5 Generic functions

38.2113GPPNRPhysical channels and modulationRelease 17TS

5.1 Modulation mapper

The modulation mapper takes binary digits, 0 or 1, as input and produces complex-valued modulation symbols as output.

5.1.1 π/2-BPSK

In case of π/2-BPSK modulation, bit is mapped to complex-valued modulation symbol according to

5.1.2 BPSK

In case of BPSK modulation, bit is mapped to complex-valued modulation symbol according to

5.1.3 QPSK

In case of QPSK modulation, pairs of bits, , are mapped to complex-valued modulation symbols according to

5.1.4 16QAM

In case of 16QAM modulation, quadruplets of bits, , are mapped to complex-valued modulation symbols according to

5.1.5 64QAM

In case of 64QAM modulation, hextuplets of bits, , are mapped to complex-valued modulation symbols according to

5.1.6 256QAM

In case of 256QAM modulation, octuplets of bits, , are mapped to complex-valued modulation symbols according to

5.1.7 1024QAM

In case of 1024QAM modulation, 10-tuplets of bits, , are mapped to complex-valued modulation symbols according to

5.2 Sequence generation

5.2.1 Pseudo-random sequence generation

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

where 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.

5.2.2 Low-PAPR sequence generation type 1

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 and .

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

5.2.2.1 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.

5.2.2.2 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

Table 5.2.2.2-1: Definition of for.

0

-3

-1

3

3

-1

-3

1

-3

3

-1

-1

3

-3

2

-3

-3

-3

3

1

-3

3

1

1

1

3

-1

-3

4

1

1

1

-3

-1

3

5

-3

1

-1

-3

-3

-3

6

-3

1

3

-3

-3

-3

7

-3

-1

1

-3

1

-1

8

-3

-1

-3

1

-3

-3

9

-3

-3

1

-3

3

-3

10

-3

1

3

1

-3

-3

11

-3

-1

-3

1

1

-3

12

1

1

3

-1

-3

3

13

1

1

3

3

-1

3

14

1

1

1

-3

3

-1

15

1

1

1

-1

3

-3

16

-3

-1

-1

-1

3

-1

17

-3

-3

-1

1

-1

-3

18

-3

-3

-3

1

-3

-1

19

-3

1

1

-3

-1

-3

20

-3

3

-3

1

1

-3

21

-3

1

-3

-3

-3

-1

22

1

1

-3

3

1

3

23

1

1

-3

-3

1

-3

24

1

1

3

-1

3

3

25

1

1

-3

1

3

3

26

1

1

-1

-1

3

-1

27

1

1

-1

3

-1

-1

28

1

1

-1

3

-3

-1

29

1

1

-3

1

-1

-1

Table 5.2.2.2-2: Definition of for.

