CN105375958A - Linear precoding method of MIMO relay system having channel feedback delays - Google Patents

Abstract

The invention provides a linear precoding method of an MIMO relay system having channel feedback delays. The method is characterized in that a base station precoding matrix, a relay forwarding matrix and a terminal decoding matrix adopted in the method respectively satisfy a minimum mean squared error criterion under the condition that both a base station and relay power are limited, so that the optimal system performance is obtained; an iteration algorithm is used for calculating precoding matrixes of the base station and relay nodes, and the iteration algorithm is good in convergence and easy to realize; in addition, the linear precoding method provided by the invention considers the condition that two channels may both have feedback delays in a practical case, so that the method is more suitable for the practical transmission condition of the MIMO relay system.

Description

A kind of linear pre-coding method that there is the MIMO relay system that channel feedback postpones

Technical field:

The invention belongs to wireless communication field, relate to the linear pre-coding method of MIMO relay system, relate to the linear pre-coding method that there is MIMO relay system under channel feedback delay condition more specifically.

Background technology:

Along with user is to the various increase of real-time multimedia traffic demand and the fast development of Internet technology, traditional single antenna transmissions technology cannot meet the requirement of wireless traffic.Multiple-input and multiple-output (Multiple-InputMultiple-Output, MIMO) technology drastically increases the frequency efficiency of communication system and improves the reliability of communication link, becomes the core technology of a kind of key of wireless communication field.Relaying technique effectively can expand mobile communications network coverage, improve capacity of communication system, relaying is introduced cordless communication network, can bring the advantage such as capacity gain and coverage rate expansion.

In practical communication situation, base station is relatively fixing to the position of via node, therefore can build the line-of-sight propagation channel of base station to relaying, and channel condition information change is relatively little, is substantially equivalent to constant-parameter channel.And via node is to the communication channel of terminal, due to the mobility of user and the complexity of reception environment, channel condition information change more complicated, feedback link there is time delay or error can make the performance such as system average error bit rate BER and Averaged Square Error of Multivariate MSE have obvious decline.Therefore, consider that information feedback has the situation of delay in via node to terminal, can be very helpful for the performance improving communication system.In recent years, the research about MIMO relaying emerges in an endless stream, but is all based on not considering the relay structure that channel feedback postpones mostly, and for considering that the research of the MIMO relay system that channel feedback existence postpones substantially also is in space state.

Summary of the invention:

The invention provides a kind of linear pre-coding method that there is the MIMO relay system that channel feedback postpones, itself and existing MIMO relay system linear pre-coding method do not consider the feedback delay that channel exists, and the present invention effectively can improve the error performance of MIMO relay system.

The present invention adopts following technical scheme: a kind of linear pre-coding method that there is the MIMO relay system that channel feedback postpones, it comprises the steps:

The first step: for the MIMO relay system of the single relaying of multi-user, builds the channel model that channel feedback exists delay situation, supposes that the channel feedback of base station-relay and backward channel and relay-terminal and forward channel all exists delay error, use represent backward channel matrix and forward channel matrix respectively;

Second step: symbol substream s forms base station transmission signal y and is transmitted to relaying after the precoding of base station, and wherein transmission signal in base station meets base station power constraint, sends signal and can obtain relay reception signal y through backward channel to relaying _s;

3rd step: via node is y to received signal _scarry out linear process and obtain y _rand be transmitted to terminal, wherein forward signal y _rmeet relay power constraint, forward signal to terminal, obtains terminal received signals y through forward channel _d, terminal is carried out detection to received signal by decoding matrix W and automated power controlling elements α and is obtained recovering signal

4th step: take least mean-square error as design criterion, compares and sends signal s and terminal recovering signal build MSE cost function with this real-time update base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix, finally obtain the optimal solution of three, improve bit error rate BER and the mean square error MSE of system with this.

