NR - Phase Tracking Reference Signal (PTRS)

• If phaseTrackingRS in DMRS-DownlinkConfig is configured,
  • If RNTI equals MCS-C-RNTI, C-RNTI, or CS-RNTI,
    • If at least timeDensity or frequencyDensity in PTRS-DownlinkConfig is configured, the time domain density (L_PT-RS) is a function of scheduled MCS (see Table 1), and frequency domain density (K_PT-RS) is a function of scheduled bandwidth (see Table 2). If not configured, the default values, L_PT-RS = 1, K_PT-RS = 2, apply.
    • If neither of timeDensity and frequencyDensity in PTRS-DownlinkConfig is configured,
      • For QPSK or scheduled bandwidth < 3 RB's, PTRS is not present;
      • Else, L_PT-RS = 1, K_PT-RS = 2.
  • If RNTI equals RA-RNTI, SI-RNTI, or P-RNTI, PTRS is not present.
• Else, PTRS is not present.

• If phaseTrackingRS in DMRS-UplinkConfig is configured,
  • If RNTI equals MCS-C-RNTI, C-RNTI, CS-RNTI, or SP-CSI-RNTI,
    • If at least timeDensity or frequencyDensity in PTRS-UplinkConfig is configured, the time domain density (L_PT-RS) is a function of scheduled MCS (see Table 1), and frequency domain density (K_PT-RS) is a function of scheduled bandwidth (see Table 2). If not configured, the default values, L_PT-RS = 1, K_PT-RS = 2, apply.
    • If neither of timeDensity and frequencyDensity in PTRS-UplinkConfig is configured, L_PT-RS = 1, K_PT-RS = 2.
  • Else, PTRS is not present.
• Else, PTRS is not present.

• If transformPrecoderEnabled in PTRS-UplinkConfig is configured,
  • If timeDensityTransformPrecoding is configured to 2, L_PT-RS = 2;
  • Else, L_PT-RS = 1.
  • With sampleDensity configured, the group pattern of PTRS is a function of scheduled bandwidth (see Table 3).

• Threshold ptrs-MCS₄ is not explicitly configured, and it equals the lowest MCS level for retransmission.
• For retransmission, the time-domain density is determined by the MCS in the initial transmission.
• Given a minislot comprising of L OFDM symbols, if L_PT-RS ≥ L, PTRS is not present.

In NR release 15, there is at most only one PTRS port in the downlink.

In order to facilitate the PTRS port association, a UE reports a layer index (LI) to its serving gNB, which indicates the index of the layer with best quality.

With LI at hand, a gNB can always associate the PTRS port to the DMRS port with the best channel quality. Moreover, for the purpose of signalling overhead reduction, a gNB can permute and reorder the precoding vectors until the lowest indexed DMRS port has the most excellent channel quality. Clearly, the operation is a completely gNB implementation related issue without any specification effort. To sum up, the PTRS port is associated to a unique DMRS port as follows.

• In single-codeword case, the PTRS port is assocated to the lowest-indexed DMRS port.
• For double-codeword, the PTRS port is associated to the lowest-indexed DMRS port corresponding to the codeword with highest MCS level.

The association between PTRS ports and DMRS ports is signalled by the field of PTRS-DMRS assocation in DCI format 0-1.

• If at least one of the following condition is satisfied, PTRS-DMRS assocation is not present.
  • CP-OFDM: PTRS-UplinkConfig is not configured.
  • DFT-S-OFDM
  • maxRank = 1
• Else, 2-bit PTRS-DMRS assocation is present (see Tables 4 and 5 for one and two PTRS ports, respectively)

The target subcarriers for PTRS mapping can be expressed as

where

• \(k_\text{ref}^\text{RE}\) is subcarrier-level offset, indicated by resourceElementOffset in PTRS-DownlinkConfig as shown in Table 6.

• \(k_\text{ref}^\text{RB}\) is PRB-level offset.

In DFT-S-OFDM case, PTRS samples are inserted before DFT operation, a.k.a. pre-DFT. Given a OFDM symbol with PTRS, PTRS samples are divided into a series of chunks/groups and then scattered in the PUSCH samples prior to DFT. The pattern depends on the number of samples in each group (\(N_\text{samp}^\text{group}\)) and the number of group (\(N_{\text{group}}^{\text{PT-RS}}\)), as shown in Table 7, where letters \(M, H, T\) mean the PTRS group is respectively inserted in the middle, head, and tail of the corresponding PUSCH sample segment.

