CN105577249A - Pre-coding method of MIMO relay system having channel estimation error and antenna correlation - Google Patents

Abstract

The invention discloses a pre-coding method of a MIMO relay system having a channel estimation error and antenna correlation. Under a condition that both the power of a transmitting end and the power of a relay end are limited, closed-form solutions of a pre-coding matrix of the transmitting end, a pre-coding matrix of the relay end and a processing matrix of a receiving end are obtained by derivation in a manner of taking a minimum mean square error as a criterion; therefore, the system performance can be improved well; a joint iterative algorithm for calculating the pre-coding matrix of the transmitting end, the pre-coding matrix of the relay end and the processing matrix of the receiving end is given; the joint iterative algorithm has good convergence and practical value and is easy to implement; the MIMO relay system is combined with problems of the channel estimation error and the antenna correlation; the condition that incomplete channel state information exists in a practical condition is considered; the pre-coding method of the MIMO relay system under the condition of the channel estimation error and the antenna correlation is implemented to improve the performance of the MIMO relay system based on the incomplete channel state information condition; and thus, the pre-coding method has wide application prospect.

Description

A kind of method for precoding that there is the MIMO relay system that channel estimation errors and antenna are correlated with

Technical field:

The invention belongs to wireless communication field, relate to the method for precoding of MIMO relay system, relate to the method for precoding that there is the MIMO relay system that channel estimation errors and antenna are correlated with more specifically.

Background technology:

Along with user is to the fast development of Internet technology since the increase, particularly 21 century of various real-time multimedia traffic demand, 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, has become the core technology of a kind of key of wireless communication field.Relaying technique effectively can expand communication network coverage, improve capacity of communication system, relaying is introduced MIMO communication system, can bring the advantage such as capacity gain and coverage rate expansion.

In practical MIMO relay system, inevitably there is channel estimation errors and Antenna Correlation.Therefore, consider the situation of channel estimation errors and Antenna Correlation in the channel, 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 mostly the relay structure based on complete channel, and is also in the stage very less for the research of the relevant MIMO relay system of the channel estimation errors existed in channel and Antenna Correlation.

Summary of the invention:

The deficiency that the present invention exists to solve prior art, a kind of method for precoding that there is the MIMO relay system that channel estimation errors and antenna are correlated with is provided, compared with traditional method for precoding, method of the present invention can improve the error performance of MIMO relay system further.

The present invention adopts following technical scheme: a kind of method for precoding that there is the MIMO relay system that channel estimation errors and antenna are correlated with, it comprises the steps:

The first step: for MIMO relay system, builds and there is the relevant channel model of channel estimation errors and antenna, suppose that transmittings-relay and relaying-receiving terminal channel all exist channel estimation errors and antenna is relevant, use represent transmitting-relay and relaying-receiving terminal channel matrix respectively, n _s, n _r, n _dtransmitting terminal respectively, relay, the antenna number of receiving terminal and meet n _s≤ min (n _r, n _d) condition;

Second step: symbol substream through transmitting terminal pre-coding matrix be transmitted to relaying after process, wherein transmitting terminal transmission signal must meet transmitting terminal power constraint, sends signal and can obtain relay reception signal through transmitting-relay channel

3rd step: Received signal strength y _rthrough relay pre-coding matrix process obtains and be transmitted to receiving terminal, wherein forward signal Y meets relay power constraint, and forward signal, through relaying-receiving terminal channel, obtains receiving terminal Received signal strength receiving terminal is by receiving terminal processing array obtain recovering signal

4th step: take least mean-square error as design criterion, compares and sends signal x and receiving terminal recovering signal build MSE cost function upgrade transmitting terminal pre-coding matrix, relay pre-coding matrix, receiving terminal processing array with this real-time iterative, finally obtain the optimal solution of three to improve the bit error rate of system.

