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 PDFInfo
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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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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
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 number2 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
be expressed as:
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,
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 )
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
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
with
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
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:
With
In formula (4),
with
represent respectively 2 * 1 dimensional vectors first and second element, vector
w lindividual different channel vector g k,isum, therefore handle
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
with
corresponding equivalent channel matrix
with
and equal respectively above 4 equivalent channel matrix F 1, l, F 2, l,
with
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
be expressed as:
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,
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 )
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
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
with
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
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:
With
In formula (4),
with
represent respectively 2 * 1 dimensional vectors first and second element, vector w lindividual different channel vector g k,isum, therefore handle
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
with
corresponding equivalent channel matrix
with
and equal respectively
above 4 equivalent channel matrix F 1, l, F 2, l,
with
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
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 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
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
represent that Kronecker is long-pending.2 * 2 dimension matrixes with
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
front8 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
front3 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
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
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
with
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
middle taking-up, by each column vector h of channel matrix H ibe expressed as
form, g wherein k,i=[h (2k-1), ih 2k, i] t, k=1 ..., n represents and code word X lin k Alamouti piece
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
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:
with represent respectively
first and second element.Again by 2 * 1 all dimensional vectors
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
In formula:
equally, be easy to obtain respectively and code word
with
corresponding equivalent channel matrix
with
they equal respectively
can find out above 4 equivalent channel matrix F 1, l, F 2, l, with
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
between minimum CGD, X wherein, and make two errors between signal be
minimum CGD is defined as
δ min ( X ) = min X , X ^ det ( ΔΔ H ) - - - ( 10 )
Suppose STBC-SM (n, k) signal X and
label in their codeword set be separately respectively l and
the symbol that they comprised is separately respectively x iwith
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
represent ECC code word c lwith
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 )
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
various combination, function
have different values, table 3 has provided different
combination minor function
value.
Listed in table 3
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
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
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 )
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 scheme3,4 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)
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