WO2004054161A1

WO2004054161A1 - A coding method of space-time trellis codes

Info

Publication number: WO2004054161A1
Application number: PCT/CN2002/000873
Authority: WO
Inventors: Yi Li; Hanyu Li; Yonghui Li; Yongsheng Zhang
Original assignee: Linkair Communications,Inc.
Priority date: 2002-12-06
Filing date: 2002-12-06
Publication date: 2004-06-24
Also published as: AU2002354129A1; CN1615604A

Abstract

The present invention provides a space-time trellis coded method comprising: at transmitting terminal: inputing signal bits are encoded using a space-time trellis code; modulating the coded data; sending modulated signals upon transmitting antenna to the communication channel; at receiving terminal: receiving antennas receive the signals upon the communication channel from said transimitting terminal; characterised: said space-time trellis code has symmetric structure, in searching said space-time trellis code must accord with symmetric configuration condition, said space-time trellis code having symmetric configuration is the best among all the corresponding space-time trellis code. Said space-time trellis code can attain the completely diversity gain and the maximal coding gain simultaneous.

Description

Space-time grid code encoding method

Technical field

The present invention belongs to the field of wireless communication technology, and particularly relates to coding under a Rayleigh fast fading channel, and in particular to a space-time trellis code coding method.

Background technique

As we all know, in a fading channel, the fading of the signal will seriously degrade the performance of the system. The most effective way to overcome fading is to use diversity technology. Space-time coding ^[1 ^'2' ^3] can be obtained at the same time space-time diversity gain and coding gain, to overcome the effects of fading and improve the reliability of the transmission, improve the utilization of spectrum have important implications for the system. References [1] and [2] have studied the design of space-time block codes in detail. It is characterized by its ability to obtain full diversity gain and simple decoding. Reference [3] pointed out that under the condition of the same data transmission rate and the same diversity gain, the performance of space-time block code cannot be better than that of space-time trellis code. This paper systematically studies the various channel conditions (including The design of space-time trellis codes for statically fading Rayleigh or Rice channels and fast-fading Rayleigh channels, etc., gives the corresponding design criteria, and gives the 4-state, 8-state, and quasi-static fading channel conditions. 16-state spatio-temporal trellis codes. The results given in this article are designed by hand. It can be proved that they can obtain full diversity gain but cannot guarantee the maximum coding gain. For this reason, there are many literatures, such as [4], [5], and [6], which are devoted to the design of optimal spatio-temporal trellis codes under quasi-static fading channel conditions, and few studies on fast fading Rayleigh channel conditions Design of Optimal Spatio-Temporal Grid Codes. These documents are dedicated to the study of spatio-temporal trellis codes under quasi-static fading Rayleigh channels because this channel environment is worse than that of fast-fading Rayleigh channels. However, when channel interleaving is long enough, quasi-static fading is similar For independent fast fading, channel interleaving will be used in practical systems. Therefore, it is necessary to research and develop the design of spatio-temporal trellis code under the fast fading Rayleigh channel.

Summary of the Invention

An object of the present invention is to provide a spatio-temporal trellis code encoding method, and in particular, a symmetric structure of the spatio-temporal trellis code encoding method is proposed for the 8-state spatio-temporal trellis code. The trellis code can get the maximum coding gain while obtaining the full diversity gain.

The technical solution of the present invention is:

A spatio-temporal trellis code encoding method includes:

Originator: encode the input bits with space-time trellis code; modulate the encoded data; transmit the modulated signal to the channel via the transmitting antenna;

Receiving end: a receiving antenna receives a signal from the transmitting end in the channel;

It is characterized by:

The spatio-temporal trellis code is a spatio-temporal trellis code having a symmetric structure. The search of the spatio-temporal trellis code must satisfy the constraint condition of the symmetric structure, and the spatio-temporal trellis code having a symmetric structure is in all The corresponding state is optimal in the space-time grid code.

The space-time grid code is an 8-state space-time grid code, and the first four rows of elements of the code matrix of the 8-state space-time grid code are different, and the last four rows of elements are also different.

The spatio-temporal trellis code with a symmetric structure may be: an 8-state spatio-temporal trellis code with a symmetric structure.

The spatio-temporal trellis code with symmetric structure refers to an 8-state spatio-temporal trellis code with symmetric structure; under the constraint of the symmetric structure, a non-linear 8-state spatio-temporal trellis code with d _lin = 48 can be searched, and The searched non-linear 8-state spatiotemporal grid code with d _min = 48 described above is the best among all 8-state codes.

