CN100454776C - Method for acquiring full marks set gain based on diagonal BLAST structure - Google Patents

Abstract

The present invention relates to a method for obtaining full diversity gain on the basis of a diagonal hierarchy space-time structure. A group of optimal random basis matrixes are firstly adopted to sterically modulate the transmission group within each symbol period in a vertical hierarchy space-time (V-BLAST) structure, and then, signals in airspace are transmitted in time domain along the direction of a diagonal line. The transmitted format can obtain full diversity gain when the spectral utilization rate of the vertical hierarchy space-time (V-BLAST) structure does not loses, and both the spectral utilization rate and the performance are optimized. Full diversity gain can be obtained when the spectral utilization rate of the V-BLAST structure is not reduced, so that the transmission performance of a system is greatly improved. In addition, an FD-DLST structure can carry out detection by adopting continuously nulling and neutralizing algorithms, so that a receiver has lower complexity for realization. Simulation results further verifies the superior performance of the FD-DLST structure.

Description

A kind of method that obtains the full diversity gain based on the diagonal angle layered space-time architecture

Technical field

The present invention relates to the space-time emission diversity technology in a kind of multi-aerial radio communication system, particularly a kind of method that obtains the full diversity gain based on the diagonal angle layered space-time architecture

Background technology

Multiple-input and multiple-output (Multiple Input Multiple Output, MIMO) (the Space-Time Coding of the Space Time Coding in the system, STC) technology provides high-speed data transmission and superior systematic function owing to can make full use of space resources, thereby wide application prospect is arranged in following radio communication.Document (MaXiaoli, Giannakis G.B.Full-diversity full-rate complex-field space-time coding.IEEETrans.on Signal Processing, 2003,51 (11): 2917-2930.) existing Space Time Coding generally is divided into two classes, i.e. (rate-oriented) of (performance-oriented) of performance type and speed type.Orthogonal space time packet (Alamouti S.M.A simple transmitter diversity scheme for wirelesscommunications.IEEE J.on Select.Areas Comm., 1998,16 (8): 1451-1458.); (TarokhV, Jafarkhani H, Calderbank A.R.Space-time block codes from orthogonal designs.IEEE Trans.on Info.Theory, 1999,45 (5): 1456-1467.) (Orthogonal Space-Time BlockCode, OSTBC) with based on Space Time Coding (the Xin Y of constellation precoding, Wang Z D, Giannakis G.B.Space-time diversity systems based on linear constellation precoding.IEEE Trans.onWireless Commun., 2003,2 (2): 294-309.) belong to the performance type, and (Vertical-Bell Labs Layered Space-Time during the Bell Laboratory vertical layered space, V-BLAST) structure (Wolniansky P.W, Foschini G.J, Golden G.D, et al.V-BLAST:An architecture for Realizing very high datarates over the rich-scattering wireless channel.In Proc.1998 URSI Int.Symp.Signals, Systems, and Electronics, New York, 1998:295-300.) and linear dispersed (LinearDispersion, LD) Space Time Coding (Hassibi B, Hochwald B.M.High-rate codes that are linearin space and time.IEEE Trans.on Info.Theory, 2002,48 (7): 1804-1824.) then be summed up as the speed type.

The OSTBC that people such as Alamouti and Tarokh proposed has can provide advantages such as full diversity gain and decoding complex degree are low, but it can not be generalized in the mimo system with any number of transmit antennas, and the symbolic number maximum of transmission can only reach 1 in its each symbol period, thereby the availability of frequency spectrum is lower.And for the V-BLAST structure of speed type, its adopts space division multiplexing form to transmit data, has the very high availability of frequency spectrum, when adopting M transmitting antenna, but in each symbol period a parallel transmission M symbol.At receiving terminal, when reception antenna number during more than or equal to number of transmit antennas, the V-BLAST structure adopts a kind of counteracting serial interference of ordering, and (Ordered Successive Interference Cancellation, OSIC) method detect to send data, has lower decoding complex degree.But the ability of V-BLAST structure opposing channel fading is relatively poor, can not make full use of the diversity gain that many antennas provide.From above-mentioned two kinds of characteristics that typical Space Time Coding had as can be seen, if can realize optimization on the availability of frequency spectrum and the performance simultaneously, will be highly significant.