Further, the channel model that described first step structure channel feedback exists delay situation comprises:

With represent backward channel matrix and the forward channel matrix of t respectively, N _s, N _r, N _dbase station respectively, via node, the antenna number of terminal and meet N _s≤ N _r≤ N _dcondition, with represent respectively through there is the feedback delay matrix postponed for Link Feedback relay and the end of τ obtain, actual channel matrix H ₁, H ₂with feedback delay matrix relation can be expressed as:

$H_1={\mathrm{\ρ}}_1{\stackrel{\‾}{H}}_1+{\mathrm{\Ξ}}_1$

$H_2={\mathrm{\ρ}}_1{\stackrel{\‾}{H}}_2+{\mathrm{\Ξ}}_2$

Wherein, ρ ₁, ρ ₂for feedback delay coefficient correlation, estimate channel matrix, Ξ ₁, Ξ ₂it is feedback delay error matrix.

Further, described second step signal is sent to relaying adopts following formula to obtain through base station precoding:

The precoding processing of base station is:

y＝Fs

The processing procedure being forwarded to relaying is:

y _s＝H ₁y+n ₁＝H ₁Fs+n ₁

Wherein, s is initialize signal data flow, and F is base station pre-coding matrix, H ₁backward channel matrix, n ₁for the additive Gaussian noise of relay, y is through the transmission signal of base station precoding processing, y _sit is relay reception signal.Send signal y and meet base station power constraints:

p(F)＝E(yy ^H)＝tr(FF ^H)≤P _s

The wherein mark of tr () representing matrix, P _sfor base station maximum transmit power.

Further, described 3rd step relay forwarding and decoding terminals obtain according to following formula:

The linear process that relaying carries out to received signal is:

y _r＝Qy _s＝QH ₁Fs+Qn ₁

Wherein, Q is the linear processing array of relaying.Relay forwarding signal y _rmeet relay power constraints:

p(Q)＝E(y _ry _r ^H)＝tr[(QH ₁Fs+Qn ₁)(QH ₁Fs+Qn ₁) ^H]≤P _r

Can terminal received signals be obtained further:

y _d＝H ₂QH ₁Fs+H ₂Qn ₁+n ₂

Wherein, H ₂for forward channel matrix, n ₁for the additive Gaussian noise of receiving terminal.The original signal that terminal is recovered:

$\tilde{s}={\mathrm{\αWy}}_d={\mathrm{\αWH}}_2{\mathrm{QH}}_1\mathrm{Fs}+{\mathrm{\αWH}}_2{\mathrm{Qn}}_1+{\mathrm{\αWn}}_2$

Wherein, W is decoding terminals matrix, and α is automated power controlling elements.

Further, described 4th step ask for base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix optimal solution processing method be obtain according to following formula:

1. be design criterion with MMSE, ask for MSE cost function:

$\begin{array}{c}\mathrm{MSE}(F,Q,W,\mathrm{\α})=\underset{F,Q,W,\mathrm{\α}}{\arg \min }J(F,Q,W,\mathrm{\α})=\underset{F,Q,W,\mathrm{\α}}{\arg \min }\left\{E{\left|\right|\tilde{s}-s\left|\right|}^2\right\}\\ ={\mathrm{\α}}^{2}E\left({\mathrm{WH}}_2{\mathrm{QH}}_1{\mathrm{FF}}^H{H}_1{Q}^H{H}_2{W}^H\right)+{\mathrm{\α}}^{2}E\left({\mathrm{WH}}_2{\mathrm{QQ}}^H{H}_2{W}^H\right)\\ -\mathrm{\αE}\left({\mathrm{WH}}_2{\mathrm{QH}}_{1}F\right)-\mathrm{\αE}\left(\right[{\left({\mathrm{WH}}_2{\mathrm{QH}}_{1}F\right)}^H]+E(I_{N_S}+{\mathrm{\α}}^2{\mathrm{\σ}}_2^2{\mathrm{WW}}^H)\end{array}$

Wherein ρ ₁for the feedback delay coefficient correlation of backward channel, here with represent additive Gaussian noise n respectively ₁and n ₂variance;

2. because base station and relay need meet power constraint, cost function will be minimized and carry out suitable abbreviation, then can be expressed as the optimization problem minimizing cost function MSE

