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SSS in LTE (secondary synchronization signals)

SSS stands for secondary synchronization signals.

SSS comes in the symbol just before PSS comes. If you don't know, how did we detect PSS, then goto this the previous post of PSS and SSS in LTE (Primary and secondary synchronization signals)

SSS is basically an m-sequence or Maximum length sequence.

Now, What is m-sequence?
M-sequence is a pseudo random binary sequence. These sequence can be generated just by cycling through every possible state of a shift register of length resulting in a sequence of length . Here, Three m-sequences, each of length 31, are used to generate the secondary synchronization signals.

SSS Generation

Two binary sequences, each of length 31, are used to generate the SSS. Sequences s0(m0) and s1(m1) are different cyclic shifts of an m-sequence, ˜s. The indices m0 and m1 are derived from the cell-identity group, NID(2) and determine the cyclic shift. The values can be read from table 6.11.2.1-1 in "Physical Channels and Modulation." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA)."
The two sequences are scrambled with a binary scrambling code (c0(n), c1(n)), which depends on NID(2).
The second SSS sequence used in each radio frame is scrambled with a binary scrambling code (z1(m0), z1(m1)) corresponding to the cyclic shift value of the first sequence transmitted in the radio frame.

Binary Sequence Generation

s0(m0) and s1(m1) are given by the following equations.
s(m0)0=˜s((n+m0)mod31)
s(m1)0=˜s((n+m1)mod31)
˜s is generated from the primitive polynomial x5+x2+1 over the finite field GF(2).
c0(n) and c1(n are given by the following equations.
c0(n)=˜c((n+N(2)ID)mod31)
c1(n)=˜c((n+N(2)ID+3)mod31)
˜c is generated from the primitive polynomial x5+x3+1 over the finite field GF(2).
z1(m0) and z1(m1) are given by the following equations.
z(m0)1=˜z((n+(m0mod8))mod31)
z(m1)1=˜z((n+(m1mod8))mod31)
˜z is generated from the primitive polynomial x5+x4+x2+x+1 over the finite field GF(2).

Mapping of the SSS

The scrambled sequences are interleaved to alternate the sequence transmitted in the first and second SSS transmission in each radio frame. This allows the receiver to determine the frame timing from observing only one of the two sequences; if the first SSS signal observed is in subframe 0 or subframe 5, synchronization can be achieved when the SSS signal is observed in subframe 0 or subframe 5 of the next frame.
The SSS is transmitted in the same subframe as the PSS but one OFDM symbol earlier. The SSS is mapped to the same subcarriers (middle 72 subcarriers) as the PSS.
The SSS is constructed using different scrambling sequences when mapped to even and odd resource elements.
  • Even resource elements:
    • Subframe 0: d(2n)=s(m0)0(n)c0(n)
    • Subframe 5: d(2n)=s(m1)1(n)c0(n)
  • Odd resource elements:
    • Subframe 0: d(2n+1)=s(m1)1(n)c1(n)z(m0)1(n)
    • Subframe 5: d(2n+1)=s(m0)0(n)c1(n)z(m1)1(n)

d(n) is mapped from lowest subcarrier to highest subcarrier.

References:
[1]mathworks.com
[2] 3GPP TS 36.211. "Physical Channels and Modulation." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA). URL: http://www.3gpp.org.

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