CN101826890B - Implementation method of ZC (Zadoff-Chu) sequence in LTE (Long Term Evolution) system - Google Patents

Abstract

The invention provides an implementation method of a ZC (Zadoff-Chu) sequence in an LTE (Long Term Evolution) system. The sequence is calculated by using a recursion mode, i.e. a value after the sequence is obtained by multiplying a value before the sequence by a coefficient, and the value of xq(n) is obtained by multiplying the value of xq(n-1) by a coefficient, wherein the ZC sequence in the LTE system can be any one signal of basic signals of a main synchronizing signal, a random access signal and an upstream reference signal. In the method, a cosine operation each time is converted into a complex multiplication operation, thereby the time of a sine operation and a division is saved and the operand is greatly reduced. In the invention, the symmetry of the ZC sequence can also be utilized, only the value of a front half of the sequence is calculated, and the value of the rear half is obtained according to the symmetry, thereby the operand is further reduced.

Description

The implementation method of ZC sequence in LTE system

Technical field

The present invention relates to mobile communication technology field, particularly relate to the implementation method of ZC sequence in third generation mobile communication long-term evolution system (hereinafter to be referred as LTE).

Background technology

The full name of ZC sequence is Zadoff-Chu sequence, and it belongs to the class in CAZAC sequence (Constant Amplitude Zero Autocorrelation sequences, constant mould and zero autocorrelation sequence).The formula of reduction of the ZC sequence of odd length is:

$\begin{array}{cc}{x}_q\left(n\right)=\exp (-\mathrm{j\πq}\frac{n(n+1)}{N})& n=0,\·\·\·N-1---\left(1\right)\end{array}$

Wherein, N represents sequence length, is odd number, and q represents sequence index.

Because ZC sequence has the characteristic in constant mould and zero auto-correlation region, be therefore widely used in the uplink and downlink system of LTE, as distinctive signal, comprising the baseband signal in master sync signal, accidental access signal and uplink reference signals.

In 3GPP TS36.211-8.4.0 agreement, master sync signal x in LTE system _q(n) be defined as:

$x_q\left(n\right)=\left\{\begin{array}{cc}{e}^{-j\frac{\mathrm{\πqn}(n+1)}{63}}& n=\mathrm{0,1},\·\·\·,30\\ e^{-j\frac{\mathrm{\πq}(n+1)(n+2)}{63}}& n=\mathrm{31,32},\·\·\·,61\end{array}\right.---\left(2\right)$

Wherein the value of q is 25,29 or 34.

Accidental access signal x in LTE system _q(n) be defined as:

$x_q\left(n\right)=e^{-j\frac{\mathrm{\πqn}(n+1)}{N}},0\≤n\≤N-1---\left(3\right)$

Sequence length N=839, the span of q value is: the integer between 1 to 838, occurrence is indicated by high level.

In LTE system, sequence length is greater than or equal to the baseband signal x in 36 uplink reference signals _q(n) be defined as:

$x_q\left(n\right)=e^{-j\frac{\mathrm{\πqn}(n+1)}{N}},0\≤n\≤N-1---\left(4\right)$

Wherein,

the length N of ZC sequence determines that by the sub-carrier number M that distributes to Physical Uplink Shared Channel (N is the largest prime that is less than M), u determine by organizing frequency hopping, span be u ∈ 0,1 ..., 29}, v determines by sequence hopping, span is v ∈ { 0,1}.

From formula 2-4, can find out that they all have the feature of formula 1.If consideration adopts formula 1 to calculate in real system, need so to do cosine and the sinusoidal computing of N time, cosine and sinusoidal computing are a kind of nonlinear computings, cosine repeatedly and sinusoidal computational complexity are very high, are unfavorable for hardware or software realization.Especially for random access leader sequence, length N=839 of this sequence, need to do cosine and the sinusoidal computing of 839 times so, and consuming time very long, such implementation method does not meet LTE system real time and requires high demand.

Summary of the invention

The invention provides the implementation method of ZC sequence in a kind of LTE system, with the recursion mode sequence of calculation, after sequence, a value is multiplied by coefficient Coeff_q by the previous value of sequence and obtains, i.e. x _q(n) value x _q(n-1) value is multiplied by a coefficient Coeff_q and obtains, change cos operation each time into complex multiplication operation in this way, saved the time of sinusoidal computing and division, greatly reduced operand, the present invention also can utilize the symmetry of ZC sequence, the value of sequence of calculation the first half, the value of later half obtains according to sequence symmetry, has further reduced operand.

