# PTRS in 5G NR: Saviour from Phase Noise

### Phase Tracking Reference Signal (PTRS)

**Jul 01, 2021**

Phase noise is present in any practical communication system and impact the system by introducing random phase variations of the received signal. For an OFDM system, this will lead to inter-carrier interference as well as to a common phase error (CPE) on all subcarriers.

With increasing carrier frequency, the variance of the phase noise increases, leading to more pronounced problems. For NR, targeting carrier frequencies of 6 GHz and above, measures need to be taken to reduce phase noise induced degradation of system performance. Millimeter-wave (mmWave) bands offer potential channel bandwidths of several GHz. Furthermore, the small carrier wavelength (e.g.,5mm at 60GHz and≈2mm at 140GHz) enables us to fit antenna arrays with a very large number of elements. Therefore, Phase Noise is a bottleneck in such a system.

Lower order modulation is less sensitive to phase errors, as compared to higher order modulation. PTRS will mainly be needed for UEs scheduled for higher order modulation, excluding UEs in unfavourable channel conditions.

The impact of phase noise is typically visible in good radio conditions and since the use case of DFT-S-OFDM in NR is for link budget limited scenarios, PTRS is present with lesser density for DFT-s-OFDM. From a resource utilization perspective, it is therefore beneficial to only transmit PTRS when needed. The following figure shows BLER vs SNR in presence of phase noise for diferent denisty of PTRS, it can be seen that more dense PTRS gives lower BLER.

# Phase Tracking Reference Signal (PTRS)

It is Intended for tracking phase variations across the transmission duration. It's main purpose is to track phase noise, the PT-RS needs to be dense in time but can be sparse in frequency as phase noise tends to change across time but tends to remains relatively constant across frequency. A Base station with multiple antenna ports may be designed to use a single local oscillator which is shared across antenna ports. 3GPP dictates transmission of PTRS on a single antenna port. Only occurs in combination with DM-RS.

## PTRS in CP-OFDM

*The above equation is taken from 3GPP Spec 38.211.*

PTRS sequence is similar to DMRS sequence

- Gold Sequence
- QPSK Modulated

## PTRS in DFT-s-OFDM

*The above equation is taken from 3GPP Spec 38.211.*

PTRS is mapped before Transform Precoding. The pattern and density of the insertion of PTRS in pre- DFT insertion is defined as shown in the table below

For CP-OFDM, the time density represents the time domain spacing between symbols allocated to PTRS.

- value of 4: every 4th symbol can include PTRS
- value of 2: every 2nd symbol can include PTRS
- Value of 1: every symbol can include PTRS

Symbol allocation algorithm avoids PTRS being allocated to the same symbol as the DMRS and also immediately after DMRS (unless time density is 1). Occurrence of PTRS resets after each DMRS occurrence

Time density of PTRS depends on MCS index. Higher the MCS index -> higher the coding rate -> lower the redundancy -> more impact of phase noise -> needs higher density of PTRS symbols

For an explanation of these equations and to understand the calculation of number of subcarriers in 1 slot for PTRS, please watch this video. https://youtu.be/VxqfjT1vEnU

For any queries or concerns on this, contact: sigpcomm@gmail.com