CN101521537A - Method for cooperative relay beamforming based on limited feedback - Google Patents

Abstract

A method for cooperative relay beamforming based on limited feedback is applicable to a communication system. The communication system comprises a transmitter, a plurality of relays and a receiver. The transmitter is provided with a plurality of antennae, each relay is provided with a single antenna, the receiver is provided with a plurality of antennae, and the plurality of the relays cooperate and adopt an amplification and forwarding protocol; the whole communication process is finished in two time slots, wherein in the first time sot, after performing transmit beamforming on a data flow, the transmitter broadcasts the data flow to all relays; and in the second time slot, all relays determine distributed beamforming code words according to limited feedback information containing code word indicators and power amplification factors from the receiver and forward receipt signals subjected to respective code word component treatment to a information sink; and the design of a code book is completed by code book design and cord word updating algorithm, the relays select code words which can maximize the instant signal to noise ratio of the receiver from the code book according to each channel condition as a beamforming vector.

Description

Cooperating relay wave beam formation method based on Limited Feedback

Technical field

The present invention relates to a kind of wireless communication system wave beam formation method that is applied to, relate in particular to a kind of cooperating relay wave beam formation method, belong to wireless communication field based on Limited Feedback.

Background technology

The auxiliary cellular radio Communication system of relaying has the Extended Cell coverage, improve the spectrum efficiency of Cell Edge User, overcome advantage such as shadow fading.In recent years, the researcher is respectively from trunk protocol, the angle of information theory and Processing Algorithm has been studied trunking traffic, for example: at the single output of single input (Single-input Single-output, SISO) wireless relay communication system, three kinds of typical trunk protocols are arranged, promptly amplify and transmit (Amplify-and-Forward, AF), (Decode-and-Forward is transmitted in decoding, DF) and compression transmit (Compress-and-Forward, CF), wherein the AF trunk protocol is not owing to needing to decode direct forward signal, and it is all very low to handle complexity and power consumption, so use more extensive.Simultaneously, multiple-input and multiple-output (MIMO) communication system can improve the validity and the reliability of communicating by letter by utilizing spatial reuse gain, space diversity gain and array gain, and MIMO technology and the relaying technique advantage that can utilize the two that combines is improved communication performance further.

At present transmit the design of optimum structure of matrix and the existing Primary Study of optimal power allocation scheme of relaying at relaying, but all be communication system at single many antennas relaying, and do not consider that the situation of a plurality of relayings, many relayings collaboration communication relate to the cooperation of distributed relay or collaborative.When the transmitter and receiver of system all is equipped with many antennas, and when using a plurality of distributed relay to carry out collaboration communication, the cooperation of this system can not only be confined on the level of relaying, and should cooperate on the receiver that comprises the transmitter of many antennas, a plurality of distributed relayings and many antennas system-level.In addition, at present mainly concentrate on the power division problem and do not consider phase place rotation (being that wave beam forms) problems of many relayings at the research of a plurality of relayings cooperations.In practical communication system, sending signal and channel all is plural number, and this makes the combined optimization of many relayings not only comprise the power division of associating but also comprise the phase place rotation of associating that promptly wave beam forms.Beam-forming technology is meant that transmitter sends pre-coherent superposition by utilizing channel condition information to transmitting, thereby realizes the purpose of transmission antenna diversity.

Present research supposes that usually each relaying all must obtain desirable channel condition information (Channel State Information, CSI), then because the channel estimating feedback inaccurate, channel information of receiver has time delay, noise pollution, make that this hypothesis is unpractical, more practical situation is that relaying is only known portion C SI.

In sum, the united beam shaping problem based on Limited Feedback has important Research Significance in the auxiliary distributed MIMO system of many relayings.

Summary of the invention

Technical problem:, the invention provides and a kind ofly can obtain the higher system throughput, the cooperating relay wave beam formation method that implementation complexity is lower based on Limited Feedback at the shortcoming of prior art.

