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Sequence generationV15.8.0

Toolbox: Pseudo-random sequence generator
(0,...30)0100000000000000000000000000000
Output sequence length
Output sequence c(n)10000010110011111000101111110011001011001001110100
Toolbox: Low-PAPR sequence generator
Sequence length MZC
Largest prime num NZC<MZC31
Group number u
Base sequence number v0
Cyclic shift
Display precision
Base sequence 1, -0.44-0.90j, 0.98+0.20j, 0.92+0.39j, 0.15-0.99j, 0.53+0.85j
0.15+0.99j, 0.98-0.20j, -0.76+0.65j, -0.99+0.10j, -0.05+1.00j, -0.25-0.97j
0.53-0.85j, -0.61-0.79j, 0.69+0.72j, -0.25+0.97j, 0.69+0.72j, -0.61-0.79j
0.53-0.85j, -0.25-0.97j, -0.05+1.00j, -0.99+0.10j, -0.76+0.65j, 0.98-0.20j
0.15+0.99j, 0.53+0.85j, 0.15-0.99j, 0.92+0.39j, 0.98+0.20j, -0.44-0.90j
1+0.00j, 1, -0.44-0.90j, 0.98+0.20j, 0.92+0.39j, 0.15-0.99j
Low-PAPR sequence 1, 0.44+0.90j, 0.98+0.20j, -0.92-0.39j, 0.15-0.99j, -0.53-0.85j
0.15+0.99j, -0.98+0.20j, -0.76+0.65j, 0.99-0.10j, -0.05+1.00j, 0.25+0.97j
0.53-0.85j, 0.61+0.79j, 0.69+0.72j, 0.25-0.97j, 0.69+0.72j, 0.61+0.79j
0.53-0.85j, 0.25+0.97j, -0.05+1.00j, 0.99-0.10j, -0.76+0.65j, -0.98+0.20j
0.15+0.99j, -0.53-0.85j, 0.15-0.99j, -0.92-0.39j, 0.98+0.20j, 0.44+0.90j
1+0.00j, -1+0.00j, -0.44-0.90j, -0.98-0.20j, 0.92+0.39j, -0.15+0.99j

Pseudo-random sequence generation

Generic pseudo-random sequences are defined by a length-31 Gold sequence. The output sequence c(n) of length , where is defined by:

where =1600 and the first m-sequence shall be initialized with . The initialization of the second m-sequence, , is denoted by with the value depending on the application of the sequence.

What it means: is the i-th bit of for i=0,...,30.

Low-PAPR sequence generation

The low-PAPR sequence is defined by a cyclic shift of a base sequence according to

where is the length of the sequence. Multiple sequences are defined from a single base sequence through different values of 𝛼 and 𝛿.

Base sequences are divided into groups, where is the group number and v is the base sequence number within the group, such that each group contains one base sequence (𝑣 = 0) of each length and two base sequences (𝑣 = 0,1) of each length . The definition of the base sequence depends on the sequence length .

What it means:

  • Each base sequence length has 30 groups of sequences.
    • For base sequence length ≤ 72, there is only one base sequence within each group, i.e., v=0.
    • For base sequence length > 72, there are two sequences within each group, i.e., v = 0 or 1.
  • Base sequence of length {6, 12, 18, 24} are generated from pre-defined tables of φ
  • Low-PAPR sequence is generated by rotating the base sequence with phase α.

Base sequences of length 36 or larger

For , the base sequence is given by

where

The length is given by the largest prime number such that

Base sequences of length less than 36

For the base sequence is given by

where the value of is given by Tables 5.2.2.2-1 to 5.2.2.2-4.