For this target, many scholars have carried out unremitting exploration.Document (Tao Meixia, Cheng R.S.Generalized layered space-time codes for high data rate wireless communications.IEEE Trans.on Wireless commun., 2004,3 (4): 1067-1075.) transmitting antenna is divided into groups, adopt the coding form of OSTBC in every group, then adopted the V-BLAST structure to send data between each group.This is actually a kind of mode of concatenated coding.Similarly thought is at document (Baro S, Bauch G, Pavlic A, etal.Improving BLAST performance using space-time block codes and turbo decoding.IEEE Proc.Globecom.2000 also can see in 2:1067-1071.).But this mode requires not only will to consider to eliminate the interference between each group when receiving terminal detects, and the interference in also will the elimination group has increased the implementation complexity of system undoubtedly.

Summary of the invention

The objective of the invention is to overcome the shortcoming of above-mentioned prior art, provide a kind of and obtained the method that full diversity gains based on the diagonal angle layered space-time architecture, we are called FD-DLST (Full Diversity-Diagonal Layered Space-Time) structure with the transmission structure that this method had.The FD-DLST structure can obtain the full diversity gain in (V-BLAST) structure availability of frequency spectrum when not losing vertical layered space, realize the dual optimization on the availability of frequency spectrum and the performance.

For achieving the above object, the technical solution used in the present invention is:

1) makes up the DLST structure

Suppose that mimo system has M transmitting antenna, the signal that N reception antenna, m antenna send in t symbol period is s _Mt, (m=1 wherein ..., M; T=1 ..., T), the signal vector that sends from transmitting terminal in t symbol period is b like this _t=[s _1ts _2tS _Mt] ^T, subscript () wherein ^TExpression is got transposition to matrix, for the emission signal vector b in T the symbol period _t, with one group of M * M dimension basic matrix Φ _tIt is done to superpose after the modulation on the space again, obtain the symbolic vector of a M * 1 dimension

$B=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\Φ}}_t{b}_t=\mathrm{Qb}---(r-1)$

In the formula: data symbol vector b is defined as $b={\left[\begin{array}{cccc}{b}_1^T& b_2^T& \·\·\·& b_T^T\end{array}\right]}^T,$ M * MT dimension matrix Q is defined as Q=[Φ ₁Φ ₂Φ _T], because matrix Q is T basic matrix Φ _tThrough what obtain after the combination, be referred to as the combination basic matrix;

Subsequently, again symbolic vector B is sent after diagonal is launched in time domain, therefore construct the DLST structure that obtains in a first step and can represent with following formula

$C=\mathrm{diag}\left(B\right)=\mathrm{diag}\left(\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\Φ}}_t{b}_t\right)=\mathrm{diag}\left(\mathrm{Qb}\right)---(r-2)$

2) select the optimal base matrix to make the DLST structure obtain the full diversity gain

The purpose of this step is exactly how to select to make up basic matrix Q=[Φ ₁Φ ₂Φ _T] just can make the DLST structure obtain the full diversity gain, the coding gain of DLST structure is expressed from the next

$g_c=\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}=\underset{e\≠0}{\min }{\left(\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\left|q_{i}e\right|}^2\right)}^{1/M}---(r-3)$

In the formula: R _EBe matrix

E is the error in label vector, the vectorial q of row of 1 * MT dimension _iThe i of representing matrix Q is capable; If the capable vector of combination basic matrix Q satisfies condition | q _iE| ²≠ 0, just can make the DLST structure obtain the full diversity gain; Further, by the expression of coding gain $g_c=\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}=\underset{e\≠0}{\min }{\left(\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\left|q_{i}e\right|}^2\right)}^{1/M}$ As can be seen, should select to make coding gain be maximum combination basic matrix Q as the optimal base matrix, the DLST structure that draws like this can not only obtain line diversity all over the sky and coding gain maximum, i.e. optimal base matrix Q _OptFor

$Q_{\mathrm{opt}}=\arg \underset{Q}{\max }\left(g_c\right)=\arg \underset{Q}{\max }\left\{\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}\right\}---(r-4)$

