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CN103684702A - Space-time coding spatial modulation method based on (n, k) error correcting codes - Google Patents

  • ️Wed Mar 26 2014

CN103684702A - Space-time coding spatial modulation method based on (n, k) error correcting codes - Google Patents

Space-time coding spatial modulation method based on (n, k) error correcting codes Download PDF

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CN103684702A
CN103684702A CN201310633122.XA CN201310633122A CN103684702A CN 103684702 A CN103684702 A CN 103684702A CN 201310633122 A CN201310633122 A CN 201310633122A CN 103684702 A CN103684702 A CN 103684702A Authority
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stbc
eff
scheme
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ecc
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2013-11-28
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王磊
陈志刚
李晓峰
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Xian Jiaotong University
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Xian Jiaotong University
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Abstract

本发明公开了一种基于(n,k)纠错码的空时编码空间调制方法,该方法利用(n,k)纠错码(Error Correcting Code,ECC)激活不同的天线对来发送Alamouti空时码。STBC-SM(n,k)方案的优点在于它可以获得可变的传输速率,且当总的发射天线数变大时还能够方便地构造出星座集合。此外,在STBC-SM(n,k)方案中,推导出编码增益的闭式解并以此作为目标函数来对两个旋转角度进行优化,从而保证STBC-SM(n,k)方案能够获得的发射分集阶数为2。STBC-SM(n,k)方案由于比STBC-SM具有更多的码字总数因而可以获得更高的频谱利用率。

The invention discloses a space-time coding space modulation method based on (n, k) error correcting codes, which uses (n, k) error correcting codes (Error Correcting Code, ECC) to activate different antenna pairs to transmit Alamouti space time code. The advantage of the STBC-SM(n,k) scheme is that it can obtain a variable transmission rate, and it can also conveniently construct a constellation set when the total number of transmitting antennas becomes larger. In addition, in the STBC-SM(n,k) scheme, the closed-form solution of the coding gain is derived and used as the objective function to optimize the two rotation angles, so as to ensure that the STBC-SM(n,k) scheme can obtain The order of transmit diversity is 2. The STBC-SM(n,k) scheme can obtain higher spectral efficiency because it has more total codewords than STBC-SM.

Description

A kind of Space Time Coding modulating method based on (n, k) error correcting code

Technical field

The invention belongs to multi-antenna wireless communication field, a kind of transmit diversity transmission technology in design multi-aerial radio communication system, particularly a kind of Space Time Coding modulating method based on (n, k) error correcting code.

Background technology

In recent years, a kind of modulator approach of Spatial Dimension transmission information of utilizing is owing to all having outstanding advantage than traditional many antennas (MIMO) transmission technology on detection complexity, hardware cost and stationary problem, thereby obtained widely and pay close attention to.Spatial modulation (Spatial Modulation, SM), sky moves keying (Space Shift Keying, SSK), the sky of promoting moves keying (Generalized SSK, GSSK) and the sky based on Hamming code and moves keying (HSSK) and all belong to this modulation system of utilizing Spatial Dimension transmission information.In SM and SSK scheme, only have antenna to activate to be used for transmission information bit, GSSK and HSSK activate many antennas and carry out transmission information bit, and the antenna number that wherein GSSK activates is fixed, and the antenna number that HSSK activates is variable.Yet above-mentioned these several schemes but have common defect, that is exactly that they can not obtain transmit diversity, can only rely on receive diversity and resist channel fading.

For this problem, in prior art respectively by space-time block code (Space-Time Block Coding, STBC) combine with SSK and SM, empty time-shift keying (Space-Time Shift Keying, STSK) and Space Time Coding spatial modulation (STBC-SM) method of transmit diversity have been proposed to obtain.When the performance of STSK is completely empty by one group, disperse set of matrices decides, yet the optimization of disperse set of matrices has but increased the design complexities of STSK during to sky.STBC-SM scheme is 2 by one group of anglec of rotation is optimized to the transmit diversity exponent number that can obtain.Yet for number of transmit antennas more than for 8 mimo system, STBC-SM needs the more anglec of rotation to be optimized, this can make again minimum coding gain distance (coding gain distance, CGD) diminish simultaneously, thereby makes the degradation of STBC-SM.Subsequently, have again scholar to propose a kind of high speed STBC-SM scheme that is applicable to 4 and 6 transmit antennas, by it referred to as H-STBC-SM scheme.Compare with previous STBC-SM, H-STBC-SM is owing to having designed space constellation matrix thereby having had higher spectrum efficiency, and it also can obtain transmit

diversity exponent number

2 by optimizing two anglecs of rotation simultaneously.Yet the optimization of these two anglecs of rotation is usingd determinant criterion and is directly carried out exhaustive search as target function, thereby can increase the complexity of search optimal angle.

Summary of the invention

The object of the invention is to solve above-mentioned the problems of the prior art, provide a kind of based on (n, k) the Space Time Coding modulating method of error correcting code, the method is utilized (n, k) error correcting code (Error Correcting Code, ECC) activates different antennas to sending the empty time-code of Alamouti.By deriving the closed solutions of coding gain and usining that this is optimized two anglecs of rotation as target function, thereby guarantee that the transmit diversity exponent number that STBC-SM (n, k) scheme can obtain is 2.STBC-SM (n, k) scheme is owing to having more code word sum than STBC-SM thereby can obtain the higher availability of frequency spectrum.

In order to achieve the above object, the technical solution adopted in the present invention comprises the following steps:

The first step: the random bit stream of input is divided into two parts, and a front k bit is used for selecting the code word c in ECC l, 2log below 2m bit is used for selecting symbol in Alamouti coding to (x 1, x 2), wherein M represents the order of modulation of symbol;

Second step: using Alamouti code and its spin matrix as basic STBC code block, Alamouti code S and its spin matrix

Figure BDA0000424913150000021

be expressed as:

S = x 1 x 2 - x 2 * x 1 *

With

S ~ = x 1 e jθ x 2 e jθ - x 2 * e - jθ x 1 * e - jθ - - - ( 1 )

Wherein, x 1and x 2be two symbols that are taken from M-PSK/QAM constellation, θ represents the anglec of rotation,

Figure BDA0000424913150000024

represent p-x 2get conjugation, expression is to x 1get conjugation;

The 3rd step: generate STBC-SM (n, k) codebook set according to Alamouti code and its spin matrix, during each transmission information, generate STBC-SM (n, k) signal from n ton individual antenna, send.

