ETSI TR 134 901-2003 Universal Mobile Telecommunications System (UMTS) Test Time Optimisation based on statistical approaches Statistical theory applied and evaluation of statistic.pdf

1、 ETSI TR 134 901 V3.0.0 (2003-06)Technical Report Universal Mobile Telecommunications System (UMTS);Test Time Optimisation based on statistical approaches;Statistical theory applied andevaluation of statistical significance(3GPP TR 34.901 version 3.0.0 Release 1999)ETSI ETSI TR 134 901 V3.0.0 (2003-

2、06) 1 3GPP TR 34.901 version 3.0.0 Release 1999 Reference DTR/TSGT-0134901v300 Keywords UMTS ETSI 650 Route des Lucioles F-06921 Sophia Antipolis Cedex - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N 348 623 562 00017 - NAF 742 C Association but non lucratif enregistre la Sous-Prfect

3、ure de Grasse (06) N 7803/88 Important notice Individual copies of the present document can be downloaded from: http:/www.etsi.org The present document may be made available in more than one electronic version or in print. In any case of existing or perceived difference in contents between such vers

4、ions, the reference version is the Portable Document Format (PDF). In case of dispute, the reference shall be the printing on ETSI printers of the PDF version kept on a specific network drive within ETSI Secretariat. Users of the present document should be aware that the document may be subject to r

5、evision or change of status. Information on the current status of this and other ETSI documents is available at http:/portal.etsi.org/tb/status/status.asp If you find errors in the present document, send your comment to: editoretsi.org Copyright Notification No part may be reproduced except as autho

6、rized by written permission. The copyright and the foregoing restriction extend to reproduction in all media. European Telecommunications Standards Institute 2003. All rights reserved. DECTTM, PLUGTESTSTM and UMTSTM are Trade Marks of ETSI registered for the benefit of its Members. TIPHONTMand the T

7、IPHON logo are Trade Marks currently being registered by ETSI for the benefit of its Members. 3GPPTM is a Trade Mark of ETSI registered for the benefit of its Members and of the 3GPP Organizational Partners. ETSI ETSI TR 134 901 V3.0.0 (2003-06) 2 3GPP TR 34.901 version 3.0.0 Release 1999 Intellectu

8、al Property Rights IPRs essential or potentially essential to the present document may have been declared to ETSI. The information pertaining to these essential IPRs, if any, is publicly available for ETSI members and non-members, and can be found in ETSI SR 000 314: “Intellectual Property Rights (I

9、PRs); Essential, or potentially Essential, IPRs notified to ETSI in respect of ETSI standards“, which is available from the ETSI Secretariat. Latest updates are available on the ETSI Web server (http:/webapp.etsi.org/IPR/home.asp). Pursuant to the ETSI IPR Policy, no investigation, including IPR sea

10、rches, has been carried out by ETSI. No guarantee can be given as to the existence of other IPRs not referenced in ETSI SR 000 314 (or the updates on the ETSI Web server) which are, or may be, or may become, essential to the present document. Foreword This Technical Report (TR) has been produced by

11、ETSI 3rd Generation Partnership Project (3GPP). The present document may refer to technical specifications or reports using their 3GPP identities, UMTS identities or GSM identities. These should be interpreted as being references to the corresponding ETSI deliverables. The cross reference between GS

12、M, UMTS, 3GPP and ETSI identities can be found under http:/webapp.etsi.org/key/queryform.asp . ETSI ETSI TR 134 901 V3.0.0 (2003-06) 3 3GPP TR 34.901 version 3.0.0 Release 1999 Contents Intellectual Property Rights2 Foreword.2 1 Scope 5 2 References 5 3. Definitions, symbols and abbreviations .5 3.1

13、 Definitions5 3.2 Symbols5 3.3 Abbreviations .5 3.4 Equations5 4 Introduction 6 5. Definitions of distribution functions and parameters to be used6 5.1 Properties of the Poisson distribution.7 5.2 Equivalence between Poisson distribution and Chi Square distribution.7 5.3 Confidence interval 12 5.4 A

14、pplication of the confidence interval to decide the outcome of the test.13 5.5 Test time reduction.14 5.6 Calculation of the intersection coordinates 16 5.7 Wrong decision risk F 17 6 F to D conversion in BER BLER tests.17 6.1 Conversion F to D 17 6.2 Introduction 17 6.3 The simulation procedure.18

15、6.3.1 Equal pass and fail probability18 6.3.2 Unequal pass and fail probability .19 6.4 Result of the simulation: M-F array .20 7. Definitions, symbols and abbreviations .20 7.1 Definitions20 7.2 Symbols21 7.3 Abbreviations .21 7.4 Equations21 8 Introduction 21 9 Statistical characteristics of testi

16、ng processes 22 9.1 Exact probability distribution functions .22 9.2 Approximation with continuous distributions 23 9.3 Simple test criteria and significance level 24 10 Early Pass/Fail termination of testing 24 10.1 Framework of test method24 10.2 Early Pass/Fail criteria25 10.3 Estimating the test