0

-3

1

-3

-3

-3

3

-3

-1

1

1

1

-3

1

-3

3

1

-3

1

3

-1

-1

1

3

3

3

2

-3

3

3

1

-3

3

-1

1

3

-3

3

-3

3

-3

-3

-1

3

3

3

-3

3

-3

1

-1

-3

4

-3

-1

-1

1

3

1

1

-1

1

-1

-3

1

5

-3

-3

3

1

-3

-3

-3

-1

3

-1

1

3

6

1

-1

3

-1

-1

-1

-3

-1

1

1

1

-3

7

-1

-3

3

-1

-3

-3

-3

-1

1

-1

1

-3

8

-3

-1

3

1

-3

-1

-3

3

1

3

3

1

9

-3

-1

-1

-3

-3

-1

-3

3

1

3

-1

-3

10

-3

3

-3

3

3

-3

-1

-1

3

3

1

-3

11

-3

-1

-3

-1

-1

-3

3

3

-1

-1

1

-3

12

-3

-1

3

-3

-3

-1

-3

1

-1

-3

3

3

13

-3

1

-1

-1

3

3

-3

-1

-1

-3

-1

-3

14

1

3

-3

1

3

3

3

1

-1

1

-1

3

15

-3

1

3

-1

-1

-3

-3

-1

-1

3

1

-3

16

-1

-1

-1

-1

1

-3

-1

3

3

-1

-3

1

17

-1

1

1

-1

1

3

3

-1

-1

-3

1

-3

18

-3

1

3

3

-1

-1

-3

3

3

-3

3

-3

19

-3

-3

3

-3

-1

3

3

3

-1

-3

1

-3

20

3

1

3

1

3

-3

-1

1

3

1

-1

-3

21

-3

3

1

3

-3

1

1

1

1

3

-3

3

22

-3

3

3

3

-1

-3

-3

-1

-3

1

3

-3

23

3

-1

-3

3

-3

-1

3

3

3

-3

-1

-3

24

-3

-1

1

-3

1

3

3

3

-1

-3

3

3

25

-3

3

1

-1

3

3

-3

1

-1

1

-1

1

26

-1

1

3

-3

1

-1

1

-1

-1

-3

1

-1

27

-3

-3

3

3

3

-3

-1

1

-3

3

1

-3

28

1

-1

3

1

1

-1

-1

-1

1

3

-3

1

29

-3

3

-3

3

-3

-3

3

-1

-1

1

3

-3

Table 5.2.2.2-3: Definition of for

0

-1

3

-1

-3

3

1

-3

-1

3

-3

-1

-1

1

1

1

-1

-1

-1

1

3

-3

3

-1

1

3

-3

-1

-3

-3

-1

-3

3

1

-1

3

-3

3

2

-3

3

1

-1

-1

3

-3

-1

1

1

1

1

1

-1

3

-1

-3

-1

3

-3

-3

3

3

3

1

-3

1

3

3

1

-3

-3

3

-1

-3

-1

1

4

1

1

-1

-1

-3

-1

1

-3

-3

-3

1

-3

-1

-1

1

-1

3

1

5

3

-3

1

1

3

-1

1

-1

-1

-3

1

1

-1

3

3

-3

3

-1

6

-3

3

-1

1

3

1

-3

-1

1

1

-3

1

3

3

-1

-3

-3

-3

7

1

1

-3

3

3

1

3

-3

3

-1

1

1

-1

1

-3

-3

-1

3

8

-3

1

-3

-3

1

-3

-3

3

1

-3

-1

-3

-3

-3

-1

1

1

3

9

3

-1

3

1

-3

-3

-1

1

-3

-3

3

3

3

1

3

-3

3

-3

10

-3

-3

-3

1

-3

3

1

1

3

-3

-3

1

3

-1

3

-3

-3

3

11

-3

-3

3

3

3

-1

-1

-3

-1

-1

-1

3

1

-3

-3

-1

3

-1

12

-3

-1

-3

-3

1

1

-1

-3

-1

-3

-1

-1

3

3

-1

3

1

3

13

1

1

-3

-3

-3

-3

1

3

-3

3

3

1

-3

-1

3

-1

-3

1

14

-3

3

-1

-3

-1

-3

1

1

-3

-3

-1

-1

3

-3

1

3

1

1

15

3

1

-3

1

-3

3

3

-1

-3

-3

-1

-3

-3

3

-3

-1

1

3

16

-3

-1

-3

-1

-3

1

3

-3

-1

3

3

3

1

-1

-3

3

-1

-3

17

-3

-1

3

3

-1

3

-1

-3

-1

1

-1

-3

-1

-1

-1

3

3

1

18

-3

1

-3

-1

-1

3

1

-3

-3

