JPS6154305B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a modulated wave phase determining device used in a receiving circuit of an 8-phase PSK modem for data communication.

Now, in an eight-phase PSK (Phase Shift Keying) modem, the phase of the carrier wave a cos ω _c t is modulated with a signal (t) as follows, and a modulated wave g(t) is sent out.

g(t)=a cos [ω _c t-(t)] …(1) Here, (i T _b )=n2π/8=π/4n …(2) However, i=0, ±1, ±2, ... n=0, 1, 2, ... 7 The instantaneous phase (i T _b ) at time i T _b is π/4n. a represents the amplitude of the carrier wave, ω _c represents the angular frequency of the carrier wave, T _b is the transmission time interval of the phase to be modulated, and its reciprocal 1/T _b is called the modulation speed, and the modulation speed is expressed in baud. Speed is expressed. Transforming the above equation (1), g(t)=a cos (t)・cos ω _c t +a sin(t)・sin ω _c t ……(3) Consider the above equation (3) as a quadrature amplitude modulation method. For example, two mutually orthogonal carrier waves a cos ω _c t and a
sin ω _c t, cos (t) and sin (t)
It is thought that they are modulated respectively. Now X=X(i T _b ) = a cos = a cos(i T _b )...(4) Y=Y(i T _b ) = a sin = a sin(i T _b )...(5) Set aside For example, g(t)=X cos ω _c t +Y sin ω _c t ...(6). From equations (4) and (5), X ² + Y ² = a ² cos ² + a ² sin ² = a ² ... (7) Since the carrier wave amplitude a is constant in the phase modulation method, X ² + Y ² = a ² is a constant.

Now, demodulation on the receiving side can be performed as follows. Now, let us consider an ideal case where there is no influence of distortion, noise, etc. due to the transmission line, and there is no time lag or phase shift of modulated waves. In other words, let us assume that the above equation (6) (we will call this the modulated wave) is received as is.

g(t)・e ^j 〓 ^ct = Xcos ω _c t ・e ^j 〓 ^ct + Ysin ω _c t・e ^j 〓 ^ct = 1/2X (e ^j 〓 ^ct +e ^-j 〓 ^ct ) e ^j 〓 ^ct + 1/2 (e ^j 〓 ^ct −e ^{-j 〓 ct} )e ^{j 〓 ct = 1/2}
) = 1/2 (X + Xcos2ω _c t + Ysin2ω _c t + 1 ^{/ 2j} (Y- _{Ycos2ω c t +} t) ...(9) I _n [g(t)・e ^j 〓 ^ct ]=1/2 (Y−Ycos2ω _c t+Xsin2ω _c t) ...(10) Here, Re[g(t)・e ^j 〓 ^ct ] is g(t)・e ^j
〓 represents the real part of ^ct , and I _n [〃] represents the imaginary part.

_{Now ,} if the _{frequency components of} By removing the components, Re[g(t)・e ^j 〓 ^ct ]→1/2X...(11) I _n [〃 〃 ]→1/2Y...(12) is obtained. Here, → means the output obtained by the low-pass filter. Therefore, 2g(t)・e ^j 〓 ^ct →X+jY = a cos + j a sin = a e ^j ...(13) Here, = arg(X+jY) ...(14) is obtained. As can be seen from the above equations (13) and (14), the phase is uniquely determined from the demodulated signal a e ^j =X+jY. However, +2k
π (k=0, ±1, ±2...) are considered to be the same.

Conversely, as can be seen from equations (1), (3), (4), and (5) on the transmitting side, X and Y are uniquely determined by. In other words, it can be said that and (X, Y) represent the same content.

Although it is generally affected by distortion and noise due to the transmission line, the demodulated signal corresponding to the above equation (13) after being affected by these is x+jy.

x+j y=(X+j Y)+( _Nx +j Ny)=(X+ _Nx )+j(Y+ _Ny )...(15) Here, _Nx and Ny are errors or noises for the X component and Y component, respectively. Now, N _x and Ny are each an appropriate distribution with a mean value of 0 (e.g. Gaussian distribution)
If this is the case, the demodulated signal (x, y) will have a distribution with a two-dimensional spread centered on the point of the signal (X, Y) originally sent from the transmitter. Note that (X+
jY) and (X, Y), the former represents a value on a complex plane, and the latter represents a value on an xy plane (orthogonal coordinates).