Wherein this problem is a convex optimization problem, uses Lagrangian extremum method to solve, and the Lagrangian of structure is

$\begin{array}{c}L(B,G,W,\mathrm{\γ},{\mathrm{\λ}}_1,{\mathrm{\λ}}_2)=\underset{F,Q,W,\mathrm{\α}}{\arg \min }J(F,Q,W,\mathrm{\α})+{\mathrm{\λ}}_1[\mathrm{tr}\left({\mathrm{FF}}^H\right)-P_s]+{\mathrm{\λ}}_2[\mathrm{tr}\left({\mathrm{Q\ΠQ}}^H\right)-P_r]\\ =\mathrm{tr}[{\mathrm{\α}}^2{W\hat{H}}_2{\mathrm{Q\ΠQ}}^H{{\hat{H}}_2}^H{W}^H+{\mathrm{\α}}^2{(1-{\mathrm{\ρ}}_2^2)}^2\mathrm{Wtr}\left({\mathrm{Q\ΠQ}}^H\right)W-{\mathrm{\αW}\hat{H}}_2{Q\hat{H}}_{1}F-\mathrm{\α}{\left({W\hat{H}}_2{Q\hat{H}}_{1}F\right)}^H\\ +{\mathrm{\α}}^2{\mathrm{\σ}}_2^2{\mathrm{WW}}^H]+{\mathrm{\λ}}_1[\mathrm{tr}\left({\mathrm{FF}}^H\right)-P_s]+{\mathrm{\λ}}_2[\mathrm{tr}\left({\mathrm{Q\ΠQ}}^H\right)-P_r]\end{array}$

Here λ ₁, λ ₂for Lagrange multiplier, order can obtain according to Caro need-Ku En-Plutarch (Karush-Kuhn-Tucker, KKT) criterion

$Q={({\hat{H}}_2^H{\stackrel{\‾}{W}}^H{\stackrel{\‾}{W}\hat{H}}_2+{\mathrm{\λ}}_2{I}_{N_r})}^{-1}{\left({\hat{H}}_2\stackrel{\‾}{W}{F\hat{H}}_1\right)}^H{\mathrm{\Π}}^{-1}$

$F={({{\hat{H}}_1}^H{Q}^H{{\hat{H}}_2}^H{\stackrel{\‾}{W}}^H\stackrel{\‾}{W}{\hat{H}}_2{Q\hat{H}}_1+{\mathrm{\λ}}_1{I}_{N_S}+{\mathrm{\λ}}_2{\hat{H}}_1^H{Q}^{H}Q{\hat{H}}_1)}^{-1}{{\hat{H}}_1}^H{Q}^H{\hat{H}}_2^H{\stackrel{\‾}{W}}^H$

The present invention has following beneficial effect:

(1), the present invention proposes a kind of linear pre-coding method being applicable to MIMO relay system, the base station pre-coding matrix that the method adopts, relay forwarding matrix and decoding terminals matrix meet, base station and the relay power least mean-square error (MinimumMeanSquaredError all under confined condition, MMSE) be criterion, thus possess optimum systematic function;

(2), present invention employs the pre-coding matrix that iterative algorithm comes calculation base station and via node place, this iterative algorithm has good convergence, is easy to realize;

(3), the linear pre-coding method that proposes of the present invention, consider two hop channels in actual conditions and all may there is the situation of feedback delay, more realistic MIMO relay system transmission situation.

Accompanying drawing illustrates:

Fig. 1 is the schematic diagram of the double bounce amplification forwarding MIMO relay structure in the present invention.

Fig. 2 adopts method of the present invention to carry out the schematic diagram of signal transmission in the MIMO relay system shown in Fig. 1.

Fig. 3 does not consider that channel feedback postpones and considers that channel feedback postpones mean square error (MSE) comparison diagram of system in two kinds of situations.

Fig. 4 does not consider that channel feedback postpones and considers that channel feedback postpones bit error rate (BER) comparison diagram of system in two kinds of situations.

Embodiment:

Below in conjunction with accompanying drawing with specifically implement that the invention will be further described.