-3

-1

-3

-3

1

1

1

-1

-1

19

3

3

3

-3

-1

-3

-1

3

-1

1

-1

-3

1

-3

-3

-1

3

3

20

-3

1

1

-3

1

1

3

-3

-1

-3

-1

3

-3

3

-1

-1

-1

-3

21

1

-3

-1

-3

3

3

-1

-3

1

-3

-3

-1

-3

-1

1

3

3

3

22

-3

-3

1

-1

-1

1

1

-3

-1

3

3

3

3

-1

3

1

3

1

23

3

-1

-3

1

-3

-3

-3

3

3

-1

1

-3

-1

3

1

1

3

3

24

3

-1

-1

1

-3

-1

-3

-1

-3

-3

-1

-3

1

1

1

-3

-3

3

25

-3

-3

1

-3

3

3

3

-1

3

1

1

-3

-3

-3

3

-3

-1

-1

26

-3

-1

-1

-3

1

-3

3

-1

-1

-3

3

3

-3

-1

3

-1

-1

-1

27

-3

-3

3

3

-3

1

3

-1

-3

1

-1

-3

3

-3

-1

-1

-1

3

28

-1

-3

1

-3

-3

-3

1

1

3

3

-3

3

3

-3

-1

3

-3

1

29

-3

3

1

-1

-1

-1

-1

1

-1

3

3

-3

-1

1

3

-1

3

-1

Table 5.2.2.2-4: Definition of for

0

-1

-3

3

-1

3

1

3

-1

1

-3

-1

-3

-1

1

3

-3

-1

-3

3

3

3

-3

-3

-3

1

-1

-3

3

1

1

-3

1

-3

-3

1

-3

-1

-1

3

-3

3

3

3

-3

1

3

3

-3

-3

2

-1

-3

-3

1

-1

-1

-3

1

3

-1

-3

-1

-1

-3

1

1

3

1

-3

-1

-1

3

-3

-3

3

1

-3

3

-1

-3

-1

3

3

1

-1

1

1

3

-3

-1

-3

-3

-3

-1

3

-3

-1

-3

-3

4

-1

3

-3

-3

-1

3

-1

-1

1

3

1

3

-1

-1

-3

1

3

1

-1

-3

1

-1

-3

-3

5

-3

-1

1

-3

-3

1

1

-3

3

-1

-1

-3

1

3

1

-1

-3

-1

-3

1

-3

-3

-3

-3

6

-3

3

1

3

-1

1

-3

1

-3

1

-1

-3

-1

-3

-3

-3

-3

-1

-1

-1

1

1

-3

-3

7

-3

1

3

-1

1

-1

3

-3

3

-1

-3

-1

-3

3

-1

-1

-1

-3

-1

-1

-3

3

3

-3

8

-3

1

-3

3

-1

-1

-1

-3

3

1

-1

-3

-1

1

3

-1

1

-1

1

-3

-3

-3

-3

-3

9

1

1

-1

-3

-1

1

1

-3

1

-1

1

-3

3

-3

-3

3

-1

-3

1

3

-3

1

-3

-3

10

-3

-3

-3

-1

3

-3

3

1

3

1

-3

-1

-1

-3

1

1

3

1

-1

-3

3

1

3

-3

11

-3

3

-1

3

1

-1

-1

-1

3

3

1

1

1

3

3

1

-3

-3

-1

1

-3

1

3

-3

12

3

-3

3

-1

-3

1

3

1

-1

-1

-3

-1

3

-3

3

-1

-1

3

3

-3

-3

3

-3

-3

13

-3

3

-1

3

-1

3

3

1

1

-3

1

3

-3

3

-3

-3

-1

1

3

-3

-1

-1

-3

-3

14

-3

1

-3

-1

-1

3

1

3

-3

1

-1

3

3

-1

-3

3

-3

-1

-1

-3

-3

-3

3

-3

15

-3

-1

-1

-3

1

-3

-3

-1

-1

3

-1

1

-1

3

1

-3

-1

3

1

1

-1

-1

-3

-3

16

-3

-3

1

-1

3

3

-3

-1

1

-1

-1

1

1

-1

-1

3

-3

1

-3

1

-1

-1

-1

-3

17

3

-1

3

-1

1

-3

1

1

-3

-3

3

-3

-1

-1

-1

-1

-1

-3

-3

-1

1

1

-3

-3

18

-3

1

-3

1

-3

-3

1

-3

1

-3

-3

-3

-3

-3

1

-3

-3

1

1

-3

1

1

-3

-3

19

-3

-3

3

3

1

-1

-1

-1

1

-3

-1

1

-1

3

-3

-1

-3

-1

-1

1

-3

3

-1

-3

20

-3

-3

-1

-1

-1

-3

1

-1

-3

-1

3