Technical scheme: embodiments of the invention disclose a kind of cooperating relay wave beam formation method based on Limited Feedback.This method is applicable to a kind of communication system, this communication system comprises a transmitter, a plurality of relaying and a receiver, many antennas of transmitter configuration, and each relaying all disposes single antenna, many antennas of receiver configuration, a plurality of relayings are cooperated mutually and are adopted the amplification retransmission protocol; Whole communication process is finished at two time slots, at first time slot, transmitter carries out being broadcast to all relayings after launching beam forms to data stream, at second time slot, all relayings are according to determining the code word that distributed wave beam forms from the Limited Feedback information that comprises the code word label and the power amplification factor of receiver, a plurality of then relayings are transmitted to the stay of two nights through code word component separately after handling with received signal.

Embodiments of the invention disclose a kind of wave beam formation method based on Limited Feedback, and concrete steps are as follows:

Step 1: transmitter is estimated the first channel response H that jumps ₁

Step 2: transmitter is according to H ₁The launching beam of design transmitter forms vectorial d ₁, ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{P_1}{V}_1(:,1),$ Wherein, P ₁Be the transmitting power of transmitter, V ₁Come from H ₁Carry out singular value decomposition $H_{}$ ${}_1={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1{V}_1^H,$ U ₁Be left singular matrix, Λ ₁Be the diagonal matrix that singular value is formed, V ₁Be right singular matrix, V ₁First row of unitary matrix are got in (:, 1) expression;

Step 3: receiver estimates that first jumps and the second channel response H that jumps ₁And H ₂

Step 4: receiver is at first according to generalized L loyd algorithm design code book subspace, combines with the designed code word update algorithm of the present invention and carries out iteration until satisfying the convergence precision requirement, obtains required code book, at last with each code word energy normalized.The code book design with code word update algorithm concrete steps is:

Step 1: the code book { w that one group of united beam of initialization forms _j, j=1 ..., 2 ^B, and produce L at random _hSecondary channel is realized

Wherein B is a number of bits of feedback, H _{I, 1}And H _{I, 2}Represent the channel realization of the i time double bounce, L _hBe that channel is realized number of times, for example L _h=10000;

Step 2: at given code book { w _j, j=1 ..., 2 ^B, channel space is divided into 2 ^BIndividual channel subspace, criteria for classifying is as follows: $S_j=\{H_{i,1},H_{i,2}|\frac{w_j^{H}A{w}_j}{w_j^{H}B{w}_j}\&GreaterEqual;\frac{w_p^{H}A{w}_p}{w_p^{H}B{w}_p},j,p=1,\&CenterDot;\&CenterDot;\&CenterDot;,2^B,j\&NotEqual;p\},$ Wherein,

A＝[H ₂diag(H ₁d ₁)] ^H[H ₂diag(H ₁d ₁)]， $B={\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_2^H{H}_2\right)+\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A200910030712E00121.png"\; state="\{\{state\}\}">P</figure-callout>}}_2}\mathrm{diag}(H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_k),$ For relaying receives noise variance,

For the stay of two nights receives noise variance, P ₂Transmitted power for all relayings;

Step 3: at 2 ^BIndividual channel subspace

The code word that each united beam is formed is upgraded by newly-designed code word algorithm respectively.The code word replacement problem can be described as:

$w_j=\underset{x}{\arg \max }\{f\left(x\right)=\underset{q=1}{\overset{L_j}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}{\log }_2\left(x^H\left\{{\left[H_{q,2}\mathrm{diag}\left(H_{q,1}{d}_{q,1}\right)\right]}^H\right[H_{q,2}\mathrm{diag}\left(H_{q,1}{d}_{q,1}\right)\left]\right\}x\right)\\ -{\log }_2\left(x^H{\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_{q,2}^H{H}_{q,2}\right)x\right)\end{array}\right\}\},$

At following formula, design code word update algorithm, concrete steps are as follows:

Step 4: initialization k=0, x ₀=0, α ₀=1, δ ₀=0;

Step?5： $\mathrm{While\; f}(x_k+{\mathrm{\&alpha;}}_k{\mathrm{\&delta;}}_k)<f\left(x_k\right)+0.45{\mathrm{\&alpha;}}_k\left({\mathrm{\&delta;}}_k^H{\mathrm{\&delta;}}_k\right)$

${\mathrm{\&delta;}}_{k+1}=\frac{\&PartialD;f\left(x_k\right)}{\&PartialD;x_k};$ x _k+1＝x _k+α _kδ _k；α _k+1＝0.75α _k；

End

Step 6: make w _j=x _K+1

Step 7: with w _jSubstitution Step2 generates the subspace of upgrading, and so circulation is until satisfying the convergence precision requirement.