In order to make principle of the present invention clearly, first the operation principle of double bounce amplification forwarding (Amplify-and-Forward, AF) the MIMO trunk line sexual system that the present invention adopts simply is introduced.Based on AF MIMO relay system model as shown in Figure 1, it is made up of base station, via node and terminal three parts, and wherein base station, via node and terminal have N respectively _s, N _r, N _droot antenna, and meet N _s≤ N _r≤ N _dcondition.The schematic diagram that composition graphs 2 signal sends, base station, via node, terminal have N respectively _s=N _r=N _d=4 antennas, symbol waiting for transmission is the QPSK modulation symbol of stochastic generation, and for reducing the complexity of relaying work, relay transmission adopts half-duplex mode, once transmits and is made up of 2 time slots.Suppose that all channels are flat Rayleigh fading, channel condition information is completely known, and remains unchanged in 2 time slots once transmitted.Backward interchannel noise n ₁with forward channel noise n ₂be the multiple Gaussian noise of zero mean unit variance, meet

The present invention is directed to the MIMO relay system that there is channel feedback and postpone, the Precoding Design method of research base station and relay.Object is by considering the system BER that the problem of channel feedback existence delay in actual conditions more is optimized and MSE performance.For solving the problems of the technologies described above, the present invention adopts following technical scheme:

The first step: for the MIMO relay system of the single relaying of multi-user, considers that the channel of base station-via node and via node-terminal all exists feedback delay, builds channel model.

The present invention supposes that the channel feedback of base station-relay (backward channel) and relay-terminal (forward channel) all exists delay error.Feedback delay error matrix Ξ in this example ₁, Ξ ₂its element obeys ε _{i, j}~ CN (0,1-ρ ²).Correlation coefficient ρ _i=J ₀(2 π f _dτ _i), i=1,2.J ₀for first kind zero Bessel function, f _dfor maximum doppler frequency.F _dτ is value 0.02,0.01,0.001 respectively.

Second step: in the 1st time slot, base station, to signal subflow s pre-coding matrix F weighting, obtains base station and sends signal y=Fs. wherein meet e () represents expectation, () ^hrepresent conjugate transpose, represent N _s× N _sunit matrix. base station meets maximum transmit power restrictions condition.Signal passes through N _sroot antenna is via backward channel H ₁issue via node, H ₁signal to noise ratio be fixed as 25dB.Send signal and can obtain relay reception signal y through backward channel to relaying _s.

3rd step: via node is y to received signal _scarry out linear process and obtain y _rand be transmitted to terminal.Wherein forward signal y _rmeet relay power constraint.Forward signal is through forward channel H ₂to terminal, obtain terminal received signals y _d, wherein H ₂the signal to noise ratio of channel is defined as SNR ₂=[0: 5: 25] (dB).Terminal is carried out detection to received signal by decoding matrix W and automated power controlling elements α and is obtained recovering signal

4th step: with least mean-square error (MinimumMeanSquaredError, MMSE) for design criterion, compares and sends signal s and terminal recovering signal build MSE cost function with this real-time update base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix, finally obtain the optimal solution of three, effectively improve BER and the mean square error MSE of system with this.

Consider that channel feedback exists to postpone, in the described first step, use represent backward channel matrix and the forward channel matrix of t respectively, N _s, N _r, N _dbase station respectively, via node, the antenna number of terminal and meet N _s≤ N _r≤ N _dcondition. with represent respectively through there is the feedback delay matrix postponed for Link Feedback relay and the end of τ obtain, actual channel matrix H ₁, H ₂with feedback delay matrix relation can be expressed as

$H_1={\mathrm{\ρ}}_1{\stackrel{\‾}{H}}_1+{\mathrm{\Ξ}}_1---\left(1\right)$

$H_2={\mathrm{\ρ}}_1{\stackrel{\‾}{H}}_2+{\mathrm{\Ξ}}_2---\left(2\right)$

Wherein, ρ ₁, ρ ₂for feedback delay coefficient correlation. estimate channel matrix, Ξ ₁, Ξ ₂feedback delay error matrix, note then formula (1) (2) can be expressed as