-3

1

-3

3

-3

3

3

1

-1

-1

1

-3

-3

21

3

-1

1

-1

3

-3

1

1

3

-1

-3

3

1

-3

3

-1

-1

-1

-1

1

-3

-3

-3

-3

22

-3

1

-3

3

-3

1

-3

3

1

-1

-3

-1

-3

-3

-3

-3

1

3

-1

1

3

3

3

-3

23

-3

-1

1

-3

-1

-1

1

1

1

3

3

-1

1

-1

1

-1

-1

-3

-3

-3

3

1

-1

-3

24

-3

3

-1

-3

-1

-1

-1

3

-1

-1

3

-3

-1

3

-3

3

-3

-1

3

1

1

-1

-3

-3

25

-3

1

-1

-3

-3

-1

1

-3

-1

-3

1

1

-1

1

1

3

3

3

-1

1

-1

1

-1

-3

26

-1

3

-1

-1

3

3

-1

-1

-1

3

-1

-3

1

3

1

1

-3

-3

-3

-1

-3

-1

-3

-3

27

3

-3

-3

-1

3

3

-3

-1

3

1

1

1

3

-1

3

-3

-1

3

-1

3

1

-1

-3

-3

28

-3

1

-3

1

-3

1

1

3

1

-3

-3

-1

1

3

-1

-3

3

1

-1

-3

-3

-3

-3

-3

29

3

-3

-1

1

3

-1

-1

-3

-1

3

-1

-3

-1

-3

3

-1

3

1

1

-3

3

-3

-3

-3

5.2.3 Low-PAPR sequence generation type 2

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

where is the length of the sequence.

Base sequences are divided into groups, where is the group number and is the base sequence number within the group, such that each group contains one base sequence () of length , . The sequence is defined by

where the definition of depends on the sequence length.

5.2.3.1 Sequences of length 30 or larger

For , the sequence is obtained as the complex-valued modulations symbols resulting from π/2-BPSK modulation as defined in clause 5.1.1 applied to the binary sequence given by clause 5.2.1, initialized with .

5.2.3.2 Sequences of length less than 30

For , the sequence is given by

where the value of is given by Table 5.2.3.2-1.

For , the sequence is obtained as the complex-valued modulations symbols resulting from π/2-BPSK modulation as defined in clause 5.1.1 applied to the binary sequence given by Tables 5.2.3.2-2 to 5.2.3.2-4.

Table 5.2.3.2-1: Definition of for .

0

-1

-7

-3

-5

-1

3

1

-1

3

7

-3

7

3

2

-1

3

1

5

-1

-5

3

-7

-3

-7

5

-7

-3

4

7

5

-1

-7

-3

1

5

3

-3

1

5

-1

-1

6

-7

-3

-7

-3

7

-5

7

-7

-3

1

-5

-1

-5

8

-7

-3

3

-3

-7

-3

9

-7

-7

-1

1

-5

1

10

-7

-3

-7

5

-1

5

11

-7

-7

-3

1

5

-1

12

5

7

-3

-5

5

-5

13

-3

7

-5

-1

-5

-1

14

5

-7

7

1

5

1

15

-7

3

1

5

-1

3

16

-7

-5

-1

-7

-5

5

17

-7

1

-3

3

7

5

18

-7

-7

3

5

1

5

19

-7

-3

3

-1

3

-5

20

-7

-5

5

3

-7

-1

21

1

5

1

5

3

7

22

1

-3

1

-5

-1

3

23

1

7

1

-5

-7

-1

24

1

-1

3

-1

-7

-3

25

1

-1

-5

-1

3

-3

26

1

-1

3

-1

3

7

27

-5

3

7

5

3

7

28

-7

1

-3

1

5

1

29

1

5

3

-7

5

-3

Table 5.2.3.2-2: Definition of for .

