CN101540929B - A digital television receiver synchronization time test system and its test method - Google Patents

Abstract

The invention relates to a digital television receiver synchronization time testing system and a testing method thereof, in particular to a method for measuring the time required for a digital television receiver from an out-of-synchronization state to a correct receiving state. The test system includes a bit error analyzer, a modulator, a combiner, a pulse generator, a Gaussian white noise generator and a receiver under test. The bit error analyzer sends data to the modulator, and the modulator sends the transmission signal to the combiner after modulation and frequency conversion of the data. The pulse generator controls the Gaussian white noise generator to output the pulse noise signal to the combiner. The combiner combines the transmission signal with the The noise signals are summed and sent to the receiver under test. The error code analyzer measures the code error seconds of the receiver under test, and calculates the synchronization time of the receiver under test by the formula. By using the method of the invention, the synchronization time of the receiver under test can be measured without accurately detecting the error position, and the system structure is simple and the operation is simple and convenient.

Description

A kind of digital television receiver test macro lock in time and method of testing thereof

Technical field

The invention belongs to the digital communication field tests, be specifically related to a kind of digital television receiver test macro lock in time and method of testing thereof.

Background technology

Along with the progress of digital television techniques, digital television broadcasting relevant device and user popularize in continuous development.China has issued the Digital Television Terrestrial Broadcasting transmission standard of independent intellectual property right in 2006, cable digital TV broadcasting has also reached widely to be popularized.At present, the receiver of Digital Television mainly contains set-top box and integrated TV etc.With the set-top box is example, and chief component is tuner, demodulation chip, picture decoding chip and controller etc.The set-top box course of work is: digital television broadcasting radiofrequency signal input tuner, tuner is down-converted to intermediate frequency with radiofrequency signal, intermediate-freuqncy signal input demodulation chip, demodulation chip through frame head synchronously, channel estimating, time-frequency conversion, deinterleaving, separate processes such as constellation mapping, channel-decoding, descrambling code, the output image code stream is given the picture decoding chip, decoding chip carries out picture decoding, and output image signal is given television set, watches for the user.

The receiving course of digital television receiver may be summarized to be:

1. the local oscillator locking frequency process of tuner and automatic gain control AGC locks the process of power;

2. the channel demodulation process of demodulation chip;

3. the picture decoding process of decoding chip.

Wherein, the picture decoding process of the decoding chip only code stream with demodulation chip output is relevant, and operating state is affected by the external environment little, decoding time delay relative fixed; And preceding two courses of work are affected by the external environment easily, and processing delay changes greatly.

Receive represented lock in time digital television receiver from the input radio frequency signal to demodulating the required time delay of correct code stream, an important parameter as receiver performance, this index and user are closely related to the use of receiver, it has reflected the size of receiver from the required time-delay of output image of starting shooting, and the user is switched the size of the required time-delay of program channel, because each user is to the switching of channel, receiver all needs the synchronous process of repetition.

There is not direct measurement means lock in time for digital television receiver at present.The equipment of measuring the code stream accuracy is called the bit error analyzing instrument, and it is 1 second the interior error rate of certain period that the development level of current bit error analyzing instrument can only be measured precision, and can not write down the moment that each error code bit takes place.That is to say when bit error analyzing instrument directly measuring receiver begins correct reception, promptly can not directly record the required time synchronously.In traditional research process, can only use the bit error analyzing instrument to carry out the rough measure of lock in time.

Therefore, need a kind of digital television receiver method of testing lock in time, accurately measure digital television receiver lock in time, and also do not mention similar method of testing in the existing document.

Summary of the invention

The present invention proposes a kind of digital television receiver test macro lock in time and method of testing thereof, specifically, the present invention relates to a kind of system and the method thereof of digital television receiver of measuring from the lock-out state to correct accepting state required time.

The synchronizing process that the present invention sets forth, mainly be meant preceding two processes in the receiving course of digital television receiver, be the local oscillator locking frequency process and automatic gain control (the Automatic Generation Control of tuner, abbreviate AGC as) process of locking power, and the channel demodulation process of demodulation chip; Just refer to this preceding two times that process is required the lock in time of receiver, promptly imports tuner to the required time of demodulation chip output code flow from signal.

Because the computing in the demodulating process is very complicated, processing parameter initial value difference is calculated in the moment homographic solution allocation and transportation that each signal arrives, particularly the parameter initial value of deinterleaving and channel-decoding process is different, can cause different locks in time, so be meant the receiver mean value of lock in time the lock in time of describing among the present invention.

The present invention mainly uses the SES statistical function of bit error analyzing instrument, and SES is meant that the second of error code appearred in the receiver demodulation, and the SES number promptly refers to occur in the timing statistics second number of error code.

In a word, the invention provides a kind of testing evaluation method, can use under various digital transmission systems and standard, test result supplies the researcher of receiving system in the reference of equipment development.

This digital television receiver test macro lock in time of the present invention is made up of bit error analyzing instrument, modulator, mixer, pulse generator, Gaussian white noise generator and tested receiver.The bit error analyzing instrument sends data to modulator, modulator obtains radio-frequency transmission signals after these data are modulated frequency conversion, and this radio-frequency transmission signals sent to mixer, the pulse generator output pulse signal is given Gaussian white noise generator, Gaussian white noise generator output white Gaussian noise signal is given mixer, mixer is with white Gaussian noise signal and radio-frequency transmission signals addition, signal after the output addition is given tested receiver, the data of output send to the bit error analyzing instrument after the tested receiver demodulation, at last by the error rate in the bit error analyzing instrument statistics code stream, method is: will be sent to the data of modulator and compare from the data that tested receiver is received, the bit definitions that receives difference between data and the transmission data is the error code bit, and the error rate is defined as: the error rate=error code bit number/total transmitted bit number.

