CN100361419C - A space-time trellis code (STTC) construction method - Google Patents

Abstract

The present invention provides a space-time trellis code (STTC) construction method which makes a matrix (called as an error matrix subsequently) obtained by the subtraction of the output of different paths which are emitted from the same state become an upper triangular matrix through constructing specific code words, and neither of diagonal elements is zero. Consequently, the error matrix is in full rank, namely full mark collection gain is obtained. Then, the optimum code with the maximum coding gain is searched from codes of the full mark collection gain. The present invention is suitable for constructing space-time trellis codes of any antenna number. The trellis codes which are searched according to the space-time trellis code (STTC) construction method also have larger coding gain. The space-time trellis codes which adopt the space-time trellis code (STTC) construction method for constructing a plurality of antennae have the characteristics of small operand, high search speed and easy realization.

Description

A kind of building method of space-time grid code

Technical field

The invention belongs to wireless communication technology, it is particularly related to the Space Time Coding technology in the wireless communication system.

Background technology:

In radio communication, because multipath effect will produce decline during signal process wireless channel.The multi-antenna diversity technology more and more is subject to people's attention as a kind of effective anti-fading technology.But the multi-antenna receive diversity technology only is fit to the base station to be used, owing to be subjected to many-sided restrictions such as volume, price and battery capacity, makes that the employing reception diversity technology is feasible hardly on down channel for portable terminal.Alamouti is at [1.Siavash M.Alamouti, " A Simple Transmit Diversity Technique forWireless Communications ", IEEE Journal on Select Areas in Communications, VOL.16, NO.8, OCTOBER1998.] propose a kind of simple transmit diversity techniques in, make transmit diversity techniques become the emphasis of down channel diversity technique.When sky on the basis of delay diversity, people such as Tarokh are at [2.Vahid Tarokh, Nambi Seshadri, A.R.Calderbank, " Space-time Codes for High Data Rate Wireless Communication:Performance Criterion and CodeConstruction ", IEEE Transactions on Information Theory, VOL.44, NO.2, MARCH 1998.] in notion based on the space-time grid code of transmit diversity has been proposed, and provided interpretational criteria---the determinant criterion and the order criterion of space-time grid code performance, become the focus of communication code area research at the grid code of these two criterion design performance excellences.Space-time grid code is a kind of combined optimization at coding, modulation, transmit diversity and the receive diversity of MIMO (multiple-input and multiple-output) channel, and the system of its transmitting terminal realizes block diagram such as Fig. 1.Grid code can obtain maximum diversity gain and coding gain, the grid code of best performance is to obtain by the method for searching for, and very huge for the search volume of the grid code of big antenna number, more than four antennas, the generator matrix search volume of the grid code of QPSK modulation is 4 at least ³², therefore, very big for the operand of the design of the space-time grid code of many antennas.

Summary of the invention:

The building method that the purpose of this invention is to provide a kind of space-time grid code adopts the space-time grid code of the many antennas of this method construct, has that operand is little, the characteristics of easy realization.

This paper then proposes a kind of grid code at any antenna number at this problem, simplifies the method for search volume.

In order to describe content of the present invention easily, at first make symbol definition:

1. number of transmit antennas n _TExpression, use the phase shift keying modulation system (be called for short: MPSK), b represents the bit number of the binary message of each the symbol correspondence after the phase shift keying modulation, then 2 ^b=M, M represent the size of constellation set in the modulation system;

The definition Ω represent (0,1 ..., 2 ^b-1) combination of arranging in any order, for example for QPSK, the size of set omega is $P_4^4=24;$

3. our purpose of search is to find out the output of all state transitions, and all these outputs can be arranged in following form:

Matrix is state-transition matrix Y above the definition, and it can regard the matrix of a three-dimensional as, if the sequence in every round bracket is regarded as a group, and certain element y then _{I, j, k}Subscript i represent the row at this element place; J represents the row (being current input) at this element place, and k represents the position in the group of this element under it, $i=\mathrm{0,1},\·\·\·2^{b(n_T-1)}-1;$ j＝0，1，…，2 ^b-1；k＝0，1，…，n _T-1。This matrix can be like this corresponding to the grid map of grid code state transitions: the line display initial state of matrix, matrix column is represented current input, each group element is then united and represented the output sequence that obtains under the condition of given initial state and current input; Then this sequence is distributed to n in order _TIndividual antenna is by n _TIndividual antenna is launched sequence.For example initial state is S _i, the current j that is input as, the then current (y that is output as of encoder _{I, j, 0}, y _{I, j, 1}..., y _{I, j, nT-1}), the element in this group output is mapped to constellation point respectively after, pass through n in order _TIndividual antenna is launched.Fig. 2 has provided the matrix Y of triantennary and the corresponding relation between the grid map.