0

0

0

0

0

0

0

1

1

0

1

1

0

1

0

0

0

0

0

1

0

0

0

1

1

1

2

0

0

0

0

0

1

1

1

0

1

1

1

3

1

1

0

1

1

0

1

0

1

0

0

0

4

1

1

0

0

1

0

1

0

1

0

0

1

5

1

0

1

1

0

1

0

0

1

0

1

1

6

0

0

0

1

0

0

1

0

0

0

1

0

7

0

1

0

0

0

1

0

0

1

0

0

0

8

1

0

1

1

1

1

0

1

1

0

1

1

9

1

0

1

1

0

1

1

1

1

0

0

0

10

1

0

1

1

0

1

0

0

0

1

1

0

11

1

0

1

0

0

1

0

0

1

0

1

0

12

1

1

0

0

0

0

0

1

1

1

1

0

13

0

1

0

0

0

1

1

0

1

0

1

1

14

0

0

0

0

0

1

1

0

0

0

1

1

15

0

0

0

0

0

1

0

0

1

0

0

1

16

0

0

1

0

0

1

0

0

0

0

0

1

17

0

0

0

0

0

1

1

0

1

1

1

0

18

0

0

0

1

1

1

1

1

0

0

0

1

19

1

0

0

0

1

0

0

0

0

0

1

1

20

0

1

1

1

1

0

1

0

1

1

1

1

21

0

1

1

1

0

1

0

0

1

1

0

1

22

0

1

1

1

1

1

0

0

1

0

0

0

23

0

1

1

1

0

0

0

0

0

1

0

0

24

0

0

1

1

1

1

1

1

1

1

0

0

25

0

1

1

1

0

0

1

1

0

1

0

0

26

0

1

1

1

0

1

1

1

0

1

1

1

27

0

1

1

1

1

1

1

0

0

0

1

1

28

0

1

1

1

1

0

0

0

0

0

1

1

29

0

1

1

1

0

1

1

1

1

0

1

1

Table 5.2.3.2-3: Definition of for .