Described pulse generator comprises:

Clock: the externally pulse of the moment generation certain width of input signal triggering, this pulse duration is the parameter preset of clock;

Selector switch: select the road output wherein of two-way input signal according to being provided with;

Manual activator: manually control by the tester, produce triggering signal in the moment of pressing;

Clocked flip-flop at random:, produce equally distributed triggering signal at random in the certain hour scope according to parameter is set.

The course of work of described pulse generator is:

The tester is provided with the pulse width parameter of clock, the triggering signal of manual activator output inputs to selector switch, the triggering signal of clocked flip-flop output also inputs to selector switch at random, selector switch wherein one the tunnel is exported to clock according to selection is set, clock the input triggering signal control under, output pulse signal.

Method of testing comprises the steps:

Step 1, connected system equipment normally receives system under the situation of plus noise not.

Open the bit error analyzing instrument, the bit error analyzing instrument sends data to modulator, and the transmission mode of operation of modulator being set and its power output is set is a definite value C ₀, to set Gaussian white noise generator and be output as closed condition, tested receiver sends to the bit error analyzing instrument with code stream after the demodulation, and the bit error analyzing instrument is shown as correct reception is not at this moment had error code state, wherein C ₀Span be-60dBm is to-40dBm.Concrete operations are:

A) open the bit error analyzing instrument, the bit error analyzing instrument sends data to modulator, sets the transmission mode of operation of modulator;

B) power output with modulator is set at a definite value C ₀, the dBm of unit closes the output of Gaussian white noise generator, and this moment, received signal was not subjected to the interference of white noise, and tested receiver normally receives;

C) tested receiver sends to the bit error analyzing instrument with the code stream after the demodulation, and the bit error analyzing instrument shows that this moment, transmission error rates was 0;

Step 2, the white Gaussian noise carrier-to-noise ratio thresholding of measuring system.

Gaussian white noise generator is set to continuous output services pattern, measures the white Gaussian noise carrier-to-noise ratio threshold value h of tested receiver this moment, and the Gaussian white noise generator power output was N when note reached white Gaussian noise carrier-to-noise ratio threshold value ₀, the dBm of unit.Concrete operations are:

A) Gaussian white noise generator is arranged on continuous output services pattern;

B) output of Gaussian white noise generator is opened, and progressively increase its power output, the white Gaussian noise of sneaking into signal is progressively strengthened, can not normally receive until tested receiver;

C) progressively reduce the power output of Gaussian white noise generator, recover to receive until tested receiver, the bit error analyzing instrument shows that the error rate is lower than error rate criterion threshold value e;

D) measure the power output of Gaussian white noise generator at this moment, be designated as N ₀, the dBm of unit;

E) with carrier-to-noise ratio C ₀/ N ₀Be designated as the white Gaussian noise carrier-to-noise ratio threshold value h of system, the dB of unit.

Step 3 increases the white noise generator power output and is set to pulse working mode.

Keep modulator output power constant, the Gaussian white noise generator power output is increased Δ N, the dB of unit, this moment, white Gaussian noise power was (N ₀+ Δ N) dBm, and Gaussian white noise generator is set to be subjected to pulse signal Control work pattern, and wherein the span of Δ N is greater than 0dB and is not more than 30dB.Concrete operations are:

A) keep modulator output power constant, the Gaussian white noise generator power output is increased Δ N, 0＜Δ N≤30 wherein, the dB of unit, promptly the Gaussian white noise generator power output is (N ₀+ Δ N) dBm, mixer are with modulator output signal and white Gaussian noise signal plus, and the signal after the output addition is given tested receiver;

B) this moment, tested receiver input carrier-to-noise ratio was (h-Δ N) dB, and less than white Gaussian noise carrier-to-noise ratio threshold value h, tested receiver enters the lock-out state;

C) Gaussian white noise generator being set is pulse signal Control work pattern, and this moment, Gaussian white noise generator output was controlled by pulse signal, only sent white noise signal in the high level time of input pulse signal.

Step 4 is provided with pulse generator output pulse signal width, and sends pulse signal.

Set pulse generator, making its output pulse signal width is W second, and the trigger interval time of adjacent pulse is random number, and wherein W is integer and 1≤W≤10.Concrete operations are:

A) the pulse generator output pulse signal is set and gives Gaussian white noise generator, and the pulsewidth of pulse signal is that high level time length is W second that wherein W is integer and 1≤W≤10;

B) pulse generator is to the Gaussian white noise generator output pulse signal, and the triggering of pulse constantly must be in tested receiver synchronously and after recovering normal the reception, promptly goes up after the error code end that tested receiver that a pulse causes produces;

C) in pulse generator inside, the generation of pulse is produced by clocked flip-flop control impuls source at random, or is produced by manual activator control impuls source at random by the tester.

Step 5 records the SES number, calculates tested receiver lock in time.

Use bit error analyzing instrument test tested receiver total SES number after continuous L the pulse period, remember that total SES number is R _Sum, calculate (R _Sum/ L)-value of W-1, result of calculation is recorded as lock in time of tested receiver, wherein L is not less than 30.

A) L pulse signal of pulse generator output, Gaussian white noise generator is exported L white Gaussian noise pulse under this signal controlling;

B) establishing the tested receiver SES number that the 1st white Gaussian noise pulse cause is R ₁, the tested receiver SES number that i white Gaussian noise pulse process causes is R _i(i=1,2 ..., L), record R ₁, R ₂..., R _L

C) calculate SES sum R _Sum=R ₁+ R ₂+ ... + R _L, and calculate (R _Sum/ L)-value of W-1, with the lock in time of result of calculation as tested receiver.

Described this kind digital television receiver method of testing lock in time adopts random time white Gaussian noise pulse and digital television transfer signal plus, and the mode of measurement SES, and the principle by statistical average records digital television receiver lock in time.