Further, the channel model that described first step structure channel estimation errors and antenna are correlated with comprises:

The antenna related matrix Kronecker model representation of H and G, definition with and Ψ _gtransmitting antenna correlation matrix, Σ _hand Σ _gbe the reception antenna correlation matrix of H and G, antenna related matrix is positive semidefinite and completely known, with element obey average to be 0 variance be 1 multiple Gaussian Profile, definition with with be with estimated matrix, Δ H and Δ G is channel estimation errors matrix, its element obey average be that 0 variance is respectively with multiple Gaussian Profile, therefore, channel model can be expressed as:

$H={\Σ}_H^{1/2}(\hat{H}+\mathrm{\Δ}H){\mathrm{\Ψ}}_H^{1/2}=\stackrel{\‾}{H}+{\Σ}_H^{1/2}{\mathrm{\ΔH\Ψ}}_H^{1/2}$

$G={\Σ}_G^{1/2}(\hat{G}+\mathrm{\Δ}G){\mathrm{\Ψ}}_G^{1/2}=\stackrel{\‾}{G}+{\Σ}_G^{1/2}{\mathrm{\ΔG\Ψ}}_G^{1/2}$

Further, described second step signal is sent to relay adopts following formula to obtain through transmitting terminal precoding:

Transmitting terminal node launches information x _i(i=1,2 ..., n _s) to relay, order ε [] represents expectation; Relay Received signal strength can be expressed as:

y _r＝HBx+w

Wherein for the pre-coding matrix of signal x, meet tr (Bxx ^hb ^h)=tr (BB ^h)≤P _s, the mark of tr [] representing matrix, P _stransmitting terminal maximum power, be the mimo channel matrix of transmitting terminal to relay, w is the additive white Gaussian noise of relay, and average is zero, and variance matrix is for its noise power, processing array is passed through in relay process to received signal, then to receiving terminal forward signal, forward signal for:

Y＝Fy _r

Wherein power constraint meets tr (YY ^h)≤P _r, P _rit is relay maximum power.

Further, described 3rd step relay forwarding and receiving terminal reduction transmit is obtain according to following formula:

Receiving terminal Received signal strength can be expressed as:

r＝GY+n＝GFHS+GFw+n

Wherein be average be zero, variance matrix is additive white Gaussian noise, it is the variance of n;

The processing array of receiving terminal is used for recovering transmitting of transmitting terminal, and order receives processing array and is then estimated signal vector for:

$\begin{array}{c}\tilde{x}=Qr=QGFHS+QGFw+Qn\\ =QGFHBa+QGFw+Qn\end{array}.$

Further, described 4th step ask for transmitting terminal pre-coding matrix, relay pre-coding matrix, receiving terminal processing array optimal solution processing method be obtain according to following formula:

(1). be design criterion with least mean-square error, ask for MSE cost function:

$\begin{array}{c}MSE(B,F,Q)=\mathrm{\ϵ}\left(\right|\tilde{x}-x{|}^2)\\ =\mathrm{\ϵ}\left(\right|QGFHBx+QGFw+Qn-x{|}^2)\\ =\mathrm{\ϵ}\left(\right|Q\left(\stackrel{\‾}{G}+{\Σ}_G^{1/2}{\mathrm{\ΔG\Ψ}}_G^{1/2}\right)F\left(\stackrel{\‾}{H}+{\Σ}_H^{1/2}{\mathrm{\ΔH\Ψ}}_H^{1/2}\right)Bx\\ +Q(\stackrel{\‾}{G}+{\Σ}_G^{1/2}{\mathrm{\ΔG\Ψ}}_G^{1/2})Fw+Qn-x{|}^2)\\ =tr\[Q\stackrel{\‾}{G}{\mathrm{FZF}}^H{\stackrel{\‾}{G}}^H{Q}^H+I_{n_s}+{\mathrm{QR}}_n{Q}^H\]\\ +tr\[{\mathrm{\σ}}_G^{2}tr\left({\mathrm{FZF}}^H{\mathrm{\Ψ}}_G\right)Q{\Σ}_G{Q}^H\]\\ -tr(Q\stackrel{\‾}{G}F\stackrel{\‾}{H}B+B^H{\stackrel{\‾}{H}}^H{F}^H{\stackrel{\‾}{G}}^H{Q}^H)\end{array}$

Wherein $Z=\[\stackrel{\‾}{H}{\mathrm{BB}}^H{\stackrel{\‾}{H}}^H+{\mathrm{\σ}}_H^{2}tr\left({\mathrm{BB}}^H{\mathrm{\Ψ}}_H\right){\mathrm{\Σ}}_H+R_w\].$

