同步信号包括（1）主同步信号（2）辅同步信号
1）主同步信号：用于小区组内侦测，符号timing对准，频率同步
2）辅同步信号：用于小区组侦测，帧timing对准，CP长度侦测
共有504个唯一的小区标识，物理层小区标志分成168个唯一的物理层小区标识组，每一个小组
包含3个唯一标识。这个分组中每一个物理小区标识是该分组的一部分，并且只有一个物理层
标识组。物理层小区标识组\(N_{ {\rm{ID}}}^{ {\rm{cell}}} = 3N_{ {\rm{ID}}}^{ {\rm{(1)}}} + N_{ {\rm{ID}}}^{ {\rm{(2)}}}\)
NID1 = floor(NIDcell/3); NID2 = mod(NIDcell,3);讯享网1）主同步信号产生：
\[{d_u}(n) = \left\{ {\begin{array}{*{20}{c}}
{
{e^{ - j\frac{
{\pi un(n + 1)}}{
{63}}}}}&{n = 0,1,...,30}\\
{
{e^{ - j\frac{
{\pi u(n + 1)(n + 2)}}{
{63}}}}}&{n = 31,32,...,61}
\end{array}} \right.\]
其中，Z-C序列（Zadoff-Chu）根序列序号为
讯享网switch NID2 case 0 u = 25; case 1 u = 29; case 2 u = 34; otherwise error('invalid NID2.'); end此时，主同步信号产生代码为
for n=1:31 PrimSync_temp(n,1) = exp(-1i*pi*u*(n-1)*n/63); PrimSync_temp(n,2) = exp(-1i*pi*u*(n+31)*(n+32)/63); end不同的帧结构有不同的映射方式，
如上图所示，对于Type1，主同步信号映射到时隙0和时隙10的最后一个OFDM符号内；
对于Type2，主同步信号映射到子帧1和子帧6的第三个OFDM符号
对于Type1，映射规则为：
\[\begin{array}{c}
{a_{k,l}} = d\left( n \right),{\rm{ }}n = 0,...,61\\
k = n - 31 + \frac{
{N_{
{\rm{RB}}}^{
{\rm{DL}}}N_{
{\rm{sc}}}^{
{\rm{RB}}}}}{2}
\end{array}\]
2）辅同步信号：
\[\begin{array}{*{20}{c}}
{d(2n) = \left\{ {\begin{array}{*{20}{l}}
{s_0^{({m_0})}(n){c_0}\left( n \right)}&{
{\rm{in subframe 0}}}\\
{s_1^{({m_1})}(n){c_0}\left( n \right)}&{
{\rm{in subframe 5}}}
\end{array}} \right.}\\
{d(2n + 1) = \left\{ {\begin{array}{*{20}{l}}
{s_1^{({m_1})}(n){c_1}\left( n \right)z_1^{({m_0})}\left( n \right)}&{
{\rm{in subframe 0}}}\\
{s_0^{({m_0})}(n){c_1}\left( n \right)z_1^{({m_1})}\left( n \right)}&{
{\rm{in subframe 5}}}
\end{array}} \right.}
\end{array}\]
其中，
\[\begin{array}{l}
{m_0} = m'\bmod 31\\
{m_1} = \left( {
{m_0} + \left\lfloor {
{
{m'} \mathord{\left/
{\vphantom {
{m'} {31}}} \right.
\kern-\nulldelimiterspace} {31}}} \right\rfloor + 1} \right)\bmod 31\\
\begin{array}{*{20}{c}}
{m' = N_{
{\rm{ID}}}^{
{\rm{(1)}}} + {
{q(q + 1)} \mathord{\left/
{\vphantom {
{q(q + 1)} 2}} \right.
\kern-\nulldelimiterspace} 2},}&{q = \left\lfloor {\frac{
{N_{
{\rm{ID}}}^{
{\rm{(1)}}} + {
{q'(q' + 1)} \mathord{\left/
{\vphantom {
{q'(q' + 1)} 2}} \right.
\kern-\nulldelimiterspace} 2}}}{
{30}}} \right\rfloor ,}&{q' = \left\lfloor {
{
{N_{
{\rm{ID}}}^{
{\rm{(1)}}}} \mathord{\left/
{\vphantom {
{N_{
{\rm{ID}}}^{
{\rm{(1)}}}} {30}}} \right.