The present invention is mainly used in the test of digital television receiver performance, development along with digital television and broadcasting transinission system, multiple digital television broadcasting transmission standard has appearred, the broadcasting system difference of various transmission standards, the implementation of receiver is also varied, be one of them important performance index the lock in time of receiver, and it is related to quality of services for users.The present invention is used to pass judgment on the requirement whether tested receiver meets index lock in time, and provides the performance between the various receivers to compare.In a word, the invention provides a kind ofly under the existing equipment condition,, record the method for receiver performance parameter lock in time, can be used for various digital television systems by repeatedly measuring the method for back statistical computation.

The advantage of a kind of digital television receiver performance test methods of the present invention is:

(1) the method for testing interface among the present invention has generality, is applicable to the test of multiple digital television system;

(2) method of testing among the present invention is not needing accurately to record under the situation of error code occurrence positions, adopts statistical method to reach a conclusion, and has avoided the restriction of appointed condition, and test just can be finished under the common apparatus condition;

(3) method of testing among the present invention adopts statistical computation, has played and has repeatedly measured the effect that is averaged, and has reduced the randomness of test, has improved result's confidence level.

Description of drawings

Fig. 1 is existing test macro equipment block diagram;

Fig. 2 is the internal frame diagram of pulse generator of the present invention;

Fig. 3 is a method of testing flow chart of the present invention;

Fig. 4 is pulse signal waveform figure of the present invention;

Concern schematic diagram between the timing statistics of Fig. 5 for pulse signal of the present invention and bit error analyzing instrument;

Fig. 6 concerns schematic diagram lock in time for single pulse noise of the present invention and receiver.

Among the figure:

1. bit error analyzing instrument 2. modulators 3. mixers

4. pulse generator 41. clocks 42. selector switches

43. manual activator 44. is clocked flip-flop 5. Gaussian white noise generators at random

6. tested receiver

Embodiment

Below in conjunction with accompanying drawing the specific embodiment of the present invention is described in further details.

Be illustrated in figure 1 as a kind of digital television receiver test macro lock in time of the present invention, this system is made up of bit error analyzing instrument 1, modulator 2, mixer 3, pulse generator 4, Gaussian white noise generator 5 and tested receiver 6.System equipment connects as shown in Figure 1, bit error analyzing instrument 1 sends data to modulator 2, modulator 2 obtains radio-frequency transmission signals after these data are modulated frequency conversion, and this radio-frequency transmission signals sent to mixer 3, pulse generator 4 output pulse signals are given Gaussian white noise generator 5, Gaussian white noise generator 5 output white Gaussian noise signals are given mixer 3, mixer 3 is with white Gaussian noise signal and radio-frequency transmission signals addition, signal after the output addition is given tested receiver 6, the data of output send to bit error analyzing instrument 1 after tested receiver 6 demodulation, at last by the error rate in the bit error analyzing instrument 1 statistics code stream, method is: will be sent to the data of modulator 2 and the data received from tested receiver 6 compare, the bit definitions that receives difference between data and the transmission data is the error code bit, and the error rate is defined as: the error rate=error code bit number/total transmitted bit number.

Be illustrated in figure 2 as the internal frame diagram of the pulse generator 4 of digital television receiver method of testing lock in time of the present invention, this pulse generator 4 comprises:

Clock 41: the externally pulse of the moment generation certain width of input signal triggering, this pulse duration is the parameter preset of clock 41;

Selector switch 42: select the road output wherein of two-way input signal according to being provided with;

Manual activator 43: manually control by the tester, produce triggering signal in the moment of pressing;

Clocked flip-flop 44 at random: according to parameter is set, produce equally distributed triggering signal at random in the certain hour scope.

The course of work of described pulse generator 4 is:

The tester is provided with the pulse width parameter of clock 41, the triggering signal of manual activator 43 outputs inputs to selector switch 42, the triggering signal of clocked flip-flop 44 outputs also inputs to selector switch 42 at random, selector switch 42 wherein one the tunnel is exported to clock 41 according to selection is set, clock 41 the input triggering signal control under, output pulse signal.

As shown in Figure 3, the concrete steps of a kind of digital television receiver method of testing lock in time of the present invention are as follows:

Step 1, connected system equipment normally receives system under the situation of plus noise not.

Open bit error analyzing instrument 1, bit error analyzing instrument 1 sends data to modulator 2, and the transmission mode of operation of modulator 2 being set and its power output is set is C ₀, to set Gaussian white noise generator 5 and be output as closed condition, tested receiver 6 sends to bit error analyzing instrument 1 with code stream after the demodulation, and bit error analyzing instrument 1 is shown as correct reception is not at this moment had error code state, wherein C ₀Span be-60dBm is to-40dBm.Concrete operations are:

A) open bit error analyzing instrument 1, bit error analyzing instrument 1 sends data to modulator 2, sets the transmission mode of operation of modulator 2;

B) power output with modulator 2 is set at certain value C ₀, the dBm of unit closes the output of Gaussian white noise generator 5, and this moment, received signal was not subjected to the interference of white noise, and tested receiver 6 normally receives;

C) tested receiver 6 sends to bit error analyzing instrument 1 with the code stream after the demodulation, and bit error analyzing instrument 1 shows that this moment, transmission error rates was 0;

Step 2, the white Gaussian noise carrier-to-noise ratio thresholding of measuring system.

Gaussian white noise generator 5 is set to continuous output services pattern, measures the white Gaussian noise carrier-to-noise ratio threshold value h of tested receiver 6 this moment, and Gaussian white noise generator 5 power outputs were N when note reached white Gaussian noise carrier-to-noise ratio threshold value ₀, the dBm of unit.Concrete operations are:

A) Gaussian white noise generator 5 is arranged on continuous output services pattern;

B) output of Gaussian white noise generator 5 is opened, and the power output that increases, the white Gaussian noise of sneaking into signal is progressively strengthened, can not normally receive until tested receiver 6;

C) progressively reduce the power output of Gaussian white noise generator 5, recover to receive until tested receiver 6, bit error analyzing instrument 1 shows that the error rate is lower than error rate criterion threshold value e;

D) measure the power output of Gaussian white noise generator 5 at this moment, be designated as N ₀, the dBm of unit;

E) with carrier-to-noise ratio C ₀/ N ₀Be designated as the white Gaussian noise carrier-to-noise ratio threshold value h of system, the dB of unit.