Adopt following method to obtain optimal base matrix Q _Opt:

Consider the power constraint condition, matrix Q is configured to satisfy the random matrix of following orthogonality condition

QQ ^H＝T·I _M (r-5)

In the formula: I _MExpression M * M ties up unit matrix, subscript () ^HExpression is got conjugate transpose to matrix, just can obtain row orthogonal matrix Q by the method for the Hermitian matrix being done the Cayley conversion;

At first all obeying average with each element is 0, and variance is that the MT * 1 dimension random vector β of 1 multiple Gaussian Profile generates Hermitian matrix A=β β ^H, A wherein ^H=A does the Cayley conversion to A, obtains the unitary matrice U of MT * MT dimension

U＝(I _MT+jA) ^-1(I _MT+jA) (r-6)

In the formula: I _MTExpression (MT) * (MT) dimension unit matrix, $j=\sqrt{-1},$ And then the preceding M that gets unitary matrice U is capable, is met the capable orthogonal matrix Q of condition (r-5), promptly

$Q=\sqrt{T}\·\mathrm{ZU}---(r-7)$

In the formula: matrix Z=[I _M0 _{M * (MT-M)}], wherein 0 _{M * (MT-M)}Expression M * (MT-M) dimension null matrix;

Can produce the process that a plurality of different random vector β repeat the capable orthogonal matrix Q of surface construction, therefore obtain a plurality of combination basic matrix Q at random, can make coding gain g from wherein choosing again _cA maximum combination basic matrix is as optimal base matrix Q _Opt, promptly the optimal base matrix satisfies formula (r-4), with this optimal base matrix Q _OptBe updated in the formula (r-2), just can obtain to obtain the DLST structure of full diversity gain.

The basic matrix at random that the present invention at first adopts one group of optimum during to vertical layered space in (V-BLAST) structure the transmission grouping in each symbol period carry out modulation on the space, again the signal in the spatial domain is sent along diagonal in time domain subsequently.Transmission form of the present invention can obtain the full diversity gain in (V-BLAST) structure availability of frequency spectrum when not losing vertical layered space, realize the dual optimization on the availability of frequency spectrum and the performance.

Description of drawings

(V-BLAST) structure sent the emitter junction composition of data when Fig. 1 was vertical layered space;

Fig. 2 is the emitter junction composition that the present invention (FD-DLST) structure sends data;

The error performance comparison diagram of (V-BLAST) structure when Fig. 3 is the present invention's (FD-DLST) structure and vertical layered space, wherein abscissa is a signal to noise ratio, ordinate is the error rate.

Embodiment

Below in conjunction with accompanying drawing the present invention is described in further detail.

The present invention realizes by following steps:

1) constructing system model

The mimo system that will have M transmitting antenna, a N reception antenna be expressed as (M, N).When adopting the V-BLAST structure to send data, its emitting structural as shown in Figure 1.When at first carrying out sky to the symbol sebolic addressing of importing, transmitting terminal along separate routes, it is divided into T the grouping b that length is M _t=[s _1ts _2tS _Mt] ^T=1,2 ..., T), subscript () ^TExpression is got transposition to matrix, in each symbol period a grouping is sent from M antenna is parallel then, wherein s _Mt(m=1 ..., M; T=1 ..., T) be illustrated in the signal that sends from m transmitting antenna in t the symbol period, so the sending metrix of V-BLAST structure should be expressed as

For make the V-BLAST structure empty, the time obtain better diversity on two-dimentional, at first use one group of basic matrix Φ _t(t=1 ..., T) to grouping b _t(t=1 ..., T) carry out modulation on the space, obtain the symbolic vector of a M * 1 dimension

$B=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\Φ}}_t{b}_t=\mathrm{Qb}---\left(2\right)$

Wherein vectorial $b={\left[\begin{array}{cccc}{b}_1^T& b_2^T& \·\·\·& b_T^T\end{array}\right]}^T$ Be data symbol vector, M * MT dimension matrix Q is defined as

Q＝[Φ ₁?Φ ₂…Φ _T] (3)

