M.6 Post-FFT equalisation

38.176-23GPPIntegrated Access and Backhaul (IAB) conformance testingNRPart 2: radiated conformance testingRelease 17TS

Perform FFTs on , one for each OFDM symbol within 10 ms measurement interval with the FFT window timing to produce an array of samples, in the time axis t by FFT size in the frequency axis f.

For the example in the annex, 1120 FFTs are performed on . The result is an array of samples, 1120 in the time axis by 4096 in the frequency axis.

The equalizer coefficients and are determined as follows:

1. Calculate the complex ratios (amplitude and phase) of the post-FFT acquired signal and the post-FFT ideal signal , for each demodulation reference signal, over 10 ms measurement interval. This process creates a set of complex ratios:

2. Perform time averaging at each demodulation reference signal subcarrier of the complex ratios, the time-averaging length is 10 ms measurement interval. Prior to the averaging of the phases an unwrap operation must be performed according to the following definition:

– The unwrap operation corrects the radian phase angles of by adding multiples of 2 * π when absolute phase jumps between consecutive time instances are greater then or equal to the jump tolerance of π radians.

– This process creates an average amplitude and phase for each demodulation reference signal subcarrier (i.e. every second subcarrier).

Where N is the number of demodulation reference signal time-domain locations from for each demodulation reference signal subcarrier f.

3. The equalizer coefficients for amplitude and phase and at the demodulation reference signal subcarriers are obtained by computing the moving average in the frequency domain of the time-averaged demodulation reference signal subcarriers. The moving average window size is 19 and averaging is over the DM-RS subcarriers in the allocated RBs. For DM-RS subcarriers at or near the edge of the channel, or when the number of available DM-RS subcarriers within a set of contiguously allocated RBs is smaller than the moving average window size, the window size is reduced accordingly as per figure M.6-1.

4. Perform linear interpolation from the equalizer coefficients and to compute coefficients , for each subcarrier.

Figure M.6-1: Reference subcarrier smoothing in the frequency domain

a) In case of FR2 EVM, to account for the common phase error (CPE) experienced in millimetre wave frequencies, , in the estimated coefficients contain phase rotation due to the CPE, , in addition to the phase of the equalizer coefficient , that is:

For OFDM symbols where PT-RS does not exist, can be estimated by performing linear interpolation from neighboring symbols where PT-RS is present.

In order to separate component of the CPE,, contained in, , estimation and compensation of the CPE needs to follow. is the common phase error (CPE), that rotates all the subcarriers of the OFDM symbol at time .

Estimate of the CPE, , at OFDM symbol time, , can then be obtained from using the PT-RS employing the expression:

In the above equation, is the set of subcarriers where PT-RS are mapped, where is the set of OFDM symbols where PT-RS are mapped while and are is the post-FFT acquired signal and the ideal PT-RS signal respectively. That is, estimate of the CPE at a given OFDM symbol is obtained from frequency correlation of the complex ratios at the PT-RS positions with the conjugate of the estimated equalizer complex coefficients. The estimated CPE can be subtracted from to remove influence of the CPE, and obtain estimate of the complex coefficient’s phase:

(t)