Step 3 increases the white noise generator power output and is set to pulse working mode.

Keep modulator 2 power outputs constant, Gaussian white noise generator 5 power outputs are increased Δ N, the dB of unit, this moment, white Gaussian noise power was (N ₀+ Δ N) dBm, and Gaussian white noise generator 5 is set to be subjected to pulse signal Control work pattern, wherein the span of Δ N is greater than 0dB and is not more than 30dB.Concrete operations are:

A) keep modulator 2 power outputs constant, Gaussian white noise generator 5 power outputs are increased Δ N, 0＜Δ N≤30 wherein, the dB of unit, promptly Gaussian white noise generator 5 power outputs are (N ₀+ Δ N) dBm, mixer 3 are with modulator 2 output signals and white Gaussian noise signal plus, and the signal after the output addition is given tested receiver 6;

B) this moment, tested receiver 6 input carrier-to-noise ratios were (h-Δ N) dB, and less than white Gaussian noise carrier-to-noise ratio threshold value h, tested receiver 6 enters the lock-out state;

C) Gaussian white noise generator 5 is set and is pulse signal Control work pattern, this moment, Gaussian white noise generator 5 outputs were controlled by pulse signal, only sent white noise signal in the high level time of input pulse signal.

Step 4 is provided with pulse generator output pulse signal width, and sends pulse signal.

Set pulse generator 4, making its output pulse signal width is W second, and the trigger interval time of adjacent pulse is random number, and wherein W is integer and 1≤W≤10.Concrete operations are:

A) pulse generator 4 output pulse signals is set and gives Gaussian white noise generator 5, and the pulsewidth of pulse signal is that high level time length is W second that wherein W is integer and 1≤W≤10;

B) pulse generator 4 is to Gaussian white noise generator 5 output pulse signals, and the triggering of pulse constantly must be in tested receiver 6 synchronously and after recovering normal the reception, promptly goes up after the error code end that tested receiver 6 that a pulse causes produces;

C) in pulse generator 4 inside, the generation of pulse is produced by the 44 control impuls sources 41 of clocked flip-flop at random, or is produced by manual activator 43 control impuls sources 41 at random by the tester.

Step 5 records the SES number, calculates tested receiver lock in time.

Use bit error analyzing instrument 1 test tested receiver 6 total SES number after continuous L the pulse period, remember that total SES number is R _Sum, calculate (R _Sum/ L)-value of W-1, result of calculation is recorded as lock in time of tested receiver 6, wherein L is not less than 30.

A) L pulse signal of pulse generator 4 outputs, Gaussian white noise generator 5 is exported L white Gaussian noise pulse under this signal controlling, and time domain waveform is as shown in Figure 4;

B) establishing the 1st tested receiver that the white Gaussian noise pulse causes 6 SES numbers is R ₁, tested receiver 6 SESs that i white Gaussian noise pulse process causes are R _i(i=1,2 ..., L), record R ₁, R ₂..., R _L

C) calculate SES sum R _Sum=R ₁+ R ₂+ ... + R _L, and calculate (R _Sum/ L)-value of W-1, with the lock in time of result of calculation as tested receiver 6.

Below part test parameter in described digital television receiver method of testing lock in time is done some explanations:

In the step 3, Gaussian white noise generator 5 power outputs increase Δ N, 0＜Δ N≤30, the dB of unit, wherein the value of Δ N to lock in time test result can exert an influence, general Δ N is big more, tested receiver is long more 6 locks in time, because need automatic gain control AGC process after the signal input tested receiver 6 through tuner, when if the value of Δ N is bigger than the value of thresholding h, the power of impulsive noise can be than the big certain numerical value Δ N-h of signal power, and within the impulsive noise width, agc circuit can be adjusted to and adapt to noise power N ₀The value of+Δ N, after impulsive noise finished, agc circuit needed the time to adjust to adaptation signal power C ₀Value, when the value of Δ N-h is big more, this adjustment time is just long more, through interpretation, the value of Δ N should not exceed more than the value 5dB of thresholding h.

In the step 4, the relation between the pulse signal that pulse generator 4 produces and the timing statistics of bit error analyzing instrument 1 as shown in Figure 5.The time that dash area indicating impulse noise continues among Fig. 5, each length is W second, and wherein W is integer and 1≤W≤10, and be M Bit Error Code Statistics second of establishing the initial moment place of the 1st pulse ₁Second, the initial moment of pulse and M ₁Time difference between second is initial is t ₁, be M Bit Error Code Statistics second at the moment place that i pulse is initial _iSecond, i=1 wherein, 2 ..., L, the initial moment of pulse and M _iTime difference between second is initial is t _i, and 0≤t as can be known _i＜1.

If if pulse generator 4 internal trigger signals are to be produced by manual activator 43 by the tester, the tester is after the error code that tested receiver 6 is produced by an impulse disturbances finishes, the manual triggers next pulse, the tester triggers and constantly can regard as at random, and time difference t _iDistribution meet [0,1) in even distribution.

If pulse generator 4 internal trigger signals are by clocked flip-flop 44 generations at random, at random clocked flip-flop 44 impulsive noise that triggers and the time difference t that adds up second initial moment _iDistribution meet [0,1) in even distribution.