0

0

0

0

0

0

1

0

0

0

1

1

1

1

1

0

0

0

1

1

0

0

0

0

0

0

0

1

1

1

1

1

0

0

1

0

0

1

2

0

0

0

0

0

1

1

1

1

0

1

1

1

0

1

1

1

1

3

0

1

0

1

1

0

1

1

0

0

0

1

1

0

1

0

1

1

4

1

1

0

1

0

0

1

0

1

0

1

0

0

1

1

1

1

0

5

0

1

0

1

0

1

1

1

0

0

1

0

1

1

0

1

1

0

6

0

0

0

1

1

1

0

0

0

1

0

0

0

1

1

1

1

1

7

0

1

0

1

0

0

0

1

1

0

1

0

0

0

0

0

1

1

8

0

0

1

0

1

0

0

0

1

0

1

0

0

1

0

0

0

1

9

1

0

1

1

0

0

1

0

1

0

1

0

0

1

0

0

0

1

10

1

0

1

1

0

0

0

1

1

1

0

0

0

0

0

0

0

1

11

1

1

0

1

1

0

1

1

1

0

1

1

1

1

1

0

0

0

12

1

0

0

0

1

0

1

0

1

0

0

0

1

1

0

1

0

1

13

1

0

1

1

0

1

0

1

1

1

0

0

0

0

0

1

1

0

14

0

0

0

0

0

1

1

1

0

1

1

0

1

0

1

1

0

0

15

0

0

1

1

1

0

1

1

0

1

0

0

0

1

1

0

1

0

16

0

1

0

0

1

0

0

0

1

1

1

0

1

0

0

1

1

1

17

0

1

0

0

1

1

0

1

1

0

0

0

0

0

0

0

1

0

18

0

0

1

0

0

1

1

1

1

0

0

0

0

0

1

1

0

0

19

0

0

0

0

0

0

0

1

0

0

1

0

0

1

1

0

1

1

20

0

0

0

0

0

1

1

0

0

0

0

1

0

0

1

1

1

1

21

1

1

1

1

0

1

0

1

1

1

1

1

0

0

1

0

0

1

22

1

0

0

1

0

0

0

1

0

0

1

1

1

1

0

1

1

1

23

0

0

1

0

0

0

1

1

1

0

0

0

1

0

0

1

0

1

24

1

1

0

1

1

0

0

0

0

0

0

0

1

1

0

1

1

0

25

1

1

0

1

0

1

0

1

1

0

0

0

0

1

0

0

1

0

26

0

1

1

1

1

1

1

1

0

0

1

0

1

0

0

1

0

0

27

0

1

1

0

1

1

1

0

0

0

0

0

0

0

1

1

0

0

28

0

0

0

1

1

0

0

0

0

0

0

0

0

0

1

1

0

0

29

0

1

1

1

0

1

1

0

1

0

1

1

1

0

1

1

0

0

Table 5.2.3.2-4: Definition of for

0

0

0

0

0

0

0

0

1

0

0

1

1

1

1

1

0

0

1

0

0

1

0

0

1

1

0

0

0

0

0

0

0

1

0

0

1

0

1

1

0

1

1

1

0

0

0

1

1

0

2

0

0

0

0

0

0

0

0

1

0

0

1

0

0

1

0

0

1

1

1

1

0

1

1

3

0

0

0

0

0

0

0

0

1

1

0

1

1

0

0

1

0

1

0

1

1

0

1

1

4

1

0

0

1

1

1

1

1

0

1

1

0

1

1

1

0

1

1

0

0

0

1

1

1

5

1

0

1

0

1

1

0

1

1

0

0

1

1

1

1

1

0

0

1

1

0

1

1

1

6

0

1

1

0

0

1

0

0

1

1

1

1

1

1

0

1

1

1

1

0

1

1

0

1

7

1

0

1

1

1

1

1

1

1

1

1

0

1

0

0

1

1

1

0

0

1

1

0

1

8

0

0

1

0

0

1

0

1

0

0

0

1

0

0

1

0

0

0

0

0

1

1

1

0

9

0

0

0

0

1

0

0

1

1

0

1

0

0

0

0

0

1

1

0

0

0

1

0

1

10

1

0

1

0

0

0

1

1

1

0

0

1

1

1

1

0

1

1

1

1

0

0

1

0

11

0

0

1

0

0

1

0

0

0

0

0

1

1

1

0

0

0

1

0

0

1

0

1

0

12

1

0

1

0

0

1

1

1

0

1

0

0

0

1

0

1

1

1

0

0

1

0

1

1

13

1

0

1

0

0

1

1

0

1

1

0

1

0

1

0

1

1

0

1

1

0

0

1

0

14

1

0

1

0

0

0

1

0

0

1

1

1

0

0

0

0

0

1

0

0

1

0

1

1

15

1

0

0

1

0

1

0

0

1

1

0

0

0

0

1

1

1

1

1

1

1

0

0

1

16

0

0

0

1

1

1

1

0

0

1

0

1

0

0

1

1

1

0

1

1

1

0

0

1

17

1

1

0

1

0

1

1

1

0

0

1

1

1

0

0

0

0

0

0

1

1

0

1

0

18

0

0

0

0

0

0

0

0

0

1

1

1

1

0

0

0

1

0

1

1

0

0

0

1

19

1

0

0

0

1

0

1

1

0

0

0

1

0

0

0

0

0

0

0

0

0

1

1

1

20

0

0

0

0

0

0

1

1

1

0

1

1

0

0

0

1

1

0

0

0

1

0

1

0

21

0

1

1

0

1

0

1

1

1

0

0

0

0

1

0

0

0

0

1

0

0

0

1

1

22

1

0

1

0

0

1

0

0

0

0

0

1

1

1

0

0

1

0

0

0

1

0

1

1

23

1

0

0

1

1

0

1

0

0

0

0

0

1

1

1

1

1

1

1

1

0

0

1

1

24

1

0

0

0

1

1

0

1

0

1

0

0

1

0

0

1

1

1

1

