Secondary Synchronization Signal for Sidelink (S-SSS)

The sidelink-secondary synchronization signal (S-SSS) is a gold-sequence of length 127 generated using \(N_{ID,1}^{SL}\) and \(N_{ID,2}^{SL}\). It is used for sidelink cell ID-2 detection and frequency synchronization which aims to mitigate the carrier offsets and centre of the S-SSB grid at the sidelink user equipment (UE). The detailed implementation of the S-SSS is provided in [3GPPTS38211_S_SSS].

Important

• S-SSS is an constituent of sidelink synchronization signal block (S-SSB). It is loaded in the middle 127 subcarrier (across frequency) of fourth and fifth symbol of the S-SSB.

If \(N_{ID,1}^{SL}\) and \(N_{ID,2}^{SL}\) is scalar:

nID1         = 25                # Cell ID-2 for SSS generation
nID2         = 1                 # Cell ID-2 for SSS generation
ssss         = S_SSS(nID1, nID2) # Generate PSS object using this cell ID-2.
ssssSequence = ssss()            # Generate [1x127] pss sequence using 'sss' object

If \(N_{ID,1}^{SL}\) is scaler and \(N_{ID,2}^{SL}\) is NumPy array:

nID1         = 204                 # Cell ID-2 for SSS generation
nID2         = np.array([1,0,1,1]) # Cell ID-2 for SSS generation
ssss         = S_SSS(nID1, nID2)   # Generate PSS object using this cell ID-2.
ssssSequence = ssss()              # Generate [4x127] pss sequence using 'sss' object for each cell-ID2

If \(N_{ID,1}^{SL}\) is NumPy array and \(N_{ID,2}^{SL}\) is scaler:

nID1         = np.array([98, 213]) # Cell ID-2 for SSS generation
nID2         = 2                   # Cell ID-2 for SSS generation
ssss         = S_SSS(nID1, nID2)   # Generate PSS object using this cell ID-2.
ssssSequence = ssss()              # Generate [2x127] pss sequence using 'sss' object for each cell-ID2

If \(N_{ID,1}^{SL}\) and \(N_{ID,2}^{SL}\) are NumPy array:

nID1         = np.array([101,45,21]) # Cell ID-2 for SSS generation
nID2         = np.array([  1, 0, 1]) # Cell ID-2 for SSS generation
ssss         = S_SSS(nID1, nID2)     # Generate PSS object using this cell ID-2.
ssssSequence = ssss()                # Generate [3x127] pss sequence using 'sss' object for each cell-ID2

The details about the input-output interface of the SSS implementation is provided below.

class toolkit5G.SequenceGeneration.S_SSS(nID1, nID2)

Generates the sidelink secondary synchronization signal (SSS) for 5G system. The constructor expects two parameters as input \(N_{ID,1}^{SL}\) and \(N_{ID,2}^{SL}\). The two IDs can be scaler and/or vector. When both the IDs are vector they should have equal length. The call method returns 1 or multiple SS sequences of length 127 based on the number of \(N_{ID,1}^{SL}\) and \(N_{ID,2}^{SL}\) passed as input. The details about the implementation of the sequence are provided in the document “Physical channels and modulation (Release 17)” TS 38.211 Section 8.4.2.3 version V17.1.0 (2022-03).

Tip

• As per 3GPP specifications, cell ID-2 \(N_{ID,1}^{SL} \in \{0, 1, 2, \dots, 335\}\).

Tip

• As per 3GPP specifications, cell ID-1 \(N_{ID,2}^{SL} \in \{0, 1\}\).

Note

The physical-layer sidelink synchronization identity is given by \(N_{ID,1}^{SL} + 336 \\times N_{ID,2}^{SL} = N_{ID}^{SL}\).

Parameters:

• nID1 (int or NumPy integer array) – denotes the \(N_{ID,1}^{SL}\). All the values should be taken from the interval \(\{0, 1, 2, \dots, 335\}\).

• nID2 (int or NumPy integer array) – denotes the \(N_{ID,2}^{SL}\). All the values should be taken from the interval {0, 1}.

Input:

None – No inputs Required.

Output:

(…,127), np.integer – sssSequence of shape \(\text{N} \times 127\) where N is the number of SSS sequences.

Note

• If both nID1 and nID2 are scalar: N(number of SS sequence) = 1.

• If nID1 is an array and nID2 is scalar: N(number of SS sequence) = length of nID1.

• If nID1 is a scalar and nID2 is an array: N(number of SS sequence) = length of nID2

• If nID1 is an array and nID2 is also an array: N(number of SS sequence) = length of nID1 or length of nID2. In this case length of nID1 and length of nID2 must be equal.

Raises:

• ValueError – [Error-S_SSS]: Size of ‘nID1’ and ‘nID2’ is inconsistent!

• Warning – [Warning S_SSS]: ‘nID1’ should belong to interval {0, 1, 2, …, 335}

• ValueError – [Error S-SSS]: ‘nID1’ must be an integer or integer numpy array!

• Warning – [Warning S_SSS]: ‘nID2’ should belong to interval {0, 1}

• ValueError – [Error S-SSS]: ‘nID2’ must be an integer or integer numpy array!

References:

[3GPPTS38211_S_SSS]

3GPP TS 38.211 “Physical channels and modulation (Release 17)”, V17.1.0 (2022-03).