Below the computing formula of 6 locks in time of tested receiver in the step 5 is explained:

As shown in Figure 6, wherein dark dash area is the duration of impulsive noise, and more shallow dash area is 6 locks in time of tested receiver, and the initial moment of i impulsive noise is apart from place Bit Error Code Statistics M _iThe time difference in second in the initial moment is t _i, establishing after i the impulsive noise 6 locks in time of tested receiver is τ _i, establishing the SES number that i impulsive noise causes is R _iBe meant after L the impulsive noise tested receiver mean value of 6 locks in time 6 locks in time of tested receiver that method of testing desire of the present invention is surveyed, and is made as τ, promptly $\stackrel{\‾}{\mathrm{\τ}}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\τ}}_i/L.$ If the integer part of τ is τ _Int(τ _Int∈ 1,2,3 ...), fractional part is τ _Dec(0≤τ _Dec＜1), τ=τ is arranged _Int+ τ _Dec

As mentioned described in the background technology, be not identical the lock in time of each tested receiver 6, particularly the parameter initial value of deinterleaving and channel-decoding is relevant with the demodulation calculation process for it, to fluctuate among a small circle lock in time, but can acute variation, can think various model tested receiver total ripple scopes within 1 second, and the lock in time of separate unit tested receiver, the variation in fluctuation range was equally distributed.If Δ τ _iBe the difference between i receiver lock in time and the τ, i.e. τ _i=τ+Δ τ _i, that is to say Δ τ _iObey [σ _τ, σ _τ] interior even distribution, wherein 0＜σ _τ≤ 1.

Note t _iCorresponding stochastic variable is ξ _i, Δ τ _iCorresponding stochastic variable is η _i, because the test 6 locks in time of L tested receiver is separate, therefore, stochastic variable ξ ₁, ξ ₂..., ξ _LAnd η ₁, η ₂..., η _LBe mutually independent.By shown in Figure 6, can get the SES that the i subpulse causes and count R _iComputing formula be:

R _i＝Int(t _i+W+τ _i)+1＝Int(t _i+W+τ _int+τ _dec+Δτ _i)+1(1)

Wherein, function Int (x) expression is to the value round numbers part of x.(1) formula can also be write as

R _i＝Int(ξ _i+W+τ _int+τ _dec+η _i)+1

＝τ _int+W+1+Int(ξ _i+τ _dec+η _i)

Thereby have $\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{R}_i/L={\mathrm{\τ}}_{\mathrm{int}}+W+1+\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\mathrm{Int}({\mathrm{\ξ}}_i+{\mathrm{\τ}}_{\mathrm{dec}}+{\mathrm{\η}}_i)/L$

Know by Chebyshev Chebyshev theorem, when L is very big

$\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{R}_i/L={\mathrm{\τ}}_{\mathrm{int}}+W+1+E\left[\mathrm{Int}({\mathrm{\ξ}}_i+{\mathrm{\τ}}_{\mathrm{dec}}+{\mathrm{\η}}_i)\right]---\left(2\right)$

Wherein, E[] to represent to ask mathematic expectaion, the value of L should be not less than 30.

As from the foregoing, ξ _iFor [0,1) interior even distribution, so ξ _iProbability density function f _X=1; η _iBe [σ _τ, σ _τ] interior even distribution, so η _iProbability density function be $f_Y=\frac{1}{{2\mathrm{\σ}}_{\mathrm{\τ}}},$ So ξ _i+ η _iJoint probability density be $f_{\mathrm{XY}}=f_X\·f_Y=1\·\frac{1}{{2\mathrm{\σ}}_{\mathrm{\τ}}}=\frac{1}{{2\mathrm{\σ}}_{\mathrm{\τ}}}.$

Calculate E[Int (ξ below _i+ τ _Dec+ η _i)]:

Int (ξ _i+ τ _Dec+ η _i) value depend on ξ _i, τ _DecAnd η _iValue and magnitude relationship because 0≤ξ _i＜1,0≤τ _Dec＜1 ,-σ _τ≤ η _i≤ σ _τSo ,-σ _τ≤ ξ _i+ τ _Dec+ η _i＜2+ σ _τ, again because 0＜σ _τ≤ 1, so Int (ξ _i+ τ _Dec+ η _i) possible value be-1,0,1,2.About ξ _i, τ _DecAnd η _iThe discussion of magnitude relationship have 6 kinds of possible situations, P[] the expression probability:

(1) works as σ _τ＜τ _Dec＜1-τ _DecThe time

Int (ξ _i+ τ _Dec+ η _i) distribution function be:

P[Int(ξ _i+τ _dec+η _i)＝-1]＝P[-σ _τ≤ξ _i+τ _dec+η _i＜0]＝0

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=0]=P[0\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<1]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;(1-{\mathrm{\&tau;}}_{\mathrm{dec}})\&CenterDot;{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}=1-{\mathrm{\&tau;}}_{\mathrm{dec}}$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=1]=P[1\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;{\mathrm{\&tau;}}_{\mathrm{dec}}\&CenterDot;{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}={\mathrm{\&tau;}}_{\mathrm{dec}}$

P[Int(ξ _i+τ _dec+η _i)＝2]＝P[2≤ξ _i+τ _dec+η _i＜2+σ _τ]＝0

So, E[Int (ξ _i+ τ _Dec+ η _i)]=0 (1)+(1-τ _Dec) 0+ τ _Dec1+02=τ _Dec

(2) work as τ _Dec≤ σ _τ＜1-τ _DecThe time

Int (ξ _i+ τ _Dec+ η _i) distribution function be:

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=-1]=P[{-\mathrm{\&sigma;}}_{\mathrm{\&tau;}}\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<0]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=0]=P[0\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<1]$

$=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+1-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2-\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2-\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}})}^2]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=1]=P[1\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}})\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}})=\frac{1}{{4\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}})}^2$

P[Int(ξ _i+τ _dec+η _i)＝2]＝P[2≤ξ _i+τ _dec+η _i＜2+σ _τ]＝0

So,

$E\left[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)\right]=\frac{1}{{4\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2\&CenterDot;(-1)+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}})}^2]\&CenterDot;0$

$+\frac{1}{{4\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}})}^2\&CenterDot;1+0\&CenterDot;2={\mathrm{\&tau;}}_{\mathrm{dec}}$