The code matrix of the 8-state spatio-temporal trellis code has a mirror-symmetric structure; and

If you use {a ₀₀ , a ₀₁ , · ■ ·, a. ₃ , a ₁₀ , an _n , a _13,. · ·, A ₇₀ , a ₇₁ , ..., a ₇ J represent 32 elements in the code matrix, then the following equations exist:

α _χγ = a _ _{x) {3} _ _y) x = 4,5,6,7 y = 0,1,2,3.

In the method of the present invention, the steps include: establishing two state sequence data files; wherein: each sequence in the first data file represents two truncated codewords, and the two truncated codewords are at time t and t + The state at time 2 is the same, and the state at time t + 1 is different;

There are 56 sequences in the first data file, and each sequence in the second data file The states of the two truncated codewords in the column are the same at time f and time ί + 3, and the states at time +1 and t + 1 are different. There are 1280 sequences in this data file;

When searching for a code: For the 8-state space-time grid code of the symmetric structure defined by the equation, only the first 16 elements of the 32 elements in the code matrix can be designed, and the last 16 elements are The above equation is obtained, and the first 16 elements must be different, that is, satisfy the condition 1, so that a. . There are 16 possible values, aw has 15 possibilities, and so on;

Each element is tested according to the sequence in the data file to see if the two "codewords" corresponding to the sequence meet the specified minimum product distance d _min . If it does not meet, the subsequent elements will not be generated any more, and It is to change the previous element to generate a new "codeword" until 16 elements that meet the conditions are generated.

The quotation marks are used here because the 32 elements have not yet been generated, so strictly speaking, they cannot be called a codeword, but because the generated elements cannot meet the conditions, it is not necessary to generate subsequent elements, which can greatly Improve search speed.

The code search also includes: For the 8-state space-time grid code, 15 36 _dniin = 48 code matrices can be searched, and if the input is 0 in the 0 state, the output is also 0, that is, the a is limited. = 00, then there are 96 trellis codes that satisfy d _nin = 48; and among all the 8-state spatiotemporal trellis codes that satisfy condition 1, these codes are optimal.

The optimal refers to: at 8 states, the minimum product distance d _min greater than 6 * 8 = 48 can only be 8 * 8 = 64, the sequence of states (0, 0, 0) and (0, 2 , 0) corresponds to two different codewords. To achieve d _min = 64, these two codewords must have a. ₂ = a ₂ . However, this does not satisfy condition one, so the maximum minimum product distance can only be 48, so the 8-state space-time grid code is optimal.

The method of the present invention is characterized in that the transmitting end can use N transmitting antennas, and the receiving end can use M receiving antennas.

The method according to the present invention is characterized in that the modulation may be 4-PSK modulation.

The beneficial effect of the present invention is that, by providing a space-time trellis code coding method, the maximum coding gain can be obtained while obtaining the full diversity gain. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a structural block diagram of a fast fading channel with two transmissions and two receptions;

Figure 2 is a 4- ¾X modulation constellation diagram;

Figure 3 is a trellis diagram of the 8-state spatiotemporal trellis code;

Figure 4 is a simulation diagram of the 8-state spatio-temporal trellis code.

detailed description

The following describes specific embodiments of the present invention with reference to the accompanying drawings:

The present invention is a spatio-temporal trellis code encoding method, including:

It is characterized by:

It is assumed that N transmitting antennas are used at the transmitting end and that receiving antennas are used at the receiving end. It is assumed that the fading of the signal in space is an independent Rayleigh fast fading. At the transmitting end, the energy of each transmitting symbol is normalized to 1, and the data sent from each transmitting antenna takes one symbol as a frame. In order to explain this article, two transmitting antennas, two receiving antennas, and 4- ¾X modulation are used. Each symbol is composed of two bits, which can be applied to the case of multiple transmitting antennas, multiple receiving antennas, and other modulations. The information transmission process is shown in Figure 1. At the receiving end, the signal received by antenna J 'at time t is:

'; _/ ( l,-, M, t = l, ..., L (1) Here: _nj (t), ..., M, t = l, ..., L is a sequence of complex Gaussian random variables, Its variance is! , The channel fading factors h _i ..., Ν,, ... are a sequence of white Gaussian random variables with a mean of zero and a variance of one. There are many representation methods of spatio-temporal trellis codes. The present invention adopts the representation method in document [3]. This method can represent all spatio-temporal trellis codes. Taking Figure 3 as an example, eight lines from top to bottom indicate the state from the state. From the eight states of Q to state 7, four branches from each state reach the four states of the next moment, and the corresponding inputs from top to bottom of the branch are 0, 1, 2, 3, and the left side of the grid The numbers in turn indicate the output on each branch from top to bottom, and the output corresponding to each branch is represented by two numbers, which respectively represent the content output from the two antennas. For convenience, a matrix is used to represent the numbers on the left of the trellis, so that each space-time grid code corresponds to a code.