Step 5: receiver feeds back to all relayings with designed code book;

Step 6: receiver is selected the code word w that can make the received signal to noise ratio maximum according to the double bounce channel information _j, calculate the relaying repeating power ξ of this code word correspondence then, then with ξ and w _jCorresponding label feeds back to all relayings;

Step 7: each relaying finds corresponding codewords according to the code word label, and then obtains own corresponding code word component, after multiply by received signal and amplifying, is transmitted to receiver at next time slot;

Step 8: receiver adopts high specific to merge (MRC) and receives, and receives vector z and is: $z=\frac{H_2{W}_r{H}_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}{{\left|\right|H_2{W}_r{H}_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\left|\right|}_F},$ W wherein _r=ξ diag (w _j);

Wherein, () ^HThe conjugate transpose of-matrix or vector; Diag ()-get diagonal element constitutes a diagonal matrix; I _KThe unit matrix of-K * K, K are the relaying number; ∑ ()-summation operation;

-function f (x) is asked local derviation to independent variable x; ‖ ‖ _F-get the Frobenius norm of matrix; Max ()-maximizing.

Beneficial effect: the present invention proposes a kind of cooperating relay wave beam formation method based on Limited Feedback, it is characterized in that, this method is applicable to a kind of communication system, this communication system comprises a transmitter, a plurality of relaying and a receiver, many antennas of transmitter configuration, each relaying all disposes single antenna, many antennas of receiver configuration, and a plurality of relayings are cooperated mutually and are adopted the amplification retransmission protocol.Whole communication process is finished at two time slots, at first time slot, transmitter carries out being broadcast to all relayings after launching beam forms to data stream, at second time slot, all relayings are according to determining the code word that distributed wave beam forms from the Limited Feedback information that comprises the code word label and the power amplification factor of receiver, a plurality of then relayings are transmitted to the stay of two nights through code word component separately after handling with received signal.The present invention has designed a kind of very practical wave beam formation method based on Limited Feedback, come design codebooks according to a kind of code book algorithm for design and the designed mutual iteration of code word update algorithm of the present invention, relaying is selected to make the code word of receiver instantaneous signal-to-noise ratio maximum form vector as wave beam from this code book according to each channel condition.The designed cooperating relay wave beam generated code instinct of the present invention obtains obvious performance gain under the very little situation of feedback overhead, the code word update algorithm is simple and practical, has obtained system spectral efficiency performance preferably with lower system's implementation complexity.

Description of drawings

Fig. 1 is that communication system of the present invention is formed structural representation, d among the figure ₁For the launching beam of transmitter forms vector, d _R1..., d _RkBe the wave beam formation component of K relaying, z is the reception vector of receiver, and M is the antenna number of transmitter, and N is the antenna number of receiver, and K is the relaying number;

Fig. 2～Fig. 4 has provided designed distributed wave beam and has formed the spectrum efficiency performance of code book under different feedback quantities and different antennae configuration.Definition ${\mathrm{\&rho;}}_1=\frac{P_1}{M{\mathrm{\&sigma;}}_1^2}$ With ${\mathrm{\&rho;}}_2=\frac{P_2}{K{\mathrm{\&sigma;}}_2^2};$

It is 4 that Fig. 2 has provided the transmitter antenna number, and the relaying number is 4, and receiver reception antenna number is 4, ρ ₁=ρ ₂Under the situation of=20dB, the system spectral efficiency cumulative distribution function curve of different number of bits of feedback B correspondences (Cumulative and Distributive Function, CDF) figure;

It is 4 that Fig. 3 has provided the transmitter antenna number, and the relaying number is 2, and receiver reception antenna number is 4, ρ ₁=ρ ₂Under the situation of=20dB, the system spectral efficiency CDF curve chart of different number of bits of feedback B correspondences;