Definition computing mod (x, y) expression integer x is divided exactly the remainder with integer y gained;

5.[x/y] expression integer x is divided by the merchant of integer y, its round numbers part;

6.c (y) expression integer y is to the mapping of constellation of complex point;

7.f _b(x) expression 2 ^bSystem is counted the mapping of x to binary number, becomes the binary number of b position after the mapping.

The invention provides a kind of building method of space-time grid code, it is characterized in that adopting following code word search step and coding step:

Described code word search step comprises following step:

Step 1: initialization

Put circulation indexed variable s=0, determine number of transmit antennas n _T, and modulation system, just can determine the value that the bit of the binary message of each the symbol correspondence after phase shift keying is modulated counts b by modulation system;

Step 2: determine and the unique corresponding matrix X of the state-transition matrix Y of code word, can generate the state-transition matrix Y of a space-time grid code, the expression formula of Y according to such X:

Choose one group of vector ${\stackrel{\‾}{x}}_0,{\stackrel{\‾}{x}}_1,\·\·\·,{\stackrel{\‾}{x}}_{n_T-1}\∈\mathrm{\Ω},$ (Ω represent (0,1 ..., 2 ^b-1) combination of arranging in any order) structural matrix then:

Because the size of Ω is 2 ^b, X is n _TOK, find X one total (2 from the expression formula of top X ^b) ^NTPlant possible situation, the search volume of expression space-time grid code is (2 ^b) ^NT

Step 3: determine first elements of all groups of code word state-transition matrix corpse according to the matrix X that determines in the step 2, their expressions are through the encode output of back first antenna of space-time grid;

Element y among the order matrix Y _{I, j, 0}=x _{0, j} $i=\mathrm{0,1},\·\·\·2^{b(n_T-1)}-1,$ j＝0，1，…，2 ^b-1；

So just determined first element of all groups among the matrix Y, guaranteed in the state transition diagram of space-time grid code (as shown in Figure 2) simultaneously when identical initial state arrives different state of termination, the output difference on first antenna;

Step 4: determine other elements except that first element of all groups of code word state-transition matrix Y according to the matrix X that determines in the step 2, when so just having determined that institute might a state transitions takes place, through the output on the different antennae behind the space-time grid coding;

Element y among the order matrix Y _{I, j, k}=x _{K, p}Wherein

p＝[mod(i，2 ^bk)/2 ^b(k-1)]， $i=\mathrm{0,1},\·\·\·2^{b(n_T-1)}-1,$ J=0,1 ..., 2 ^b-1, k=1 ..., n _T-1 (special oeprator is wherein seen symbol definition 4,5)

At this moment just determined all elements of Y, note state-transition matrix Y at this moment is Y _sThis step has guaranteed that the grid code of structure is a upper triangular matrix from the pairing mistake matrix in the different paths of same state;

Step 5: the coding gain that calculates the space-time grid code of this search

Get all integers that satisfy following relation to (l, m): 0＜l＜2 ^b, 0≤m≤l, calculate each to (l, m) pairing $\underset{q=0}{\overset{n_T-1}{\mathrm{\Π}}}|c\left(x_{q,l}\right)-c\left(x_{q,m}\right)|,$ (seeing symbol definition 6) also got minimum one and is designated as J _s

So draw the coding gain J of the code word of search this time _s

Put s=s+1,

Repeating step 2～5 can obtain (2 ^b) ^NTIndividual different space-time grid code coding gain J _s, wherein $s=\mathrm{0,1},\·\·\·,{(2^b!)}^{n_T},$ Repeating step 2～5 o'clock matrix X chooses and can not repeat;

Step 6: the state-transition matrix Y that determines optimum space-time grid code correspondence _s

Find out maximum J _sBe designated as J _S0And at this moment corresponding Y _S0, Y then _S0Be the state-transition matrix of the optimum code that searches;

Step 7: the state-transition matrix Y of the space-time grid code of the optimum that obtains according to step 6 _S0, obtain the generator matrix G of optimum space-time grid code _S0:

$\stackrel{\‾}{g_i}=\left\{\begin{array}{c}{[f_b\left(y_{0,2^{b-i-1},0}\right),f_b\left(y_{0,2^{b-i-1},1}\right),\·\·\·,f_b\left(y_{0,2^{b-i-1},n_T-1}\right)]}^T,i=\mathrm{0,1},\·\·\·,b-1\\ {[f_b\left(y_{2^{b(n_T-1)-i-1},\mathrm{0,0}}\right),f_b\left(y_{2^{b(n_T-1)-i-1},\mathrm{0,1}}\right),\·\·\·,f_b\left(y_{2^{b(n_T-1)-i-1},0,n_T-1}\right)]}^T,i=b,b+1,\·\·\·,{\mathrm{bn}}_T-1\end{array}\right.$

(f _b(x) see symbol definition 7)

Order $G_{s_0}=\left[\begin{array}{cccc}{\stackrel{\‾}{g}}_0& {\stackrel{\‾}{g}}_1& \·\·\·& {\stackrel{\‾}{g}}_{{\mathrm{bn}}_T-1}\end{array}\right];$ G then _S0The generator matrix of the space-time grid code of the optimum that searches exactly;

Step 1～7 are the code word search step, and its programming realization flow figure as shown in Figure 6;

Described coding step is:

Step 8: according to the generator matrix G of space-time grid code _S0Carry out Space Time Coding:

Obtain the generator matrix G of optimum code _S0After, the grid code coding method is described below: if the encoder current state is S _i, the binary form of i is shown m ₀, m ₁..., m _{B (nT-2)-1}, the binary form of current input is shown u ₀, u ₁..., u _B-1, then the binary vector form of output this moment is: $V=[u_0,u_1,\·\·\·,u_{b-1},m_0,m_1,\·\·\·,m_{b(n_T-2)-1}]*{G_{s_0}}^T\mathrm{mod}\left(2\right),$ The columns of V is bn _T, V can be expressed as: $V=[v_0,v_1,\·\·\·,v_{{\mathrm{bn}}_T-1}],$ Can obtain the constellation symbol of space-time grid coding output thus:

C (v ₀, v ₁..., v _B-1), c (v _B+0, v _B+1..., v _B+b-1) ..., c (v _{B (nT-1)+0}, v _{B (nT-1)+1}..., v _{B (nT-1)+b-1}) ((v wherein ₀, v ₁..., v _B-1), (v _B+0, v _B+1..., v _B+b-1) ..., (v _{B (nT-1)+0}, v _{B (nT-1)+1}..., v _{B (nT-1)+b-1}) represent n respectively _TThe binary number of individual b position), these constellation symbol are mapped to n respectively _TThe root antenna is launched; Suppose that the new state that arrives is S _{I '}, then the binary form of the sequence number i ' of this new state is shown: [u ₀, u ₁..., u _B-1, m ₀, m ₁..., m _{B (nT-2)-1}], so just finished the process of whole Space Time Coding.

Design the hardware of encoder according to coding rule of the present invention and generator matrix easily and realize (its block diagram as shown in Figure 3); Can use the viterbi interpretation method during decoding.

Characteristics of the present invention:

The search volume of optimum code of grid code that the present invention is directed to big number of antennas is too huge, the present operational speed of a computer is difficult to realize that this problem has proposed under a kind of accurate flat fading channel, be applicable to the simplification searching method of the space-time grid code of any number of antennas, the basic ideas of this method are the specific code words of structure, make that subtracting each other the matrix (hereinafter referred to as the mistake matrix) that obtains from the output in the different paths of same state is upper triangular matrix, and diagonal entry is non-vanishing entirely, thereby mistake matrix full rank--promptly obtain the full diversity gain, and then in the sign indicating number of these full diversity gains, search optimum code with maximum coding gain.The superiority of this method maximum is that the search volume is less, and computing is simple, and is as follows with the searching method contrast of the traditional total space:

● suppose 2 ^bConstellation point number in the modulation system that expression is used, n _TThe expression number of transmit antennas needs the generator matrix G that searches for to have 2 in the conventional method ^{(bnT) 2}Individual, the number of the G that this method need be searched for is (2 ^b) ^NT, can find, along with n _TIncrease, the former than the latter increase many rapidly.