(3) work as τ _Dec＜1-τ _Dec≤ σ _τThe time

Int (ξ _i+ τ _Dec+ η _i) distribution function be:

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=-1]=P[{-\mathrm{\&sigma;}}_{\mathrm{\&tau;}}\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<0]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=0]=P[0\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<1]=\frac{1}{2{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+1-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2-{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=1]=P[1\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2]=\frac{1}{2{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}(2-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+1)\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}}-1)+\frac{1}{2}]$

$=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}(3-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}}-1)+\frac{1}{2}]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=2]=P[2\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}}-1)}^2$

So

$E\left[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)\right]=\frac{1}{{4\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2\&CenterDot;(-1)+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+1-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2-\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2]\&CenterDot;0$

$+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}(3-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})\&CenterDot;({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}}-1)+\frac{1}{2}]\&CenterDot;1+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}+{\mathrm{\&tau;}}_{\mathrm{dec}}-1)}^2\&CenterDot;2={\mathrm{\&tau;}}_{\mathrm{dec}}$

(4) work as σ _τ＜1-τ _Dec≤ τ _DecThe time

Int (ξ _i+ τ _Dec+ η _i) distribution function be:

P[Int(ξ _i+τ _dec+η _i)＝-1]＝P[-σ _τ≤ξ _i+τ _dec+η _i＜0]＝0

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=0]=P[0\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<1]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[(1-{\mathrm{\&tau;}}_{\mathrm{dec}})\&CenterDot;{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=1]=P[1\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}{[2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}{\&CenterDot;(1-1+{\mathrm{\&tau;}}_{\mathrm{dec}})]=\mathrm{\&tau;}}_{\mathrm{dec}}$

P[Int(ξ _i+τ _dec+η _i)＝2]＝P[2≤ξ _i+τ _dec+η _i＜2+σ _τ]＝0

So, $E\left[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)\right]=0\&CenterDot;(-1)+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\left[(1-{\mathrm{\&tau;}}_{\mathrm{dec}}\&CenterDot;{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}})\right]\&CenterDot;0+{\mathrm{\&tau;}}_{\mathrm{dec}}\&CenterDot;1+0\&CenterDot;2={\mathrm{\&tau;}}_{\mathrm{dec}}$

(5) as 1-τ _Dec≤ σ _τ＜τ _DecThe time

P[Int(ξ _i+τ _dec+η _i)＝-1]＝P[-σ _τ≤ξ _i+τ _dec+η _i＜0]＝0

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=0]=P[0\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<1]=\frac{1}{2{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\left[\frac{1}{2}{\left({1-{\mathrm{\&tau;}}_{\mathrm{dec}}+\mathrm{\&sigma;}}_{\mathrm{\&tau;}}\mathrm{\&tau;}\right)}^2\right]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=1]=P[1\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2]=\frac{1}{2{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2-\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=2]=P[2\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2$

So

$E\left[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)\right]=0\&CenterDot;(-1)+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\left[\frac{1}{2}(1-{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}{)}^2\right]\&CenterDot;0$

$+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-\frac{1}{2}(1-{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}{)}^2-\frac{1}{2}\&CenterDot;(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}{)}^2]\&CenterDot;1+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2\&CenterDot;2={\mathrm{\&tau;}}_{\mathrm{dec}}$

(6) as 1-τ _Dec≤ τ _Dec≤ σ _τThe time

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=-1]=P[{-\mathrm{\&sigma;}}_{\mathrm{\&tau;}}\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<0]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=0]=P[0\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<1]=\frac{1}{2{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2-{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=1]=P[1\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2]=\frac{1}{2{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[1-\frac{1}{2}{(2-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2]$

$P[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)=2]=P[2\&le;{\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i<2+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2$

So

$E\left[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)\right]=\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2\&CenterDot;(-1)+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2-{({\mathrm{\&sigma;}}_{\mathrm{\&tau;}}-{\mathrm{\&tau;}}_{\mathrm{dec}})}^2]\&CenterDot;0$

$+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}[1-\frac{1}{2}(2-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}}{)}^2]\&CenterDot;1+\frac{1}{{2\mathrm{\&sigma;}}_{\mathrm{\&tau;}}}\&CenterDot;\frac{1}{2}{(1-{\mathrm{\&tau;}}_{\mathrm{dec}}-{\mathrm{\&sigma;}}_{\mathrm{\&tau;}})}^2\&CenterDot;2={\mathrm{\&tau;}}_{\mathrm{dec}}$

In sum, under 6 kinds of possible situations, E[Int (ξ _i+ τ _Dec+ η _i)] value all be τ _Dec

By (2) Shi Kede

$\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{R}_i/L={\mathrm{\&tau;}}_{\mathrm{int}}+W+1+E\left[\mathrm{Int}({\mathrm{\&xi;}}_i+{\mathrm{\&tau;}}_{\mathrm{dec}}+{\mathrm{\&eta;}}_i)\right]={\mathrm{\&tau;}}_{\mathrm{int}}+{\mathrm{\&tau;}}_{\mathrm{dec}}+W+1=\stackrel{\&OverBar;}{\mathrm{\&tau;}}+W+1$

So be the lock in time that can get tested receiver 6 $\stackrel{\&OverBar;}{\mathrm{\&tau;}}=\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{R}_i/L-W-1=(R_{\mathrm{sum}}/L)-W-1.$

Be example with China's digital TV ground radio transmission standard (Digital Terrestrial MultimediaBroadcasting abbreviates DTMB as) receiver below, the principle and the course of work of method of testing of the present invention be described:

The digital TV ground wireless broadcast system is a kind of widely used digital television broadcasting system, its mode of operation has multifarious characteristics, the combination of different frame head modes, coding mode, mapped mode, interlace mode, a large amount of different mode of operations have been produced, from receiving on the principle, be every kind of pattern needed lock in time inequality.And, Digital Television Terrestrial Broadcasting user's broad covered area, receiving equipment is of a great variety, and different demodulation techniques also can produce different time-delays.