As is clear from the above equations (2), (4), and (5),
(X, Y) takes only a finite number of discrete values.
Here, there are eight. As can be seen from equation (7) above,
They lie on the circumference of a circle with radius a centered at the origin. Therefore, (x, y) is a different point in (X, Y)
P ₀ , P ₁ ... each has a two-dimensional distribution centered on P ₇ . Here, if the absolute values of error components (noise components) N _x , Ny |N _x |, |Ny |
If is small enough, the originally sent signal of (x, y) will be sent to eight different points of (X, Y) P ₀ , P ₁ , . . .
It can be estimated that it is the closest value among _P7 . As can be seen from the above, it can be said that P ₀ , P ₁ , . . . P ₇ represent the same content.

This invention relates to a device that determines which of P ₀ , P ₁ , P ₂ , ...P ₇ is, and receives modulated waves that have the same frequency but a phase difference of 90 degrees (i.e., orthogonal waves). ) The above describes a method for performing synchronous detection using two reference carrier waves (regenerated carrier waves) and determining (estimates) the phase of the modulated wave that was originally supposed to be sent from the demodulated signal (x, y). . Note that P ₀ , P ₁ , ... P ₇ are sometimes expressed as symbols. Also, instead of the phase, it may be referred to as the phase of P ₀ , P ₁ , . . . P ₇ or the phase of the symbol.

Figure 1 shows the above x
FIG. 3 is a signal constellation diagram showing the correspondence between the values of and y and eight possible phase states of the received modulated wave. In the same figure,
P ₀ to P ₇ are signal points, each representing a possible phase state of the received modulated wave.

Now, in FIG. 1, consider eight regions partitioned by four straight lines A to D, and consider a case where it is determined to which region the phase state of a received modulated wave belongs. In addition, the straight line A is y=(tan22.5
゜) x, straight line B is y = (tan67.5゜)
゜) It is assumed that it is represented by x. As an example,
If the relationship between demodulated signals x and y is y<(tan67.5°)x and y>(tan22.5°)x, then the phase state of the received modulated wave is _P1 . Judgment is possible.

In the conventional judgment circuit configured based on this principle, the boundaries of the area for judgment classification are y=±(tan22.5°)x and y=±(tan67.5°)x
Since there are four straight lines, the value of y and ±(tan22.5
It was necessary to compare the values of x) and ±(tan67.5°), and to do so, it was necessary to multiply x by the values of tan22.5° and tan67.5°. By the way, tan22.5゜=0.4142...
tan67.5°=2.4142... Therefore, if the above comparison were to be performed digitally, a multiplier would be required for the above multiplication. Assume that this multiplier is not omitted, and the approximate expressions tan22.5°≒1/2 and tan67.5°≒2 are used. When representing a number in binary, multiplying by 1/2 or 2 can be easily done without the need for a multiplier by shifting the binary digit by one bit to the right or left. However, this method does not require a multiplier, but has the drawback of increasing the rate of determination errors. arc tan1/2=26.6° and arc tan2=63.4°, which have an error of about 4° compared to 22.5° and 67.5°, respectively. This means that in Fig. 1, the judgment area for signal points P ₀ , P ₂ , P ₄ , and P ₆ is approximately 8° wider than the original angular range of 45°, and the signal points
That of P ₁ , P ₃ , P ₅ , and P ₇ means that it becomes narrower by about 8°.

This invention has been made to overcome the drawbacks of the prior art as described above, and an object of the invention is to eliminate the need for expensive multipliers and theoretically avoid the occurrence of judgment errors. An object of the present invention is to provide a novel phase determining device for eight-phase modulated waves.

The main points of the configuration of the present invention are a polarity determiner for each of the demodulated signals x and y, a detector that detects whether or not the determination outputs of each determiner match and generates a corresponding detection output, and a polarity selector that receives either one of x and y and inverts the signal polarity according to the detection output from the detector or outputs it as non-inverted; and one of x and y that is not input to the polarity selector. and a comparator that compares and determines the magnitude of the signal and the output signal from the polarity selector, and each determination output from the first and second polarity determiner and a comparison determination output from the comparator. The point is that the phase of the received modulated wave is determined from

Next, one embodiment of the present invention will be described in detail with reference to the drawings.