In described the 3rd step, the method that generates STBC-SM (n, k) codebook set is specially:

Suppose that it is L=2 that (n, k) ECC can generate a size kcodeword set A eCC, for n t=2n transmitting antenna, two code book X in STBC-SM (n, k) constellation set 1and X 2be configured to

X 1 = { X l , X ~ l } , X 2 = { X l , X ~ l } e jφ , - - - ( 2 )

Wherein, X lwith

Figure BDA0000424913150000031

be defined as respectively:

X l = Δ c l ⊗ S / w l = B l ( 1 ) B l ( 2 ) . . . B l ( n ) X ~ l = Δ c l ⊗ S ~ / w l = B ~ l ( 1 ) B ~ l ( 2 ) . . . B ~ l ( n ) - - - ( 3 )

In formula (2), each code book comprises 2L code word X lwith

Figure BDA0000424913150000033

wherein, l=0 ..., L-1, φ is two anglecs of rotation between code book; In formula (3), c l∈ A eCCthe ECC code word of 1 * n dimension, w leCC code word c lhamming weight, symbol represent that Kronecker is long-pending; 2 * 2 dimension matrixes

Figure BDA0000424913150000035

with

Figure BDA0000424913150000036

represent respectively code word X lwith

Figure BDA0000424913150000037

in n Alamouti piece, c wherein l(n) represent c ln element; STBC-SM (n, the k) constellation set finally obtaining is expressed as

Figure BDA0000424913150000038

The detection of the 4th step: STBC-SM (n, k):

Adopt STBC-SM (n, k) scheme when transmission, because accessing its channel matrix of equal value, the orthogonality of STBC-SM (n, k) code word also there is orthogonality, thereby the maximum likelihood algorithm of this modulation scheme will be reduced to a linear process, concrete grammar is as follows:

When the system equation that sends STBC-SM (n, k) code word being reduced to the system equation of transmission Alamouti coding, draw and code word X l∈ X 1and X le j φ∈ X 2corresponding 2n r* 2 dimension channel matrixes, and there is respectively following form:

F 1 , l = Δ g p , 1 l , eff ( 1 ) g p , 1 l , eff ( 2 ) g p , 1 l , eff ( 2 ) * - g p , 1 l , eff ( 1 ) * g p , 2 l , eff ( 1 ) g p , 2 l , eff ( 2 ) g p , 2 l , eff ( 2 ) * - g p , 2 l , eff ( 1 ) * . . . . . . g p , n R l , eff ( 1 ) g p , n R l , eff ( 2 ) g p , n R l , eff ( 2 ) * - g p , n R l , eff ( 1 ) *

With

Figure BDA00004249131500000310

In formula (4),

Figure BDA00004249131500000311

with

Figure BDA00004249131500000312

represent respectively 2 * 1 dimensional vectors first and second element, vector

Figure BDA00004249131500000314

w lindividual different channel vector g k,isum, therefore handle

Figure BDA00004249131500000315

be called and code word X l∈ X 1the channel vector of corresponding equivalence, has w lthe vectorial p of individual element represents code word X lthe right label of middle activated antenna; And vectorial g k,i=[h (2k-1), ih 2k, i] t, k=1 ..., n, element h wherein 2k, iexpression is from 2k transmitting antenna to the channel gain i reception antenna, and T represents vector to make transposition; Equivalent channels matrix F 1, land F 2, lcomprise respectively the realization that L kind is different;

Equally, obtain respectively and code word

Figure BDA0000424913150000041

with

Figure BDA0000424913150000042

corresponding equivalent channel matrix

Figure BDA0000424913150000043

with

Figure BDA0000424913150000044

and equal respectively above 4 equivalent channel matrix F 1, l, F 2, l,

Figure BDA0000424913150000046

with

Figure BDA0000424913150000047

each has the column vector of two quadratures, they have identical structure with the equivalent channel matrix of STBC-SM scheme, therefore the ML detector of STBC-SM scheme also can be applied to STBC-SM (n, k) scheme, this detector has linear decoding complexity, and its decoding complexity is 2cM.

Compared with prior art, the present invention has following technique effect:

The advantage of STBC-SM of the present invention (n, k) scheme is that it can obtain variable transmission rate, and can also construct easily constellation set when total number of transmit antennas becomes large.In addition, in STBC-SM (n, k) scheme, derive the closed solutions of coding gain and using that this is optimized two anglecs of rotation as target function, thereby guarantee that the transmit diversity exponent number that STBC-SM (n, k) scheme can obtain is 2.STBC-SM (n, k) scheme is owing to having more code word sum than STBC-SM thereby can obtain the higher availability of frequency spectrum.

Accompanying drawing explanation

Fig. 1 is STBC-SM of the present invention (n, k) modulating system block diagram;

Fig. 2 is the theoretical BER curve of STBC-SM of the present invention (n, k) and the comparison diagram of emulation BER curve;

To be STBC-SM of the present invention (3,2), STBC-SM and H-STBC-SM scheme be respectively 3,4 and BER comparison diagram during 5bits/s/Hz in spectrum efficiency to Fig. 3;

Fig. 4 is that STBC-SM of the present invention (4,3) and STBC-SM scheme are at n tthe BER comparison diagram of=8 o'clock.