PTRS samples are generated according to \[ r_m(m^{\prime}) = w(k^{\prime}) \frac{1 + j}{\sqrt{2}}[1 - 2c(m^{\prime})]e^{j\frac{\pi}{2}(m \mod 2)}, \] where

• \(c(\cdot)\) is a Gold sequence initialized with \(c_{\text{init}} = [2^{17}(N_{\text{symb}}^{\text{slot}} n_{s,f}^{\mu} + \ell + 1)(2N_{\text{ID}} + 1) + 2 N_{\text{ID}}] \mod 2^{31}\).
• \(m\) is the global index of a PTRS sample with PUSCH samples considered.
• \(m^{\prime} = N_{\text{samp}}^{\text{group}} s^{\prime} + k^{\prime}\) is the intra-sequence index of a PTRS sample.
• \(s^{\prime} = 0, 1, \ldots, N_{\text{group}}^{\text{PT-RS}} - 1\) are the indices of PTRS groups.
• \(k^{\prime} = 0, 1, \ldots, N_{\text{samp}}^{\text{group}} - 1\) are the intra-group indices of samples.
• \(w(\cdot)\) is the orthogonal cover code (OCC) for port multiplexing purpose, which is essentially a Walse code of length \(N_{\text{samp}}^{\text{group}}\), implicitly indicated by \(n_{\text{RNTI}} \mod N_{\text{samp}}^{\text{group}}\).

On each PTRS subcarrier, the QPSK symbol of the assocated DMRS port on the same subcarrier is reused and placed on the PTRS RE's.

For clear description, taking a PTRS port for instance, we suppose that a PTRS symbol \(x_{m, n}\) is transmitted over its associated DMRS port on a RE \((k_m, l_n)\), which corresponds to subcarrier \(k_m\) and OFDM symbol \(l_n\), i.e.,

where \(y_{k_m, l_n}\), \(H_{k_m, l_n}\), and \(n_{k_m, l_n}\) are the received signal, channel fading, and the additive white Gaussian noise on RE \((k_m, l_n)\), respectively; \(\theta_{l_n}\) represents the phase noise on \(l_n\) th OFDM symbol.

Since phase noise fluctuates as time, the impairment of phase noise can be completely complemented by a phase difference relative to a reference. Without loss of generality, we identify the phase noise on the first PTRS symbol as the reference, and the phase noise on the symbol is zero, i.e. \(\theta_{l_1} = 0\). Then, the phase noise on PTRS symbol \(l_n\) can be estimated according to

Then, if the time density of the PTRS is less than 1, i.e., \(L_\text{PTRS} > 1\), the phase noise of the OFDM symbols without PTRS can be obtained by interpolation.

In DFT-S-OFDM case, which is different from CP-OFDM waveform, the PTRS samples are inserted into PUSCH samples before the DFT operation, i.e., in the time domain. Accordingly, the phase noise should also be estimated and complemented in the time domain, i.e., after the IDFT processing. Taking \(X\) PTRS groups/chunks with each comprised of \(K\) samples for instance, the received signal can be expressed as

where the subscript tuple \((m, g, l_n)\) means \(m\) th sample position within \(g\) th PTRS group in DFT-S-OFDM symbol \(l_n\); accordingly, \(x_{m, g, l_n}\), \(\theta_{m, g, l_n}\), \(r_{m, g, l_n}\), \(h_{m, g, l_n}\), and \(n_{m, g, l_n}\) are the PTRS sample, the phase noise, the received signal (after IDFT), the effective channel fading and the effective additive white Gaussian noise at the sample position.

Then, the phase noises can be estimated by \[ \theta_{m, g+1, l_n} - \theta_{m, g, l_n} = \arg \left(\sum_{m=1}^K r_{m, g+1, l_n} x_{m, g+1, l_n}^*\right) \left(\sum_{m=1}^K r_{m, g, l_n}^* x_{m, g, l_n}\right), \quad g = 1, \ldots, X - 1. \]