Subsequently, again symbolic vector B after launching, diagonal is sent code word matrix in the time of to obtain FD-DLST structure empty thus in time domain

$C=\mathrm{diag}\left(B\right)=\mathrm{diag}\left(\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\Φ}}_t{b}_t\right)---\left(4\right)$

Definition availability of frequency spectrum R is the information bit of emission in average every symbol period, and unit is bps/Hz.This transmission form of FD-DLST has sent MT symbol in M symbol period, so its availability of frequency spectrum is R=TL bps/Hz, and wherein L represents the bit number that every symbol contains.In order to make FD-DLST keep the identical availability of frequency spectrum with the V-BLAST structure, the present invention gets T=M.

The assumed wireless channel is the smooth Rayleigh fading channel of quasistatic, and then N * M dimensional signal the Y that receives on N reception antenna can be expressed as

Y＝HC+W (5)

Wherein H is that N * M ties up channel matrix, the element h among the H _JiRepresent that i transmitting antenna is to the multiple path gain between j the reception antenna; W is that N * M ties up additive white Gaussian noise; The vectorial q of row with 1 * MT dimension _t(i=1 ..., M) i of representing matrix Q is capable, and the code word matrix C of transmission is

C＝diag(q ₁b，q ₂b，…，q _Mb) (6)

Be the FD-DLST structure the transmission form as shown in Figure 2.Like this, received signal can be expressed as again

At receiving terminal, for data symbol vector b is separated from code word matrix, to Y ^TBoth sides are done to obtain by row stretching computing vec ()

In the formula: y=vec (Y ^T), n=vec (W ^T), the vectorial h among the matrix G _j(j=1 ..., N) j of expression channel matrix H is capable.Can see that the relational expression (7) that will import, export by conversion is equivalent to (MT, mimo system MN), thereby output can use formula (8) to represent;

2) diversity gain of FD-DLST structure and coding gain

Suppose that receiving terminal has desirable channel condition information (CSI) and known basic matrix Q, for the FD-DLST structure, code word C=diag (Qb) misjudge is if receiving terminal will send when empty $\hat{C}=\mathrm{diag}\left(Q\hat{b}\right),$ The symbolic vector of mistaken verdict wherein $\hat{b}\≠b,$ Then make the code word error matrix $E=C-\hat{C},$ The error in label vector $e=b-\hat{b}.$ Definition M * M ties up matrix

In the formula: subscript () ^HExpression is got conjugate transpose to matrix.By the design criterion of Space Time Coding as can be known, if receiving terminal has N antenna, the diversity gain of Space Time Coding is defined as $g_d=\underset{e\≠0}{\min }\mathrm{rank}\left(R_E\right)\·N$ (Tarokh V, SeshadriN, Calderbank A.R.Space time codes for high data rate wireless communication:Performance analysis and code construction.IEEE Trans.on Info.Theory, 1998,44 (2): 744-765.), wherein rank of matrix is asked in rank () expression.From formula (9) as can be seen, if | q _iE| ²≠ 0 (i=1 ..., M), then can make matrix R _EFull rank, the FD-DLST structure just can obtain full diversity gain MN like this.

If matrix R _EMinimum order be r, establish R _ER nonzero eigenvalue be λ _i(i=1 ..., r), then the coding gain of Space Time Coding should be defined as $g_c=\underset{e\≠0}{\min }{\left(\underset{i=1}{\overset{r}{\mathrm{\Π}}}{\mathrm{\λ}}_i\right)}^{1/r}$ (Tarokh V, Seshadri N, Calderbank A.R.Space-timecodes for high data rate wireless communication:Performance analysis and codeconstruction.IEEE Trans.on Info.Theory, 1998,44 (2): 744-765.), as matrix R _EDuring full rank, coding gain then is $g_c=\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}.$ Be easy to find out from formula (9), work as R _EDuring full rank, the coding gain of FD-DLST structure is

$g_c=\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}=\underset{e\≠0}{\min }{\left(\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\left|q_{i}e\right|}^2\right)}^{1/M}---\left(10\right)$