Power constraint is:

tr(BB ^H)≤P _s

tr(YY ^H)＝tr[F(HBB ^HH ^H+R _w)F ^H]

＝tr[FZF ^H]≤P _r

(2). because transmitting terminal and relay need meet power constraint, then can be expressed as the optimization problem minimizing cost function MSE:

$\begin{array}{c}\arg \underset{B,F,Q}{\min }\left\{MSE\right\}\\ \begin{array}{cc}s.t& tr\left({\mathrm{BB}}^H\right)\≤P_s\end{array}\\ \begin{array}{cc}& tr\[{\mathrm{FZF}}^H\]\≤P_r\end{array}\end{array}$

The present invention has following beneficial effect:

(1) the present invention proposes a kind of method for precoding being applicable to MIMO relay system, under transmitting terminal and relay power all confined condition, with least mean-square error MMSE for criterion, derive and obtain the closed solutions of transmitting terminal pre-coding matrix, relay pre-coding matrix and receiving terminal processing array, systematic function can be improved admirably;

(2) give the Joint iteration algorithm calculating transmitting terminal pre-coding matrix, relay pre-coding matrix and receiving terminal processing array, this iterative algorithm has good convergence, is easy to realize, and has good practical value;

(3) problem that MIMO relay system and channel exist evaluated error and Antenna Correlation combines by the present invention, consider the situation of the incomplete channel condition information existed in actual conditions, there is good practicality, therefore, the performance that the enforcement that there is the MIMO relay system method for precoding under evaluated error and Antenna Correlation condition based on channel promotes MIMO relay system under based on incomplete channel condition information condition has a wide range of applications.

Accompanying drawing illustrates:

Fig. 1 is the schematic diagram of the MIMO relay system 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 gives SNR _sr=SNR _rdtime to adopt the bit error rate comparison diagram of Joint iteration design method and other methods for designing based on the MIMO relay system of different channels evaluated error.

Fig. 4 gives SNR _sr=SNR _rdtime to adopt the bit error rate comparison diagram of Joint iteration design method and other methods for designing based on the MIMO relay system of different antennae correlation.

Embodiment:

The present invention be directed to and there is the relevant MIMO relay system of channel estimation errors and antenna, the Precoding Design method of research transmitting terminal and relay.Object is by considering the system performance of BER that channel in actual conditions exists problem that evaluated error and antenna be correlated with and more optimizes.

In order to make principle of the present invention clearly, first the operation principle of the MIMO relay system that the present invention adopts simply is introduced.As shown in Figure 1, it is made up of transmitting terminal, relay and receiving terminal three parts MIMO relay system model, and wherein transmitting terminal, relay and receiving terminal have n respectively _s, n _r, n _droot antenna, and meet n _s≤ min (n _r, n _d) condition.The schematic diagram that composition graphs 2 signal sends, transmitting terminal, relay and receiving terminal configure 4 antennas respectively, transmitting information is the QPSK modulation symbol of stochastic generation, for reducing the complexity of relaying work, relay transmission adopts half-duplex mode, once transmit and be made up of 2 time slots, suppose that channel is flat Rayleigh fading, channel condition information remains unchanged in 2 time slots once transmitted.

The present invention adopts following technical scheme, a kind of method for precoding that there is the MIMO relay system that channel estimation errors and antenna are correlated with, and concrete steps are:

The first step: for MIMO relay system, builds and a kind ofly there is the relevant channel model of channel estimation errors and antenna.The present invention supposes that transmitting-relay and relaying-receiving terminal channel all exist antenna and be correlated with and channel estimation errors.With represent transmitting-relay and relaying-receiving terminal channel matrix respectively.

Second step: symbol substream through transmitting terminal pre-coding matrix be transmitted to relaying after process, wherein transmitting terminal transmission signal must meet transmitting terminal power constraint.Send signal and can obtain relay reception signal through transmitting-relay channel

3rd step: Received signal strength y _rthrough relay pre-coding matrix process obtains and be transmitted to receiving terminal.Wherein forward signal Y meets relay power constraint.Forward signal, through relaying-receiving terminal channel, obtains receiving terminal Received signal strength receiving terminal is by receiving terminal processing array obtain recovering signal

4th step: with least mean-square error (MinimumMeanSquaredError, MMSE) for design criterion, compares and sends signal x and receiving terminal recovering signal build MSE cost function upgrade transmitting terminal pre-coding matrix, relay pre-coding matrix, receiving terminal processing array with this iteration, finally obtain the optimal solution of three, effectively improve the BER of system with this.