● in the search procedure, at each selected generator matrix G, suppose that a code word all launches (afterbody that the encoder buffer status is made zero of ignoring is imported) by l symbol time, conventional method need be at C ₂₁ ²In the right mistake matrix of possible difference input do and ask the computing of sum of ranks determinant; And this numeral only is C in this method _2b ²

● in the conventional method, need ask the sum of ranks determinant at each mistake matrix, and the mistake matrix that this method is searched for all is a full rank, and is that therefore the calculating of its determinant only need be to its diagonal entry quadrature for upper triangular matrix.

The present invention is to provide a kind of building method of space-time grid code, adopt the space-time grid code of the many antennas of this method construct, have the advantages that operand is little, search speed fast, realize easily.The grid code that searches out of this method also has bigger coding gain in addition, and Fig. 4,5 has provided this method performance curve that the method for delay diversity is compared during with simple sky at the code word of 4,5 transmit antennas search respectively.

Description of drawings:

Fig. 1 is to use the realization block diagram of transmitting terminal of the multiaerial system of space-time grid code

Fig. 2 is the corresponding relation schematic diagram of the matrix Y of definition in 4 corresponding to the grid code grid map

Wherein, on grid map, arrange the arrival state for some given initial states according to the input size sequence, for example initial state is S ₀It is current that to be input as 00 o'clock arrival state be S topmost ₀, the state that is input as arrival in 01 o'clock is ensuing S ₁, be input as the state that arrived at 10 o'clock and be under S ₂, the state that arrives when being input as 11 is nethermost S ₃

Fig. 3 realizes block diagram by the hardware of the encoder of the generator matrix G decision of the optimum code that searches

D wherein represents register, u ₀... u _B-1The binary number of representing current input, v ₀, v ₁..., v _BnT-1The binary system output sequence that the presentation code device is current.Certain element g among the G _{C, d}For the breakpoint place at its place of null representation disconnects g _{C, d}The breakpoint place that is 1 its place of expression connects.

Fig. 4 is the performance curve comparison diagram of the method for space-time grid code when utilizing the 4 transmit antennas QPSK modulation that this method searches out and 4 antenna delay diversities.

Fig. 5 is the performance curve comparison diagram of the delay diversity method of space-time grid code when utilizing the QPSK modulation of 5 transmit antennas that this method searches out and 5 antennas.

Fig. 6 is the flow chart (not comprising coding) that the code word search utility is realized.

Embodiment

Provide the grid code generator matrix that utilizes the inventive method search to obtain below at 4,5,6 transmit antennas:

4 transmit antennas:

$G=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& 1& 1\end{array}\right]$

5 transmit antennas:

$G=\left[\begin{array}{cccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\end{array}\right]$

6 transmit antennas:

$G=\left[\begin{array}{cccccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\end{array}\right]$

Claims (1)

1, a kind of building method of space-time grid code is characterized in that adopting following code word search step and coding step:

Described code word search step comprises following step:

Step 1: initialization

Put circulation indexed variable s=0, determine number of transmit antennas n _T, and modulation system, just determined the value that the bit of the binary message of each the symbol correspondence after phase shift keying is modulated counts b by modulation system;

Step 2: determine and the unique corresponding matrix X of code word state-transition matrix Y, generate a code word state-transition matrix Y, the expression formula of Y according to such X:

Choose one group of vector ${\stackrel{\‾}{x}}_0,{\stackrel{\‾}{x}}_1,\·\·\·,{\stackrel{\‾}{x}}_{n_T-1}\∈\mathrm{\Ω},$ Ω represent (0,1 ..., 2 ^b-1) combination of arranging in any order, then structural matrix:

Because the size of Ω is 2 ^b, X is n _TOK, find X one total (2 from the expression formula of top X ^b) ^NTPlant possible situation, the search volume of expression space-time grid code is (2 ^b) ^NT

Step 3: determine first elements of all groups of code word state-transition matrix Y according to the matrix X that determines in the step 2, their expressions are through the encode output of back first antenna of space-time grid;

Element y among the order matrix Y _{I, j, 0}=x _{0, j}I=0,1 ... 2 ^{B (nT-1)-1}, j=0,1 ..., 2 ^b-1;

So just determined first element of all groups among the matrix Y, guaranteed simultaneously in the state transition diagram of space-time grid code when identical initial state arrives different state of termination, the output difference on first antenna;

Step 4: determine other elements except that first element of all groups of code word state-transition matrix Y according to the matrix X that determines in the step 2, when so just having determined that institute might a state transitions takes place, through the output on the different antennae behind the space-time grid coding;