17、 time 31 10.4 Minimizing the test time.33 10.4.1 Truncation.33 10.4.2 Decimation35 10.4.3 Composite criteria.35 11 Accuracy of Continuous Distributions.36 Annex A: Change history .40 History 41 ETSI ETSI TR 134 901 V3.0.0 (2003-06) 4 3GPP TR 34.901 version 3.0.0 Release 1999 Foreword This Technical

18、Report has been produced by the 3rdGeneration Partnership Project (3GPP). The contents of the present document are subject to continuing work within the TSG and may change following formal TSG approval. Should the TSG modify the contents of the present document, it will be re-released by the TSG wit

19、h an identifying change of release date and an increase in version number as follows: Version x.y.z where: x the first digit: 1 presented to TSG for information; 2 presented to TSG for approval; 3 or greater indicates TSG approved document under change control. y the second digit is incremented for

20、all changes of substance, i.e. technical enhancements, corrections, updates, etc. z the third digit is incremented when editorial only changes have been incorporated in the document. ETSI ETSI TR 134 901 V3.0.0 (2003-06) 5 3GPP TR 34.901 version 3.0.0 Release 1999 1 Scope The present document descri

21、bes the statistical theory and concepts applied in the conformance test of the user equipment (UE) so as to improve test speed. 2 References The following documents contain provisions which, through reference in this text, constitute provisions of the present document. References are either specific

22、 (identified by date of publication, edition number, version number, etc.) or non-specific. For a specific reference, subsequent revisions do not apply. For a non-specific reference, the latest version applies. In the case of a reference to a 3GPP document (including a GSM document), a non-specific

23、reference implicitly refers to the latest version of that document in the same Release as the present document. 1 3GPP TS 34.121: “Terminal Conformance Specification; Radio transmission and reception (FDD)“. 2 3GPP TS 34.122: “ Terminal Conformance Specification; Radio transmission and reception (TD

24、D)“. 3. Definitions, symbols and abbreviations Definitions, symbols, abbreviations and equations used in the present document are listed in TR 21.905 5 and TR 25.990 6. 3.1 Definitions For the purposes of the present document, the following additional terms and definitions apply. 3.2 Symbols For the

25、 purposes of the present document, the following symbols apply: Values included in square bracket must be considered for further studies, because it means that a decision about that value was not taken 3.3 Abbreviations For the purposes of the present document, the following abbreviations apply: BER

26、 Bit Error Ratio BLER Block Error Ratio DUT Device under Test 3.4 Equations Void. ETSI ETSI TR 134 901 V3.0.0 (2003-06) 6 3GPP TR 34.901 version 3.0.0 Release 1999 4 Introduction This technical report includes two distinct approaches made to determine total test time optimisation. For ease of unders

27、tanding they are just referred to here as the first and second approach. Furthermore the two approaches differ a little in that they use slightly different terminology. 4.1 First approach The first approach is found in clauses 5 and 6. It reflects TS 34.121 in that the symbols, abbreviations and equ

28、ations are consistent with TS 34.121. 4.2 Second approach The second approach is found in clauses 7 to 11 and does not directly reflect TS 34.121 although it does use the existing theory from TS 34.121. The difference is that it refines the theory and derives further approaches for test time reducti

29、on. Some of the symbols, abbreviations and equations have local meaning and these are identified in clause 7. 5. Definitions of distribution functions and parameters to be used Summary 5.1 Properties of the Poisson Distribution Description of a statistical experiment by a distribution function and b

30、asic characteristics of the distribution. 5.2 Equivalence between Poisson Distribution and Chi Square Distribution Here it is shown, that both distributions are equal. Just the form is different. On the other hand there are two inverse cumulative operations. One of them is useful for our purpose. 5.

31、3 Confidence interval Introduction into the notion. 5.4 Application of the confidence interval to decide the outcome of the test Using the notion of the confidence interval, we calculate the early pass and early fail limit. 5.6 Test time reduction Using 5.4 the outcome of the test is connected with

32、two qualities, a good one and a worse and variable one. Introducing the bad DUT factor M, the quality of the test is now uniform and test time is further reduced. 5.7 Calculation of the intersection coordinates (maximum number of sample and the normalized test limit) Calculus for intersection co-ord

33、inates of the early pass and early fail limit. 5.8 Wrong decision risk F 5.1 to 5.6 applies the wrong decision risk for a single test step D. However it is desirable to have a predefined wrong decision risk for the entire test F. The approach to derive F from D this is explained here. ETSI ETSI TR 1

34、34 901 V3.0.0 (2003-06) 7 3GPP TR 34.901 version 3.0.0 Release 1999 5.1 Properties of the Poisson distribution NOTE: The following text is expressed in terms of BER=bit error ratio. However it can be used for BLER (Block error ratio) as well. Even for 1- Success Ratio, used in RRM delay tests, the t

35、heory can be used. With a finite number of samples (ns), the final bit error ratio BER cannot be determined exactly. Applying a finite ns, we measure a number of errors (ne). ne/ns =ber is the preliminary bit error ratio. In a single test we apply a predefined number of samples ns and we measure a n

36、umber of errors (ne). ne is connected with a certain differential probability in the Poisson distribution. We dont know the probability and the position in the distribution conducting just one single test. Repeating this test infinite times, applying repeatedly the same ns, we get the complete Poiss