Embodiment

Below in conjunction with drawings and Examples, the present invention is further detailed explanation:

Referring to Fig. 1, the present invention includes following steps:

The first step: the random bit stream of input is divided into two parts, and a front k bit is used for selecting the code word c in ECC l, 2log below 2m bit is used for selecting symbol in Alamouti coding to (x 1, x 2), wherein M represents the order of modulation of symbol;

Second step: using Alamouti code and its spin matrix as basic STBC code block, Alamouti code S and its spin matrix

Figure BDA0000424913150000051

be expressed as:

S = x 1 x 2 - x 2 * x 1 *

With

S ~ = x 1 e jθ x 2 e jθ - x 2 * e - jθ x 1 * e - jθ - - - ( 1 )

Wherein, x 1and x 2be two symbols that are taken from M-PSK/QAM constellation, θ represents the anglec of rotation,

Figure BDA0000424913150000054

represent p-x 2get conjugation, expression is to x 1get conjugation;

The 3rd step: generate STBC-SM (n, k) codebook set according to Alamouti code and its spin matrix

Suppose that it is L=2 that (n, k) ECC can generate a size kcodeword set A eCC, for n t=2n transmitting antenna, two code book X in STBC-SM (n, k) constellation set 1and X 2can be configured to

X 1 = { X l , X ~ l } , X 2 = { X l , X ~ l } e jφ , - - - ( 2 )

Wherein, X lwith

Figure BDA0000424913150000057

be defined as respectively:

X l = Δ c l ⊗ S / w l = B l ( 1 ) B l ( 2 ) . . . B l ( n ) X ~ l = Δ c l ⊗ S ~ / w l = B ~ l ( 1 ) B ~ l ( 2 ) . . . B ~ l ( n ) - - - ( 3 )

In formula (2), each code book comprises 2L code word X lwith

Figure BDA0000424913150000059

wherein, l=0 ..., L-1, φ is two anglecs of rotation between code book; In formula (3), c l∈ A eCCthe ECC code word of 1 * n dimension, w leCC code word c lhamming weight, symbol

Figure BDA00004249131500000510

represent that Kronecker is long-pending; 2 * 2 dimension matrixes

Figure BDA00004249131500000511

with

Figure BDA00004249131500000512

represent respectively code word X lwith in n Alamouti piece, c wherein l(n) represent c ln element; STBC-SM (n, the k) constellation set finally obtaining is expressed as

Figure BDA00004249131500000514

during each transmission information, generate STBC-SM (n, k) signal from n ton individual antenna, send.

The detection of the 4th step: STBC-SM (n, k):

Adopt STBC-SM (n, k) scheme when transmission, because accessing its channel matrix of equal value, the orthogonality of STBC-SM (n, k) code word also there is orthogonality, thereby the maximum likelihood algorithm of this modulation scheme will be reduced to a linear process, concrete grammar is as follows:

When the system equation that sends STBC-SM (n, k) code word being reduced to the system equation of transmission Alamouti coding, draw and code word X l∈ X 1and X le j φ∈ X 2corresponding 2n r* 2 dimension channel matrixes, and there is respectively following form:

F 1 , l = Δ g p , 1 l , eff ( 1 ) g p , 1 l , eff ( 2 ) g p , 1 l , eff ( 2 ) * - g p , 1 l , eff ( 1 ) * g p , 2 l , eff ( 1 ) g p , 2 l , eff ( 2 ) g p , 2 l , eff ( 2 ) * - g p , 2 l , eff ( 1 ) * . . . . . . g p , n R l , eff ( 1 ) g p , n R l , eff ( 2 ) g p , n R l , eff ( 2 ) * - g p , n R l , eff ( 1 ) *

With

In formula (4),

Figure BDA0000424913150000063

with

Figure BDA0000424913150000064

represent respectively 2 * 1 dimensional vectors first and second element, vector w lindividual different channel vector g k,isum, therefore handle

Figure BDA0000424913150000067

be called and code word X l∈ X 1the channel vector of corresponding equivalence, has w lthe vectorial p of individual element represents code word X lthe right label of middle activated antenna; And vectorial g k,i=[h (2k-1), ih 2k, i] t, k=1 ..., n, element h wherein 2k, iexpression is from 2k transmitting antenna to the channel gain i reception antenna, and T represents vector to make transposition; Equivalent channels matrix F 1, land F 2, lcomprise respectively the realization that L kind is different;

Equally, obtain respectively and code word

Figure BDA0000424913150000068

with

Figure BDA0000424913150000069

corresponding equivalent channel matrix

Figure BDA00004249131500000610

with

Figure BDA00004249131500000611

and equal respectively

Figure BDA00004249131500000612

above 4 equivalent channel matrix F 1, l, F 2, l,

Figure BDA00004249131500000613

with

Figure BDA00004249131500000614

each has the column vector of two quadratures, they have identical structure with the equivalent channel matrix of STBC-SM scheme, therefore the ML detector of STBC-SM scheme also can be applied to STBC-SM (n, k) scheme, this detector has linear decoding complexity, and its decoding complexity is 2cM.

Embodiment:

Concrete modulation and the detection algorithm of this programme are as follows:

1) STBC-SM (n, k) modulator approach

In STBC-SM (n, the k) scheme proposing, STBC and (n, k) ECC can be used for transmission information bit, and wherein (n, k) ECC has determined the antenna label activating.Using Alamouti code and its spin matrix as basic STBC code block, they can be expressed as respectively

S = x 1 x 2 - x 2 * x 1 * ,

With

S ~ = x 1 e jθ x 2 e jθ - x 2 * e - jθ x 1 * e - jθ - - - ( 1 )

X wherein 1and x 2be two symbols that are taken from M-PSK/QAM constellation, θ represents the anglec of rotation.Suppose that it is L=2 that (n, k) ECC can generate a size kcodeword set A eCC, for n t=2n transmitting antenna, two code book X in STBC-SM (n, k) constellation set 1and X 2can be configured to

X 1 = { X l , X ~ l } , X 2 = { X l , X ~ l } e jφ , - - - ( 2 )