It is 4 that Fig. 4 has provided the transmitter antenna number, and the relaying number is 2, and receiver reception antenna number is 2, ρ ₁=ρ ₂Under the situation of=20dB, the system spectral efficiency CDF curve chart of different number of bits of feedback B correspondences;

Embodiment

As shown in Figure 1, communication system of the present invention comprises a transmitter, a plurality of relaying and a receiver, many antennas of transmitter configuration, and each relaying all disposes single antenna, many antennas of receiver configuration, a plurality of relayings are cooperated mutually and are adopted the amplification retransmission protocol.Whole communication process is finished at two time slots, at first time slot, transmitter carries out being broadcast to all relayings after launching beam forms to data stream, at second time slot, all relayings are according to determining the code word that distributed wave beam forms from the Limited Feedback information that comprises the code word label and the power amplification factor of receiver, a plurality of then relayings are transmitted to the stay of two nights through code word component separately after handling with received signal.

For doing performance relatively with the designed cooperating relay wave beam formation method of the present invention based on Limited Feedback, the present invention has also designed many relayings of cooperation Optimal Distribution formula wave beam formation method that a kind of relaying need be known whole channel condition informations, and concrete implementation step is as follows:

Step 1: transmitter estimates that first jumps the channel response H of (transmitter is to all relayings) ₁

Step 2: transmitter is according to H ₁The launching beam of design transmitter forms vectorial d ₁, ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{P_1}{V}_1(:,1),$ Wherein, P ₁Be the transmitting power of transmitter, V ₁Come from H ₁Carry out singular value decomposition (Singular Value Decomposition, SVD) ${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">H</figure-callout>}}_1=U_1{\mathrm{\&Lambda;}}_1{V}_1^H,$ U ₁Be left singular matrix, Λ ₁Be the diagonal matrix that singular value is formed, V ₁Be right singular matrix, V ₁First row of unitary matrix are got in (:, 1) expression;

Step 3: receiver is estimated the channel response H of first jumping and second jumping (all are relayed to receiver) ₁And H ₂

Step 4: receiver is determined optimum collaboration type forwarding processing array D according to receiver received signal to noise ratio maximization criterion _r=diag (d _r), then this matrix information is fed back to all relayings.The Mathematical Modeling of received signal to noise ratio maximization problems is:

$\underset{D_r}{\max }\left\{\frac{d_1^H{H}_1^H{D}_r^H{H}_2^H{H}_2{D}_r{H}_r{d}_1}{n_1^H{D}_r^H{H}_2^H{H}_2{\mathrm{<figure-callout\; id="1"\; label="D\; r\; n"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">D</figure-callout>}}_r{n}_{}{}_1+\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A200910030712E00121.png"\; state="\{\{state\}\}">P</figure-callout>}}_2}\mathrm{tr}\left\{D_r[H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_k]D_r^H\right\}}\right\}$

s.t. $\mathrm{tr}\left\{D_r\right[H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_K\left]D_r^H\right\}={\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A200910030712E00121.png"\; state="\{\{state\}\}">P</figure-callout>}}_2$

The optimal solution D of this maximization problems _r=diag (d _r) be $d_r=\mathrm{\&xi;}\&CenterDot;{\stackrel{\&RightArrow;}{d}}_r,$ Wherein,

${\stackrel{\&RightArrow;}{d}}_r={\left(L^{-1}\right)}^H\&CenterDot;v_{\max }\left\{\left(L^{-1}\right)\mathrm{diag}{\left(H_1{d}_1\right)}^H{H}_2^{\mathrm{<figure-callout\; id="2"\; label="H\; H"\; filenames="A200910030712E00121.png"\; state="\{\{state\}\}">H</figure-callout>}}{H}_{}{}_2\mathrm{diag}\left(H_1{d}_1\right){\left(L^{-1}\right)}^H\right\}$

$\mathrm{\&xi;}=\sqrt{\frac{P_2}{{\stackrel{\&RightArrow;}{d_r}}^H\mathrm{diag}(H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_k)\stackrel{\&RightArrow;}{d_r}}}$

$Q=[{\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_2^H{H}_2\right)+\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A200910030712E00121.png"\; state="\{\{state\}\}">P</figure-callout>}}_2}\mathrm{diag}(H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_k)]={\mathrm{LL}}^H$

Wherein, P ₂The power constraint of representing all relayings respectively, the mark of tr () representing matrix,

With

Represent that respectively relaying receives noise variance and the stay of two nights receives noise variance, Q=LL ^HFor Choleskey decomposes, v _MaxThe normalization characteristic vector of { } expression eigenvalue of maximum correspondence, L ^-1Expression is got contrary,

Expression is got diagonal element and is constituted a diagonal matrix.