FIG. 2 is a block diagram showing one embodiment of the present invention. In the figure, the oscillator 6 oscillates at the frequency f _c of the carrier wave, and the 90° phase shifter 3 has the function of delaying the phase of the output of the oscillator 6 by 90°. cos(2
π f _c +θ), 90° phase shifter 3
The output of is expressed as sin(2π f _c +θ). Multipliers 1 and 2 are multipliers for demodulation, respectively, and low-pass filters 4 and 5 are for extracting a baseband signal that is a demodulated signal component. The demodulator 7 is configured by each of the above circuits, but
The configuration of the demodulator itself is unchanged from the conventional one. Now, it is assumed that a modulated wave received as an 8-phase phase modulated wave is demodulated by this demodulator 7 and demodulated signals x and y are output. Note that the reproduction of the carrier wave during demodulation and the like are not directly related to this invention, so the explanation is omitted. Since the demodulated signals x and y are orthogonal to each other, they are generally expressed on a plane of an orthogonal coordinate system. Therefore, x is expressed on the x-axis on a plane, and y is expressed on the y-axis orthogonal to the x-axis. Each of the signal polarity determiners 8 to 10 is a circuit that outputs logic 1 or 0 depending on whether the polarity of the input signal to the determiner is positive or negative.
Now, assuming that x0, the output D ₀ of the signal polarity determiner 8 is D ₀ =logic 1, and if x<0, D ₀ =logic 0. The same applies to signal polarity determiners 9 and 10. The exclusive OR gate 11 plays the role of a detector that detects whether the judgment outputs D ₀ and D ₁ of the two signal polarity judgment devices 8 and 9 match or do not match. When , outputs logic 0. The polarity selector 12 selects the input signal y when the output of the exclusive OR gate 11 is logic 1.
Inverts the polarity of and outputs it as -y to subtracter 1.
Send to 3. The output of exclusive OR gate 11 is logic 0
In this case, the polarity selector 12 does not perform the inversion operation, and therefore, the input signal y becomes the output y and is sent to the subtracter 13 as it is. The subtracter 13 outputs a value obtained by subtracting the output of the polarity selector 12 from the input x, and the polarity of this output signal is determined by the signal polarity determiner 1.
0, and if positive, its output D ₂ becomes logic 1; if negative, it becomes logic 0. In other words, subtractor 13
The signal polarity determiner 10 and the signal polarity determiner 10 constitute a comparator that compares the signal x with the output signal of the polarity selector 12. To explain in detail, when the signs (polarity) of x and y are equal, the output of the exclusive OR gate 11 is logic 0, and if x-y≧0 (i.e. xy), the output of the signal polarity determiner 10 is
D ₂ is a logic 1 and becomes a logic 0 if x-y<0 (ie, x<y). When x and y have different signs (polarity), the output of exclusive-OR gate 11 is logic 1, and x-(-y)=x+y0 (i.e. x-
y), then output D ₂ is logic 1, x-(-y) = x+
If y<0 (that is, x<-y), it becomes logic 0.

From the above, in the modulated wave phase determination circuit shown in FIG. 2, x=0, y=0, x=y, x=-
It can be seen that it is convenient to assume eight regions partitioned by four straight lines y and to determine which region the phase state of the received modulated wave belongs to.