X wherein l,

Figure BDA0000424913150000074

be defined as respectively

X l = Δ c l ⊗ S / w l = B l ( 1 ) B l ( 2 ) . . . B l ( n ) ; X ~ l = Δ c l ⊗ S ~ / w l = B ~ l ( 1 ) B ~ l ( 2 ) . . . B ~ l ( n ) , - - - ( 3 )

(2) in formula, each code book comprises 2L code word X lwith

Figure BDA0000424913150000076

l=0 ..., L-1, c l∈ A eCCthe ECC code word of 1 * n dimension, w leCC code word c lhamming weight, φ is two anglecs of rotation between code book, symbol

Figure BDA0000424913150000077

represent that Kronecker is long-pending.2 * 2 dimension matrixes with

Figure BDA0000424913150000079

represent respectively code word X lwith in n Alamouti piece, c wherein l(n) represent c ln element.STBC-SM (n, the k) constellation set finally obtaining can be expressed as

In table 1, provided at n tthe example of STBC-SM (4, the 3) code under=8 transmitting antennas, this code word is to mend 1 rear generation by last bit of (4,3) parity check code.In table 1, only provided first codebook set X 1in

front

8 code words, the vectorial p in table 1 represents the right number of antenna that each code word activates, wherein n t=2n transmitting antenna is divided into n couple, and every pair is 2 antennas.When two symbols in Alamouti coding all adopt BPSK modulation, 8 code words in table 1 can be transmitted the information of 5 bits in two continuous symbol periods, wherein

front

3 bit (b 1, b 2, b 3) determine to adopt which code word, and latter two bit (b 4, b 5) determine two symbols in Alamouti coding.For example, when current 3 bits are (010), corresponding code word is X 2, what also now activate is second pair of antenna.

Table 1n tsTBC-SM (4,3) code under=8 transmitting antennas

Figure BDA0000424913150000081

From formula (2), the code word sum in STBC-SM (n, k) constellation set equals c=4L=2 (k+2).When two symbols in Alamouti coding adopt M-PSK/QAM modulation, each code word has M 2middle different realization.Therefore the availability of frequency spectrum of STBC-SM (n, k) scheme equals η=(1/2) log 2(cM 2)=(k+2)/2+log 2mbits/s/Hz, wherein 1/2 is because STBC-SM (n, k) signal has taken two symbol periods.When adopting identical order of modulation, the spectrum efficiency of different STBC-SM schemes depends on the size of code word sum c completely, and the c value that can design is larger, and the spectrum efficiency obtaining is higher.In table 2, provided STBC-SM, H-STBC-SM and STBC-SM (n, k) scheme are in the situation that the c value of different number of transmit antennas.

The comparison of the code word sum c of table 2 different schemes

? n T=4 n T=6 n T=8 n T=10 n T=12
STBC-SM 4 8 16 32 64
H-STBC-SM 8 16 / / /
STBC-SM(n,k) 8 16 32 64 128

2) detection algorithm of STBC-SM (n, k)

While adopting the transmission of STBC-SM (n, k) scheme, its maximum likelihood (ML) detection algorithm will be reduced to a linear process, below it be carried out to detailed derivation.For thering is n tindividual transmitting antenna and n rthe mimo system of individual reception antenna, 2 * n rthe reception signal matrix of dimension

Figure BDA0000424913150000082

can be expressed as

Y = ρ XH + N - - - ( 4 )

In formula: X ∈ X is 2 * n tsTBC-SM (n, the k) transmission matrix of dimension, ρ is the average signal-to-noise ratio (SNR) at each reception antenna place, matrix

Figure BDA00004249131500000913

with

Figure BDA00004249131500000914

represent respectively n t* n rdimension channel matrix and 2 * n rdimension noise matrix, wherein each element is all that average is 0, the multiple Gaussian random variable that variance is 1.(j, i) individual element h of matrix H j,iexpression is from j transmitting antenna to the channel gain i reception antenna.Suppose that channel matrix H remains unchanged in two continuous symbol periods (two continuous symbol periods are called a frame), and in next frame independent variation.In addition, receiving terminal has channel information accurately, and transmitting terminal Unknown Channel information.

Below with the code word X in first codebook set l∈ X 1for the example derivation equivalent channels matrix corresponding with it, this result is easy to extend to other code word.Suppose that the X that transmits is from code word

Figure BDA0000424913150000092

middle taking-up, by each column vector h of channel matrix H ibe expressed as

Figure BDA0000424913150000093

form, g wherein k,i=[h (2k-1), ih 2k, i] t, k=1 ..., n represents and code word X lin k Alamouti piece

Figure BDA0000424913150000094

relevant channel vector.Like this, 2 * 1 dimensional signals at i reception antenna place can be expressed as

y i = ρ Σ k = 1 n B l ( k ) g k , i + n i = ρ w l S g p , i l , eff + n i - - - ( 5 )

In formula: there is w lthe vectorial p of individual element represents code word X lthe right label of middle activated antenna (in Table listed in 1), 2 * 1 dimensional vectors

Figure BDA0000424913150000096

w lindividual different channel vector g k,isum, therefore handle be called and code word X l∈ X 1the channel vector of corresponding equivalence.