For reaching above object, in LTE system of the present invention, the realization approach of ZC sequence is, according to the length N of sequence and sequence index value q, calculates the coefficient needing

then with the mode of recursion calculate successively ZC sequence value a little.

Its simplified operation principle is as follows:

$x_q\left(n\right)=e^{-j\frac{\mathrm{\πqn}(n+1)}{N}},0\≤n\≤N-1---\left(5\right)$

Initialization x _q(0)=1

$\begin{array}{c}{x}_q\left(n\right)/x_q(n-1)=e^{-j\frac{\mathrm{\πqn}(n+1)}{N}}/e^{-j\frac{\mathrm{\π}(n-1)n}{N}}\\ =e^{-j\frac{2\mathrm{\πqn}}{N}},1\≤n\≤N-1\end{array}---\left(6\right)$

Order

1≤n≤N-1, initialization a (0)=1

$\begin{array}{c}a\left(n\right)/a(n-1)=e^{-j\frac{2\mathrm{\πqn}}{N}}/e^{-j\frac{2\mathrm{\πq}(n-1)}{N}}\\ =e^{-j\frac{2\mathrm{\πq}}{N}},1\≤n\≤N-1\end{array}$

Order $\mathrm{Coeff}\_q=e^{-j\frac{2\mathrm{\πq}}{N}},$ And then obtain

$a\left(n\right)=a(n-1)\×\mathrm{Coeff}\_q,1\≤n\≤N-1---\left(7\right)$

According to formula 6 and formula 7, and x _q(0)=1, obtains

x _q(n)=x _q(n-1)×a(n),1≤n≤N-1 (8)

Wherein, x={x _q(0), x _q(1) ..., x _q(N-1) } be sequence array, for depositing sequential value, a={a (0), a (1) ..., a (N-1) } and be coefficient array, for depositing coefficient value.

Its concrete operation step is as follows:

According to signal type, determine length N and the sequence index value q of sequence;

To master sync signal, N=63, q=25,29 or 34, is determined by UE;

To accidental access signal, N=839, the span of q value is: the integer between 1 to 838, occurrence is indicated by high level;

Baseband signal to uplink reference signals, N determines (N is the largest prime that is less than M) by the sub-carrier number M that distributes to Physical Uplink Shared Channel, q value is determined by group frequency hopping and sequence hopping.

According to the length N of sequence and sequence index value q, calculate

Initialization a (0)=1, utilize formula a (n)=a (n-1) * Coeff_q, 1≤n≤N-1, calculates a (1)=a (0) * Coeff_q, a (2)=a (1) * Coeff_q, the rest may be inferred, until calculate a (N-1).

Initialization x _q(0)=1, utilizes formula x _q(n)=x _q(n-1) * a (n), 1≤n≤N-1, calculates x _q(1)=x _q(0) * a (1), x _q(2)=x _q(1) * a (2), the rest may be inferred, until calculate x _q(N-1).

Can further utilize the symmetry of ZC sequence, simplify the value of (N+1)/2 point before calculating, then according to the symmetry of ZC sequence, obtain whole sequential value

Symmetry proof is as follows:

$\begin{array}{c}\frac{x_q\left(n\right)}{x_q(N-1-n)}=\frac{e^{-j\frac{\mathrm{\πqn}(n+1)}{N}}}{e^{-j\frac{\mathrm{\πq}(N-1-n)(N-n)}{N}}}=e^{j\frac{\mathrm{\πq}(N^2-\mathrm{Nn}-N+n-\mathrm{Nn}+n^2-n^2-n)}{N}}\\ =e^{j\frac{\mathrm{\πq}(N^2-2\mathrm{Nn}-N)}{N}=e^{\mathrm{j\πq}(N-2n-1)}}\end{array}$

Analyze: no matter what value n gets, and 2n is even number; N is odd number, and N-1 is even number so; So N-2n-1 is even number, so e ^{j π q (N-2n-1)}be constantly equal to 1.

Therefore no matter why sequence index q is worth, x _q(n) all there is symmetry, be expressed as x _q(n)=x _q(N-1-n).

