samples as being due to modulation, the original ΔωT can be observed. Another way of thinking is that for a k-phase modulated signal, the phase change due to modulation is 2π/k
Since the signal is in radians, there is a method of raising both the same signal and the receiving side reference carrier signal to the k power and comparing the phases. In this case, the phase error will be k times, but the 2π/k radian change due to modulation will be an integer multiple of 2π,
Virtually disappear. According to this idea, the receiving side reference signal f _i =
The frequency and phase differences Δω and θ ₀ between e ^j( 〓 ^0t+ 〓 ⁰⁾ and the phase modulated wave y _i after quasi-synchronous detection with the phase modulated wave can be estimated. These estimated values are written as Δ~ω and θ~o, respectively, and fi is f _i =ej {ωo+Δ~ω)t+(θo+θ~o)}
The input signal carrier wave can be reproduced by changing Δω and θ ₀ to be equal to the previous Δω and θ ₀ .

One way to make (Δω-Δ~ω) and (θo-θ~o) zero from N yi sample series is to
There is a multiplicative estimation method. This method determines Δω and θo so as to minimize the sum of squares of errors at each time ti between the yi time series and fi that are disturbed by input noise. Let A _i (i=1 to N) be the phase difference observed at each time t _i (i=1 to N). N observed values
Consider a problem that is approximated by a function P _n (t). For example, for a plot of N observed values A _i = (i = 1 to N), the straight line θ(t) = Δ to ωt that minimizes the squared error
If +θ~ _p can be estimated, this θ(t) can be said to be the optimal reproduced carrier signal in terms of squared error. Therefore, we will consider estimating such a straight line (which does not have to be a straight line).

Generalizing, suppose that N observed values can be approximated by a function P _n (t).

Pm(t)=a ₀・t ⁰ +a ₁・t ¹ +a ₂・t ² +……+a _n・t ^m
(1) Here, from the principle of least squares estimation, _N 〓 ⁱ⁼¹ ρi ² = _N 〓 ⁱ⁼¹ [p _n (t _i )−A _i ] ² (ρi: error with respect to expected value) is minimized. All you have to do is find a ₀ , a ₁ , ...an _{such that} . That is, ρ ₁ δ〓 ₁ / δa _s + ρ ₂ δ〓 ₂ / δa _s +……ρ _o δ〓 ₂ / δa _s
=0 (S=0,1,2,...m) (2) It is sufficient to find a ₀ , a ₁ , ... _an that satisfy m+1 conditions. The approximate expression (1) includes an error ρi for the observed value A _i and can be expressed as follows.

a ₀・t ⁰ +a ₁・t ¹ _i +a ₂・t ² _i +……+a _n・t ^m _i =A _i- 〓 _i (
i
=1~N) (3) From this, −δ〓 _i /δa ₀ =t ⁰ _i , −δ〓 _i /δa ₁ =t ¹ _i ,……, −
δ〓 _i / δa _n =t ^m _i Therefore, if we set the condition of equation (2) for S=0, 1, 2...m, we get _N 〓 ⁱ⁼¹ ρit ⁰ _i =0 _N 〓 ⁱ⁼¹ ρit ¹ _i = 0,..., _N 〓 ⁱ⁼¹ ρit ^m _i =0 (4) is obtained. From equations (3) and (4), get. In normal demodulation, it is only necessary to find Δω and θ ₀ , so the estimated values of θ _{0 and} Δω of a 0 and a ₁ in equation (1) are θ~ ₀ ,
Considering Δ~ω, equation (5) becomes the following simultaneous equations.

The above formula A _i represents the phase difference between the carrier waves between transmitting and receiving, and if the receiving side reference signal is f _i and the phase modulated wave after quasi-synchronous detection of the phase modulated wave and f _i is y _i , then A _i =I _n (f _i・yi ^* ).

Here, as described above, since the phase error multiplied by K is obtained from the signal obtained by raising the phase modulated wave to the k power, (6) becomes as follows.

However, since fi ^k and yi ^*k (complex conjugate of yi) are the original signals raised to the k power, both δθo and δΔω have values k times their original values.

Therefore, new θo and Δω can be considered as follows.

Note that Im (fi ^k・yi ^*k ) on the right side of equation (1) above is
It shows a first-order approximation of the phase difference between fi ^k and yi ^k , and in addition to this expression, tan ^-1 (fi ^k · yi ^*k ) may be used.

Generally, any term that indicates the phase difference between fi and yi is sufficient.

The matrices on the right and left sides of equation (1) above will be constant matrices if the input signal is sampled at the same period every time. Therefore, the quantity required to find δθo and δΔω is only the matrix on the right side of the right side.

This is the product sum of the complex conjugate of the input signal k-th power signal yi ^*k and the k-th power signal fi ^k of the received reference carrier signal, and ti.
It is the sum of products with yi ^*k fi ^k .

If the correct θ~ ₀ and Δ~ω are found from equations (7) and (8), each sample value X _i is set as X _i・ej (−θ~0−Δ~ω(ti−t1)) This results in demodulation with the correct phase.

FIG. 2 embodies the above principle for a four-phase phase modulation signal.