The channel model that wherein first step structure channel estimation errors and antenna are correlated with comprises: use represent transmitting-relay and relaying-receiving terminal channel matrix respectively, n _s, n _r, n _dtransmitting terminal respectively, relay, the antenna number of receiving terminal and meet n _s≤ min (n _r, n _d) condition.The antenna related matrix of H and G commonly uses Kronecker model representation, definition with Ψ _hand Ψ _gtransmitting antenna correlation matrix, Σ _hand Σ _gbe the reception antenna correlation matrix of H and G, antenna related matrix adopts correlation of indices model, and antenna related matrix is positive semidefinite and completely known.Σ _helement be Σ _h(m, n)=ρ ^{| m-n|}, 1≤m, n≤n _r, ρ represents coefficient correlation, ρ=0.4.In like manner, Ψ _h, Σ _gand Ψ _gadopt identical coefficient correlation. with element obey average to be 0 variance be 1 multiple Gaussian Profile.But, in practical communication system, be difficult to obtain complete CSI, therefore definition with with be with estimated matrix, Δ H and Δ G is evaluated error matrix, its element obey average be that 0 variance is respectively with multiple Gaussian Profile, therefore, channel model can be expressed as:

$H={\Σ}_H^{1/2}(\hat{H}+\mathrm{\Δ}H){\mathrm{\Ψ}}_H^{1/2}=\stackrel{\‾}{H}+{\Σ}_H^{1/2}{\mathrm{\ΔH\Ψ}}_H^{1/2}---\left(1\right)$

$G={\Σ}_G^{1/2}(\hat{G}+\mathrm{\Δ}G){\mathrm{\Ψ}}_G^{1/2}=\stackrel{\‾}{G}+{\Σ}_G^{1/2}{\mathrm{\ΔG\Ψ}}_G^{1/2}---\left(2\right).$

Wherein second step signal is sent to relay adopts following formula to obtain through transmitting terminal precoding:

Transmitting terminal node launches information x _i(i=1,2 ..., n _s) to relay, order ε [] represents expectation; Relay Received signal strength can be expressed as:

y _r＝HBx+w(3)

Wherein for the pre-coding matrix of signal x, meet tr (Bxx ^hb ^h)=tr (BB ^h)≤P _s, the mark of tr [] representing matrix, P _sit is transmitting terminal maximum power. be the mimo channel matrix of transmitting terminal to relay, w is the additive white Gaussian noise of relay, and average is zero, and variance matrix is for its noise power.

Pre-coding matrix is passed through in relay process to received signal, then to receiving terminal forward signal, forward signal for:

Y＝Fy _r(4)

Wherein power constraint meets tr (YY ^h)≤P _r, P _rit is relay maximum power.

Wherein the 3rd step relay forwarding and receiving terminal reduction transmit is obtain according to following formula:

Order for relay is to the mimo channel matrix of receiving terminal, receiving terminal Received signal strength can be expressed as:

r＝GY+n＝GFHS+GFw+n(5)

Wherein be average be zero, variance matrix is additive white Gaussian noise (AWGN), it is the variance of n.

The processing array of receiving terminal is used for recovering transmitting of transmitting terminal, and order receives processing array and is then estimated signal vector for:

$\begin{array}{c}\tilde{x}=Qr=QGFHS+QGFW+Qn\\ =QGFHBa+QGFw+Qn\end{array}---\left(6\right)$

Described 4th step ask for transmitting terminal pre-coding matrix, relay pre-coding matrix, receiving terminal processing array optimal solution processing method be obtain according to following formula:

Be design criterion with MMSE, ask for MSE cost function:

