Sequence generationV15.8.0

Pseudo-random sequence generation

Generic pseudo-random sequences are defined by a length-31 Gold sequence. The output sequence c(n) of length $M_{PN}$, where $n=0,1,...,M_{PN}-1$ is defined by:

where $N_C$ =1600 and the first m-sequence $x_1(n)$ shall be initialized with $x_1(0)=1, x_1(n)=0 \text{ for } n=1,2,...,30$. The initialization of the second m-sequence, $x_2(n)$, is denoted by $c_{init}=\sum_{i=0}^{30}x_2(i)\cdot 2^i$ with the value depending on the application of the sequence.

What it means: $x_2(i)$ is the i-th bit of $c_{init}$ for i=0,...,30.

Low-PAPR sequence generation

The low-PAPR sequence $r_{u,v}^{(\alpha,\delta)}(n)$ is defined by a cyclic shift $\alpha$ of a base sequence $\bar{r}_{u,v}(n)$ according to

where $M_{ZC}=mN_{sc}^{RB}/2^{\delta}$ is the length of the sequence. Multiple sequences are defined from a single base sequence through different values of 𝛼 and 𝛿.

Base sequences $\bar{r}_{u,v}(n)$ are divided into groups, where $u \in \{0,1,...,29\}$ 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 $M_{ZC}=mN_{sc}^{RB}/2^{\delta}\text{, }1/2\le m/2^{\delta}\le5$ and two base sequences (𝑣 = 0,1) of each length $M_{ZC}=mN_{sc}^{RB}/2^{\delta}\text{, }6\le m/2^{\delta}$. The definition of the base sequence $\bar{r}_{u,v}(0),...,\bar{r}_{u,v}(M_{ZC}-1)$ depends on the sequence length $M_{ZC}$.

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 $M_{ZC} \le 3N_{sc}^{RB}$, the base sequence $\bar{r}_{u,v}(0),...,\bar{r}_{u,v}(M_{ZC-1})$ is given by

where

The length $N_{ZC}$ is given by the largest prime number such that $N_{ZC} < M_{ZC}$

Base sequences of length less than 36

For $M_{ZC} \in \{6, 12, 18, 24\}$ the base sequence is given by

where the value of $\phi(n)$ is given by Tables 5.2.2.2-1 to 5.2.2.2-4.

For $M_{ZC}=30$, the base sequence is given by