## C.2 Statistical Testing of E-DPDCH Throughput

25.1413GPPBase Station (BS) conformance testing (FDD)Release 17TS

## C.2.1 Definition

Information Bit Throughput R:

The measured information bit throughput R is defined as the sum (in kilobits) of the information bit payloads (excluding the 24-bit CRC) successfully received during the test interval, divided by the duration of the test interval (in seconds).

## C.2.2 Mapping throughput to block error ratio

a) In measurement practice the BS indicates successfully received information bit payload by signalling an ACK to the tester.

If payload is received, but damaged and cannot be decoded, the BS signals a NACK.

b) Only the ACK and NACK signals, not the data bits received, are accessible to the tester.

The number of bits is known in the tester from knowledge of what payload was sent.

c) For fixed reference channel the number of bits in a TTI is fixed during one test.

d) The time in the measurement interval is composed of successful TTIs (ACK), unsuccessful TTIs (NACK) and DTX-TTIs.

e) DTX-TTIs occur statistically when the BS is not responding ACK or NACK where it should. (statDTX)

This may happen when the BS misses data, that are intended for it.

The pass / fail decision is done by observing the:

– number of NACKs

– number of ACKs and

– number of statDTXs

The ratio (NACK + statDTX)/(NACK+ statDTX +ACK)is the Bock Error Ratio BLER. Taking into account the time consumed by the ACK-, NACK-, and statDTX-TTIs, BLER can be mapped unambiguously to throughput for any single FRC test.

## C.2.3 Bad DUT factor

NOTE: A statistical test of limited test duration and confidence level >1/2 exhibits limited selectivity. The Bad DUT factor ≠ 1 is a measure of limited selectivity.

Data throughput in a communication system is of statistical nature and must be measured and decided pass or fail. The specified limit of throughput related to the ideal throughput in different throughput tests is in the range of a few % to near 100%. To make it comparable with BER, we define the complement of the relative throughput: BLER as defined above. Complementary this is in the range of near 100% down to a few % For e.g. BLER = 1%, the currently in BER BLER used Bad DUT factor M=1.5 is highly meaningful. For e.g. BLER = 99%, the currently used M=1.5 is obviously meaningless.

An appropriate definition of the bad DUT factor is illustrated in figure C.2.3: constant and variable Bad DUT factor.

It illustrates how to find the Bad BLER when the nominal BLER is given.

1) In the range 0%< nominal BLER>10% the Bad DUT factor is constant 1.5

2) In the range 90%< bad BLER>100% it decreases to 1. (symmetrical to (1))

3) The range in between is interpolated by an arc section.

The example shows: nominal BLER=35,6% 🡪 bad BLER=47.67.5% 🡪 M=1.34

(blue mapping)

Figure C.2.3: constant and variable Bad DUT factor

Formula:

For 0 < BLER<= 0.1 M = 1.5

For 0.1 <BLER <.85

For 0.85 <= BLER < 1 M(BLER)= 2/3BLER + 1/3

With BLER: nominal Block Error Ratio (0<BLER<1)

With r = 2.70415 (Radius of the arc)

### C.2.3.1 Bad DUT factor, range of applicability

Inaccuracy is one practical reason to avoid the grey shaded area of figure C.2.3: constant and variable Bad DUT factor. For BLER near 1 the Bad DUT factor M is near 1. For M=1,exactly, the pass and fail criteria do not intersect. The test never is finalised.

For M near 1 the pass and fail criteria exhibit a very smooth intersection. In addition the binomial distribution and its inverse are of discrete nature. Therefore the test limit and the number of samples is calculable only very ambiguous.

It is proposed to apply the bad DUT factor only in the not shaded area of figure C.2.3.

This is done by the following:

BLER mode:

Use BLER as defined above in the range of 0 to 50%, use M >1 as defined above.

The Test Limit will be > the Minimum Requirement in the table C.10 below.

Relative Throughput mode:

If BLER is in the range 50 to 100%, use 1-BLER instead. Use m<1 instead of M.

1-BLER is the relative throughput with respect to the ideal throughput.

As a consequence, the Test Limit < the Minimum Requirement

Formula for m:

For 0 < (1-BLER) <= 0.15, m = 1/1.5

For 0.15 <(1-BLER) <.85,

In the figure C.2.3 this is represented by the red mapping.

The table** **C.10 below distinguishes between m and M.

## C.2.4 Minimum Test time

Same as with BER BLER there is a minimum test time necessary for multipath fading profiles with the same justification: Table C.2 in Annex C.1applies for throughput tests as well.

The minimum Test Time is

1) the minimum test time due to statistical reasons

( To ensure the confidence level, the test must be continued until a certain number of samples (NACK+ statDTX +ACK) is reached.)