00 02 22 20

13 11 31 33

12 10 30 32

Matrix, the spatio-temporal trellis code of Figure 3 can be used as a code matrix 01 03 23 21

21 23 03 01 to represent _t

32 30 10 12

33 31 11 13

20 22 02 00

For the search criteria of spatio-temporal trellis codes, Tarokh in [3] derived the design principles of spatio-temporal trellis codes under fast fading Rayleigh channels. Let c and e be two different codewords in the codeword sequence, e = ^^… ^^ .. ^… ^^… ^,

When transmitting the codeword c at the transmitting end, it is mistranslated into e at the receiving end, and the pairwise code error probability under the fast fading Rayleigh channel satisfies:

Here in any two yards

The words c and e, in the time sequence l≤t≤Z, if | _c , _{-e (} | ² ≠ 0, the time is in the time set s (c, e). Let s ( _C , _e ) | be the set , E), the diversity weight that can be obtained under the fast fading Rayleigh channel is M | s ( _C , _e ) |, in order to obtain the maximum coding gain, we must make:

to reach maximum. Since diversity gain plays a large role, it determines the slope of the BER curve, so In the design of space-time codes, we must first ensure that we can obtain the maximum diversity gain.

As for the design of the optimal 8-state spatio-temporal trellis code, the case of two transmitting antennas is used as an example for description, that is, N = 2, which can also be generalized to the case of other multiple transmitting antennas.

It can be seen from the trellis structure in Fig. 3 that if the elements in the code matrix of the 8-state spatio-temporal trellis code satisfy:

Condition 1: The elements of the first four rows of the code matrix of the 8-state space-time grid code are different, and the elements of the last four rows are also different.

Then the output of any two different codewords of the 8-state spatio-temporal trellis code must be different at some two times, so that 2yl re-diversity gain must be obtained. Therefore, the difficulty in designing the 8-state spatio-temporal trellis code is how to obtain the maximum Encoding gain.

For the 8-state spatiotemporal grid code, if the search is performed, the calculation will be very large, but the search method described below can be used to perform a search in the range of linear codes, and 44 minimum product distances d can be found. _Rain = 32 linear 8-state spatio-temporal grid codes. These codes are optimal in linear codes, but if there is no constraint condition of linear structure, there can be better codes. This paper presents an 8-state spatio-temporal grid code based on a symmetric structure. Using the search method described below, a non-linear 8-state spatio-temporal grid code with d _min = 48 can be found under the constraint of the symmetric structure. It can be proved that these codes are All 8 status codes are optimal. Details are described below.

This article assumes that the code matrix of the 8-state spatiotemporal trellis code has a mirror-symmetrical structure. If {a ₀₀₃ a ₀₁ , a ₀₃ , a ₁₀ , an _n , a ₁₃ , a _{7 is used} . , A ₇₁ , ..., a ₇₃ } represent the 32 elements in the code matrix, then:

^ _X y = u- _x) (3-y) ^x = ⁴ ' ⁵ ' ⁶ ' ⁷ = 0,1,2,3 (4)

First, two state sequence data files are created. Each sequence in the first data file represents two truncated codewords. The states of the two truncated codewords are the same at time and +2, and at t + 1 Different states, such as the state sequence P ii, 0, 0), (0, 2, 0)}, the first three elements of the sequence {0, 0, 0} represent a truncated codeword, and the truncated codeword runs from time to The state at time t + 1 is state 0, 0, 0 in sequence. For the trellis code shown in FIG. 3, it represents the truncated code word. {00, 00}, the last three elements {0, 2, 0} of the same sequence ρ _λ represent truncated codeword dB = [22, 12}, assuming that codeword ^ and codeword are before time t and time ί + 2 After that, it is the same. At time t to time t + 2, the truncated codewords (1A and dB, respectively, then the output of codeword 4 and at two times are different. Under modulation (as shown in Figure 2), (3) calculates the product distance between them as 48. Through simple analysis, we can know that there are 56 sequences in the sequence data file, and the two truncated codewords represented by each sequence in the second data file are at time t. The state at time +3 is the same, and the state at time ί + l and time ί + 2 is different. There are 1280 sequences in this data file. The following code search is performed. The search method is: for (4) The 8-state space-time grid code of the symmetrical structure defined by the formula, only the first 16 elements of the 32 elements in the code matrix can be designed. The last 16 elements are obtained by the formula (4), and the first 16 elements are required. different conditions is met a, so, a _QQ there are 16 possible values, a _fll 15 possible, Such push Each element generates a data file according to the sequence of the subject face to see two "codeword" corresponding to the sequence is not a product meets the specified minimum distance d _min, then not continue if not generated later , But change the previous element to generate a new "codeword", until 16 elements that meet the conditions are generated. The codewords are quoted here because 32 elements have not yet been generated, so strictly speaking they cannot be called. Is a codeword, but because the generated elements cannot meet the conditions, there is no need to generate subsequent elements, which can greatly improve the search speed.

