3GPP TS 38.211 / TS 38.213

PUCCH Format 0 Test Bench Report

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1. Configuration Parameters

Test bench parameters derived from non-dedicated common resource sets with intra-slot frequency hopping across 2 OFDM symbols.

Parameter 3GPP Symbol Value / Setting Description
Channel / Format — PUCCH Format 0 Sequence-based short format (≤ 2 bits)
Resource Type — Common / Non-Dedicated Configured via pucch-ResourceCommon (SIB1 / Initial Access)
Resource Set Index r_PUCCH Index 0 Selects row entry from 3GPP TS 38.213 Table 9.2.1-1
Interlace Allocation — Disabled Licensed spectrum operation (contiguous PRB mapping)
Allocated RBs N_PRB 1 RB (M_sc = 12) 12 contiguous subcarriers per hop
Start Symbol S 12 Occupies symbols 12 and 13 (S=12, N_symb=2)
Frequency Hopping — Enabled (Mandatory) Implicit rule for pucch-ResourceCommon (Hop 0: Sym 12, Hop 1: Sym 13)
Group Hopping pucch-GroupHopping Neither (f_gh = 0) Sequence group u = N_ID mod 30 = 11
Initial Cyclic Shift Index m_0 0 Initial shift index derived from Resource Set Index 0
UCI Payload — 1-bit HARQ-ACK (ACK = 1) Maps to m_cs = 6
Cell ID N_ID 101 Drives PRN seed c_init = 101 and sequence group u = 11
Slot Number n_s 0 Frame 0, Subframe 0, Slot 0

2. Expected Intermediate Values

Mathematical metrics and sequence generation parameters derived during physical layer execution.

PRN Initialization Seed: c_init = N_ID = 101
Sequence Group Index: u = 101 mod 30 = 11 | Base Base Sequence Length: M_sc = 12 (v = 0)
Symbol / Hop Absolute Symbol (l) PRN Bit Offset Shift Index (shift_idx) Phase Shift (α)
Hop 0 (Symbol 12) l = 12 Offset 96 shift_idx = 3 α = 1.5708 rad (π/2)
Hop 1 (Symbol 13) l = 13 Offset 104 shift_idx = 2 α = 1.0472 rad (π/3)

3. Expected Reference Values (Low-PAPR Base Sequence)

Base sequence &rbar;u,v(n) values for M_sc = 12, Group u = 11 according to 3GPP TS 38.211 Table 5.2.2.2-1.

Subcarrier Index (n) Base Phase Phase φ(n) Complex Base Sequence Value &rbar;u,v(n)
n = 0-1(+0.7071, -0.7071)
n = 13(-0.7071, +0.7071)
n = 21(+0.7071, +0.7071)
n = 3-3(-0.7071, -0.7071)
n = 41(+0.7071, +0.7071)
n = 5-1(+0.7071, -0.7071)
n = 6-1(+0.7071, -0.7071)
n = 73(-0.7071, +0.7071)
n = 81(+0.7071, +0.7071)
n = 93(-0.7071, +0.7071)
n = 10-1(+0.7071, -0.7071)
n = 111(+0.7071, +0.7071)

4. Time-Domain Cyclic Shift & Resource Grid Architecture

Physical resource grid mapping illustrating sequence generation and HARQ-ACK cyclic shift phase rotation (α) across 12 contiguous subcarriers without separate DM-RS pilots.

================================================================================
                    PUCCH FORMAT 0 RESOURCE GRID ARCHITECTURE                   
================================================================================

  Subcarrier Index (k)
  within 1 PRB (0 to 11)
  ^
  |  +-----------------------------+-----------------------------+
  |  |  Subcarrier 11 (Sequence)   |  Subcarrier 11 (Sequence)   |
  |  |  Subcarrier 10 (Sequence)   |  Subcarrier 10 (Sequence)   |
  |  |  Subcarrier 9  (Sequence)   |  Subcarrier 9  (Sequence)   |
  |  |  Subcarrier 8  (Sequence)   |  Subcarrier 8  (Sequence)   |
  |  |  Subcarrier 7  (Sequence)   |  Subcarrier 7  (Sequence)   |
  |  |  Subcarrier 6  (Sequence)   |  Subcarrier 6  (Sequence)   |
  |  |  Subcarrier 5  (Sequence)   |  Subcarrier 5  (Sequence)   |
  |  |  Subcarrier 4  (Sequence)   |  Subcarrier 4  (Sequence)   |
  |  |  Subcarrier 3  (Sequence)   |  Subcarrier 3  (Sequence)   |
  |  |  Subcarrier 2  (Sequence)   |  Subcarrier 2  (Sequence)   |
  |  |  Subcarrier 1  (Sequence)   |  Subcarrier 1  (Sequence)   |
  |  |  Subcarrier 0  (Sequence)   |  Subcarrier 0  (Sequence)   |
  |  +-----------------------------+-----------------------------+
  +-------------------------------------------------------------------> Time
         OFDM Symbol l_0 (Hop 0)       OFDM Symbol l_1 (Hop 1)
         [PRB = startPRB]              [PRB = secondHopPRB]

================================================================================
                           SEQUENCE & PHASE MAPPING
================================================================================

  Base Sequence:      Low-PAPR Base Sequence r_u,v(n)  [Length M_sc = 12]
                      (Group u = N_ID mod 30)

  UCI Mapping:        HARQ-ACK / SR bits select Cyclic Shift offset m_cs:
                      * ACK (1 bit):  m_cs = 6  --> Phase shift α = π
                      * NACK (1 bit): m_cs = 0  --> Phase shift α = 0

  Symbol Equation:    x(n) = r_u,v(n) * e^(j * α * n)   for n = 0, ..., 11

  Structure Notes:    - No separate DM-RS pilots (Sequence itself carries UCI)
                      - 1 PRB Allocation (12 contiguous subcarriers)
                      - Short duration: 1 or 2 OFDM symbols
================================================================================

5. Signal Visualizations

Time-domain waveform envelope and Power Spectral Density (PSD) plots generated from the signal analytics pipeline.

PUCCH Format 0 Time Domain Plot
Figure 1: Time Domain Waveform
PUCCH Format 0 Power Spectral Density Plot
Figure 2: Power Spectral Density (PSD)