$\begin{array}{c}MSE(B,F,Q)=\mathrm{\ϵ}\left(\right|\tilde{x}-x{|}^2)\\ =\mathrm{\ϵ}\left(\right|QGFHBx+QGFw+Qn-x{|}^2)\\ =\mathrm{\ϵ}\left(\right|Q\left(\stackrel{\‾}{G}+{\Σ}_G^{1/2}{\mathrm{\ΔG\Ψ}}_G^{1/2}\right)F\left(\stackrel{\‾}{H}+{\Σ}_H^{1/2}{\mathrm{\ΔH\Ψ}}_H^{1/2}\right)Bx\\ +Q(\stackrel{\‾}{G}+{\Σ}_G^{1/2}{\mathrm{\ΔG\Ψ}}_G^{1/2})Fw+Qn-x{|}^2)\\ =tr\[Q\stackrel{\‾}{G}{\mathrm{FZF}}^H{\stackrel{\‾}{G}}^H{Q}^H+I_{n_s}+{\mathrm{QR}}_n{Q}^H\]\\ +tr\[{\mathrm{\σ}}_G^{2}tr\left({\mathrm{FZF}}^H{\mathrm{\Ψ}}_G\right)Q{\Σ}_G{Q}^H\]\\ -tr(Q\stackrel{\‾}{G}F\stackrel{\‾}{H}B+B^H{\stackrel{\‾}{H}}^H{F}^H{\stackrel{\‾}{G}}^H{Q}^H)\end{array}---\left(7\right)$

Wherein $Z=\[\stackrel{\‾}{H}{\mathrm{BB}}^H{\stackrel{\‾}{H}}^H+{\mathrm{\σ}}_H^{2}tr\left({\mathrm{BB}}^H{\mathrm{\Ψ}}_H\right){\mathrm{\Σ}}_H+R_w\].$

Power constraint is

tr(BB ^H)≤P _s

tr(YY ^H)＝tr[F(HBB ^HH ^H+R _w)F ^H](8)

＝tr[FZF ^H]≤P _r

Because transmitting terminal and relay need meet power constraint, then can be expressed as the optimization problem minimizing cost function MSE

$\begin{array}{c}\arg \underset{B,F,Q}{\min }\left\{MSE\right\}\\ \begin{array}{cc}s.t& tr\left({\mathrm{BB}}^H\right)\≤P_s\end{array}\\ \begin{array}{cc}& tr\[{\mathrm{FZF}}^H\]\≤P_r\end{array}\end{array}---\left(9\right)$

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). transmitting terminal pre-coding matrix:

Fixing F and Q optimization B, is converted into formula:

$\begin{array}{c}\underset{B}{\min }{b}^H{A}_{1}b-2\×R\left({C_1}^{H}b\right)+D_1\\ \begin{array}{cc}s.t& b^H{A}_{2}b-2\×R\left({C_2}^{H}b\right)+D_2\≤0\end{array}\\ \begin{array}{cc}& b^H{A}_{3}b-2\×R\left({C_3}^{H}b\right)+D_3\≤0\end{array}\end{array}---\left(10\right)$

Parameter is defined as:

$b=vec\left(B\right)---\left(11\right)$

$\begin{array}{c}{A}_1=(I\⊗{\stackrel{\‾}{H}}^H{F}^H{\stackrel{\‾}{G}}^H{Q}^{H}Q\stackrel{\‾}{G}F\stackrel{\‾}{H})\\ +{\mathrm{\σ}}_H^{2}tr\left(F^H{\stackrel{\‾}{G}}^H{Q}^{H}Q\stackrel{\‾}{G}F{\Σ}_H\right)(I\⊗{\mathrm{\Ψ}}_H)\\ +{\mathrm{\σ}}_G^{2}tr\left(Q^{H}Q{\Σ}_G\right)(I\⊗{\stackrel{\‾}{H}}^H{F}^H{\mathrm{\Ψ}}_{G}F\stackrel{\‾}{H})\end{array}---\left(12\right)$

$A_2=(I\⊗I)---\left(13\right)$

$A_3=(I\⊗{\stackrel{\‾}{H}}^H{F}^{H}F\stackrel{\‾}{H})+{\mathrm{\σ}}_H^{2}tr\left(F^H{\mathrm{F\Σ}}_H\right)(I\⊗{\mathrm{\Ψ}}_H)---\left(14\right)$

$C_1=vec\[{\left(Q\stackrel{\‾}{G}F\stackrel{\‾}{H}\right)}^H\]---\left(15\right)$

