PUCCH Format 1 Test Bench Report | 5G NR Physical Layer

1. Configuration Parameters

Test setup configured using long PUCCH sequence allocation with intra-slot frequency hopping and time-domain OCC spreading.

Parameter	3GPP Symbol	Value / Setting	Description
Channel / Format	—	PUCCH Format 1	Sequence-based long format (≤ 2 bits) with TD-OCC
Resource Type	—	COMMON_NON_DEDICATED	Common resource set for initial access / random access
Resource Set Index	r_PUCCH	7	Resource set entry selector
Allocated RBs	N_PRB	1 PRB (M_sc = 12)	Single physical resource block transmission
Initial Cyclic Shift Index	m_0	1	Base initial cyclic shift index
Group Hopping	pucch-GroupHopping	Group Hopping Enabled	Dynamic group index switching (Hop 0: u=10, Hop 1: u=7)
Frequency Hopping	intraSlotFrequencyHopping	Enabled (ISFH_ENABLE)	Intra-slot frequency hopping across 2 hops
Orthogonal Cover Code Index	i_OC	1	Time-domain orthogonal cover code index
Modulation Scheme	—	QPSK	QPSK modulation mapping for UCI payload
Cell ID	N_ID	100	Drives PRN seed c_init = 100 and base sequence group u = 10
Slot Number	n_s,f^μ	1	Slot index within radio frame

2. Expected Intermediate Values & Symbol Multiplexing

Derivation of pilot vs data symbol allocations and group hopping indices evaluated across the 10-symbol slot allocation for Cell ID 100.

PRN Initialization Seed: c_init = N_ID = 100 Total Allocated Symbols: N_symb = 10 | Allocated Grid Size: 12 x 10 = 120 elements Data (UCI) Symbol Indices: {1, 3, 6, 8} (4 elements) Pilot (DM-RS) Symbol Indices: {0, 2, 4, 5, 7, 9} (6 elements)

Hop Index	OFDM Symbol Range	Sequence Group Index (u)	Sequence Base Length	Hopping Status
Hop 0	Symbols 0 – 4	u = 10 (100 mod 30)	M_sc = 12 (v = 0)	PRB Index 0
Hop 1	Symbols 5 – 9	u = 7 (Group Hopped)	M_sc = 12 (v = 0)	PRB Index 1

3. Time-Domain OCC Spreading & Multiplexing Architecture

Physical resource mapping illustrating interleaved DM-RS/UCI symbols and Orthogonal Cover Code (w_i) vector spreading across hops.

* Relative Symbol Index:    [ 0 ]   [ 1 ]   [ 2 ]   [ 3 ]   [ 4 ]   [ 5 ]
* Resource Allocation:    | Pilot  | Data  | Pilot  | Data | Pilot  | Data  |
*                                                     (0)
*
* Subcarriers
*  ^
*  |  [Column 1]        [Column 3]        [Column 5]        [Column 7]
*  | +------------+   +------------+   +------------+   +------------+
   | |            |   |            |   |            |   |            |
   | | d(0)*w[0]*R|   | d(0)*w[1]*R|   | d(0)*w[2]*R|   | d(0)*w[3]*R|
   | |            |   |            |   |            |   |            |
   | +------------+   +------------+   +------------+   +------------+
   +--------------------------------------------------------------------> Time (Symbols)
                       (Note: Columns 0, 2, 4, 6 are the interleaved DM-RS pilots)   
                       
                       
 Relative Index:      0          1          2      :      3          4          5          6
                  +----------+----------+----------+  : +----------+----------+----------+----------+
Physical Grid:    |  PILOT   |   DATA   |  PILOT   | : |  PILOT   |   DATA   |  PILOT   |   DATA   |
                  +----------+----------+----------+  : +----------+----------+----------+----------+
                   \______________________________/   :  \________________________________________/
                          HOP 1 (3 Symbols)           :               HOP 2 (4 Symbols)
                            (startingPRB)             :                (secondHopPRB)
                                                      :
Data OCC Vector:   w_i[0]        -        w_i[1]      :   w_i[0]        -        w_i[1]        -
Data SF (Length):  [====== Length = 2 ======]         :   [====== Length = 2 ======]
                                                      :
Pilot OCC Vector:    -         w_n[0]       -         :     -         w_n[0]       -         w_n[1]
Pilot SF (Length):             [= 1 =]                :               [====== Length = 2 ======]

3. 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 1 Power Spectral Density Plot

Figure 2: Power Spectral Density (PSD)