$H_1={\hat{H}}_1+{\mathrm{\Ξ}}_1---\left(3\right)$

$H_2={\hat{H}}_2+{\mathrm{\Ξ}}_2---\left(4\right)$

Wherein in second step, the precoding processing of signal is:

y＝Fs(5)

The processing procedure being forwarded to relaying is:

y _s＝H ₁y+n ₁＝H ₁Fs+n ₁(6)

Wherein, s is initialize signal data flow, and F is base station pre-coding matrix, H ₁backward channel matrix, n ₁for the additive Gaussian noise of relay, y is through the transmission signal of base station precoding processing, y _sit is relay reception signal.Send signal y and meet base station power constraints:

p(F)＝E(yy ^H)＝tr(FF ^H)≤P _s(7)

The wherein mark of tr () representing matrix, P _sfor base station maximum transmit power.

The linear process that wherein the 3rd step relaying carries out to received signal is:

y _r＝Qy _s＝QH ₁Fs+Qn ₁(8)

Wherein, Q is the linear processing array of relaying.Relay forwarding signal y _rmeet relay power constraints:

p(Q)＝E(y _ry _r ^H)＝tr[(QH ₁Fs+Qn ₁)(QH ₁Fs+Qn ₁) ^H]≤P _r(9)

Can terminal received signals be obtained further:

y _d＝H ₂QH ₁Fs+H ₂Qn ₁+n ₂(10)

Wherein, H ₂for forward channel matrix, n ₁for the additive Gaussian noise of receiving terminal.The original signal that terminal is recovered:

$\tilde{s}={\mathrm{\αWy}}_d={\mathrm{\αWH}}_2{\mathrm{QH}}_1\mathrm{Fs}+{\mathrm{\αWH}}_2{\mathrm{Qn}}_1+{\mathrm{\αWn}}_2---\left(11\right)$

Wherein, W is decoding terminals matrix, and α is automated power controlling elements.

Wherein the 4th step ask for base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix optimal solution step be:

1. be design criterion with MMSE, ask for MSE cost function:

$\begin{array}{c}\mathrm{MSE}(F,Q,W,\mathrm{\α})=\underset{F,Q,W,\mathrm{\α}}{\arg \min }J(F,Q,W,\mathrm{\α})=\underset{F,Q,W,\mathrm{\α}}{\arg \min }\left\{E{\left|\right|\tilde{s}-s\left|\right|}^2\right\}\\ ={\mathrm{\α}}^{2}E\left({\mathrm{WH}}_2{\mathrm{QH}}_1{\mathrm{FF}}^H{H}_1{Q}^H{H}_2{W}^H\right)+{\mathrm{\α}}^{2}E\left({\mathrm{WH}}_2{\mathrm{QQ}}^H{H}_2{W}^H\right)\\ -\mathrm{\αE}\left({\mathrm{WH}}_2{\mathrm{QH}}_{1}F\right)-\mathrm{\αE}\left(\right[{\left({\mathrm{WH}}_2{\mathrm{QH}}_{1}F\right)}^H]+E(I_{N_S}+{\mathrm{\α}}^2{\mathrm{\σ}}_2^2{\mathrm{WW}}^H)\end{array}---\left(12\right)$

Wherein ρ ₁for the feedback delay coefficient correlation of backward channel, here with represent additive Gaussian noise n respectively ₁and n ₂variance.

2. because base station and relay need meet power constraint, cost function will be minimized and carry out suitable abbreviation, then can be expressed as the optimization problem minimizing cost function MSE

Wherein this problem is a convex optimization problem, uses Lagrangian extremum method to solve, and the Lagrangian of structure is