When to y isecond element get after conjugation, can from (5) formula, isolate two symbol x in Alamouti coding 1and x 2, receive like this signal y ithe equivalent form of value that can be expressed as

y ~ i = ρ w l g p , i l , eff ( 1 ) g p , i l , eff ( 2 ) g p , i l , eff ( 2 ) * - g p , i l , eff ( 1 ) * x 1 x 2 + n ~ i - - - ( 6 )

In formula:

Figure BDA0000424913150000099

with represent respectively

Figure BDA00004249131500000911

first and second element.Again by 2 * 1 all dimensional vectors

Figure BDA00004249131500000912

be stacked into a 2n rthe equivalence of * 1 dimension receives signal y, and it can be expressed as

y = ρ w l F 1 , l x 1 x 2 + n - - - ( 7 )

In formula: n represents 2n rthe noise vector of equal value of * 1 dimension, F 1, lbe and code word X l∈ X 1corresponding 2n r* 2 dimension channel matrixes.Matrix F 1, lcomprise the realization that L kind is different, its expression is

F 1 , l = Δ g p , 1 l , eff ( 1 ) g p , 1 l , eff ( 2 ) g p , 1 l , eff ( 2 ) * - g p , 1 l , eff ( 1 ) * g p , 2 l , eff ( 1 ) g p , 2 l , eff ( 2 ) g p , 2 l , eff ( 2 ) * - g p , 2 l , eff ( 1 ) * . . . . . . g p , n R l , eff ( 1 ) g p , n R l , eff ( 2 ) g p , n R l , eff ( 2 ) * - g p , n R l , eff ( 1 ) * - - - ( 8 )

Equally, can obtain and code word X le j φ∈ X 2corresponding equivalent channel matrix F 2, l

Figure BDA0000424913150000103

In formula:

Figure BDA0000424913150000104

equally, be easy to obtain respectively and code word

Figure BDA0000424913150000105

with

Figure BDA0000424913150000106

corresponding equivalent channel matrix

Figure BDA0000424913150000107

with

Figure BDA0000424913150000108

they equal respectively

Figure BDA0000424913150000109

can find out above 4 equivalent channel matrix F 1, l, F 2, l, with

Figure BDA00004249131500001011

each has the column vector of two quadratures, they have identical structure with the equivalent channel matrix of STBC-SM scheme, therefore the ML detector of STBC-SM scheme also can be applied to STBC-SM (n, k) scheme, this detector has linear decoding complexity, and its decoding complexity is 2cM.

3) optimization and the performance evaluation of STBC-SM (n, k) scheme

Minimum code gain distance (Coding Gain Distance, CGD) by derivation STBC-SM (n, k) scheme is optimized its anglec of rotation, and the performance of this scheme is analyzed.

3.1) minimum CGD and scheme optimization

The design criterion of Space Time Coding be ask any two STBC-SM (n, k) signal X and

Figure BDA0000424913150000111

between minimum CGD, X wherein, and make two errors between signal be

Figure BDA0000424913150000114

minimum CGD is defined as

δ min ( X ) = min X , X ^ det ( ΔΔ H ) - - - ( 10 )

Suppose STBC-SM (n, k) signal X and

Figure BDA0000424913150000116

label in their codeword set be separately respectively l and

Figure BDA0000424913150000117

the symbol that they comprised is separately respectively x iwith

Figure BDA0000424913150000118

can calculate error correlation matrix Δ Δ hthere is following form

ΔΔ H = β 1 ( | x 1 | 2 + | x 2 | 2 ) I 2 + β 2 ( | x ^ 1 | 2 + | x ^ 2 | 2 ) I 2 + k l , l ^ DD H - - - ( 11 )

In formula:

β 1 = w l - k l , l ^ w l , β 2 = w l ^ - k l , l ^ w l ^ , k l , l ^ = w l + w l ^ - d l , l ^ 2 ,

Wherein

Figure BDA00004249131500001111

represent ECC code word c lwith

Figure BDA00004249131500001112

between Hamming matrix, matrix D is defined as

D = 1 w l x 1 e j θ ^ x 2 e j θ ^ - x 2 * e - j θ ^ x 1 * e - j θ ^ - e jφ w l ^ x ^ 1 e jθ x ^ 2 e jθ - x ^ 2 * e - jθ x ^ 1 * e - jθ - - - ( 12 )

Use function

Figure BDA00004249131500001114

represent error correlation matrix Δ Δ hdeterminant, have

ζ ( φ , θ ^ , θ ) = Δ det ( ΔΔ H ) = κ 2 - 4 κ · cos φ · k l , l ^ · R { ( x ^ 1 x 1 * + x ^ 2 x 2 * ) e j ( θ - θ ^ ) } / w 1 w l ^ + 2 k l , l ^ 2 [ | x ^ 1 x 1 * + x ^ 2 x 2 * | 2 - 2 sin 2 φ · ( | x 1 | 2 + | x 2 | 2 ) ( | x ^ 1 | 2 + | x ^ 2 | 2 ) + R { ( x ^ 1 x 1 * + x ^ 2 x 2 * ) 2 e j 2 ( θ - θ ^ ) } ] / ( w l w l ^ ) - - - ( 13 )

In formula:

κ = Σ i = 1 2 ( | x i | 2 + | x ^ i | 2 ) .

For signal X and

Figure BDA00004249131500001117

various combination, function

Figure BDA00004249131500001118

have different values, table 3 has provided different

Figure BDA00004249131500001119

combination minor function

Figure BDA00004249131500001120

value.

Table 3 is different

Figure BDA00004249131500001121

combination minor function

Figure BDA00004249131500001122

value

Figure BDA00004249131500001123

1annotation: due to

Figure BDA00004249131500001124

the 3rd parameter be zero, therefore by its second parameter

Figure BDA00004249131500001125

with θ, represent.

Listed in table 3

Figure BDA0000424913150000121

functional value in, due to ζ (φ, 0,0)=ζ (φ, θ, θ), the minimum CGD that therefore obtains STBC-SM (n, k) scheme is

δ min ( X ) = min x i , x ^ i ∈ γ 0 ≤ l , l ^ ≤ L - 1 { ζ ( 0,0 , θ ) , ζ ( φ , 0,0 ) , ζ ( φ , 0 , θ ) , ζ ( φ , θ , 0 ) } - - - ( 14 )

In formula: γ represents M-PSK/QAM constellation.Therefore,, in order to obtain best performance, the optimal value of two anglecs of rotation is elected as

( φ opt , θ opt ) = arg max φ , θ δ min ( X ) - - - ( 15 )

(φ in (15) formula of employing opt, θ opt) time, can obtain δ min(X) >0, from the design criterion of Space Time Coding, so can guarantee that the exponent number of the emission diversity gain that STBC-SM (n, k) scheme obtains is 2.For STBC-SM (n, k) scheme at number of transmit antennas n t=4,6 and 8 o'clock, the optimal angle while adopting BPSK modulation is θ=pi/2 and φ=π/3, and the optimal angle while adopting QPSK modulation is θ=π/4 and π/143, φ=60, and the optimal angle while adopting 8-QAM modulation is θ=π/4 and π/180, φ=73.

