## E.6 EVM for PRACH

36.521-13GPPEvolved Universal Terrestrial Radio Access (E-UTRA)Part 1: Conformance testingRadio transmission and receptionRelease 17TSUser Equipment (UE) conformance specification

The description below is generic in the sense that all 5 PRACH formats are covered. The numbers, used in the text below are taken from PRACH format#0 without excluding the other formats. The sampling rate for the PUSCH, 30.72 Msps in the time domain, is re-used for the PRACH. The carrier spacing of the PUSCH is 12 (format 0 to 3) and 2 (format 4) times of the PRACH. This results in an oversampling factor of 12 (format 0 to 3) and 2 (format 4), when acquiring the time samples for the PRACH. The pre-FFT algorithms (clauses E.6.6 and E.6.7) use all time samples, although oversampled. For the FFT the time samples are decimated by the factor of 12 (format 0 to 3) and 2 (format 4), resulting in the same FFT size as for the other transmit modulation tests (2048). Decimation requires a decision, which samples are used and which ones are rejected. The algorithm in E.6.6, Timing of the FFT window, can also be used to decide about the used samples.

## E.6.1 Basic principle

The basis principle is the same as described in E.2.1

## E.6.2 Output signal of the TX under test

The output signal of the TX under test is processed same as described in E.2.2

The measurement period is different:

– 2 PRACH preambles are recorded for format 0and 1,

– 1 PRACH preamble is recorded for format 2 and 3, each containing 1 CP and 2 preamble sequences

– 10 RPRACH preambles are recorded for format 4.

## E.6.3 Reference signal

The test description in 6.5.2.1.4.1A is based on non contention based access:

– PRACH configuration index (responsible for Preamble format, System frame number and subframe number)

– Preamble ID

– Preamble power

signalled to the UE, defines the reference signal unambiguously, such that no demodulation process is necessary to gain the reference signal.

The reference signal i(ν) is constructed by the measuring equipment according to the relevant TX specifications, using the following parameters: the applicable Zadoff Chu sequence, nominal carrier frequency, nominal amplitude and phase for each subcarrier, nominal timing, no carrier leakage. It is represented as a sequence of samples at a sampling rate of 30.72 Msps in the time domain.

## E.6.4 Measurement results

The measurement result is:

– EVMPRACH

## E.6.5 Measurement points

The measurement points are illustrated in the figure below:

Figure E.6.5-1

## E.6.6 Pre FFT minimization process

The pre-FFT minimization process is applied to each PRACH preamble separately. The time period for the pre- FFT minimisation process includes the complete CP and Zadoff-Chu sequence (in other words, the power transition period is per definition outside of this time period) Sample timing, Carrier frequency and carrier leakage in** **z(ν) are jointly varied in order to minimise the difference between z(ν) and i(ν). Best fit (minimum difference) is achieved when the RMS difference value between z(ν) and i(ν) is an absolute minimum.

After this process the samples z(ν) are called z^{0}(ν).

RF error, and carrier leakage are necessary for best fit of the measured signal towards the ideal signal in the pre FFT domain. However they are not used to compare them against the limits.

## E.6.7 Timing of the FFT window

The FFT window length is 24576 samples for preamble format 0, however in the measurement period is at least 27744 samples are taken. The position in time for FFT must be determined.

In an ideal signal, the FFT may start at any instant within the cyclic prefix without causing an error. The TX filter, however, reduces the window. The EVM requirements shall be met within a window W<CP.

The reference instant for the FFT start is the centre of the reduced window, called ,

EVM is measured at the following two instants: –W/2 and +W/2.

The timing of the measured signal z^{0}(ν) with respect to the ideal signal i(ν) is determined in the pre FFT domain as follows:

Correlation between z^{0}(ν) and i(ν) will result in a correlation peak. The meaning of the correlation peak is approx. the “impulse response” of the TX filter. The correlation peak, (the highest, or in case of more than one, the earliest) indicates the timing in the measured signal with respect to the ideal signal.

W is different for different preamble formats and shown in TableE.6.7-1.

Table E.6.7-1EVM window length for PRACH

Preamble format |
Cyclic prefix length |
Nominal FFT size |
EVM window length |
Ratio of |

0 |
3168 |
24576 |
3072 |
96.7% |

1 |
21024 |
24576 |
20928 |
99.5% |

2 |
6240 |
49152 |
6144 |
98.5% |

3 |
21024 |
49152 |
20928 |
99.5% |

4 |
448 |
4096 |
432 |
96.4% |

Note 1: The unit is number of samples, sampling rate of 30.72MHz is assumed Note 2: Decimation of time samples by 12(format 0 to 3) and factor 2 (format 4) is assumed, leading to a uniform FFT size of 2048 for all formats. Note 3: These percentages are informative |

The number of samples, used for FFT is reduced compared to z^{0}(ν). This subset of samples is called z’’(ν).

The sample frequency 30.72 MHz is oversampled with respect to the PRACH-subcarrier spacing of 1.25kHz (format 0 to 3) and 7.5kHz (format 4). EVM is based on 2048 samples per PRACH preamble and requires decimation of the time samples by the factor of 12 (format 0 to 3) and factor 2 (format 4). The final number of samples per PRACH preamble, used for FFT is reduced compared to z^{’’}(ν) by the factor of 12 (format 0 to 3) and factor 2 (format 4). This subset of samples is called z’(ν).

## E.6.8 Post FFT equalisation

Equalisation is not applicable for the PRACH.

## E.6.9 Derivation of the results

### E.6.9.1 EVM_{PRACH}

Perform FFT on z’(ν) and i(ν) using the FFT timing –W/2 and +W/2.

For format 2 and 3 the first and the repeated preamble sequence are FFT-converted separately. using the standard FFT length 0f 2048

The EVM_{PRACH} is the difference between the ideal waveform and the measured and equalized waveform for the allocated RB(s).

,

where

f covers the count of demodulated symbols within the allocated bandwidth.

are the samples of the signal evaluated for the EVM_{PRACH}

is the ideal signal reconstructed by the measurement equipment, and

is the average power of the ideal signal. For normalized modulation symbols is equal to 1.

is random access preamble sequence length.

From the acquired samples 4 EVM_{PRACH} value can be derived, 2 values for the timing –W/2 and 2 values for the timing +W/2 (4 and 2 applies for format 0,1,2,3. 20 and 10 applies for format 4).

### E.6.9.2 Averaged EVM_{PRACH}

The PRACH EVM, , is averaged over two preamble sequence measurements for preamble formats 0, 1, 2, 3, and it is averaged over 10 preamble sequence measurements for preamble format 4.

for preamble formats 0,1,2,3

for preamble format 4

The averaging is done separately for timing¦ –W/2 and +W/2 leading to and

is compared against the test requirements.