Step 5: receiver is transmitted processing array D with collaboration type _r=diag (d _r) feed back to many relayings;

Step 6: each relaying forms vectorial d with received signal separately through wave beam _rComponent forward again after handling;

Step 7: receiver adopts high specific to merge (MRC) and receives, and receives vector z and is: $z=\frac{H_2{D}_r{H}_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}{{\left|\right|H_2{D}_r{H}_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\left|\right|}_F};$

The concrete steps of a kind of wave beam formation method based on Limited Feedback of the present invention are as follows:

Step 1: transmitter is estimated the first channel response H that jumps ₁

Step 2: transmitter is according to H ₁The launching beam of design transmitter forms vectorial d ₁, ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{P_1}{V}_1(:,1),$ Wherein, V ₁Come from H ₁Carry out singular value decomposition $H_{}$ ${}_1={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Lambda;}}_1{V}_1^H,$ V ₁First row of unitary matrix are got in (:, 1) expression;

Step 3: receiver estimates that first jumps and the second channel response H that jumps ₁And H ₂

Step 4: receiver is at first according to generalized L loyd algorithm design code book subspace, combines with the designed code word update algorithm of the present invention and carries out iteration until satisfying the convergence precision requirement, obtains required code book, at last with each code word energy normalized.The code book design with code word update algorithm concrete steps is:

Step 1: the code book { w that one group of united beam of initialization forms _j,, j=1 ..., 2 ^B, and produce L at random _hSecondary channel is realized

Wherein B is a number of bits of feedback, H _{I, 1}And H _{I, 2}Represent the channel realization of the i time double bounce, L _hBe that channel is realized number of times, for example L _h=10000;

Step 2: at given code book { w _j, j=1 ..., 2 ^B, channel space is divided into 2 ^BIndividual channel subspace, criteria for classifying is as follows: $S_j=\{H_{i,1},H_{i,2}|\frac{w_j^{H}A{w}_j}{w_j^{H}B{w}_j}\&GreaterEqual;\frac{w_p^{H}A{w}_p}{w_p^{H}B{w}_p},j,p=1,\&CenterDot;\&CenterDot;\&CenterDot;,2^B,j\&NotEqual;p\},$ Wherein,

A＝[H ₂diag(H ₁d ₁)] ^H[H ₂diag(H ₁d ₁)]， $B={\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_2^H{H}_2\right)+\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A200910030712E00121.png"\; state="\{\{state\}\}">P</figure-callout>}}_2}\mathrm{diag}(H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_k),$

For relaying receives noise variance, For the stay of two nights receives noise variance, P ₂Transmitted power for all relayings;

Step 3: at 2 ^BIndividual channel subspace The code word that each united beam is formed is upgraded by newly-designed code word algorithm respectively.The code word replacement problem can be described as:

$w_j=\underset{x}{\arg \max }\{f\left(x\right)=\underset{q=1}{\overset{L_j}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}{\log }_2\left(x^H\left\{{\left[H_{q,2}\mathrm{diag}\left(H_{q,1}{d}_{q,1}\right)\right]}^H\right[H_{q,2}\mathrm{diag}\left(H_{q,1}{d}_{q,1}\right)\left]\right\}x\right)\\ -{\log }_2\left(x^H{\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_{q,2}^H{H}_{q,2}\right)x\right)\end{array}\right\}\},$

At following formula, design code word update algorithm, concrete steps are as follows:

Step 4: initialization k=0, x ₀=0, α ₀=1, δ ₀=0;

Step?5： $\mathrm{While\; f}(x_k+{\mathrm{\&alpha;}}_k{\mathrm{\&delta;}}_k)<f\left(x_k\right)+0.45{\mathrm{\&alpha;}}_k\left({\mathrm{\&delta;}}_k^H{\mathrm{\&delta;}}_k\right)$

${\mathrm{\&delta;}}_{k+1}=\frac{\&PartialD;f\left(x_k\right)}{\&PartialD;x_k};$ x _k+1＝xl _k+α _kδ _k；α _k+1＝0.75α _k；

End

Step 6: make w _j=x _K+1

Step7: with w _jSubstitution Step2 generates the subspace of upgrading, and so circulation is until satisfying the convergence precision requirement.