Element y among the order matrix Y _{I, j, k}=x _{K, p}Wherein

p＝[mod(i，2 ^bk)/2 ^b(k-1)]，i＝0，1，…2 ^b(nT-1)-1，j＝0，1，…，2 ^b-1，k＝1，…，n _T-1；

At this moment just determined all elements of Y, note code word state-transition matrix Y at this moment is Y _sThis step has guaranteed that the grid code of structure is a upper triangular matrix from the pairing mistake matrix in the different paths of same state;

Step 5: the coding gain that calculates the space-time grid code of this search

Get all integers that satisfy following relation to (l, m): 0＜l＜2 ^b, 0≤m≤l, calculate each to (l, m) pairing $\underset{q=0}{\overset{n_T-1}{\mathrm{\Π}}}|c\left(x_{q,1}\right)-c\left(x_{q,m}\right)|,$ And get minimum one and be designated as J _s: c (y) expression integer y is to the mapping of constellation of complex point; So draw the coding gain J of the code word of search this time _sPut s=s+1,

Repeating step 2～5 obtains (2 ^b) ^NTIndividual different space-time grid code coding gain J _s, s=0 wherein, 1 ..., (2 ^b) ^NT, repeating step 2～5 o'clock matrix X chooses and can not repeat;

Step 6: determine optimum code word state-transition matrix Y _s

Find out maximum J _sBe designated as J _S0And at this moment corresponding Y _S0, T then _S0Be the code word state-transition matrix of the optimum that searches;

Step 7: the code word state-transition matrix Y of the optimum that obtains according to step 6 _S0, obtain optimum code word generator matrix G _S0:

$\stackrel{\‾}{g_i}=\left\{\begin{array}{c}{[f_b\left(y_{\mathrm{0,}{2}^{b-i-1},0}\right),f_b\left(y_{0,2^{b-i-1},1}\right),\·\·\·,f_b\left(y_{0,2^{b-i-1},n_T-1}\right)]}^T,i=\mathrm{0,1},\·\·\·,b-1\\ {[f_b\left(y_{2^{b(n_T-1)-i-1},\mathrm{0,0}}\right),f_b\left(y_{2^{b(n_T-1)-i-1},\mathrm{0,1}}\right),\·\·\·,f_b\left(y_{2^{b(n_T-1)-i-1},0,n_T-1}\right)]}^T,i=b,b+1,\·\·\·,{\mathrm{bn}}_T-1\end{array}\right.$

f _b(x) expression 2 ^bSystem is counted the mapping of x to binary number, becomes the binary number of b position after the mapping;

Order

G then _S0The code word generator matrix of the optimum that searches exactly;

Step 1～7 are the code word search step;

Described coding step is:

Step 8: according to the code word generator matrix G of optimum _S0Carry out Space Time Coding:

Obtain optimum code word generator matrix G _S0After, the grid code coding method is described below: if the encoder current state is S _i, the binary form of i is shown m ₀, m ₁..., m _{B (nT-2)-1}, the binary form of current input is shown u ₀, u ₁..., u _B-1, then the binary vector form of output this moment is: $V={[u}_0,u_1,\·\·\·,u_{b-1},m_0,m_1,\·\·\·,m_{b(n_T-2)-1}]*{G_{s_0}}^T\mathrm{mod}\left(2\right),$ The columns of V is b _NT, V is expressed as: V=[v ₀, v ₁..., v _BnT-1], mod (2) represents Modulo-two operation, obtains the constellation symbol of space-time grid coding output thus:

C (v ₀, v ₁..., v _B-1), c (v _B+0, v _B+1..., v _B+b-1) ..., c (v _{B (nT-1)+0}, v _{B (nT-1)+1}..., v _{B (nT-1)+b-1}) (v wherein ₀, v ₁..., v _B-1), (v _B+0, v _B+1..., v _B+b-1) ..., (v _{B (nT-1)+0}, v _{B (nT-1)+1}..., v _{B (nT-1)+b-1}) represent n respectively _TThe binary number of individual b position, these constellation symbol are mapped to n respectively _TThe root antenna is launched; Suppose that the new state that arrives is S _{I '}, then the binary form of the sequence number i ' of this new state is shown: [u ₀, u ₁..., u _B-1, m ₀, m ₁..., m _{B (nT-2)-1}], so just finished the process of whole Space Time Coding.

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