C ₂＝0(16)

C ₃＝0(17)

D ₁＝0(18)

D ₂＝-P _s(19)

D ₃＝-P _r+tr(FR _wF ^H)(20)

Introduce variable t, this problem can be converted into semi definite programming problem:

$\begin{array}{c}\begin{array}{cc}\underset{B,t}{\min }& t\end{array}\\ \begin{array}{cc}s.t.& \left[\begin{array}{cc}I& {A_1}^{1/2}b\\ {\left({A_1}^{1/2}b\right)}^H& t+2\×R\left({C_1}^{H}b\right)-D_1\end{array}\right]\≥0\end{array}\\ \begin{array}{cc}& \left[\begin{array}{cc}I& {A_i}^{1/2}b\\ {\left({A_1}^{1/2}b\right)}^H& 2\×R\left({C_i}^{H}b\right)-D_i\end{array}\right]\≥0,i=2,3\end{array}\end{array}---\left(21\right)$

This problem can be solved by interior point method or MATLABCVX tool box.

(2). relaying pre-coding matrix F

Optimization problem (9) is converted into the subproblem that fixing B and Q solves F:

$\begin{array}{c}\arg \underset{F}{\min }\left\{MSE\right\}\\ \begin{array}{cc}s.t& tr\[{\mathrm{FZF}}^H\]\≤P_r\end{array}\end{array}---\left(22\right)$

Be easy to prove that this problem is convex optimization problem.Therefore, F can try to achieve with KKT algorithm, and the Lagrangian of formula (23) is:

L(F,λ)＝MSE(B,F,Q)+λ(tr[FZF ^H]-P _r)(23)

Wherein, λ is Lagrange multiplier.By to L (F, λ) differentiate, and following power constraint to be met:

$\frac{\∂L(F,\mathrm{\λ})}{\∂\stackrel{\‾}{F}}{|}_{\stackrel{\‾}{F}=F^{*}}=0---\left(24\right)$

tr[FZF ^H]-P _r＜0(25)

λ＞0(26)

λ(tr[FZF ^H]-P _r)＝0(27)

Therefore, relaying pre-coding matrix F can be obtained:

$\begin{array}{c}F={({\stackrel{\‾}{G}}^H{Q}^{H}Q\stackrel{\‾}{G}+{\mathrm{\σ}}_G^{2}tr(Q^{H}Q{\Σ}_G){\mathrm{\Ψ}}_G+{\mathrm{\λI}}_{n_r})}^{+}\\ {\stackrel{\‾}{G}}^H{Q}^H{B}^H{\stackrel{\‾}{H}}^H{Z}^{+}\end{array}---\left(28\right)$

Optimization λ must meet and, the constraints of λ is λ optimum in formula can adopt dichotomy to solve.

In order to simplify optimization problem, lead-in property coefficient η > 0 in receiving terminal processing array, and Q is replaced with η ^-1q.Through series of computation, can obtain:

$\begin{array}{c}F=\mathrm{\η}{({\stackrel{\‾}{G}}^H{Q}^{H}Q\stackrel{\‾}{G}+{\mathrm{\σ}}_G^{2}tr(Q^{H}Q{\Σ}_G){\mathrm{\Ψ}}_G+{\mathrm{\θI}}_{n_r})}^{+}\\ {\stackrel{\‾}{G}}^H{Q}^H{B}^H{\stackrel{\‾}{H}}^H{Z}^{+}\end{array}---\left(29\right)$

Order

$\mathrm{\θ}=\frac{tr\left({\mathrm{QR}}_n{Q}^H\right)}{P_r}---\left(30\right)$

$\begin{array}{c}{\mathrm{MSE}}_{\min }(B,Q)=tr\left(I_{n_s}\right)-tr\[B^H{\stackrel{\‾}{H}}^H{Z}^{+}\stackrel{\‾}{H}BQ\stackrel{\‾}{G}\\ {({\stackrel{\‾}{G}}^H{Q}^{H}Q\stackrel{\‾}{G}+{\mathrm{\σ}}_G^{2}tr(Q^{H}Q{\Σ}_G){\mathrm{\Ψ}}_G+{\mathrm{\θI}}_{n_r})}^{+}{\stackrel{\‾}{G}}^H{Q}^H\]\end{array}---\left(31\right)$

