## E.2 Definition of the process

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

## E.2.1 Basic principle

The process is based on the comparison of the actual **output signal of the TX under test**, received by an ideal receiver, with a **reference signal**, that is generated by the measuring equipment and represents an ideal error free received signal. The reference signal shall be composed of the same number of codes at the correct spreading factors as contained In the test signal. Note, for simplification, the notation below assumes only codes of one spreading factor although the algorithm is valid for signals containing multiple spreading factors. All signals are represented as equivalent (generally complex) baseband signals.

## E.2.2 Output signal of the TX under test

The output signal of the TX under test is acquired by the measuring equipment, filtered by a matched filter (RRC 0.22, correct in shape and in position on the frequency axis) and stored for further processing

The following form represents the physical signa l in the entire measurement interval:

one vector **Z**, containing N = ns x sf complex samples;

with

ns: number of symbols in the measurement interval;

sf: number of chips per symbol. (sf: spreading factor) (see Note: Symbol length)

## E.2.3 Reference signal

The reference signal is constructed by the measuring equipment according to the relevant TX specifications.

It is filtered by the same matched filter, mentioned in E.2.2., and stored at the Inter-Symbol-Interference free instants. The following form represents the reference signal in the entire measurement interval:

one vector **R**, containing N = ns x sf complex samples

where

ns: number of symbols in the measurement interval;

sf: number of chips per symbol. (see Note: Symbol length)

## E.2.4 Classification of measurement results

The measurement results achieved by the global in-channel TX test can be classified into two types:

– Results of type "deviation", where the error-free parameter has a non-zero magnitude. (These are the parameters that quantify the integral physical characteristic of the signal).These parameters are:

RF Frequency

Power (in case of single code)

Code Domain Power (in case of multi code)

Timing (only for UE) (see Note: Deviation)

(Additional parameters: see Note: Deviation)

– Results of type "residual", where the error-free parameter has value zero. (These are the parameters that quantify the error values of the measured signal, whose ideal magnitude is zero). These parameters are:

Error Vector Magnitude (EVM);

Peak Code Domain Error (PCDE).

(Additional parameters: see Note: Residual)

## E.2.5 Process definition to achieve results of type "deviation"

The reference signal (**R**; see clause E.2.3) and the signal under Test (Z; see clause E.2.2) are varied with respect to the parameters mentioned in clause E.2.4 under "results of type deviation" in order to achieve best fit. Best fit is achieved when the RMS difference value between the varied signal under test and the varied reference signal is an absolute minimum.

Overview:

Z : Signal under test.

R: Reference signal,

with frequency f, the timing t, the phase ϕ, gain of code1 (g_{1}), gain of code2 (g_{2}) etc, and the gain of the synch channel g_{synch }See Note: Power Step

The parameters marked with a tilde in Z and R are varied in order to achieve a best fit.

For most measurement results the best fit process is to be carried out over the whole measurement interval corresponding to the duration of one slot, i.e. ns * sf = 2560 chips in E.2.2 and E.2.3. Some measurements are, however, defined for a measurement interval corresponding to the duration of one frame, i.e. ns * sf = 38400 chips. In this latter case, the best fit with respect to **Z **and **R **is to be carried out successively over multiple best fit intervals (segments) corresponding to the duration of one slot each, i.e. 15 times for a measurement interval corresponding to the duration of one frame.

Detailed formula: see Note: Formula for the minimum process

The varied reference signal, after the best fit process, will be called **R’.**

The varied signal under test, after the best fit process, will be called **Z’.**

**R’** and **Z’** are each of length ns * sf and depending on the length of the measurement interval result of possibly multiple successive applications of the minimum process.

The varying parameters, leading to **R’ and Z** represent directly the wanted results of type "deviation". These measurement parameters are expressed as deviation from the reference value with the same units as the reference value.

In the case of multi code, the type-"deviation"-parameters (frequency, timing and (RF-phase)) are varied commonly for all codes such that the process returns one frequency-deviation, one timing deviation, (one RF-phase -deviation).

(These parameters are not varied on the individual code signals such that the process would return kr frequency errors… . (kr: number of codes)).

The only type-"deviation"-parameters varied individually are the code domain gain factors (g1, g2, …)

See Note: Power Step.

### E.2.5.1 Decision Point Power

The mean-square value of the signal-under-test, sampled at the best estimate of the of Intersymbol-Interference-free points using the process defined in clause 2.5, is referred to the* Decision Point Power* (DPP):

### E.2.5.2 Code-Domain Power

The samples, Z’, are separated into symbol intervals to create ns time-sequential vectors **z** with sf complex samples comprising one symbol interval. The *Code Domain Power* is calculated according to the following steps:

1) Take the vectors **z** defined above.

