NR-Physical Broadcast Channel

NR-PBCH

• UE needs to first decode PBCH in order to receive system information
• MIB is transmitted on PBCH

NR-Secondary Synchronization Signal

NR-SSS(Secondary Synchronization Signal)

• SSS sequences are based on maximum length sequences, known as M-sequences made up of 127 values
• SSS determines Physical Layer Cell ID

NR-SSS Sequence Generation Algorithm

NR-SSS Python Code

def nr_sss_gen(N_id1, N_id2):

LEN = 127
x0 = np.zeros(LEN)
x0[0:7] = [1, 0, 0, 0, 0, 0, 0]
for i in range(0, LEN - 7):

x0[i + 7] = (x0[i + 4] + x0[i]) % 2 x1 = np.zeros(LEN)

x1[0:7] = [1, 0, 0, 0, 0, 0, 0]
for i in range(0, LEN - 7):

x1[i + 7] = (x1[i + 1] + x1[i]) % 2 d_sss = np.zeros(LEN)

m0 = int(15 * math.floor(N_id1/ 112) + 5 * N_id2)
m1 = N_id1 % 112
for n in range(0, LEN):

d_sss[n] = (1 - 2 * x0[((n + m0) % LEN)]) * (1 - 2 * x1[(n + m1) % LEN]) 

return d_sss

[Reference]

• 3GPP TS 38.211 V15.8.0 (2019-12), "NR; Physical channels and modulation"

NR-Primary Synchronization Signal

NR-PSS(Primary Synchronization Signal)

• PSS sequences are based on maximum length sequences, known as M-sequences made up of 127 values
• PSS sequence uses NR Downlink Frame Synchronization
• PSS determines Physical Layer Cell ID and provides Group ID value

NR-PSS Sequence Generation Algorithm

• It is generated by d(n) and it is determined by N(2)ID

NR-PSS Python Code

• It is based on python 2.7 and numpy Package
• nr_pss_gen python function

def nr_pss_gen(N_id2):
    len = 127
    len_intial = 7
    d = np.empty(len)
    x = np.zeros(len)
    x[0:7] = np.array([0,1,1,0,1,1,1])
    for i in range(len_intial,len):
         x[i] = (x[i+4-len_intial] + x[i-len_intial]) % 2
    for n in range(len):
        m = (n + 43*N_id2) % len
        d[n] = 1 -2*x[m]
    return d

• nr_pss_gen python plot 
• N_id2 = 0, PSS sequence 

• N_id2 = 1, PSS sequence 

• N_id2 = 2, PSS sequence 

NR-PSS Sequence Correlation Characteristic

• Auto Correlation of PSS sequence

• Cross Correlation   
• N_id2 =0 , N_id2 = 1  

• N_id2 =0 , N_id2 = 2  

• Cross Correlation between PSS with circular shift 

 [Reference]

• 3GPP TS 38.211 V15.8.0 (2019-12), "NR; Physical channels and modulation"