According to the search method introduced above, for the 8-state spatio-temporal grid code, 1536 d _min = 48 code matrices can be searched. If the input is limited to Q in the Q state, the output is also 0, that is, a is limited. = 00, then there are 96 grid codes that satisfy d _min = 48. Figure 4 shows one of them. It can be proved that among all 8-state spatio-temporal trellis codes that satisfy the condition 1, these codes are optimal, and the proof is as follows: In the 8-state, the minimum product distance d _{min is} larger than 6 * 8 = 48, which can only be 8 * 8-64. From the 8-state lattice diagram shown in Figure 4, you can know that the state sequences (0, 0, 0) and (0, 2, 0) correspond to two different codewords. These two codewords must be To reach d _rain = 64, we must have a _D2 = a ₂ . However, this does not satisfy condition one, so the maximum minimum product distance can only be 48, so the 8-state space-time grid code in this paper is optimal. The simulation results are as follows:

In order to verify the previous results and compare with the codes given in other literatures, the simulation results given in this paper are shown in Figure 4, the codes used are shown in Table 1, and the parameters used in the simulation are shown in Table 2. It can be seen from the figure that the 8-state space-time grid code based on the symmetric structure given in this paper is optimal under the Rayleigh fast fading channel. The linear optimal 8-state space-time grid found by the search method introduced in this article The performance of the code is worse than the optimal code given in this paper, but it is better than that of other codes.

The present invention proposes an 8-state space-time trellis code based on a symmetric structure. A code search method is designed, and the design criteria of the space-time trellis code under the fast-fading Rayleigh channel given in reference [3] are designed. An optimal 8-state spatio-temporal trellis code is constructed. The theory and search show that the code given by the present invention has the largest minimum product distance, can obtain the maximum coding gain while obtaining the full diversity gain, and gives the simulation results. The verification shows that the code given in this paper has a larger coding gain than the space-time trellis code given in other literatures. Under the fast fading Rayleigh channel, the code given by the present invention is optimal.

: Codewords used in simulation

State number Tamkh's code [3] K.gx's code [4] Stephan's code [5] Code given in this article

S state 00 01 02 03 00 22 02 20 00 01 22 23 00 02 22 20 00 02 21 23

10 11 12 13 10 32 12 30 10 11 32 33 13 11 31 33 12] 0 33 31

20 21 22 23 23 01 21 03 20 21 02 03 12 10 30 32 22 20 03 01

30 31 32 33, ^ 33 11 31 13 _Λ 30 31 12 13, 01 03 23 21 30 32 Π 13 d _m ; = 16 Η. = 24

22 23 20 21 ^mm 01 23 03 21 ^η 22 23 00 01 21 23 03 01 12 10 33 31

32 33 30 31 11 33 13 31 32 33 10 11 32 30 10 12 20 22 01 03

02 03 00 01 20 02 22 00 02 03 20 21 33 31 11 13 30 32 11 13

12 13 10 11 30 12 32 10 12 13 30 31 20 22 02 00 02 00 23 21

¾ Good code linear optimal code d _mi = 32

Table 2: Parameters used in the simulation

Trust environment fast a Rayleigh channel

Antenna

Frame 130 symbols

Simulation statistics 10 ⁸ input information bits or 10 ⁷ error bits It can be known from the above specific embodiments that the present invention has the beneficial effect that, by providing a space-time trellis code coding method, the maximum coding gain can be obtained while obtaining the full diversity gain. At the same time, it should be pointed out that J Zhen Shi Gu Yi ifi Qian said too

invention. references:

[1] Siavash M Alamouti. A simple Transmit Diversity Technique for Wireless Communications. IEEE Journal on select areas in communications, 1998, 16 (8).

[2] Va id Tarokh, Hamid Jafarkhani and A Robert Calderbank. Space Time Block Coding for Wireless Communications: Performance Results. IEEE Journal on select areas in communications, 1999, 17 (3).

[3] V Tarokh, N Seshadri and A R Calderbank. Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction. IEEE Trans. IT, 1998, 44 (2): 744-765.