3.2) BER performance analysis

When transmitted signal is X, be mistaken for

Figure BDA0000424913150000124

pair-wise error probability (Pairwise error probability, PEP) be defined as

P ( X → X ^ ) = 1 π ∫ 0 π 2 ( 4 sin 2 θ 4 sin 2 θ + ρ λ 1 ) n R ( 4 sin 2 θ 4 sin 2 θ + ρ λ 2 ) n R dθ - - - ( 16 )

In formula: λ 1and λ 2it is error correlation matrix Δ Δ htwo characteristic values.Due in each transmission intercal, STBC-SM (n, k) scheme is transmitted a 2 η bit, will

Figure BDA0000424913150000126

all 2 2 η=4LM 2in individual different code word, ask statistical average can obtain the upper bound of average bit error probability (BEP)

P b ≤ 1 2 2 η Σ X Σ X ^ N ( X , X ^ ) 2 η P ( X → X ^ ) - - - ( 17 )

In formula:

Figure BDA0000424913150000128

representing matrix X and

Figure BDA0000424913150000129

between different bit numbers.

4) experiment simulation

Simulation result when the present invention provides STBC-SM (n, k) scheme and adopts different transmit antennas to count, and compare with the error performance of STBC-SM and H-STBC-SM scheme.The reception antenna number that all emulation adopts is n r=4.In all analogous diagram, transverse axis represents the average signal-to-noise ratio (ρ) at each reception antenna place, and the longitudinal axis represents bit error rate (BER).All Performance Ratios are more all to get 10 in BER value -5in time, is made.

In Fig. 2, provide STBC-SM (n, k) scheme and adopted respectively n t=4 and n tthe performance curve in the BER performance curve of=6 o'clock and the BEP upper bound that calculated by (17) formula, the modulation system of employing is respectively BPSK and QPSK.Work as n t=4 o'clock, the ECC of employing was c 0=[0 1] and c 1=[1 0].Work as n t=6 o'clock, adopt (3,2) ECC, wherein last position of each code word mends 1, has c 0=[0 0 1], c 1=[0 1 0], c 2=[1 0 0] and c 3=[1 1 1].As seen from Figure 2, derive and approach very much between the BEP upper bound drawing and the BER curve obtaining by Monte Carlo simulation, particularly in the higher region of SNR.

In Fig. 3 to having adopted n tthe STBC-SM of=6 transmitting antennas (3,2) and H-STBC-

SM scheme

3,4 and the transmission rate of 5bits/s/Hz under BER performance compare.Because STBC-SM scheme is at n t=8 o'clock, state two schemes and there is identical spectrum efficiency (2+log identical order of modulation M is lower and upper 2m) bits/s/Hz, compares so also provided the BER curve of STBC-SM in Fig. 3.As seen from Figure 3, work as n t=6 and transmission rate while being 5bits/s/Hz, STBC-SM (3,2) and H-STBC-SM scheme have all adopted 8-QAM modulation, and now the performance of two schemes is almost identical; When adopting QPSK modulation, the spectrum efficiency of these three kinds of schemes is 4bits/s/Hz, see now STBC-SM (3,2) performance is better than H-STBC-SM slightly, and the performance of STBC-SM (3,2) and H-STBC-SM is all approached with having adopted the performance of the STBC-SM of 8 transmit antennas very much.Now the performance difference between these three kinds of schemes can be made an explanation by minimum CGD by the normalization of its acquisition, and the minimum CGD value of normalization of STBC-SM, STBC-SM (3,2) and H-STBC-SM is respectively 1.22,1.0 and 0.42.When adopting BPSK modulation, these three kinds of schemes can obtain the spectrum efficiency of 3bits/s/Hz.Can see, now STBC-SM (3,2) has the SNR gain of about 1dB than H-STBC-SM, and the performance of STBC-SM (3,2) is approached the STBC-SM scheme that has adopted 8 transmitting antennas very much.Performance difference between three kinds of schemes can be made an explanation by minimum CGD by their normalization equally in this case, and the minimum CGD value of the now normalization of STBC-SM, STBC-SM (3,2) and H-STBC-SM is respectively 4.69,2.86 and 1.21.As seen from Figure 3, the BER slope of a curve of these three kinds of schemes remains unchanged, and this illustrates that they can obtain 2n rdiversity order.In Fig. 3, can draw, compare with STBC-SM, the algorithm proposing in this patent can be take very little BER loss as 2 transmitting antennas of cost saving, thereby has reduced the hardware complexity of transmitting terminal.

In Fig. 4, provided while adopting 8 transmitting antennas the BER performance curve of STBC-SM (4,3) and STBC-SM scheme.Because this two schemes is at n twithin=8 o'clock, their code word sum c is unequal, in order under identical spectrum efficiency, this two schemes to be carried out to fair comparison, and when spectrum efficiency is 4bits/s/Hz, the symbol x in STBC-SM (4,3) scheme 1from BPSK, take out, and x 2from QPSK, take out, corresponding optimal angle is respectively θ=pi/2 and π/143, φ=60.When spectrum efficiency is 6bits/s/Hz, the symbol x in STBC-SM (4,3) scheme 1from 8-QAM, take out, and x 2from 16-QAM, take out, corresponding optimal angle is respectively θ=π/4 and π/158, φ=47.As can be seen from Figure 4, the performance of STBC-SM when 6bits/s/Hz (4,3) scheme and the performance of STBC-SM are very approaching, and STBC-SM (4,3) has the performance gain of about 0.8dB than STBC-SM when 4bits/s/Hz.But, STBC-SM (4,3) scheme 4 and during 6bits/s/Hz calculative maximum likelihood searching number of times be respectively 192 and 768 times, and the calculation times of STBC-SM is respectively 128 and 512 times.Therefore work as n t=8 o'clock, the decoding complexity of STBC-SM (4,3) was a little more than STBC-SM scheme.