Step 5: receiver feeds back to all relayings with designed code book;

Step 6: receiver is selected the code word w that can make the received signal to noise ratio maximum according to the double bounce channel information _j, calculate the relaying repeating power ξ of this code word correspondence then, then with ξ and w _jCorresponding label feeds back to all relayings;

Step 7: each relaying finds corresponding codewords according to the code word label, and then obtains own corresponding code word component, after multiply by received signal and amplifying, is transmitted to receiver at next time slot;

Step 8: receiver adopts high specific to merge (MRC) and receives, and receives vector z and is: $z=\frac{H_2{W}_r{H}_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}{{\left|\right|H_2{W}_r{H}_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A200910030712E00101.png,A200910030712E00131.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\left|\right|}_F},$ W wherein _r=ξ diag (w _j);

Wherein, () ^HThe conjugate transpose of-matrix or vector; Diag ()-get diagonal element constitutes a diagonal matrix; I _KThe unit matrix of-K * K, K are the relaying number; ∑ ()-summation operation;

-function f (x) is asked local derviation to independent variable x; ‖ ‖ _F-get the Frobenius norm of matrix; Max ()-maximizing.

Fig. 3～Fig. 5 has provided designed distributed wave beam and has formed the spectrum efficiency performance of code book under different feedback quantities and different antennae configuration.Wherein the situation of feedback is many relayings of cooperation Optimal Distribution formula wave beam formation method that the designed relaying of the present invention need be known whole channel condition informations fully.

As seen from Figure 3, when B is increased at 2,5 o'clock from 1, spectrum efficiency obviously increases, and when B=5, obtains the gain of about 0.6b/s/Hz.As seen, designed code book obtains spectral efficiency gain clearly under the smaller situation of feedback overhead.

Fig. 4 and Fig. 5 have provided the situation of two distributed relay, and under the reception antenna number of two kinds of receivers, the spectrum efficiency of system is all very approaching performance ideally when number of bits of feedback B=5.As seen put forward distributed wave beam formation scheme and under designed code book, obtained tangible system performance gain with very little feedback quantity.

Claims (3)

1. cooperating relay wave beam formation method based on Limited Feedback, it is characterized in that, this method is applicable to a kind of communication system, this communication system comprises a transmitter, a plurality of relaying and a receiver, many antennas of transmitter configuration, each relaying all disposes single antenna, many antennas of receiver configuration, and a plurality of relayings are cooperated mutually and are adopted the amplification retransmission protocol; Whole communication process is finished at two time slots, at first time slot, transmitter carries out being broadcast to all relayings after launching beam forms to data stream, at second time slot, all relayings are according to determining the code word that distributed wave beam forms from the Limited Feedback information that comprises the code word label and the power amplification factor of receiver, a plurality of then relayings are transmitted to the stay of two nights through code word component separately after handling with received signal; Finish the design of code book by code book design and code word update algorithm, relaying is selected to make the code word of receiver instantaneous signal-to-noise ratio maximum form vector as wave beam from this code book according to channel condition at every turn.