2) To achieve meaningful results it is necessary to descramble **z,** leading to **z’** (see Note: Scrambling code)

3) Take the orthogonal vectors of the channelization code set **C **(all codes belonging to one spreading factor) as defined in TS 25.213 and TS 25.223 (range +1, -1), and normalize by the norm of the vectors to produce **C**norm=**C**/sqrt(sf). (see Note: Symbol length)

4) Calculate the inner product of **z’** with **C**norm**.**. Do this for all symbols of the measurement interval and for all codes in the code space.

This gives an array of format k x ns, each value representing a specific symbol and a specific code, which can be exploited in a variety of ways.

k: total number of codes in the code space

ns: number of symbols in the measurement interval

5) Calculate k mean-square values, each mean-square value unifying ns symbols within one code.

(These values can be called "*Absolute CodeDomainPower *(CDP)" [Volt^{2}].) The sum of the k values of CDP is equal to DPP.

6) Normalize by the decision point power to obtain

## E.2.6 Process definition to achieve results of type "residual"

The difference between the varied reference signal (**R’**; see clauseE.2.5.) and the varied TX signal under test (**Z’**; see clauseE.2.5)** **is the error vector **E** versus time:

**E** = **Z’** – **R’**

Depending on the parameter to be evaluated, it is appropriate to represent **E** in one of the following two different forms:

Form EVM (representing the physical error signal in the entire measurement interval)

One vector **E**, containing N = ns x sf complex samples;

with

ns: number of symbols in the measurement interval

sf: number of chips per symbol (see Note: Symbol length)

Form PCDE (derived from Form EVM by separating the samples into symbol intervals)

ns time-sequential vectors **e** with sf complex samples comprising one symbol interval.

**E **and** e** give results of type "residual" applying the two algorithms defined in clauses E.2.6.1 and E.2.6.2.

### E.2.6.1 Error Vector Magnitude (EVM)

The Error Vector Magnitude (EVM) is calculated according to the following steps:

1) Take the error vector **E** defined in clause E.2.6 (Form EVM) and calculate the RMS value of **E**; the result will be called RMS(**E**).

2) Take the varied reference vector **R’** defined in clause E.2.5 and calculate the RMS value of **R’**; the result will be called RMS(**R’**).

3) Calculate EVM according to:

(here, EVM is relative and expressed in %)

(see Note: Formula for EVM)

### E.2.6.2 Peak Code Domain Error (PCDE)

The Peak Code Domain Error is calculated according to the following steps:

1) Take the error vectors **e** defined in clause E.2.6 (Form PCDE)

2) To achieve meaningful results it is necessary to descramble **e,** leading to **e’** (see Note: Scrambling code)

3) Take the orthogonal vectors of the channelization code set **C **(all codes belonging to one spreading factor) as defined in TS 25.213 and TS 25.223 (range +1, -1). (see Note: Symbol length) and normalize by the norm of the vectors to produce **C**norm= **C**/sqrt(sf). (see Note: Symbol length)

4) Calculate the inner product of **e’** with **C**norm. Do this for all symbols of the measurement interval and for all codes in the code space.

This gives an array of format k x ns, each value representing an error-vector representing a specific symbol and a specific code, which can be exploited in a variety of ways.

k: total number of codes in the code space

ns: number of symbols in the measurement interval

5) Calculate k RMS values, each RMS value unifying ns symbols within one code.

(These values can be called "*Absolute CodeEVMs*" [Volt].)

6) Find the peak value among the k "*Absolute CodeEVMs*".

(This value can be called "*Absolute PeakCodeEVM*" [Volt].)

7) Calculate PCDE according to:

(a relative value in dB).

(see Note IQ)

(see Note Synch channel)

### E.2.6.3 Relative Code Domain Error (RCDE)

The Relative Code Domain Error is calculated for a wanted code according to the following steps:

1) Calculate the value "*Absolute CodeEVM*" [Volt] for the wanted code according to E.2.6.2, as an RMS value unifying ns = 2400 symbols corresponding to the measurement interval of 1 frame.

2) Calculate the value "*Absolute CodeDomainPower *(CDP)" [Volt^{2}] for the wanted code according to E.2.5.2, with ns = 2400 symbols corresponding to the measurement interval of 1 frame.

3) Calculate RCDE according to:

4) The average RCDE across a set of wanted codes is defined as the mean of the linear RCDE values and subsequently expressed in dB.