1

1

0

0

0

25

1

0

1

0

1

1

0

0

0

1

0

0

0

1

1

1

1

1

1

0

0

1

0

0

26

0

1

0

0

1

0

1

0

1

1

0

0

0

1

1

1

1

1

1

0

0

1

0

0

27

0

1

0

1

1

0

1

0

1

0

1

0

1

1

0

1

1

0

0

1

0

0

1

1

28

0

1

0

0

0

1

1

0

1

0

1

0

1

1

1

0

1

0

0

1

0

0

1

1

29

0

1

0

0

1

0

0

1

1

1

1

1

1

1

1

1

1

0

0

1

0

0

1

1

5.3 OFDM baseband signal generation

5.3.1 OFDM baseband signal generation for all channels except PRACH and RIM-RS

The time-continuous signal on antenna port and subcarrier spacing configuration for OFDM symbol in a subframe for any physical channel or signal except PRACH is defined by

where at the start of the subframe,

and

is given by clause 4.2;

is the subcarrier spacing configuration;

– is the largest value among the subcarrier spacing configurations by scs-SpecificCarrierList for each of uplink and downlink and by sl-SCS-SpecificCarrierList for sidelink.

In case of cyclic prefix extension of the first OFDM symbol allocated for PUSCH, SRS, or PUCCH transmission, the time-continuous signal for the interval preceding the first OFDM symbol for PUSCH, SRS, or PUCCH is given by

where refers to the signal in the previous subframe and

– for dynamically scheduled PUSCH, SRS, and PUCCH transmissions

where is given by Table 5.3.1-1 with for , for , and and given by the higher-layer parameters cp-ExtensionC2 and cp-ExtensionC3, respectively, and given by clause 4.3.1. For contention-based random access, or in absence of higher-layer configuration of and , the value of shall be set to the largest integer fulfilling for each of the values of . Text is applied to the first UL transmission scheduled by the scheduling DCI.

– for a PUSCH transmission using configured grant

where is given by Table 5.3.1-2 with the index given by the procedure in [6, TS 38.214].

The starting position of OFDM symbol for subcarrier spacing configuration in a subframe is given by

Table 5.3.1-1: The variables and for cyclic prefix extension

index

0

1

2

3

Table 5.3.1-2: The variable for cyclic prefix extension with configured grants.

index

0

1

2

3

4

5

6

5.3.2 OFDM baseband signal generation for PRACH

The time-continuous signal on antenna port for PRACH is defined by

where and

is given by clause 6.3.3;

is the subcarrier spacing of the initial uplink bandwidth part during initial access. Otherwise, is the subcarrier spacing of the active uplink bandwidth part;

– is the largest value among the subcarrier spacing configurations by the higher-layer parameter scs-SpecificCarrierList;

– is the lowest numbered resource block of the initial uplink bandwidth part and is derived by the higher-layer parameter initialUplinkBWP during initial access. Otherwise, is the lowest numbered resource block of the active uplink bandwidth part and is derived by the higher-layer parameter BWP-Uplink;

– is the frequency offset of the lowest PRACH transmission occasion in frequency domain with respect to physical resource block 0 of the active uplink bandwidth part. The quantity is given by the higher-layer parameter msgA-RO-FrequencyStart if configured and a type-2 random-access procedure is initiated as described in clause 8.1 of [5, TS 38.213], otherwise by msg1-FrequencyStart as described in clause 8.1 of [5 TS 38.213];

– is the PRACH transmission occasion index in frequency domain for a given PRACH transmission occasion in one time instance as given by clause 6.3.3.2;

– is the number of resource blocks occupied and is given by the parameter allocation expressed in number of RBs for PUSCH in Table 6.3.3.2-1.