(3). receiving terminal processing array Q

Optimization problem (9) is converted into the subproblem that fixing B and F solves Q:

$\begin{array}{c}MSE\left(Q\right)=tr\left(I_{n_s}\right)-tr\[B^H{\stackrel{\‾}{H}}^H{Z}^{+}\stackrel{\‾}{H}BQ\stackrel{\‾}{G}\\ {({\stackrel{\‾}{G}}^H{Q}^{H}Q\stackrel{\‾}{G}+{\mathrm{\σ}}_G^{2}tr(Q^{H}Q{\Σ}_G){\mathrm{\ψ}}_G+{\mathrm{\θI}}_{n_r})}^{+}{\stackrel{\‾}{G}}^H{Q}^H\]\\ =tr\left(E_H\right)+tr\left(E_G\right)-tr\[E_H{E}_G\]\end{array}---\left(32\right)$

Definition:

$E_H=I_{n_s}-B^H{\stackrel{\‾}{H}}^H{Z}^{+}\stackrel{\‾}{H}B---\left(33\right)$

$\begin{array}{c}{\mathrm{\β}}_n={\mathrm{\σ}}_G^{2}tr\left(Q^{H}Q{\Σ}_G\right){\mathrm{\Ψ}}_G+{\mathrm{\θI}}_{n_r}\\ ={\mathrm{\σ}}_G^{2}tr\left(Q^{H}Q{\Σ}_G\right){\mathrm{\Ψ}}_G+{\mathrm{\θI}}_{n_r}\\ \≤{\mathrm{\σ}}_G^{2}tr\left(Q^{H}Q\right){\mathrm{\λ}}_{\max }\left({\Σ}_G\right){\mathrm{\Ψ}}_G+{\mathrm{\θI}}_{n_r}\\ =\left({\mathrm{\σ}}_G^2{P}_r{\mathrm{\λ}}_{\max }\right({\Σ}_G)R_n^{-1}{\mathrm{\Ψ}}_G+I_{n_r}){\mathrm{\θ}}_n\end{array}---\left(34\right)$

$E_G={(I_{n_s}+Q_n\stackrel{\‾}{G}{{\mathrm{\β}}_n}^{-1}{\stackrel{\‾}{G}}^H{Q_n}^H)}^{-1}---\left(35\right)$

This Unconstrained Optimization Problem can adopt gradient linearity search method to solve

$\begin{array}{c}{\mathrm{\ΔQ}}_n=-{\▿}_{Q^{*}}MSE\left(Q\right)\\ =-{{\mathrm{\η}}_n}^{-2}{\mathrm{QR}}_n+E_G{B}^H{\stackrel{\‾}{H}}^H{Z}^{+}\stackrel{\‾}{H}{\mathrm{BE}}_{G}Q\stackrel{\‾}{G}{{\mathrm{\β}}_n}^{-1}{\stackrel{\‾}{G}}^H\end{array}---\left(36\right)$

Corresponding solution procedure is as shown in algorithm 1:

(4). Joint iteration designs

This algorithm is as follows:

Following table is the simulated conditions that the present embodiment adopts.

In order to verify the superiority of Joint iteration algorithm in this paper, the method and additive method are contrasted, the method contrasted in emulation is:

iteration B and F pre-coding scheme: Q ∝ I.

iteration F and Q pre-coding scheme:

joint iteration pre-coding scheme

Fig. 3 and Fig. 4 sets forth SNR _sr=SNR _rdtime based on the bit error rate comparison diagram of MIMO relay system under different evaluated error and different antennae correlation, find out from simulation result, when low signal-to-noise ratio, the performance of iteration F and Q method is better than iteration B and F method, and along with the increase of signal to noise ratio, Joint iteration method is significantly better than other two kinds of methods, and keeps the snr gain of 2-4dB, it can thus be appreciated that scheme can obtain lower BER really, demonstrate validity and the superiority of put forward algorithm herein.

