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"