Adopt receiver method of testing lock in time among the present invention, can be to testing lock in time with the receiver of different vendor under the different modulating pattern, the test result that draws provides important references for the development and the use of equipment as these performance index of this receiver.

Digital Television Terrestrial Broadcasting transmission standard receiver method of testing lock in time, equipment connecting relation as shown in Figure 1, step is:

Step 1 is opened bit error analyzing instrument 1, and bit error analyzing instrument 1 sends data to modulator 2, and the transmission mode of operation of modulator 2 being set and its power output is set is C ₀=-53dBm sets Gaussian white noise generator 5 and is output as closed condition, and tested receiver 6 sends to bit error analyzing instrument 1 with code stream after the demodulation, and bit error analyzing instrument 1 is shown as correct reception is not at this moment had the error code state.Concrete operations are:

Open bit error analyzing instrument 1, bit error analyzing instrument 1 sends data to modulator 2, sets the transmission mode of operation of modulator 2;

The power output of modulator 2 is set at-53dBm, the output of Gaussian white noise generator 5 is closed, this moment, received signal was not subjected to the interference of white noise, and tested receiver 6 normally receives;

Tested receiver 6 sends to bit error analyzing instrument 1 with the code stream after the demodulation, and bit error analyzing instrument 1 shows that this moment, transmission error rates was 0;

Step 2, Gaussian white noise generator 5 are set to continuous output services pattern, measure the white Gaussian noise carrier-to-noise ratio thresholding h of tested receiver 6 this moment, establish that Gaussian white noise generator 5 power outputs are N when reaching white Gaussian noise carrier-to-noise ratio threshold value ₀, the dBm of unit.Concrete operations are:

Gaussian white noise generator 5 is arranged on continuous output services pattern;

The output of Gaussian white noise generator 5 is opened, and the power output that increases, the white Gaussian noise of sneaking into signal is progressively strengthened, can not normally receive until tested receiver 6;

Progressively reduce the power output of Gaussian white noise generator 5, recover to receive until tested receiver 6, bit error analyzing instrument 1 shows that the error rate is lower than error rate criterion threshold value 3 * 10 ^-6

Measure the power output of Gaussian white noise generator 5 this moment, be designated as N ₀, the dBm of unit;

With carrier-to-noise ratio C ₀/ N ₀As the white Gaussian noise carrier-to-noise ratio threshold value h of system, the dB of unit.

Step 3 keeps modulator 2 power outputs constant, and Gaussian white noise generator 5 power outputs are increased Δ N=5dB, and this moment, white Gaussian noise power was (N ₀+ 5) dBm, and Gaussian white noise generator 5 is set to be subjected to pulse signal Control work pattern.Concrete operations are:

Keep modulator 2 power outputs constant, Gaussian white noise generator 5 power outputs are increased Δ N=5dB, promptly Gaussian white noise generator 5 power outputs are (N ₀+ 5) dBm, mixer 3 are with modulator 2 output signals and white Gaussian noise signal plus, and the signal after the output addition is given tested receiver 6;

This moment, tested receiver 6 input carrier-to-noise ratios were (h-5) dB, and less than white Gaussian noise carrier-to-noise ratio threshold value h, tested receiver 6 enters the lock-out state;

Gaussian white noise generator 5 is set is pulse signal Control work pattern, this moment, Gaussian white noise generator 5 outputs were controlled by pulse signal, only sent white noise signal in the high level time of input pulse signal.

Step 4 is set pulse generator 4, and making its output pulse signal width is W=1 second, and the trigger interval time of adjacent pulse is random number.Concrete operations are:

Pulse generator 4 output pulse signals are set give Gaussian white noise generator 5, and the pulsewidth of pulse signal is that high level time length is W=1 second;

Pulse generator 4 is to Gaussian white noise generator 5 output pulse signals, and the triggering of pulse constantly must be in tested receiver 6 synchronously and after recovering normal the reception, promptly goes up after the error code end that tested receiver 6 that a pulse causes produces;

In pulse generator 4 inside, the generation of pulse is produced by manual activator 43 control impuls sources at random by the tester.

Step 5 is used bit error analyzing instrument 1 test tested receiver 6 total SES number after continuous L=30 the pulse period, and establishing total SES number is R _Sum, calculate (R _Sum/ L)-value of W-1, result of calculation is recorded as the lock in time of tested receiver.

30 pulse signals of pulse generator 4 outputs, Gaussian white noise generator 5 is exported 30 white Gaussian noise pulses under this signal controlling;

If the 1st tested receiver that the white Gaussian noise pulse causes 6 SES numbers are R ₁, tested receiver 6 SESs that i white Gaussian noise pulse process causes are R _i(i=1,2 ..., L), record R ₁, R ₂..., R _L

Calculate SES sum R _Sum=R ₁+ R ₂+ ... + R _L, and calculate (R _Sum/ L)-value of W-1, with the lock in time of result of calculation as tested receiver 6.

In a specific embodiment of receiver of the present invention method of testing lock in time, with China's digital TV ground radio transmission standard DTMB receiver is tested object, the modulator mode of operation is 4QAM, FEC0.4, PN420, multicarrier, longly interweave, no pilot tone, frame head are rotated, pulse number is 30, pulse duration is 1 second, and the receiver SES that records each subpulse noise is as shown in table 1:

Table 1DTMB receiver test result lock in time

The pulse sequence number	The SES number (unit: second)	The pulse sequence number	The SES number (unit: second)	The pulse sequence number	The SES number (unit: second)
						1	3	11	3	21	3
2	4	12	4	22	2
						3	2	13	2	23	3
4	5	14	5	24	3
						5	5	15	4	25	4
6	5	16	3	26	3
						7	6	17	4	27	4
8	4	18	3	28	4
						9	4	19	4	29	3
10	5	20	4	30	5

Total as shown in Table 1 SES number is 113 seconds, can get: second receiver lock in time=(113/30)-1-1=3.77-2=1.77.