Technique effect of the present invention can compare from the availability of frequency spectrum and two aspects of error performance and existing STBC-SM and H-STBC-SM scheme.

1) availability of frequency spectrum

The availability of frequency spectrum of the spatial modulation scheme of Space Time Coding is

η=(1/2)log 2(cM 2)=(1/2)log 2c+log 2M

In formula: parameter c is total code word number of spatial modulation, the order of modulation of M is-symbol, the 1/2nd, because STBC-SM signal has taken two symbol periods.From above formula, the spectrum efficiency of STBC-SM forms by two: first is to spatial modulation, the availability of frequency spectrum also selection of antenna being obtained; Second is to two availability of frequency spectrums that symbol transmission obtains in Alamouti.When adopting identical order of modulation, the spectrum efficiency of different STBC-SM schemes depends on the size of code word sum c completely, and the c value that can design is larger, and the spectrum efficiency obtaining is higher.In table 2, provided STBC-SM, H-STBC-SM and STBC-SM (n, k) scheme are in the situation that the c value of different number of transmit antennas.

2) error performance

Referring to Fig. 2~Fig. 4, the present invention utilizes this algorithm fairly obvious with respect to prior art to the lifting effect of systematic function.

Claims (3)

1.一种基于(n,k)纠错码的空时编码空间调制方法,其特征在于,包括以下步骤:1. a space-time coded space modulation method based on (n, k) error correction code, it is characterized in that, comprises the following steps: 第一步:将输入的随机比特流分为两个部分,前k个比特用来选择ECC中的码字cl,后面的2log2M个比特用来选择Alamouti编码中的符号对(x1,x2),其中M表示符号的调制阶数;Step 1: Divide the input random bit stream into two parts, the first k bits are used to select the code word c l in ECC, and the latter 2log 2 M bits are used to select the symbol pair (x 1 , x 2 ), where M represents the modulation order of the symbol; 第二步:将Alamouti码和其旋转矩阵作为基本的STBC码块,则Alamouti码S和其旋转矩阵分别表示为:The second step: take the Alamouti code and its rotation matrix as the basic STBC code block, then the Alamouti code S and its rotation matrix Respectively expressed as: S = x 1 x 2 - x 2 * x 1 * 和 S ~ = x 1 e jθ x 2 e jθ - x 2 * e - jθ x 1 * e - jθ - - - ( 1 ) S = x 1 x 2 - x 2 * x 1 * and S ~ = x 1 e jθ x 2 e jθ - x 2 * e - jθ x 1 * e - jθ - - - ( 1 ) 其中,x1和x2是两个取自于M-PSK/QAM星座的符号,θ表示旋转角度,

Figure FDA0000424913140000014

表示对-x2取共轭,

Figure FDA0000424913140000015

表示对x1取共轭;
Among them, x 1 and x 2 are two symbols taken from the M-PSK/QAM constellation, θ represents the rotation angle,

Figure FDA0000424913140000014

means to take the conjugate of -x 2 ,

Figure FDA0000424913140000015

Represents the conjugate of x 1 ;
第三步:根据Alamouti码和其旋转矩阵生成STBC-SM(n,k)码本集合,每次传输信息时,生成STBC-SM(n,k)信号从nT个天线上发送出去。Step 3: Generate a STBC-SM(n,k) codebook set according to the Alamouti code and its rotation matrix, and generate a STBC-SM(n,k) signal to send out from n T antennas each time information is transmitted. 2.根据权利要求1所述的基于(n,k)纠错码的空时编码空间调制方法,其特征在于:所述第三步中,生成STBC-SM(n,k)码本集合的方法具体为:2. the space-time coding space modulation method based on (n, k) error correcting code according to claim 1, it is characterized in that: in the described 3rd step, generate STBC-SM (n, k) code book collection The method is specifically: 假定(n,k)ECC能够生成一个大小为L=2k的码字集合AECC,则对于nT=2n个发射天线,STBC-SM(n,k)星座集合中的两个码本X1和X2构造为Assuming that (n,k)ECC can generate a codeword set A ECC of size L=2 k , then for n T =2n transmit antennas, two codebooks X in the STBC-SM(n,k) constellation set 1 and X 2 are constructed as Xx 11 == {{ Xx ll ,, Xx ~~ ll }} ,, Xx 22 == {{ Xx ll ,, Xx ~~ ll }} ee jφjφ ,, -- -- -- (( 22 )) 其中,Xl

Figure FDA0000424913140000017

分别定义为:
Among them, X l and

Figure FDA0000424913140000017

are defined as:
Xx ll == ΔΔ cc ll ⊗⊗ SS // ww ll == BB ll (( 11 )) BB ll (( 22 )) .. .. .. BB ll (( nno )) Xx ~~ ll == ΔΔ cc ll ⊗⊗ SS ~~ // ww ll == BB ~~ ll (( 11 )) BB ~~ ll (( 22 )) .. .. .. BB ~~ ll (( nno )) -- -- -- (( 33 )) 公式(2)中每个码本包含2L个码字Xl

Figure FDA0000424913140000019

其中,l=0,…,L-1,φ是两个码本之间的旋转角度;公式(3)中,cl∈AECC是一个1×n维的ECC码字,wl是ECC码字cl的汉明重量,符号

Figure FDA00004249131400000110

表示Kronecker积;2×2维矩阵

Figure FDA00004249131400000111

Figure FDA00004249131400000112

分别表示码字Xl中的第n个Alamouti块,其中cl(n)表示cl的第n个元素;最后得到的STBC-SM(n,k)星座集合则表示为

Figure FDA00004249131400000114

Each codebook in formula (2) contains 2L codewords X l and

Figure FDA0000424913140000019

Among them, l=0,...,L-1, φ is the rotation angle between the two codebooks; in formula (3), c lA ECC is a 1×n-dimensional ECC codeword, w l is the ECC Hamming weight of codeword c l , sign