3) selection of optimal base matrix

We need seek the basic matrix of one group of optimum, make the FD-DLST structure can obtain full diversity gain and maximum coding gain.Be without loss of generality, the energy of establishing each incoming symbol is 1, i.e. E{|s _Mt| ²}=1 (m=1 ..., M; T=1 ..., T).Transmit signal power on the every day line in the symbol period is carried out normalization, and the energy that obtains sending the FD-DLST structure is $E\left\{{\left|\right|C\left|\right|}_F^2\right\}=\mathrm{MT},$ ‖ ‖ wherein _FThe Frobenius norm of representing matrix, again because

$E\left\{{\left|\right|C\left|\right|}_F^2\right\}=E\left\{{\left|\right|B\left|\right|}_2^2\right\}=E\left\{B^{H}B\right\}=E\left\{\mathrm{tr}(B\·B^H)\right\}=\mathrm{tr}\left(\mathrm{QE}\right\{b\·b^H\left\}{Q}^H\right)---\left(11\right)$

‖ ‖ in the following formula ₂The 2-norm of expression vector, matrix trace is asked in tr () expression.Because E{bb ^H}=I _MT, so basic matrix Q=[Φ ₁Φ ₂Φ _T] should satisfy the power constraint condition

tr(Q·Q ^H)＝MT (12)

Consider power constraint formula (12), structure satisfies the random matrix Q as descending orthogonality condition

QQ ^H＝T·I _M (13)

In the formula: I _MExpression M * M ties up unit matrix, to this, we are by making method (the Jing Ymdi of Cayley conversion to the Hermitian matrix, Hassibi B.Unitary space-time modulation via cayley transform.IEEE Trans. on Signal Processing, 2003,51 (11): 2891-2904.) obtain row orthogonal matrix Q;

At first all obeying average with each element is 0, and variance is that the MT * 1 dimension random vector β of 1 multiple Gaussian Profile generates Hermitian matrix A=β β ^H, be easy to verify A ^H=A.A is done the Cayley conversion, can obtain the unitary matrice U of MT * MT dimension

U＝(I _MT+jA) ^-1(I _MT+jA) (14)

In the formula: $j=\sqrt{-1}.$ And then the preceding M that gets unitary matrice U is capable, is met the capable orthogonal matrix Q of condition (13)

$Q=\sqrt{T}\·\mathrm{ZU}---\left(15\right)$

In the formula: matrix z=[I _M0 _{M * (MT-M)}], wherein 0 _{M * (MT-M)}Expression M * (MT-M) dimension null matrix.At last, we adopt method (the Xin Y of random search, Wang Z D, Giannakis G.B.Space-time diversity systemsbased on linear constellation precoding.IEEE Trans.on Wireless Commun., 2003,2 (2): 294-309.); (Heath Jr R W, Paulraj A.J.Linear dispersion codes for MIMO systemsbased on frame theory.IEEE Trans.on Signal Processing, 2002,50 (10): 2429-2441.), from basic matrix (15), select the optimal base matrix.

Take all factors into consideration the diversity gain and the coding gain of FD-DLST structure, we select to make formula (10) to be one group of maximum basic matrix.Because formula has comprised matrix R in (10) _EBe this condition of full rank, the basic matrix Q of gained can make the FD-DLST structure obtain full diversity gain and maximum coding gain like this, and promptly Zui You one group of basic matrix should be

$Q_{\mathrm{opt}}=\arg \underset{Q}{\max }\left(g_c\right)=\arg \underset{Q}{\max }\left\{\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}\right\}---\left(16\right)$

4) detection of FD-DLST structure

At receiving terminal, we detect the data symbol vector in the FD-DLST structure from the input of equivalence, output relation formula (8) $b={\left[\begin{array}{cccc}{b}_1^T& b_2^T& \·\·\·& b_T^T\end{array}\right]}^T.$ For in the formula (8) (channel matrix of equal value is x=GQ for MT, MN) mimo system.Suppose that receiving terminal has desirable channel estimating and known basic matrix Q, optimum detection scheme is that maximum likelihood (ML) detects, and it can detect a plurality of transmission signals simultaneously from received signal.But because the FD-DLST structure has very high transmission rate, if contain 2 in the constellation at input data symbol place ^LIndividual symbol need search for 2 when then adopting Maximum Likelihood Detection ^LMTIndividual possible symbolic vector, so its decoding complex degree is the index increase with LMT.