$\begin{array}{c}L(B,G,W,\mathrm{\γ},{\mathrm{\λ}}_1,{\mathrm{\λ}}_2)=\underset{F,Q,W,\mathrm{\α}}{\arg \min }J(F,Q,W,\mathrm{\α})+{\mathrm{\λ}}_1[\mathrm{tr}\left({\mathrm{FF}}^H\right)-P_s]+{\mathrm{\λ}}_2[\mathrm{tr}\left({\mathrm{Q\ΠQ}}^H\right)-P_r]\\ =\mathrm{tr}[{\mathrm{\α}}^2{W\hat{H}}_2{\mathrm{Q\ΠQ}}^H{{\hat{H}}_2}^H{W}^H+{\mathrm{\α}}^2{(1-{\mathrm{\ρ}}_2^2)}^2\mathrm{Wtr}\left({\mathrm{Q\ΠQ}}^H\right)W-{\mathrm{\αW}\hat{H}}_2{Q\hat{H}}_{1}F-\mathrm{\α}{\left({W\hat{H}}_2{Q\hat{H}}_{1}F\right)}^H\\ +{\mathrm{\α}}^2{\mathrm{\σ}}_2^2{\mathrm{WW}}^H]+{\mathrm{\λ}}_1[\mathrm{tr}\left({\mathrm{FF}}^H\right)-P_s]+{\mathrm{\λ}}_2[\mathrm{tr}\left({\mathrm{Q\ΠQ}}^H\right)-P_r]\end{array}---\left(14\right)$

Here λ ₁, λ ₂for Lagrange multiplier, order can obtain according to Caro need-Ku En-Plutarch (Karush-Kuhn-Tucker, KKT) criterion

$Q={({\hat{H}}_2^H{\stackrel{\‾}{W}}^H{\stackrel{\‾}{W}\hat{H}}_2+{\mathrm{\λ}}_2{I}_{N_r})}^{-1}{\left({\hat{H}}_2\stackrel{\‾}{W}{F\hat{H}}_1\right)}^H{\mathrm{\Π}}^{-1}---\left(15\right)$

$F={({{\hat{H}}_1}^H{Q}^H{{\hat{H}}_2}^H{\stackrel{\‾}{W}}^H\stackrel{\‾}{W}{\hat{H}}_2{Q\hat{H}}_1+{\mathrm{\λ}}_1{I}_{N_S}+{\mathrm{\λ}}_2{\hat{H}}_1^H{Q}^{H}Q{\hat{H}}_1)}^{-1}{{\hat{H}}_1}^H{Q}^H{\hat{H}}_2^H{\stackrel{\‾}{W}}^H---\left(17\right)$

After obtaining base station pre-coding matrix, the linear processing array of relaying, the optimum solution's expression of decoding terminals matrix, ask for base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix optimal solution employing iterative algorithm in this example, concrete steps are:

(1) initialization pre-coding matrix:

(2) with the formula (16) calculate λ is obtained again by (18) (19) ₁and λ ₂.

(3) upgrade Q and F by formula (15) and formula (17), Q and F meets the power limitation condition of relay point and base station here, namely needs to meet formula (7) and formula (9).

(4) step (1) and step (2) is repeated, until tr [(Q ⁱ) (Q ⁱ) ']≤ξ and tr [(F ⁱ) (F ⁱ) ']≤ξ, in formula: the mark of tr () representing matrix, ζ is the threshold value (getting ξ=0.0001) preset.Here ξ is the threshold value of setting in advance, represent that (note, the size of ξ value all has impact to the precision of algorithm and complexity to the size that in adjacent 2 iteration, matrix value changes, and occupies value less, result of calculation is more accurate, but time complexity is also higher).Q ⁱand F ⁱrepresent i-th iteration of Q and F respectively.In above-mentioned iterative process, mean square error MSE (F, Q, W, α) be dull reduction, in addition, the lower bound of square mean error amount is zero, this two promise convergence of this iterative algorithm. in addition, it should be noted that, introduce auxiliary parameter α just conveniently the solving of optimization problem, α on the BER performance of convergence and system all without affecting.

Following table is be the simulated conditions that the present embodiment adopts:

Simulation parameter configured list

In the present embodiment, have stochastic generation 10000 accidental channels altogether, all have sent 1000 QPSK modulation symbols at every turn.The effect that the present embodiment obtains can be further described by the concrete data obtained in Fig. 3, Fig. 4 emulation experiment.We can see, and do not consider compared with the situation that channel feedback postpones, and consider that channel feedback postpones to obtain better bit error rate and mean square error performance, and along with the increase of signal to noise ratio, this performance boost seems further obvious.

