PUCCH Format 3 Test Bench Report | 5G NR Physical Layer

1. Configuration Parameters

Test setup configured for long PUCCH Format 3 with DFT-s-OFDM precoding and intra-slot frequency hopping.

Parameter	3GPP Symbol	Value / Setting	Description
Channel / Format	—	PUCCH Format 3	DFT-s-OFDM long format (> 2 bits) without OCC
RNTI	n_RNTI	12345	Scrambling sequence seed parameter
Allocated PRBs	N_PRB	2 PRBs (24 subcarriers)	Multi-PRB allocation (M_sc = 24)
Allocated Symbols	N_symb	4 Symbols (l = 10 to 13)	Long PUCCH symbol allocation duration
Start Symbol Index	S	10	First OFDM symbol index in slot
Group Hopping	pucch-GroupHopping	Disabled (NEITHER)	Constant sequence group index (u = 10)
Frequency Hopping	intraSlotFrequencyHopping	Enabled (ISFH_ENABLE)	Intra-slot frequency hopping across 2 hops
Modulation Scheme	—	QPSK	QPSK constellation mapping
Cell ID	N_ID	100	Base sequence group index u = 100 mod 30 = 10
Slot Number	n_s,f^μ	0	Slot index within radio frame

2. Expected Intermediate Values & Symbol Multiplexing

Derivation of pilot vs data symbol allocations and frequency hopping indices across the 4-symbol slot allocation.

Total Allocated Symbols: N_symb = 4 | Grid Dimensions: 24 subcarriers × 4 symbols = 96 elements Data (UCI) Symbol Indices: {11, 13} (2 OFDM symbols) Pilot (DM-RS) Symbol Indices: {10, 12} (2 OFDM symbols)

Hop Index	OFDM Symbol Indices	Frequency Hopping Index	Sequence Group Index (u)	DM-RS Phase Shift (α)
Hop 0	Symbol 10 (DM-RS), Symbol 11 (UCI)	0	u = 10	α = 2.6180 rad
Hop 1	Symbol 12 (DM-RS), Symbol 13 (UCI)	1	u = 10	α = 4.7124 rad

3. DFT-s-OFDM Precoding & Resource Grid Architecture

Resource grid mapping illustrating full-symbol DM-RS pilots and DFT-precoded UCI data symbols across 2 PRBs.

================================================================================
                    PUCCH FORMAT 3 RESOURCE GRID ARCHITECTURE                   
================================================================================

  Subcarriers (Y-Axis)
  M_sc = 24 (2 PRBs)
  ^
  |  +--------------------+--------------------+--------------------+--------------------+
  |  | DM-RS Symbol       | UCI Data Symbol    | DM-RS Symbol       | UCI Data Symbol    |
  |  | (Full PRBs)        | (DFT Precoded)     | (Full PRBs)        | (DFT Precoded)     |
  |  |                    |                    |                    |                    |
  |  | Low-PAPR Base      | Scrambled + QPSK   | Low-PAPR Base      | Scrambled + QPSK   |
  |  | Sequence r_u,v(n)  | + M_sc point DFT   | Sequence r_u,v(n)  | + M_sc point DFT   |
  |  +--------------------+--------------------+--------------------+--------------------+
  +--------------------------------------------------------------------------------------> Time (OFDM Symbols)
        Symbol l = 10        Symbol l = 11        Symbol l = 12        Symbol l = 13
        \____________________________________/    \____________________________________/
                   HOP 0 (startPRB)                          HOP 1 (secondHopPRB)

================================================================================
                         TRANSFORM PRECODING PIPELINE
================================================================================

  UCI Bits --> [ Scrambling ] --> [ QPSK Mod ] --> [ M_sc DFT Precode ] --> Grid REs

  Notes:      - No Time-Domain OCC (Allows higher spectral efficiency)
              - DM-RS occupies dedicated, un-multiplexed OFDM symbols
              - Low PAPR maintained via Transform Precoding (DFT-s-OFDM)
================================================================================

4. Python Signal Analytics & Visualizations

Time-domain envelope and Power Spectral Density (PSD) plots exported from the Python test analytics pipeline.

Figure 1: Time Domain Waveform

PUCCH Format 3 Power Spectral Density Plot

Figure 2: Power Spectral Density (PSD)