FIG. 3 is a signal point arrangement diagram taken in the embodiment of the invention shown in FIG. x=0
As shown in the figure, signals Q ₀ to Q _{7 are located in eight regions partitioned by a straight line H, where y=0, a straight line H, where x=y, a straight line G, where x=y, and a straight line H} , where x=-y. FIG. 3 also shows the correspondence between the values of the logical outputs D ₀ , D ₁ , D ₂ of the signal polarity determiners 8 to 10 and the signal points Q ₀ to Q ₇ . An example of correspondence will be explained. Now, when D ₀ is logic 1, it is x0, so the signal point is any one of Q ₆ , Q ₇ , Q ₀ , and Q ₁ . Furthermore, when D ₁ is logic 1, it is y0, so the signal point is any one of Q ₀ , Q ₁ , Q ₂ , and Q ₃ .
Also, when D ₂ is logical 1, in the current case, D ₀ and D ₁
Since both are logic 1 and x and y have the same positive polarity,
x-y≧0, that is, xy, and the signal point is Q ₀
Must be. Therefore, the logical output D ₀ ,
If D ₁ and D ₂ are (1, 1, 1), the signal point is Q ₀ . Let me explain one more example. Now, if D ₀ is logic 0, since x<0, the signal points are Q ₂ , Q ₃ ,
Either Q ₄ or Q ₅ . . Furthermore, if D ₁ is also set to logic 0, since y<0, the signal points are Q ₄ , Q ₅ , Q ₆ ,
Q: Any of ₇ . Next, if D ₂ is logical 0,
In this case, both D ₀ and D ₁ are logic 0, and x and y have the same negative polarity, so x−y<0, that is, x<
y, so the signal point is _Q4 . Therefore D ₀ ,
When D ₁ and D ₂ are (0, 0, 0), the signal point is Q ₄ .

Comparing FIG. 1 and FIG. 3, the signal point arrangement diagram shown in FIG. 3 corresponds to that of FIG. 1 rotated by 45°/2=22.5°. Therefore, the signal point of the received modulated wave must also be rotated by 22.5 degrees from that shown in FIG. This rotation only requires shifting the phase of the recovered carrier by 22.5°. This will be explained below.

Consider the case where the phase of the reproduced carrier wave e ^j 〓 ^ct in the above equation (8) is shifted by θ.

g(t)・e ^j( 〓 ^ct+ 〓 ⁾ = [g(t)・e ^j 〓 ^ct ] e ^j 〓 ...(16) Therefore, the demodulated output obtained through the low-pass filter is given by the above equation (13). 2g(t)・e ^j( 〓 ^ct+ 〓 ⁾ → (X+jY) e jθ=a e ^{j( +} 〓 ⁾ ...(17) Thus, the demodulated output (X,
Y) rotated by θ. Here, if θ=22.5°, it is clear that P ₀ , P ₁ , ...P ₇ in Fig. 1 correspond to Q ₀ , Q ₁ , ...Q ₇ in Fig. 3, so the reproduction It turns out that it is sufficient to shift the phase of the carrier wave by 22.5 degrees.

As described above, the present invention has the advantage of providing an excellent phase determination device that does not require expensive multipliers and does not cause logical determination errors.

[Brief explanation of the drawing]

Fig. 1 is a diagram showing the arrangement of signal points in an 8-phase PSK modem, Fig. 2 is a block diagram showing an embodiment of the present invention, and Fig. 3 is a diagram showing the arrangement of signal points adopted in the embodiment of the invention. It is. In the figure, 1 and 2 are multipliers, and 3 is 90
゜Phase shifter, 4 and 5 are each a low-pass filter, 6 is an oscillator, 7 is a demodulator, 8 to 10 are each a signal polarity determiner, 11 is an exclusive OR gate, 12 is a polarity selector, 13 is a subtracter, shows.

Claims (1)

[Claims] 1. A phase determination device for determining the phase of a received modulated wave in an 8-phase PSK modem from a first signal and a second signal that are orthogonal to each other obtained by demodulating the modulated wave, the phase determination device comprising: a first polarity determiner that determines the polarity of the first signal, a second polarity determiner that determines the polarity of the second signal, and a match between the determination outputs of the first and second polarity determiners; a match that detects a mismatch and produces a detection output accordingly;
a mismatch detector; and a polarity selection device that receives either the first signal or the second signal and inverts the polarity of the signal depending on the detection output from the detector, or outputs the polarity as it is not inverted. and a comparator that compares and determines the magnitude of the signal that is not input to the polarity selector out of the first signal and the second signal and the output signal from the polarity selector. A phase determination device characterized in that the phase of a received modulated wave is determined from each determination output from the first and second polarity determination devices and a comparison determination output from the comparator.