– is the start CRB index of uplink RB set corresponding to the quantity . The UE assumes that the RB set is defined as when the UE is not provided IntraCellGuardBandsPerSCS for an UL carrier as described in Clause 7 of [6, TS 38.214]

– is the index of the RB set which contains the lowest PRACH transmission occasion in frequency domain indicated by . The UE may assume that is configured such that each PRACH transmission occasion is fully contained within an RB set.

and are given by clause 6.3.3

– where

– for ,

– for kHz, is the number of times the interval overlaps with either time instance 0 or time instance in a subframe

The starting position of the PRACH preamble in a subframe (for ) or in a 60 kHz slot (for kHz) is given by

where

– the subframe or 60 kHz slot is assumed to start at ;

– a timing advance value shall be assumed;

– and are given by clause 5.3.1;

– shall be assumed for kHz, otherwise the value of corresponds to kHz and the symbol position is given by

where

– is given by the parameter "starting symbol" in Tables 6.3.3.2-2 to 6.3.3.2-4;

– is the PRACH transmission occasion within the PRACH slot, numbered in increasing order from 0 to within a RACH slot where is given Tables 6.3.3.2-2 to 6.3.3.2-4 for and fixed to 1 for ;

– is given by Tables 6.3.3.2-2 to 6.3.3.2-4;

– is given by

– if kHz, then

– if kHz and either of "Number of PRACH slots within a subframe" in Tables 6.3.3.2-2 to 6.3.3.2-3 or "Number of PRACH slots within a 60 kHz slot" in Table 6.3.3.2-4 is equal to 1, then , otherwise

– if kHz and

– the "Number of PRACH slots within a 60 kHz slot" in Table 6.3.3.2-4 is equal to 1, then for kHz and for kHz, or

– the "Number of PRACH slots within a 60 kHz slot" in Table 6.3.3.2-4 is equal to 2, then for kHz and for kHz.

If the preamble format given by Tables 6.3.3.2-2 to 6.3.3.2-4 is A1/B1, A2/B2 or A3/B3, then

– if , then the PRACH preamble with the corresponding PRACH preamble format from B1, B2 and B3 is transmitted in the PRACH transmission occasion;

– otherwise the PRACH preamble with the corresponding PRACH preamble format from A1, A2 and A3 is transmitted in the PRACH transmission occasion

5.3.3 OFDM baseband signal generation for RIM-RS

The time-continuous signal on antenna port for RIM-RS is defined by

where

and

– where is the subcarrier spacing configuration for the RIM-RS;

– is the starting frequency offset of the RIM-RS as given by clause 7.4.1.6.4.3;

– is the length of the RIM-RS sequence where is the bandwidth of the RIM-RS in resource blocks;

– is the starting symbol given by clause 7.4.1.6.3;

– is given by clause 5.3.1 with ;

– is given by clause 5.3.1 with .

5.4 Modulation and upconversion

Modulation and upconversion to the carrier frequency of the complex-valued OFDM baseband signal for antenna port , subcarrier spacing configuration , and OFDM symbol in a subframe assumed to start at is given by

– for PRACH

– for RIM-RS

where is the configured reference point for RIM-RS;

– for all other channels and signals

NOTE: For the uplink, the signal and the baseband signals part thereof should be filtered per UE implementation, as required, to meet the minimum requirements as specified in [38.101-1] and [38.101-2] for the respective frequency range.