CN101672877B - Amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis - Google Patents

Abstract

The method provides an amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis, and a mainly used device is a vector signal analyzer. Traditionally, measurement accompanying phase modulation utilizes a frequency spectrum analysis method with more limitations and complex computation. The method reasonably sets the parameters of the vector signal analyzer so as to measure amplitude-modulated signal by a vector demodulation way, has wide applicability and clear and simple mathematic relation.

Description

A kind of amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis

Technical field

The present invention relates to fields such as radio communication, radio and television, especially relate to amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis.

Background technology

In fields such as radio communication, radio and television, amplitude modulation (AM) signal is a kind of widely used signal, and form as shown in Equation (1) is for desirable AM signal, β=0.But because device property is undesirable, in amplitude modulation, follow phase modulation, cause β ≠ 0, β is called the phase-modulation index of following of amplitude modulation, be in the measurement of amplitude-modulated signal accompanying phase modulation (incidental PM at AM is hereinafter to be referred as following phase modulation), weigh the important parameter of AM signal non-ideal characteristic.

Since two thousand six, there is the researchist to use the method for spectrum analysis to calculate β.But the limitation of this method is bigger:

1, used the Bessel's function approximation method, complexity height but degree of accuracy is not high.

2, with regard to signal shown in the formula (1), classic method only is applicable to the situation of β＜=0.2rad and φ=0 in principle.

Summary of the invention

Because the deficiency of previous methods, fundamental purpose of the present invention is to provide a kind of amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis, realizes amplitude-modulated signal is measured accurately.

In order to realize purpose of the present invention, a kind of amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis is proposed, this method may further comprise the steps:

(1) uses VSA, tested amplitude-modulated signal is carried out the vector demodulation measure Measurement Phase mean square of error root PhaseErr _RMS

(2) according to root-mean-square value PhaseErr _RMSFollow phase-modulation index by 4 calculating of following formula,

$\mathrm{\β}=\sqrt{2}\×{\mathrm{PhaseErr}}_{\mathrm{RMS}}---\left(4\right)$

When described VSA is asked amplitude-modulated signal accompanying phase-modulation index β, carry out following parameter setting:

Demodulation modes: BPSK, QPSK or 8PSK generally recommend the BPSK pattern; During greater than 0.7rad, must use the BPSK pattern at the β of expection;

Demodulation carrier frequency: f _c± f _d, f _dValue see formula (1)

f _d=N _sf _aN _s〉=10, recommend N _sFor integer and 〉=40 (4)

Character rate: M * f _d, demodulation modes is BPSK, M=2; Demodulation modes is QPSK, M=2 or 4; Demodulation modes is 8PSK, M=2,4 or 8

Catch symbol quantity: use L _RFormula (2) is seen in expression

L _R=[N _T* N _s* M] N _TBe positive integer, recommendation N _T〉=5, [] is for rounding symbol (5)

Base band is measured wave filter: recommend to be provided with " closing ";

Described amplitude-modulated signal exists follows the expression formula under the phase modulation situation to be:

S(t)＝(1+Dcos2πf _at)sin[2πf _ct+βcos(2πf _at+φ)] (6)

Wherein, f _cBe carrier frequency, D is the amplitude modulation degree of depth, f _aBe modulating frequency.

Method mathematical relation of the present invention is simple, is under the situation of arbitrary value at β＜=lrad and φ, can both realize measuring accurately.

Description of drawings

The test that Fig. 1 is based on the inventive method is provided with figure;

Fig. 2 is based on the fa=25kHz that this patent method obtains, D=60%, and β=30deg, φ=0deg, demodulation modes are the demodulation polar plot of QPSK.

Embodiment

In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is described in further detail below in conjunction with accompanying drawing.

The test that Fig. 1 is based on the inventive method is provided with figure.VSA used in the present invention can adopt the VSA VSA of Agilent company, R﹠amp; The FSQ vector signal analysis module of S company etc.

When carrier wave is f _d+ f _b(f _df _b), the amplitude modulation degree of depth is that D, modulating frequency are f _aThe AM signal follow in existence under the situation of phase modulation β, expression formula is:

S(t)＝(1+Dcos2πf _at)sin[2π(f _d+f _b)t+βcos2πf _at] (7)

Frequency of utilization is f _dThe CW signal S (t) is carried out quadrature demodulation, then the vector form of the orthogonal waveforms after the demodulation is:

V(t)＝(1+Dcos2πf _at)exp[j(2πf _bt+βcos2πf _at)] (8)

V (t) is handled the phase error Phase Err parameter that (this is according to the QPSK signal Processing) analyzes V (t) according to mpsk signal, and then Phase Err is by following phase modulation to cause, if the amplitude modulation period T _aMuch larger than symbol period T _s, that is:

(establish T _aBe T _sM _aMore than the multiple, M _a〉=30) (9)

And the integral multiple that the sampled sequence persistence length is approximately equal to the amplitude modulation cycle is promptly:

N _aT _a＝NT _s (10)

The code element number that N catches when being the VSA measurement, N _aBe positive integer, recommendation N _a〉=10, then statistical average effect helps improving the accuracy of Phase Err reading.(typical with regard to general VSA table as Agilent VSA and R﹠amp; S FSQ), the code element number N that catches when it is measured is limited, bigger in this case N _aBigger M _aBe that certain contradiction is arranged, recommendation is: N=4000, f _b=1MHz, f _a=25kHz.Then the sampled sequence V (n) of V (t) is:

V(n)＝(1+Dcos2πf _anT _s)exp[j(2πf _bnT _s+βcos2πf _anT _s)] (11)