Figure FDA00004249131400000110

Represents the Kronecker product; 2×2-dimensional matrix

Figure FDA00004249131400000111

and

Figure FDA00004249131400000112

represent the codewords X l and The nth Alamouti block in , where c l (n) represents the nth element of c l ; the finally obtained STBC-SM (n, k) constellation set is expressed as

Figure FDA00004249131400000114

3.根据权利要求1或2所述的基于(n,k)纠错码的空时编码空间调制方法,其特征在于,还包括以下步骤:3. the space-time coded spatial modulation method based on (n, k) error correction code according to claim 1 and 2, is characterized in that, also comprises the following steps: 第四步:STBC-SM(n,k)的检测:Step 4: Detection of STBC-SM(n,k): 采用STBC-SM(n,k)方案传输时,由于STBC-SM(n,k)码字的正交性能够得到其等价的信道矩阵也具有正交性,因而该调制方案的最大似然检测算法将简化为一个线性过程,具体方法如下:When the STBC-SM(n,k) scheme is used for transmission, due to the orthogonality of the STBC-SM(n,k) codewords, its equivalent channel matrix also has orthogonality, so the maximum likelihood of the modulation scheme The detection algorithm will be reduced to a linear process as follows: 当将发送STBC-SM(n,k)码字的系统方程简化为传输Alamouti编码的系统方程时,得出与码字Xl∈X1和Xle∈X2所对应的2nR×2维信道矩阵,且分别具有如下的形式:When the system equations for transmitting STBC-SM(n,k ) codewords are simplified to the system equations for transmitting Alamouti codes, the 2n R × 2-dimensional channel matrix, and respectively have the following forms: F 1 , l = Δ g p , 1 l , eff ( 1 ) g p , 1 l , eff ( 2 ) g p , 1 l , eff ( 2 ) * - g p , 1 l , eff ( 1 ) * g p , 2 l , eff ( 1 ) g p , 2 l , eff ( 2 ) g p , 2 l , eff ( 2 ) * - g p , 2 l , eff ( 1 ) * . . . . . . g p , n R l , eff ( 1 ) g p , n R l , eff ( 2 ) g p , n R l , eff ( 2 ) * - g p , n R l , eff ( 1 ) * 和 f 1 , l = Δ g p , 1 l , eff ( 1 ) g p , 1 l , eff ( 2 ) g p , 1 l , eff ( 2 ) * - g p , 1 l , eff ( 1 ) * g p , 2 l , eff ( 1 ) g p , 2 l , eff ( 2 ) g p , 2 l , eff ( 2 ) * - g p , 2 l , eff ( 1 ) * . . . . . . g p , no R l , eff ( 1 ) g p , no R l , eff ( 2 ) g p , no R l , eff ( 2 ) * - g p , no R l , eff ( 1 ) * and 公式(4)中,

Figure FDA0000424913140000023

Figure FDA0000424913140000024

分别表示2×1维向量

Figure FDA0000424913140000025

的第一个和第二个元素,向量

Figure FDA0000424913140000026

是wl个不同的信道向量gk,i之和,因此把

Figure FDA0000424913140000027

称为与码字Xl∈X1所对应的等效的信道向量,具有wl个元素的向量p表示码字Xl中所激活的天线对的标号;而向量gk,i=[h(2k-1),i h2k,i]T,k=1,…,n,其中的元素h2k,i表示从第2k个发射天线到第i个接收天线之间的信道增益,T表示对向量作转置;等价信道矩阵F1,l和F2,l分别包含L种不同的实现;
In formula (4),

Figure FDA0000424913140000023

and

Figure FDA0000424913140000024

represent 2×1-dimensional vectors respectively

Figure FDA0000424913140000025

The first and second elements of , a vector

Figure FDA0000424913140000026

is the sum of w l different channel vectors g k,i , so put

Figure FDA0000424913140000027

is called the equivalent channel vector corresponding to the codeword X l ∈ X 1 , the vector p with w l elements represents the label of the activated antenna pair in the codeword X l ; and the vector g k,i = [h (2k-1),i h 2k,i ] T , k=1,…,n, where the element h 2k,i represents the channel gain from the 2kth transmit antenna to the i-th receive antenna, and T represents Transpose the vector; the equivalent channel matrix F 1,l and F 2,l respectively contain L different realizations;
同样,得到分别与码字

Figure FDA0000424913140000029

所对应的等效信道矩阵

Figure FDA00004249131400000210

Figure FDA00004249131400000211

且分别等于

Figure FDA00004249131400000212

以上4个等效的信道矩阵F1,l、F2,l

Figure FDA00004249131400000213

Figure FDA00004249131400000214

每一个都具有两个正交的列向量,它们与STBC-SM方案的等效信道矩阵具有相同的结构,因此STBC-SM方案的ML检测器也能够应用于STBC-SM(n,k)方案,该检测器具有线性译码复杂度,其译码复杂度为2cM。
Similarly, get the code words respectively and and

Figure FDA0000424913140000029

The corresponding equivalent channel matrix

Figure FDA00004249131400000210

and

Figure FDA00004249131400000211

and are equal to

Figure FDA00004249131400000212

The above four equivalent channel matrices F 1,l , F 2,l ,

Figure FDA00004249131400000213

and

Figure FDA00004249131400000214

Each has two orthogonal column vectors, which have the same structure as the equivalent channel matrix of the STBC-SM scheme, so the ML detector of the STBC-SM scheme can also be applied to the STBC-SM(n,k) scheme , the detector has linear decoding complexity, and its decoding complexity is 2cM.
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