Claims (2)

1. A digital television receiver synchronous time test system, the system includes: error code analyzer, modulator, combiner, pulse generator, Gaussian white noise generator and receiver under test; The modulator sends the data, the modulator modulates the data and obtains the radio frequency transmission signal after frequency conversion, and sends the radio frequency transmission signal to the combiner, the pulse generator outputs the pulse signal to the Gaussian white noise generator, and the Gaussian white noise generator outputs Gaussian The white noise signal is sent to the combiner, and the combiner adds the Gaussian white noise signal and the radio frequency transmission signal, and outputs the added signal to the receiver under test, and the demodulated output data of the receiver under test is sent to the error analysis The bit error analyzer compares the data sent to the modulator with the data received from the receiver under test to obtain the bit error rate, and the bit difference between the received data and the sent data is defined as an error bit, and the bit error rate is defined as: bit error rate=error bit number/total transmission bit number; it is characterized in that, The pulse generator (4) in this system is made up of pulse source (41), selection switch (42), manual trigger (43) and random timing trigger (44); The tester sets the pulse width parameters of the pulse source (41), the trigger signal output by the manual trigger (43) is input to the selector switch (42), and the trigger signal output by the random timing trigger (44) is also input to the selector switch (42) , the selection switch (42) selects one of them to output to the pulse source (41) according to the setting, and the pulse source (41) outputs a pulse signal under the control of the input trigger signal. 2. A digital television receiver synchronization time test method, the method may further comprise the steps: Step 1. Connect the system equipment so that the system can receive normally without adding noise; Turn on the bit error analyzer (1), the bit error analyzer (1) sends data to the modulator (2), set the transmission working mode of the modulator (2) and set its output power to C ₀ , set the Gaussian white noise generation The output of the device (5) is in a closed state, and the code stream after the demodulation is sent to the error code analyzer (1) by the receiver under test (6). At this time, the code error analyzer (1) shows that it is correctly received and has no code error state, wherein The value range of C ₀ is -60dBm to -40dBm; Step 2, measuring the Gaussian white noise carrier-to-noise ratio threshold of the system; The Gaussian white noise generator (5) is set to the continuous output mode of operation, and the Gaussian white noise carrier-to-noise ratio threshold value h of the receiver under test (6) is measured at this time, and the Gaussian white noise carrier-to-noise ratio threshold value h is recorded when reaching the Gaussian white noise carrier-to-noise ratio threshold value. The output power of the white noise generator (5) is N ₀ , the unit is dBm; It is characterized in that, Step 3, increase the output power of the Gaussian white noise generator and set it to the working mode controlled by the pulse signal; Keep the output power of the modulator (2) unchanged, increase the output power of the Gaussian white noise generator (5) by ΔN, the unit is dB, at this time the Gaussian white noise output power is (N ₀ +ΔN)dBm, and generate the Gaussian white noise The device (5) is set to be controlled by the pulse signal mode of operation, wherein the value range of ΔN is greater than 0dB and not greater than 30dB; the specific operations are: a) keep the output power of the modulator (2) constant, and increase the output power of the Gaussian white noise generator (5) by ΔN, where 0<ΔN≤30, the unit is dB, that is, the output power of the Gaussian white noise generator (5) is ( N ₀ +ΔN)dBm, the combiner (3) adds the output signal of the modulator (2) to the Gaussian white noise signal, and outputs the added signal to the receiver under test (6); b) At this time, the carrier-to-noise ratio at the input terminal of the receiver under test (6) is (h-ΔN) dB, which is less than the Gaussian white noise carrier-to-noise ratio threshold value h, and the receiver under test (6) enters an out-of-synchronization state; c) Set the Gaussian white noise generator (5) to work mode controlled by the pulse signal, at this time the output of the Gaussian white noise generator (5) is controlled by the pulse signal, and the Gaussian white noise is only sent during the high level time of the input pulse signal Signal; Step 4, set the pulse generator output pulse signal width, and send the pulse signal; Set the pulse generator (4) so that the output pulse signal width is W seconds, and the trigger interval of adjacent pulses is a random number, where W is an integer and 1≤W≤10; the specific operations are: a) The pulse generator (4) is set to output a pulse signal to the Gaussian white noise generator (5), and the pulse signal width, that is, the high level time length, is W seconds, where W is an integer and 1≤W≤10; b) The pulse generator (4) outputs a pulse signal to the Gaussian white noise generator (5), and the triggering moment of the pulse is after the receiver under test (6) is synchronized and resumes normal reception, that is, the receiver under test caused by the previous pulse (6) After the generated bit error ends; c) Inside the pulse generator (4), the pulse is generated by a random timing trigger (44) controlling the pulse source (41), or by the tester randomly controlling the pulse source (41) through a manual trigger (43); Step five, measure the number of errored seconds, and calculate the synchronization time of the receiver under test; Use the bit error analyzer (1) to test the total number of errored seconds of the receiver under test (6) after L consecutive pulse periods, record the total number of errored seconds as R _sum , and calculate (R _sum /L)-W-1 The value of the calculation result is recorded as the synchronization time of the receiver under test (6), wherein L is not less than 30; the specific operations are: A) the pulse generator (4) outputs L pulse signals, and the Gaussian white noise generator (5) outputs L Gaussian white noise pulses under the control of the signal; b) Suppose the number of errored seconds of the receiver under test (6) caused by the first Gaussian white noise pulse is R ₁ , and the number of errored seconds of the receiver under test (6) caused by the i-th Gaussian white noise pulse is R _i (i=1, 2, ..., L), record R ₁ , R ₂ , ..., R _L ; Calculate the total number of errored seconds R _sum =R ₁ +R ₂ +...+ _RL , and calculate the value of (R _sum /L)-W-1, and use the calculation result as the synchronization time of the receiver under test (6).

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