For this reason, output signal in the formula (8) has been adopted continuous ZF and cancellation algorithms (the Wolniansky P.W of V-BLAST, Foschini G.J, Golden G.D, et al.V-BLAST:An architecture forRealizing very high data rates over the rich-scattering wireless channel.In Proc.1998URSI Int.Symp.Signals, Systems, and Electronics, New York 1998:295-300.) detects.This algorithm has adopted the thought of serial interference elimination (SIC), its detection order at first detects the strongest signal according to the size of signal to noise ratio, offsets the interference of this signal to other signal then from received signal, iteration successively is until the data that detect all layers.Adopt the V-BLAST detection algorithm, can make the FD-DLST structure have lower decoding complex degree, but with respect to the V-BLAST structure, its shortcoming is that decoding delay becomes greatly.

The present invention is by the Monte-Carlo emulation experiment, and the error performance of the FD-DLST structure that proposed is verified.In the emulation experiment, the average transmit power on the every day line is taken as 1, represents the output signal-to-noise ratio at each reception antenna place with SNR, and noise is chosen as real part and imaginary part all is that average is 0, and variance is the multiple Gaussian random variable of M/ (2SNR).Channel between each sending and receiving antenna is separate, and the real part of channel gain and imaginary part obey all that average is 0, variance is 0.5 Gaussian Profile, and channel parameter remains unchanged in T symbol period.

Referring to Fig. 3, when incoming symbol adopts the BPSK modulation system, in T=2 symbol period, the FD-DLST structure of from the mimo system of (2,2), transmitting and the characteristic curve of error code of V-BLAST structure.In the simulation curve of Fig. 3, the optimal base matrix that the FD-DLST structure is adopted is

$Q=\left[\begin{array}{cccc}0.8918-0.1479j& 0.1042-0.4793j& 0.5261-0.3708j& 0.4478+0.5722j\\ -0.1625+0.4628j& 0.9879-0.1207j& -0.3050-0.4951j& 0.5409-0.3718j\end{array}\right]$

When adopting basic matrix Q, the minimum order of FD-DLST structure code word error matrix is 2, and coding gain is 1.4971.From the simulation result of Fig. 3 as can be seen, adopt the optimal base matrix to the transmission in each symbol period of V-BLAST structure be grouped in sky, the time modulate resulting FD-DLST structure owing to can obtain the full diversity gain on the two dimension, the ability of its opposing channel fading is stronger, thereby error performance obviously is better than the V-BLAST structure.

This invention is to be target with the ability that improves V-BLAST structure opposing channel fading, abundant thought in conjunction with linear dispersed space-time coding, by the basic matrix of selecting one group of optimum make in the V-BLAST structure all signals as much as possible " dispersion " in the space and on the time, thereby can when not reducing the V-BLAST structure availability of frequency spectrum, obtain the full diversity gain, improve the transmission performance of system greatly.In addition, the FD-DLST structure can adopt continuous ZF and cancellation algorithms to detect, and makes its receiver have lower implementation complexity.The nearly step of simulation result has been demonstrate,proved the superior performance of this FD-DLST structure.

Claims (1)

1, a kind of method that obtains the full diversity gain based on the diagonal angle layered space-time architecture, its main thought is to make up diagonal angle layered space-time architecture Diagonal Layered Space-Time, make this structure obtain full diversity gain Full Diversity by the basic matrix of selecting optimum on the basis of abbreviation DLST, be called for short FD, therefore will propose empty the time transmission structure be called the FD-DLST structure, the realization flow of this method is divided into following two steps:

1) makes up the DLST structure

Suppose that mimo system has M transmitting antenna, the signal that N reception antenna, m antenna send in t symbol period is s _Mt, m=1 wherein ..., M; T=1 ..., T, the signal vector that sends from transmitting terminal in t symbol period is b like this _t=[s _1ts _2tS _Mt] ^T, subscript () wherein ^TExpression is got transposition to matrix, for the emission signal vector b in T the symbol period _t, with one group of M * M dimension basic matrix Φ _tIt is done to superpose after the modulation on the space again, obtain the symbolic vector of a M * 1 dimension