\kern-\nulldelimiterspace} {30}}} \right\rfloor }
\end{array}
\end{array}\]
序列\(s_0^{({m_0})}(n)\)和\(s_1^{({m_1})}(n)\)是m序列\(\tilde s(n)\)的循环位移
\[\begin{array}{l}
s_0^{({m_0})}(n) = \tilde s\left( {(n + {m_0})\bmod 31} \right)\\
s_1^{({m_1})}(n) = \tilde s\left( {(n + {m_1})\bmod 31} \right)
\end{array}\]
其中，m序列\(\tilde s(i) = 1 - 2x(i)\)
\[x(\bar i + 5) = \left( {x(\bar i + 2) + x(\bar i)} \right)\bmod 2,{\rm{ }}0 \le \bar i \le 25\]
初始状态为\(\begin{array}{*{20}{c}}
{x(0) = 0,}&{x(1) = 0,}&{x(2) = 0,}&{x(3) = 0,}&{x(4) = 1}
\end{array}\)
讯享网PN_gen = commsrc.pn('GenPoly', [1 0 0 1 0 1], ... 'InitialStates', [1 0 0 0 0], ... 'Shift', 0, ... 'NumBitsOut', 31); PN_seq_temp = generate(PN_gen).'; PN_seq = 1-2*PN_seq_temp;
两个扰码序列\({c_0}(n)\)和\({c_1}(n)\)依赖与主同步信号，由m序列\(\tilde c(n)\)循环移位得到
\[\begin{array}{l}
{c_0}(n) = \tilde c((n + N_{
{\rm{ID}}}^{(2)})\bmod 31)\\
{c_1}(n) = \tilde c((n + N_{
{\rm{ID}}}^{(2)} + 3)\bmod 31)
\end{array}\]
其中，\(\tilde c(i) = 1 - 2x(i)\)为
\[x(\bar i + 5) = \left( {x(\bar i + 3) + x(\bar i)} \right)\bmod 2{\rm{, }}0 \le \bar i \le 25\]
初始状态为\(\begin{array}{*{20}{c}}
{x(0) = 0,}&{x(1) = 0,}&{x(2) = 0,}&{x(3) = 0,}&{x(4) = 1}
\end{array}\)
两个扰码序列\(z_1^{({m_0})}(n)\)和\(z_1^{({m_1})}(n)\)由m序列\(\tilde z(n)\)循环位移得到
\[z_1^{({m_0})}(n) = \tilde z((n + ({m_0}\bmod 8))\bmod 31)\]
\[z_1^{({m_1})}(n) = \tilde z((n + ({m_1}\bmod 8))\bmod 31)\]
同理，有\(\tilde z(i) = 1 - 2x(i)\)，
\[x(\bar i + 5) = \left( {x(\bar i + 4) + x(\bar i + 2) + x(\bar i + 1) + x(\bar i)} \right)\bmod 2{\rm{, }}0 \le \bar i \le 25\]
初始状态为\(\begin{array}{*{20}{c}}
{x(0) = 0,}&{x(1) = 0,}&{x(2) = 0,}&{x(3) = 0,}&{x(4) = 1}
\end{array}\)
SC_gen1 = commsrc.pn('GenPoly', [1 0 1 0 0 1], ... 'InitialStates', [1 0 0 0 0], ... 'Shift', 0, ... 'NumBitsOut', 31); SC_seq1_temp = generate(SC_gen1).'; SC_seq1 = 1-2*SC_seq1_temp; SC_gen2 = commsrc.pn('GenPoly', [1 1 0 1 1 1], ... 'InitialStates', [1 0 0 0 0], ... 'Shift', 0, ... 'NumBitsOut', 31); SC_seq2_temp = generate(SC_gen2).'; SC_seq2 = 1-2*SC_seq2_temp; SecSync = zeros(62,1); for n=0:30 switch subframe case 1 SecSync(2*n+1) = PN_seq(mod(n+m0,31)+1).*SC_seq1(mod(n+NID2, 31)+1); SecSync(2*n+2) = PN_seq(mod(n+m1,31)+1).*SC_seq1(mod(n+NID2+3,31)+1).*SC_seq2(mod(n+mod(m0,8),31)+1); case 6 SecSync(2*n+1) = PN_seq(mod(n+m1,31)+1).*SC_seq1(mod(n+NID2, 31)+1); SecSync(2*n+2) = PN_seq(mod(n+m0,31)+1).*SC_seq1(mod(n+NID2+3,31)+1).*SC_seq2(mod(n+mod(m1,8),31)+1); otherwise end end辅同步信号映射到资源块
\[\begin{array}{c}
{a_{k,l}} = d\left( n \right),{\rm{ }}n = 0,...,61\\
k = n - 31 + \frac{
{N_{
{\rm{RB}}}^{
{\rm{DL}}}N_{
{\rm{sc}}}^{
{\rm{RB}}}}}{2}\\
l = \left\{ {\begin{array}{*{20}{l}}
{N_{
{\rm{symb}}}^{
{\rm{DL}}} - 2}&{
{\rm{in slots 0 and 10}}}&{
{\rm{for frame structure type 1}}}\\
{N_{
{\rm{symb}}}^{
{\rm{DL}}} - 1}&{
{\rm{in slots 1 and 11}}}&{
{\rm{for frame structure type 2}}}
\end{array}} \right.
\end{array}\]
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