The signal entering the input terminal 100 is a k-phase modulated signal, ideally with a frequency equal to that of its carrier.
This is a complex signal obtained by performing remainder product detection using a reference signal on the receiving side that has a phase. Actually, the above frequency,
Since the phase is different from that of the carrier wave on the transmitting side, the signal subjected to the residual product detection rotates on the complex plane due to the difference in frequency and phase between the transmitting and receiving signals. Figure 1 shows this situation. This type of detection method is called a quasi-synchronous detection method.

1 in Fig. 2 is the symbol root sampling of the k-phase modulated wave from the input terminal 100 at the timing when the data eye is most open, and the sample values from X ₁ to X _N are sampled over time. from t ₁
A sample circuit 2 is a reference wave oscillator on the receiving side that obtains and stores data up to t _N , and outputs fi=e ^j( 〓 ^ot+ 〓 ^o) , and ωo and θo are variable. 3 is a complex conjugate circuit 30 that inverts the polarity of the imaginary part of the sample circuit output, a quadruple circuit 31 that raises the output to the 4th power, and a 4th power circuit 32 that also raises the output of the receiving side reference wave oscillator to the 4th power; An error detector consisting of a multiplication circuit 33 that takes the product of the multiplication circuit outputs and outputs only the imaginary part thereof.
Output fi ⁴・yi ^*4 . 4 is an adder to obtain _N 〓 ⁱ⁼¹ fi ⁴・yi ^*4 , and 5 is a product-sum circuit consisting of a multiplier 50 and an adder 51 to obtain _N 〓 ⁱ⁼¹ ti・fi ⁴・yi ^*4 . . 6 is the previous (7), (8)
A phase difference estimating circuit that calculates equations and derives estimated values Δ~ω and θ~o of Δω and θo.

7 is the complex conjugate value of ti prior to the sample value X _i
A complex conjugate circuit 70 for multiplying by fi ^*2 , a multiplier 71 for imparting π/4 phase rotation for moving the signal point of the four-phase modulated wave to ±π/4, ±3/4π, and a sample value. This multiplier includes a multiplier 72 for multiplying Xi by fi ^* ·e ^j 〓 ^/4 to obtain a demodulated signal. The demodulated output is output from the output terminal 101.

In this embodiment, the case where N data is received individually has been described. In the case of voice communication, etc.
Data is received continuously. In such a case, two additional sample circuits 1 are required. That is, it is for storing the next N data received while the first N data are being received and processed. The third N data can be used again because the sample circuit that received and processed the first N data is already used. Similarly, continuous data can be processed one after another as long as there are two sample circuits.

At this time, ωo and θo of the reference signal oscillator for the new N data can be determined by using the corrected values (ωo+Δ~ω) and (θo+θ~o) obtained from the previous N data, so that the next Δ~ω, θ~ The promotion of o becomes more accurate.

In this embodiment, only θo and Δω were estimated, but as N becomes larger, the square term, that is, the term e ^j 〓〓 ^o2 also influences the synchronization accuracy. In this case, in addition to the product-sum circuit 2 in the embodiment shown in FIG. 2, (Σt ² _i ·f ^k _i ·y ^*k _i ) is calculated.

By adding the third product-sum circuit, From this, Δωa can be found. In this case as well, the right-hand side and left matrix are constant matrices.

As described above, according to the present invention, it is possible to provide a demodulator that receives a burst digital signal that does not include a synchronizing pre-signal and supplies a modulated signal that is synchronized with the carrier phase. Another feature of the demodulator is that it operates stably even when the noise level of the input signal is relatively high.

[Brief explanation of drawings]

FIG. 1 is a diagram for explaining the state of phase rotation due to a frequency shift of a transmission carrier wave in two-phase PSK. FIG. 2 is a diagram showing a block diagram of an embodiment of the present invention. In the figure, 1... sample circuit, 2... reference signal oscillator, 3... error detector, 4... adder, 5...
A product-sum circuit, 6...a phase difference estimation circuit, and 7...a multiplier are shown, respectively.

Claims (1)

[Claims] 1 A sampling circuit that samples the k-phase modulated wave after quasi-synchronous detection at the symbol rate and obtains N sample values from X ₁ to X _N between time t ₁ and t _N.
a reference signal oscillator that outputs exp(j(ω ₀ ti + θ ₀ ) and whose ω ₀ and θ ₀ are variable; and an error detector that obtains a value k times the phase difference between the output of the reference signal oscillator and the output of the sample circuit. an adder that obtains a cumulative value A of the error detector output A _i from i=1 to N; and a product-sum circuit that obtains a sum B of the product of the A _i and the t _i from i=1 to N. The initial phase error estimate θ~ ₀ and the phase rotation speed estimate Δ~ω of the sample value X _i with respect to the reference signal oscillator output
and a phase difference estimating circuit that calculates the above by a linear combination of the constant coefficients of A and B, and the ω ₀ and θ ₀ of the reference signal oscillator are changed to ω ₀ +Δ~ω and θ ₀ +θ~ ₀ , respectively. A phase modulation demodulator comprising: a multiplier that multiplies the sample X _i by a complex conjugate value of an oscillator output, and obtains a demodulated signal in carrier phase synchronization from the multiplier output.