$B=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\Φ}}_t{b}_t=\mathrm{Qb}---(r-1)$

In the formula: data symbol vector b is defined as $b={\left[\begin{array}{cccc}{b}_1^T& b_2^T& ...& b_T^T\end{array}\right]}^T,$ M * MT dimension matrix Q is defined as Q=[Φ ₁Φ ₂Φ _T], because matrix Q is T basic matrix Φ _tThrough what obtain after the combination, be referred to as the combination basic matrix;

Subsequently, again symbolic vector B is sent after diagonal is launched in time domain, therefore construct the DLST structure that obtains in a first step and can represent with following formula

$C=\mathrm{diag}\left(B\right)=\mathrm{diag}\left(\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\Φ}}_t{b}_t\right)=\mathrm{diag}\left(\mathrm{Qb}\right)---(r-2)$

2) select the optimal base matrix to make the DLST structure obtain the full diversity gain

The purpose of this step is exactly how to select to make up basic matrix Q=[Φ ₁Φ ₂Φ _T] just can make the DLST structure obtain the full diversity gain, the coding gain of DLST structure is expressed from the next

$g_c=\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}=\underset{e\≠0}{\min }{\left(\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\left|q_{i}e\right|}^2\right)}^{1/M}---(r-3)$

In the formula: R _EBe matrix

E is the error in label vector, the vectorial q of row of 1 * MT dimension _iThe i of representing matrix Q is capable; If the capable vector of combination basic matrix Q satisfies condition | q _iE| ²≠ 0, just can make the DLST structure obtain the full diversity gain; Further, by the expression of coding gain $g_c=\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}=\underset{e\≠0}{\min }{\left(\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\left|q_{i}e\right|}^2\right)}^{1/M}$ As can be seen, should select to make coding gain be maximum combination basic matrix Q as the optimal base matrix, the DLST structure that draws like this can not only obtain line diversity all over the sky and coding gain maximum, i.e. optimal base matrix Q _OptFor

$Q_{\mathrm{opt}}=\arg \underset{Q}{\max }\left(g_c\right)=\arg \underset{Q}{\max }\left\{\underset{e\≠0}{\min }{\left(\det \left(R_E\right)\right)}^{1/M}\right\}---(r-4)$

Adopt following method to obtain optimal base matrix Q _Opt:

Consider the power constraint condition, matrix Q is configured to satisfy the random matrix of following orthogonality condition

QQ ^H＝T·I _M (r-5)

In the formula: I _MExpression M * M ties up unit matrix, subscript () ^HExpression is got conjugate transpose to matrix, just can obtain row orthogonal matrix Q by the method for the Hermitian matrix being done the Cayley conversion;

At first all obeying average with each element is 0, and variance is that the MT * 1 dimension random vector β of 1 multiple Gaussian Profile generates Hermitian matrix A=β β ^H, A wherein ^H=A does the Cayley conversion to A, obtains the unitary matrice U of MT * MT dimension

U＝(I _MT+jA) ^-1(I _MT+jA) (r-6)

In the formula: I _MTExpression (MT) * (MT) dimension unit matrix, $j=\sqrt{-1},$ And then the preceding M that gets unitary matrice U is capable, is met the capable orthogonal matrix Q of condition (r-5), promptly

$Q=\sqrt{T}\·\mathrm{ZU}---(r-7)$

In the formula: matrix Z=[I _M0 _{M * (MT-M)}], wherein 0 _{M * (MT-M)}Expression M * (MT-M) dimension null matrix;

Can produce the process that a plurality of different random vector β repeat the capable orthogonal matrix Q of surface construction, therefore obtain a plurality of combination basic matrix Q at random, can make coding gain g from wherein choosing again _cA maximum combination basic matrix is as optimal base matrix Q _Opt, promptly the optimal base matrix satisfies formula (r-4), with this optimal base matrix Q _OptBe updated in the formula (r-2), just can obtain to obtain the DLST structure of full diversity gain.

Images