In addition, due to the generation formula 2 of master sync signal and the fundamental formular (formula 1) of ZC sequence difference slightly, the sequence length of the baseband signal of accidental access signal and uplink reference signals is all N, and the sequence length of master sync signal is N-1, thereby it is slightly variant that master sync signal symmetry is represented, its symmetry is expressed as x _q(n)=x _q(N-2-n).

Wherein, x={x _q(0), x _q(1) ..., x _q(N-1) } be sequence array, for depositing sequential value, a={a (0), a (1) ..., a (N-1) } and be coefficient array, for depositing coefficient value.

By the method (formula 8) that the method defining in agreement (formula 1) and the present invention propose, carry out complexity comparison, as table 1.

Table 1

By the method that the present invention proposes, can greatly reduce as can be seen from Table 1 the operation times of cosine, sine and real number division, especially N value is larger, reduces more obvious.While considering that software is realized, the instruction cycle that the instruction cycle that complex multiplication needs needs than cosine calculating is few, has also saved the time of real number division and sinusoidal computing with formula 8 simultaneously, greatly reduces the complexity of computing.

Accompanying drawing explanation

Fig. 1 is ZC sequence recursion implementation method;

Fig. 2 is the implementation method of utilizing the symmetric recursive algorithm of ZC sequence.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the implementation method of ZC sequence in a kind of LTE system of the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.

ZC sequence recursion implementation method in a kind of LTE system of the present invention, as shown in Figure 1, it comprises the steps:

Step 101: determine length N and the sequence index value q of sequence according to different signal types, in the present embodiment, signal type is master sync signal, value N=63, q=25;

Optionally, as another kind of embodiment, signal type is accidental access signal, N=839, and the span of q value is: the integer between 1 to 838, occurrence is indicated by high level;

Optionally, as another kind of embodiment, the baseband signal that signal type is uplink reference signals, N is definite by the sub-carrier number M that distributes to Physical Uplink Shared Channel, and q value is determined by group frequency hopping and sequence hopping;

Wherein, during baseband signal that signal type is uplink reference signals, N is the largest prime that is less than M.

Step 102: determine length N and the sequence index value q of sequence according to signal type, design factor $\mathrm{Coeff}\_q=e^{-j\frac{2\mathrm{\πq}}{N}};$

Step 103: initialization a (0)=1, utilize formula a (n)=a (n-1) * Coeff_q, 1≤n≤N-1, calculates a (1)=a (0) * Coeff_q, a (2)=a (1) * Coeff_q, the rest may be inferred, until calculate a (N-1);

Step 104: initialization x _q(0)=1, utilizes formula x _q(n)=x _q(n-1) * a (n), 1≤n≤N-1, calculates x _q(1)=x _q(0) * a (1), x _q(2)=x _q(1) * a (2), the rest may be inferred, until calculate x _q(N-1).

Optionally, as another kind of embodiment, step 103 to step 104 can be taked an a (n) and an x _q(n) account form one to one.

Wherein, N represents sequence length, is odd number, and q represents sequence index value, x={x _q(0), x _q(1) ..., x _q(N-1) } be sequence array, for depositing sequential value, a={a (0), a (1) ..., a (N-1) } and be coefficient array, for depositing coefficient value.

In a kind of LTE system of the present invention, utilize symmetric ZC sequence implementation method, as shown in Figure 2, it comprises the steps:

Step 201: determine length N and the sequence index value q of sequence according to different signal types, in the present embodiment, signal type is master sync signal, value N=63, q=25;

Optionally, as another kind of embodiment, signal type is accidental access signal, N=839, and the span of q value is: the integer between 1 to 838, occurrence is indicated by high level;

Optionally, as another kind of embodiment, the baseband signal that signal type is uplink reference signals, N is definite by the sub-carrier number M that distributes to Physical Uplink Shared Channel, and q value is determined by group frequency hopping and sequence hopping;

Wherein, during baseband signal that signal type is uplink reference signals, N is the largest prime that is less than M.

Step 202: according to the length N of sequence and sequence index value q, calculate

Step 203: initialization a (0)=1, utilize formula a (n)=a (n-1) * Coeff_q to calculate a (1)=a (0) * Coeff_q, a (2)=a (1) * Coeff_q, the rest may be inferred, until calculate a ((N-1)/2)

Step 204: initialization x _q(0)=1, utilizes formula x _q(n)=x _q(n-1) * a (n), calculates x _q(1)=x _q(0) * a (1), x _q(2)=x _q(1) * a (2), the rest may be inferred, until calculate x _q((N-1) 2)

Optionally, as another kind of embodiment, step 203 to step 204 can be taked an a (n) and an x _q(n) account form one to one.