The above is only the preferred embodiment of the present invention, it should be pointed out that for those skilled in the art, can also make some improvement under the premise without departing from the principles of the invention, and these improvement also should be considered as protection scope of the present invention.

Claims (5)

1. there is a linear pre-coding method for the MIMO relay system that channel feedback postpones, it is characterized in that: comprise the steps

The first step: for the MIMO relay system of the single relaying of multi-user, builds the channel model that channel feedback exists delay situation, supposes that the channel feedback of base station-relay and backward channel and relay-terminal and forward channel all exists delay error, use represent backward channel matrix and forward channel matrix respectively;

Second step: symbol substream s forms base station transmission signal y and is transmitted to relaying after the precoding of base station, and wherein transmission signal in base station meets base station power constraint, sends signal and can obtain relay reception signal y through backward channel to relaying _s;

3rd step: via node is y to received signal _scarry out linear process and obtain y _rand be transmitted to terminal, wherein forward signal y _rmeet relay power constraint, forward signal to terminal, obtains terminal received signals y through forward channel _d, terminal is carried out detection to received signal by decoding matrix W and automated power controlling elements α and is obtained recovering signal

4th step: take least mean-square error as design criterion, compares and sends signal s and terminal recovering signal build MSE cost function with this real-time update base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix, finally obtain the optimal solution of three, improve bit error rate BER and the mean square error MSE of system with this.

2. a kind of linear pre-coding method of MIMO relay system that there is channel feedback and postpone as claimed in claim 1, is characterized in that: the described first step builds the channel model that channel feedback exists delay situation and comprises:

With represent backward channel matrix and the forward channel matrix of t respectively, N _s, N _r, N _dbase station respectively, via node, the antenna number of terminal and meet N _s≤ N _r≤ N _dcondition, with represent respectively through there is the feedback delay matrix postponed for Link Feedback relay and the end of τ obtain, actual channel matrix H ₁, H ₂with feedback delay matrix relation can be expressed as:

$H_1={\mathrm{\ρ}}_1{\stackrel{\‾}{H}}_1+{\mathrm{\Ξ}}_1$

$H_2={\mathrm{\ρ}}_1{\stackrel{\‾}{H}}_2+{\mathrm{\Ξ}}_2$

Wherein, ρ ₁, ρ ₂for feedback delay coefficient correlation, estimate channel matrix, Ξ ₁, Ξ ₂it is feedback delay error matrix.

3. a kind of linear pre-coding method of MIMO relay system that there is channel feedback and postpone as claimed in claim 1, is characterized in that: described second step signal is through base station precoding and be sent to relaying and adopt following formula to obtain:

The precoding processing of base station is:

y＝Fs

The processing procedure being forwarded to relaying is:

y _s＝H ₁y+n ₁＝H ₁Fs+n ₁

Wherein, s is initialize signal data flow, and F is base station pre-coding matrix, H ₁backward channel matrix, n ₁for the additive Gaussian noise of relay, y is through the transmission signal of base station precoding processing, y _sbe relay reception signal, send signal y and meet base station power constraints:

p(F)＝E(yy ^H)＝tr(FF ^H)≤P _s

The wherein mark of tr () representing matrix, P _sfor base station maximum transmit power.

4. a kind of linear pre-coding method of MIMO relay system that there is channel feedback and postpone as claimed in claim 1, is characterized in that: described 3rd step relay forwarding and decoding terminals obtain according to following formula:

The linear process that relaying carries out to received signal is:

y _r＝Qy _s＝QH ₁Fs+Qn ₁

Wherein, Q is the linear processing array of relaying, relay forwarding signal y _rmeet relay power constraints:

p(Q)＝E(y _ry _r ^H)＝tr[(QH ₁Fs+Qn ₁)(QH ₁Fs+Qn ₁) ^H]≤P _r

Can terminal received signals be obtained further:

y _d＝H ₂QH ₁Fs+H ₂Qn ₁+n ₂

Wherein, H ₂for forward channel matrix, n ₂for the additive Gaussian noise of receiving terminal, the original signal that terminal is recovered:

$\tilde{s}={\mathrm{\αWy}}_d={\mathrm{\αWH}}_2{\mathrm{QH}}_{1}Fs+{\mathrm{\αWH}}_2{\mathrm{Qn}}_1+{\mathrm{\αWn}}_2$

Wherein, W is decoding terminals matrix, and α is automated power controlling elements.