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 method for precoding for the MIMO relay system that channel estimation errors and antenna are correlated with, it is characterized in that: comprise the steps

The first step: for MIMO relay system, builds and there is the relevant channel model of channel estimation errors and antenna, suppose that transmittings-relay and relaying-receiving terminal channel all exist channel estimation errors and antenna is relevant, use represent transmitting-relay and relaying-receiving terminal channel matrix respectively, n _s, n _r, n _dtransmitting terminal respectively, relay, the antenna number of receiving terminal and meet n _s≤ min (n _r, n _d) condition;

Second step: symbol substream through transmitting terminal pre-coding matrix be transmitted to relaying after process, wherein transmitting terminal transmission signal must meet transmitting terminal power constraint, sends signal and can obtain relay reception signal through transmitting-relay channel

3rd step: Received signal strength y _rthrough relay pre-coding matrix process obtains and be transmitted to receiving terminal, wherein forward signal Y meets relay power constraint, and forward signal, through relaying-receiving terminal channel, obtains receiving terminal Received signal strength receiving terminal is by receiving terminal processing array obtain recovering signal

4th step: take least mean-square error as design criterion, compares and sends signal x and receiving terminal recovering signal build MSE cost function upgrade transmitting terminal pre-coding matrix, relay pre-coding matrix, receiving terminal processing array with this real-time iterative, finally obtain the optimal solution of three to improve the bit error rate of system.

2. there is the method for precoding of the MIMO relay system that channel estimation errors and antenna are correlated with as claimed in claim 1, it is characterized in that: the described first step builds channel estimation errors and the relevant channel model of antenna comprises:

The antenna related matrix Kronecker model representation of H and G, definition with Ψ _hand Ψ _gtransmitting antenna correlation matrix, Σ _hand Σ _gbe the reception antenna correlation matrix of H and G, antenna related matrix is positive semidefinite and completely known, with element obey average to be 0 variance be 1 multiple Gaussian Profile, definition with with be with estimated matrix, Δ H and Δ G is channel estimation errors matrix, its element obey average be that 0 variance is respectively with multiple Gaussian Profile, therefore, channel model can be expressed as:

3. there is the method for precoding of the MIMO relay system that channel estimation errors and antenna are correlated with as claimed in claim 1, it is characterized in that: described second step signal is through transmitting terminal precoding and be sent to relay and adopt following formula to obtain:

Transmitting terminal node launches information x _i(i=1,2 ..., n _s) to relay, order ε [] represents expectation; Relay Received signal strength can be expressed as:

y _r＝HBx+w

Wherein for the pre-coding matrix of signal x, meet tr (Bxx ^hb ^h)=tr (BB ^h)≤ _sthe mark of P, tr [] representing matrix, P _stransmitting terminal maximum power, be the mimo channel matrix of transmitting terminal to relay, w is the additive white Gaussian noise of relay, and average is zero, and variance matrix is for its noise power, processing array is passed through in relay process to received signal, then to receiving terminal forward signal, forward signal for:

Y＝Fy _r

Wherein power constraint meets tr (YY ^h)≤P _r, P _rit is relay maximum power.

4. there is the method for precoding of the MIMO relay system that channel estimation errors and antenna are correlated with as claimed in claim 1, it is characterized in that: it is obtain according to following formula that described 3rd step relay forwarding and receiving terminal reduction transmit:

Receiving terminal Received signal strength can be expressed as:

r＝GY+n＝GFHS+GFw+n

Wherein be average be zero, variance matrix is additive white Gaussian noise, it is the variance of n;

The processing array of receiving terminal is used for recovering transmitting of transmitting terminal, and order receives processing array and is then estimated signal vector for:

。

5. there is the method for precoding of the MIMO relay system that channel estimation errors and antenna are correlated with as claimed in claim 1, it is characterized in that: described 4th step ask for transmitting terminal pre-coding matrix, relay pre-coding matrix, receiving terminal processing array optimal solution processing method be obtain according to following formula:

(1). be design criterion with least mean-square error, ask for MSE cost function:

Wherein

Power constraint is:

tr(BB ^H)≤P _s

tr(YY ^H)＝tr[F(HBB ^HH ^H+R _w)F ^H]

＝tr[FZF ^H]≤P _r

(2). because transmitting terminal and relay need meet power constraint, then can be expressed as the optimization problem minimizing cost function MSE:

s.ttr(BB ^H)≤P _s。

tr[FZF ^H]≤P _r。