37、on distribution. The average number of errors is NE. NE/ns is the final BER. Poisson Distribution: dpois(ne,NE)=(NEne/ne!)e-NE(1) TOL 1010:=e.g. : ns 500:=BER 0.01:= NE ns BER:= ne 1 2, 50:= 0 102030405000.050.10.150.2dpois ne NE,()neFigure 5-1: Example of Poisson distribution curve The Poisson dist

38、ribution has the variable ne and is characterised by the parameter NE. Real probabilities to find ne between two limits are calculated by integrating between such limits. Note: The Poisson distribution is an approximation: Independent error occurrence is described by the binomial distribution. If th

39、e BER approaches 0 the Poisson distribution approximates the binomial distribution. 5.2 Equivalence between Poisson distribution and Chi Square distribution The experiment, the Poisson distribution is based on, is having observed a certain number of samples (ns), the number of events (ne) is counted

40、 to calculate the ratio ne/ns. The experiment, the Chi Square distribution is based on, is having observed a certain number of events (ne), the number of samples (ns) is counted to calculate the ratio ne/ns. Poisson and Chi Square are valid only if ne0. This explains that the Poisson distribution ne

41、eds one event more, to equal in its form the Chi Square distribution 2*dchisq(2*NE,2*ne) = dpois(ne-1,NE) describes the experiment, terminated by an error. 2*dchisq(2*NE,2*(ne+1) = dpois(ne,NE) describes the experiment, terminated by any sample. The terminating error may be the artificial error at t

42、he beginning of the test, or the last error, causing the fail. In the next comparison shows dpois versus dchisq. The first 3D plot shows the Poisson distribution: (Figure 5-1) Variable: ne Range 0 to 10 Column in the table 0 to 10- axis in the plot Parameter: NE Range 0 to 10 Row in the table 0 to 1

43、00 axis in the plot The second 3D plot shows the Chi Square distribution: (Figure 5-4) Variable: NE Range 0 to 10 Column in the table 0 to 100- axis in the plot Parameter: ne Range 0 to 10 Row in the table 0 to 10 axis in the plot Columne 0 is degenerated Pne NE,( ) dpois ne 0.1NE 0.000001+,():=m10:

44、=n 100:=Omatrixmn, P,():=ETSI ETSI TR 134 901 V3.0.0 (2003-06) 9 3GPP TR 34.901 version 3.0.0 Release 1999 Table 5-1: Poisson distribution calculation O01234567891010123456789101 0.905 0.819 0.741 0.67 0.607 0.549 0.497 0.449 0.407 0.368 0.3331010 -70.09 0.164 0.222 0.268 0.303 0.329 0.348 0.359 0.3

45、66 0.368 0.366510 -134.52410 -30.016 0.033 0.054 0.076 0.099 0.122 0.144 0.165 0.184 0.2010 1.50810 -41.09210 -33.33410 -37.1510 -30.013 0.02 0.028 0.038 0.049 0.061 0.0740 3.7710 -65.45810 -52.510 -47.1510 -41.5810 -32.96410 -34.96810 -37.66910 -30.011 0.015 0.020 7.54110 -82.18310 -61.510 -55.7210

46、 -51.5810 -43.55610 -46.95510 -41.22710 -32.00110 -33.06610 -34.46710 -30 1.25710 -97.27810 -87.50110 -73.81310 -61.31610 -53.55610 -58.11410 -51.63610 -43.00110 -45.10910 -48.1910 -40 1.79510 -112.07910 -93.21510 -82.17910 -79.40210 -73.04810 -68.11410 -61.8710 -53.85810 -57.29910 -51.28710 -40 2.2

47、4410 -135.19810 -111.20610 -91.0910 -85.87610 -82.28610 -77.110 -71.8710 -64.34110 -69.12410 -61.7710 -50 2.49410 -151.15510 -124.01810 -114.84210 -103.26510 -91.52410 -85.52210 -81.66210 -74.34110 -71.01410 -62.16310 -6=OFigure 5-3: 3D plot for Poisson distribution CNEne,()2dchisq20.1NE( ) 2 ne .00

48、0001+(),:=m 100:=n10:= Dmatrixmn, C,():=ne ETSI ETSI TR 134 901 V3.0.0 (2003-06) 103GPP TR 34.901 version 3.0.0 Release 1999 Table 5-2: Chi-squared distribution calculation D012345678910012345678910111213141516171800000000009.04810 -60.905 0.09 4.52410 -31.50810 -43.7710 -67.5410 -81.25710 -91.79510

49、 -112.24410 -134.09410 -60.819 0.164 0.016 1.09210 -35.45810 -52.18310 -67.27810 -82.07910 -95.19810 -112.46910 -60.741 0.222 0.033 3.33410 -32.510 -41.510 -57.50110 -73.21510 -81.20510 -91.67610 -60.67 0.268 0.054 7.1510 -37.1510 -45.7210 -53.81310 -62.17910 -71.0910 -81.21310 -60.607 0.303 0.076 0.013 1.5810 -31.5810 -41.31610 -59.40210