2) the minimum test time due to multipath fading.

The longer test time applies.

## C.2.5 Statistical independence

If a process works within an incremental redundancy sequence, the samples and errors are not independent. The incremental redundancy sequence for every process must be finalised, successfully or unsuccessfully, on or beyond the minimum test time.

Then the BLER (or 1-BLER) is compared with the Test Limit to decide pass or fail.

The distribution of errors in an HARQ process with dependent errors is narrower, than the equivalent binomial distribution.

The distribution of errors, where the current BLER fluctuates due to the multipath propagation channel, is narrower than the equivalent binomial distribution.

Hence the application of the binomial distribution and its inverse function yields a conservative decision in the sence that the true confidence level is slightly higher than the given one.

(The binomial distribution describes a time-independent statistical process, where the errors occur memoryless)

## C.2.6 Formula

True BLER in the range of near 0% to near 100% does not allow to use any approximated distributions. The binomial distribution and its inverse cumulative function: qbinom is appropriate for this test.

a) For the BLER test mode:

ne_{low}=qbinom(D,ns,M*BLER_{limit}) (1)

ne_{high}=qbinom(1-D,ns,BLER_{limit}) (2)

given: 1-D: confidence level= 99.8%

BLER_{limit}=Block error ratio at the limit

M: Bad DUT factor >1

Input: ns: number of samples (NACK+ statDTX + ACK)

Output ne: number of events (NACK+ statDTX)

The intersection of (1) and (2) is the Test Limit with the coordinates: ns and ne

b) For the Relative Throughput test mode:

ne_{low}=qbinom(D,ns,1-BLER_{limit}) (3)

ne_{high}=qbinom(1-D,ns,m*(1-BLER_{limit)}) (4)

given: 1-D: confidence level= 99.8%

1-BLER_{limit}= Relative Throughtput at the limit

m: Bad DUT factor <1

Input: ns: number of samples (NACK+ statDTX + ACK)

Output ne: number of events (ACK)

The intersection of (3) and (4) is the Test Limit with the coordinates: ns and ne

NOTE: In contrast to BER BLER test, this approach does not contain any test time optimisation.

(early pass, early fail)

## C.2.7 Meaning of a decision

After the minimum test time in terms of ns, ne is compared against the test limit and an idividual throughput test is decided accordingly.

A pass means: The true throughput is not worse than a Bad Throughput with 99.8% confidence level.

A fail means: The true throughput is not better than a Limit Throughput with 99.8% confidence level.

NOTE: A single throughput test measured on a marginal receiver will be correctly decided with 99.8% probability, but incorrectly with 0.2% probability. A single throughput test is repeated in 112 variations. (7 FRCs * 4 fading profiles * 2 diversity modes * 2 limits). A marginal DUT, marginal on each variation, will experience one fail due to statistical reasons with approx. 22% probability. This situation is accepted but may be revised in future.

## C.2.8 The test limit

– NACK+ statDTX + ACK is summarised as No of samples (ns)

– NACK+ statDTX is summarised as No of errors

– ACK is summarised as No of successes

– In the BLER test mode the ratio: No of errors/ No of samples is recorded. In this mode the test limit is above the minimum requirement and a pass is below the test limit.

– In the Relative Throughput test mode (1-BLER) the ratio: No of successes/ No of samples is recorded. In this mode the test limit is below the minimum requirement and a pass is above the test limit.

– The test mode, used, is indicated by bold versus gray-shading

– The generic term for No of errors (BLER mode) or No of successes (Relative Throughput mode) is No of events (ne). This is used in the table columns Test Limit and pass condition.

Table C.11: Test limit

Relative throughput Minimum requirement |
BLER Minimum requirement |
Bad DUT factor |
Test limit expressed as No of events / statistical min No of samples |
Pass |
Test time |

30% |
(70%) |
m=0.692 |
183/725 |
ne/ns≥183/725 |
The test time is determined by the propagation condition or by the minimum No of samples, which ever is greater. See table C.2 and C.12 |

(70%) |
30% |
M=1.378 |
209/587 |
ne/ns≤209/587 |

Table C.12 Test time

Relative Throughput =30% |
BLER=30% |
|||

Fading condition |
TTI=2ms |
TTI=10ms |
TTI=2ms |
TTI=10ms |

3 Km/h |
164 s |
164s |
164s |
164s |

30Km/h |
16.4s |
16.4s |
16.4s |
16.4s |

120Km/h |
4.1s |
725 TTI (7.25s) |
4.1s |
587 TTI (5.78s) |

Annex D (normative):

Propagation conditions