For , the base sequence is given by

φ(n) for Mzc=6
u
0-3-133-1-3
1-33-1-13-3
2-3-3-331-3
31113-1-3
4111-3-13
5-31-1-3-3-3
6-313-3-3-3
7-3-11-31-1
8-3-1-31-3-3
9-3-31-33-3
10-3131-3-3
11-3-1-311-3
12113-1-33
131133-13
14111-33-1
15111-13-3
16-3-1-1-13-1
17-3-3-11-1-3
18-3-3-31-3-1
19-311-3-1-3
20-33-311-3
21-31-3-3-3-1
2211-3313
2311-3-31-3
24113-133
2511-3133
2611-1-13-1
2711-13-1-1
2811-13-3-1
2911-31-1-1
φ(n) for Mzc=12
u
0-31-3-3-33-3-1111-3
1-331-313-1-11333
2-3331-33-113-33-3
3-3-3-1333-33-31-1-3
4-3-1-11311-11-1-31
5-3-331-3-3-3-13-113
61-13-1-1-1-3-1111-3
7-1-33-1-3-3-3-11-11-3
8-3-131-3-1-331331
9-3-1-1-3-3-1-3313-1-3
10-33-333-3-1-1331-3
11-3-1-3-1-1-333-1-11-3
12-3-13-3-3-1-31-1-333
13-31-1-133-3-1-1-3-1-3
1413-313331-11-13
15-313-1-1-3-3-1-131-3
16-1-1-1-11-3-133-1-31
17-111-1133-1-1-31-3
18-3133-1-1-333-33-3
19-3-33-3-1333-1-31-3
2031313-3-1131-1-3
21-3313-311113-33
22-3333-1-3-3-1-313-3
233-1-33-3-1333-3-1-3
24-3-11-31333-1-333
25-331-133-31-11-11
26-113-31-11-1-1-31-1
27-3-3333-3-11-331-3
281-1311-1-1-113-31
29-33-33-3-33-1-113-3
φ(n) for Mzc=18
u
0-13-1-331-3-13-3-1-1111-1-1-1
13-33-113-3-1-3-3-1-331-13-33
2-331-1-13-3-111111-13-1-3-1
3-3-33331-31331-3-33-1-3-11
411-1-1-3-11-3-3-31-3-1-11-131
53-3113-11-1-1-311-133-33-1
6-33-1131-3-111-3133-1-3-3-3
711-33313-33-111-11-3-3-13
8-31-3-31-3-331-3-1-3-3-3-1113
93-131-3-3-11-3-333313-33-3
10-3-3-31-33113-3-313-13-3-33
11-3-3333-1-1-3-1-1-131-3-3-13-1
12-3-1-3-311-1-3-1-3-1-133-1313
1311-3-3-3-313-3331-3-13-1-31
14-33-1-3-1-311-3-3-1-13-31311
1531-31-333-1-3-3-1-3-33-3-113
16-3-1-3-1-313-3-13331-1-33-1-3
17-3-133-13-1-3-11-1-3-1-1-1331
18-31-3-1-131-3-3-3-1-3-3111-1-1
19333-3-1-3-13-11-1-31-3-3-133
20-311-3113-3-1-3-13-33-1-1-1-3
211-3-1-333-1-31-3-3-1-3-11333
22-3-31-1-111-3-13333-13131
233-1-31-3-3-333-11-3-131133
243-1-11-3-1-3-1-3-3-1-3111-3-33
25-3-31-3333-1311-3-3-33-3-1-1
26-3-1-1-31-33-1-1-333-3-13-1-1-1
27-3-333-313-1-31-1-33-3-1-1-13
28-1-31-3-3-31133-333-3-13-31
29-331-1-1-1-11-133-3-113-13-1
φ(n) for Mzc=24
u
0-1-33-1313-11-3-1-3-113-3-1-3333-3-3-3
1-1-3311-31-3-31-3-1-13-3333-3133-3-3
2-1-3-31-1-1-313-1-3-1-1-31131-3-1-13-3-3
31-33-1-3-1331-1113-3-1-3-3-3-13-3-1-3-3
4-13-3-3-13-1-11313-1-1-3131-1-31-1-3-3
5-3-11-3-311-33-1-1-3131-1-3-1-31-3-3-3-3
6-3313-11-31-31-1-3-1-3-3-3-3-1-1-111-3-3
7-313-11-13-33-1-3-1-33-1-1-1-3-1-1-333-3
8-31-33-1-1-1-331-1-3-113-11-11-3-3-3-3-3
911-1-3-111-31-11-33-3-33-1-313-31-3-3
10-3-3-3-13-33131-3-1-1-31131-1-3313-3
11-33-131-1-1-133111331-3-3-11-313-3
123-33-1-3131-1-1-3-13-33-1-133-3-33-3-3
13-33-13-13311-313-33-3-3-113-3-1-1-3-3
14-31-3-1-1313-31-133-1-33-3-1-1-3-3-33-3
15-3-1-1-31-3-3-1-13-11-131-3-1311-1-1-3-3
16-3-31-133-3-11-1-111-1-13-31-31-1-1-1-3
173-13-11-311-3-33-3-1-1-1-1-1-3-3-111-3-3
18-31-31-3-31-31-3-3-3-3-31-3-311-311-3-3
19-3-3331-1-1-11-3-11-13-3-1-3-1-11-33-1-3
20-3-3-1-1-1-31-1-3-13-31-33-3331-1-11-3-3
213-11-13-3113-1-331-33-1-1-1-11-3-3-3-3
22-31-33-31-331-1-3-1-3-3-3-313-11333-3
23-3-11-3-1-111133-11-11-1-1-3-3-331-1-3
24-33-1-3-1-1-13-1-13-3-13-33-3-1311-1-3-3
25-31-1-3-3-11-3-1-311-111333-11-11-1-3
26-13-1-133-1-1-13-1-31311-3-3-3-1-3-1-3-3
273-3-3-133-3-131113-13-3-13-131-1-3-3
28-31-31-31131-3-3-113-1-331-1-3-3-3-3-3
293-3-113-1-1-3-13-1-3-1-33-1311-33-3-3-3