According to the definition of QPSK signal phase error, the corresponding Phase Err sequence of corresponding each the vector sampling of (11) formula is as can be known:

PhaseErr(n)＝βcos2πf _anT _s (12)

Then obviously have:

PhaseErr _Peak＝max(βcos2πf _anT _s)≈β (13)

But because sampled point is not necessarily at function cos2 π f _aThe extreme point of t, so the principle maximum error of (13) is:

${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="H2009101775957E00012.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=\mathrm{\&beta;}-\mathrm{\&beta;}\cos 2\mathrm{\&pi;}{f}_a{T}_s\&ap;\mathrm{\&beta;}-\mathrm{\&beta;}\cos \frac{2\mathrm{\&pi;}}{M_a}\&ap;\mathrm{\&beta;}{\left(\frac{2\mathrm{\&pi;}}{M_a}\right)}^2---\left(14\right)$

Consider (12) formula, then sequence PhaseErr (n) repeats in the cycle, and then the RMS value of Phase Err can be expressed as:

${\mathrm{PhaseErr}}_{\mathrm{RMS}}=\sqrt{\frac{\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left(\mathrm{\&beta;}\sin 2\mathrm{\&pi;n}{T}_s{f}_a\right)}^2}{N}}---\left(15\right)$

In conjunction with preceding formula, then (15) can be rewritten as the form of integration:

${\mathrm{PhaseErr}}_{\mathrm{RMS}}=\sqrt{\frac{\underset{0}{\overset{N_a{T}_a}{\&Integral;}}{\left(\mathrm{\&beta;}\sin 2\mathrm{\&pi;}{f}_{a}t\right)}^2\mathrm{dt}}{N_a{T}_a}}=\frac{\mathrm{\&beta;}}{\sqrt{2}}---\left(16\right)$

(16) be a clear and definite succinct conclusion, numerical evaluation shows, if (3) formula lowest term is met, then since the error that the mathematics of (15) to (16) conversion is caused in β * 10 ^-14Magnitude can be ignored.Accuracy analysis from principle is beneficial to (16) and asks the precision of β will be higher than utilization (13) to ask β.

Provided some demonstration tests based on this method example as a result below, waveform definition-the download function of Agilent E4438C Vector Modulation signal source is adopted in test, by the software mode generation form as (1) formula, have different amplitude modulation depth D, follow the signal of phase-modulation index β and phase difference, measure β based on patented method then, whether preset value and the measured value of checking β be variant, and different amplitude modulation frequency fa, depth D, β setting value, φ setting value and demodulation modes can be set respectively.Fig. 2 has provided the I-Q demodulation image that measures based on patented method, and fa=25kHz is set, D=60%, β=45deg, φ=0deg, the demodulation polar plot of demodulation modes QPSK;

From the demodulation polar plot of contrast different parameters under being provided with, it is as follows that its physical significance is made summary description:

1, the vector demodulation modes is can be used for analyzing having the AM signal of following phase modulation.

2, the vector length of each point has reflected the amplitude of signal at that time on the I-Q image, and the rotation at the relative center of curve has then reflected the degree of following phase modulation, and the value of setting of β is big more, and curve rotation trend is remarkable more.Simultaneously, parameter

Influential to the polar plot curve shape, but evidence is for almost not influence of measurement result.

Below table 1 provided the error of demonstration test, at first, come the mathematical definition and the physical significance of specification error.Produce a signal with different fa, D, β and φ by the aforementioned software mode, measure β based on patented method then, whether preset value and the measured value of checking β be variant, and then measuring error is defined as:

Table 1 is the systematic measurement error of this test.

Claims (3)

1. amplitude-modulated signal accompanying phase modulation measurement method based on vector analysis is characterized in that comprising step:

(1) uses VSA, tested amplitude-modulated signal is carried out the vector demodulation measure, the root-mean-square value PhaseErr of the phase error of the amplitude-modulated signal after the demodulation of measurement vector _RMS

(2) according to root-mean-square value PhaseErr _RMSFollow phase-modulation index by following formula (4) calculating,

$\mathrm{\&beta;}=\sqrt{2}\&times;{\mathrm{PhaseErr}}_{\mathrm{RMS}}---\left(4\right)$

2. accompanying phase modulation measurement method according to claim 1 is characterized in that,

When described VSA is asked amplitude-modulated signal accompanying phase-modulation index β, carry out following parameter setting:

Demodulation modes: BPSK, QPSK or 8PSK; During greater than 0.7rad, must use the BPSK pattern at the β of expection;

Demodulation carrier frequency: f _c± f _d, f _dValue see formula (1)

f _d＝N _Sf _a N _S≥10 (1)

Character rate: M * f _d, demodulation modes is BPSK, M=2; Demodulation modes is QPSK, M=2 or 4; Demodulation modes is 8PSK, M=2,4 or 8

Catch symbol quantity: use L _RFormula (2) is seen in expression

L _R=[N _T* N _S* M] N _TFor positive integer [] for rounding symbol (2)

Described amplitude-modulated signal exists follows the expression formula under the phase modulation situation to be:

S(t)＝(1+Dcos2πf _at)sin[2πf _ct+βcos(2πf _at+φ)] (3)

Wherein, f _cBe carrier frequency, D is the amplitude modulation degree of depth, f _aBe modulating frequency, φ is a phase differential.

3. accompanying phase modulation measurement method according to claim 2 is characterized in that, described parameter is set to: base band is measured wave filter and is set to " closing "; Demodulation modes is the BPSK pattern; In the described formula (1), N _SFor integer and 〉=40; In the described formula (2), N _T〉=5.

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