5. a kind of linear pre-coding method of MIMO relay system that there is channel feedback and postpone as claimed in claim 1, is characterized in that: described 4th step ask for base station pre-coding matrix, the linear processing array of relaying, decoding terminals matrix optimal solution processing method be obtain according to following formula:

1. be design criterion with MMSE, ask for MSE cost function:

$\begin{array}{c}MSE(F,Q,W,\mathrm{\α})=\underset{F,Q,W,\mathrm{\α}}{\mathrm{argmin}}J(F,Q,W,\mathrm{\α})=\underset{F,Q,W,\mathrm{\α}}{\mathrm{argmin}}\left\{E\right||\tilde{s}-s|{|}^2\}\\ ={\mathrm{\α}}^{2}E\left({\mathrm{WH}}_2{\mathrm{QH}}_1{\mathrm{FF}}^H{H}_1{Q}^H{H}_2{W}^H\right)+{\mathrm{\α}}^{2}E\left({\mathrm{WH}}_2{\mathrm{QQ}}^H{H}_2{W}^H\right)\\ -\mathrm{\α}E\left({\mathrm{WH}}_2{\mathrm{QH}}_{1}F\right)-\mathrm{\α}E(\[{\left({\mathrm{WH}}_2{\mathrm{QH}}_{1}F\right)}^H\]+E(I_{N_S}+{\mathrm{\α}}^2{\mathrm{\σ}}_2^2{\mathrm{WW}}^H)\end{array}$

Wherein ρ ₁for the feedback delay coefficient correlation of backward channel, here with represent additive Gaussian noise n respectively ₁and n ₂variance;

2. because base station and relay need meet power constraint, cost function will be minimized and carry out suitable abbreviation, then can be expressed as the optimization problem minimizing cost function MSE

Wherein this problem is a convex optimization problem, uses Lagrangian extremum method to solve, and the Lagrangian of structure is

$\begin{array}{c}L(B,G,W,\mathrm{\γ},{\mathrm{\λ}}_1,{\mathrm{\λ}}_2)=\underset{F,Q,W,\mathrm{\α}}{\mathrm{argmin}}J(F,Q,W,\mathrm{\α})+{\mathrm{\λ}}_1\[tr\left({\mathrm{FF}}^H\right)-P_s\]+{\mathrm{\λ}}_2\[tr\left({\mathrm{Q\ΠQ}}^H\right)-P_r\]\\ =tr\[{\mathrm{\α}}^{2}W{\hat{H}}_2{\mathrm{Q\ΠQ}}^H{{\hat{H}}_2}^H{W}^H+{\mathrm{\α}}^2{(1-{\mathrm{\ρ}}_2^2)}^{2}Wtr\left({\mathrm{Q\ΠQ}}^H\right)W-\mathrm{\α}W{\hat{H}}_{2}Q{\hat{H}}_{1}F-\mathrm{\α}{\left(W{\hat{H}}_{2}Q{\hat{H}}_{1}F\right)}^H\\ +{\mathrm{\α}}^2{\mathrm{\σ}}_2^2{\mathrm{WW}}^H\]+{\mathrm{\λ}}_1\[tr\left({\mathrm{FF}}^H\right)-P_s\]+{\mathrm{\λ}}_2\[tr\left({\mathrm{Q\ΠQ}}^H\right)-P_r\]\end{array}$

Here λ ₁, λ ₂for Lagrange multiplier, order can obtain according to Caro need-Ku En-Plutarch (Karush-Kuhn-Tucker, KKT) criterion