Step 205: utilize symmetry, obtain x _q((N-1) 2+1) ... x _q(N-1).

Wherein, when signal type is the baseband signal of accidental access signal and uplink reference signals, symmetry calculating formula is x _q(n)=x _q(N-1-n); When signal type is master sync signal, symmetry calculating formula is x _q(n)=x _q(N-2-n).

Wherein, N represents sequence length, is odd number, and q represents sequence index value, x={x _q(0), x _q(1) ..., x _q(N-1) } be sequence array, for depositing sequential value, a={a (0), a (1) ..., a (N-1) } and be coefficient array, for depositing coefficient value.

It will be apparent to those skilled in the art that and understand, system and method for the present invention for above embodiment only for the present invention is described, and be not limited to the present invention.Although effectively described the present invention by embodiment, one skilled in the art will appreciate that the present invention exists many variations and do not depart from spirit of the present invention.In the situation that not deviating from spirit of the present invention and essence thereof, those skilled in the art be when can make various corresponding changes or distortion according to the inventive method, but these corresponding change or within distortion all should be included in protection scope of the present invention.

Claims (7)

1. In 1.LTE system, the implementation method of ZC sequence, is characterized in that, with the recursion mode sequence of calculation, after sequence, a value is multiplied by coefficient Coeff_q by the previous value of sequence and obtains, and concrete steps are:

   According to signal type, determine length N and the sequence index value q of sequence;

   Design factor $\mathrm{Coeff}\_q=e^{-j\frac{2\mathrm{\πq}}{N}};$

   Initialization a (0)=1, utilize formula a (n)=a (n-1) * Coeff_q, 1≤n≤N-1, calculates a (1)=a (0) * Coeff_q, a (2)=a (1) * Coeff_q, the rest may be inferred, until calculate a (N-1);

   Initialization x _q(0)=1, utilizes formula x _q(n)=x _q(n-1) * a (n), 1≤n≤N-1, calculates x _q(1)=x _q(0) * a (1), x _q(2)=x _q(1) * a (2), the rest may be inferred, until calculate x _q(N-1);

   Wherein, N represents sequence length, is odd number, and q represents sequence index value, x={x _q(0), x _q(1) ..., x _q(N-1) } be sequence array, for depositing sequential value, a={a (0), a (1) ..., a (N-1) } and be coefficient array, for depositing coefficient value.
2. 2. the implementation method of ZC sequence in LTE system as claimed in claim 1, is characterized in that, described signal type refers to any one signal in the baseband signal in master sync signal, accidental access signal and the uplink reference signals in LTE system.
3. 3. the implementation method of ZC sequence in LTE system as claimed in claim 1 or 2, is characterized in that, when described signal type refers to the master sync signal in LTE system, its parameter N=63, q=25,29 or 34, q by UE, determined.
4. 4. the implementation method of ZC sequence in LTE system as claimed in claim 1 or 2, it is characterized in that, when described signal type refers to the accidental access signal in LTE system, its parameter N=839, the span of q value is: the integer between 1 to 838, occurrence is indicated by high level.
5. 5. the implementation method of ZC sequence in LTE system as claimed in claim 1 or 2, it is characterized in that, when described signal type refers to the baseband signal in the uplink reference signals in LTE system, its parameter N is definite by the sub-carrier number M that distributes to Physical Uplink Shared Channel, and q value is determined by group frequency hopping and sequence hopping.
6. 6. the implementation method of ZC sequence in LTE system as claimed in claim 5, is characterized in that, described parameter N determines that by the sub-carrier number M that distributes to Physical Uplink Shared Channel method is that N is the largest prime that is less than M.
7. 7. the implementation method of ZC sequence in the LTE system as described in claim 1-2,6 any one, is characterized in that, utilize the symmetry of ZC sequence, before calculating, the value of (N+1)/2 point, then according to the symmetry of ZC sequence, obtains whole sequential value;

   Wherein, when signal type is the baseband signal of accidental access signal and uplink reference signals, symmetry calculating formula is x _q(n)=x _q(N-1-n); When signal type is master sync signal, symmetry calculating formula is x _q(n)=x _q(N-2-n);

   Wherein, N represents sequence length, is odd number, and q represents sequence index value, 1≤n≤N-1.

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