[4] K.guixia. Searching Good Space-time Trellis Codes of High Complexity. IEEE WCNC'2002 (1): 109-113.

[5] S. Baro, G. Bauch, and A. Hansmann. Improved codes for space-time trellis coded modulation. IEEE Commun. Lett., Vol.4, pp.20-22, Jan. 2000.

[6] Kang Guixia. Theory and technology of space-time code design and application. PhD dissertation of Beijing University of Posts and Telecommunications: 990073009.

Claims

Rights request

1. A spatio-temporal trellis code encoding method, comprising:

It is characterized by:

The spatio-temporal trellis code is a spatio-temporal trellis code having a symmetric structure. The search of the spatio-temporal trellis code must satisfy the constraint condition of the symmetric structure, and the spatio-temporal trellis code having the symmetric structure is in all The corresponding state is optimal in the space-time grid code.

2. The method according to claim 1, wherein the space-time grid code is an 8-state space-time grid code, and the first four rows of the code matrix of the 8-state space-time grid code are 2. Each is different, and the last four rows are also different.

3. The method according to claim 1, wherein the spatio-temporal trellis code having a symmetric structure is: an 8-state spatio-temporal trellis code having a symmetric structure.

4. The method according to claim 1, wherein the spatio-temporal trellis code is an 8-state spatio-temporal trellis code, and the first four rows of elements of the code matrix of the 8-state spatio-temporal trellis code are not The same, the last four rows of elements are also different;

The spatio-temporal trellis code with a symmetric structure refers to an 8-state spatio-temporal trellis code with a symmetric structure; a non-linear 8-state spatio-temporal trellis code with d _fflin = 48 can be searched under the constraint of the symmetric structure, and the The searched nonlinear 8-state spatiotemporal grid code with d _min = 48 is the best among all 8-state codes.

5. The method according to claim 4, wherein the code matrix of the 8-state spatiotemporal grid code has a mirror-symmetrical structure; and

If fe ₀₀ , a ₀₁ , ..., a ₀₃ , a ₁₀ , an _n , a _13,. ·., A ₇₀ , a ₇₁ , ..., a ₇₃ } represent the 32 elements in the code matrix, then there is The following equation: a _xy = a _a _ _{x) (3} _ _y) x = 4,5,6,7 y = 0,1,2,3.

6. The method according to claim 5, comprising the steps of: establishing two state sequence data files; wherein:

Each sequence in the first data file represents two truncated codewords, and the states of the two truncated codewords are the same at time t and time, but different at + ι;

There are a total of 56 sequences in the first data file, and the states of the two truncated codewords represented by each sequence in the second data file are the same at time t and time ί + 3, and at time t + 1 The state of time is different, there are 1280 sequences in this data file;

When searching for a code: For the 8-state space-time grid code of the symmetric structure defined by the equation, only the first 16 elements of the 32 elements in the code matrix can be designed, and the last 16 elements are The above equation is obtained, and the first 16 elements must be different, that is, satisfy the condition 1, so that a. There are 16 possible values for _D , 15 possibilities, and so on;

Every time an element is generated, it is tested according to the sequence in the data file to see if the two "codewords" corresponding to the sequence meet the specified minimum product distance d _min . If it does not meet, the subsequent elements will not be generated any more, and Is to change the previous element to generate a new "codeword" until 16 elements that meet the conditions are generated;

The quoted codeword is because 32 elements have not been generated yet, so it cannot be called a codeword strictly, but because the generated elements cannot meet the conditions, it is not necessary to generate subsequent elements. Greatly improve search speed.

7. The method according to claim 6, wherein the code search further comprises: for a space-time grid code of 8 states, 1536 _dmin = 48 code matrices can be searched, if limited to a state of 0 When the input is 0, the output is also 0, that is, if a _Q = 00 is defined, there are 96 grid codes that satisfy d _min = 48;

And among all the 8-state spatio-temporal trellis codes that satisfy Condition 1, these codes are optimal.

8. The method according to claim 7, characterized in that the optimal means: in the 8 state, the minimum product distance d _{rain is} larger than 6 * 8 = 48, and can only be 8 * 8 = 64 Order of states The columns (0, 0, 0) and (0, 2, 0) correspond to two different codewords. To reach d _min = 64, these two codewords must have a _Q2 = a _2D , but this way Condition 1 is not satisfied, so the maximum minimum product distance can only be 48, so the 8-state space-time grid code is optimal.

9. The method according to any one of claims 1 to 8, wherein the transmitting end can use N transmitting antennas, and the receiving end can use M receiving antennas.

10. The method according to any one of claims 1 to 8, wherein the modulation is 4-PSK modulation.