2. the cooperating relay wave beam formation method based on Limited Feedback according to claim 1 is characterized in that the concrete steps of this method are as follows:

Step 1: transmitter is estimated the first channel response H that jumps ₁

Step 2: transmitter is according to H ₁The launching beam of design transmitter forms vectorial d ₁, $d_1=\sqrt{P_1}{V}_1(:,1)$ , wherein, P ₁Be the transmitting power of transmitter, V ₁Come from H ₁Carry out singular value decomposition H ₁=U ₁A ₁V ₁ ^H, U ₁Be left singular matrix, A ₁Be the diagonal matrix that singular value is formed, V ₁Be right singular matrix, V ₁First row of unitary matrix are got in (:, 1) expression;

Step 3: receiver estimates that first jumps and the second channel response H that jumps ₁And H ₂

Step 4: receiver combines with the code word update algorithm and carries out iteration until satisfying the convergence precision requirement at first according to generalized L loyd algorithm design code book subspace, obtains required code book, at last with each code word energy normalized;

Step 5: receiver feeds back to all relayings with designed code book;

Step 6: receiver is selected the code word w that can make the received signal to noise ratio maximum according to the double bounce channel information _j, calculate the relaying repeating power ξ of this code word correspondence then, then with ξ and w _jCorresponding label feeds back to all relayings;

Step 7: each relaying finds corresponding codewords according to the code word label, and then obtains own corresponding code word component, after multiply by received signal and amplifying, is transmitted to receiver at next time slot;

Step 8: receiver adopts high specific to merge (MRC) and receives, and receives vector z and is: $z=\frac{H_2{W}_r{H}_1{d}_1}{{||H_2{W}_r{H}_1{d}_1||}_F}$ W wherein _r=ξ diag (w _j);

3. the cooperating relay wave beam formation method based on Limited Feedback according to claim 1 is characterized in that, the code book design with code word update algorithm concrete steps is:

Step 1: the code book { w that one group of united beam of initialization forms _j, j=1 ..., 2 ^B, and produce L at random _hSecondary channel is realized

, wherein B is a number of bits of feedback, H _{I, 1}And H _{I, 2}Represent the channel realization of the i time double bounce, L _hBe that channel is realized number of times, for example L _h=10000;

Step 2: at given code book { w _j, j=1 ..., 2 ^B, channel space is divided into 2 ^BIndividual channel subspace, criteria for classifying is as follows: $S_j=\{H_{i,1},H_{i,2}|\frac{w_j^H{\mathrm{Aw}}_j}{w_j^H{\mathrm{Bw}}_j}\&GreaterEqual;\frac{w_p^H{\mathrm{Aw}}_p}{w_p^H{\mathrm{Bw}}_p},j,p=1,\&CenterDot;\&CenterDot;\&CenterDot;,2^B,j\&NotEqual;p\}$ , wherein, A=[H ₂Diag (H ₁d ₁)] ^H[H ₂Diag (H ₁d ₁)], $B={\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_2^H{H}_2\right)+\frac{{\mathrm{\&sigma;}}_2^2}{P_2}\mathrm{diag}(H_1{d}_1{d}_1^H{H}_1^H+{\mathrm{\&sigma;}}_1^2{I}_K),$

For relaying receives noise variance,

For the stay of two nights receives noise variance, P ₂Transmitted power for all relayings;

Step 3: at 2 ^BIndividual channel subspace , the code word that each united beam is formed is upgraded by newly-designed code word algorithm respectively, and the code word replacement problem can be described as:

$w_j=\underset{x}{\arg \max }\{f\left(x\right)=\underset{q=1}{\overset{L_j}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}{\log }_2\left(x^H\left\{{\left[H_{q,2}\mathrm{diag}\left(H_{q,I}{d}_{q,I}\right)\right]}^H\left[H_{q,2}\mathrm{diag}\left(H_{q,I}{d}_{q,I}\right)\right]\right\}x\right)\\ {-\log }_2\left(x^H{\mathrm{\&sigma;}}_1^2\mathrm{diag}\left(H_{q,2}^H{H}_{q,2}\right)x\right)\end{array}\right\}\},$

At following formula, design code word update algorithm, concrete steps are as follows:

Step 4: initialization k=0, x ₀=0, α ₀=1, δ ₀=0;

Step 5: $\mathrm{Whilef}(x_k+{\mathrm{\&alpha;}}_k{\mathrm{\&delta;}}_k)<f\left(x_k\right)+0.45{\mathrm{\&alpha;}}_k\left({\mathrm{\&delta;}}_k^H{\mathrm{\&delta;}}_k\right)$

${\mathrm{\&delta;}}_{k+1}=\frac{\&PartialD;f\left(x_k\right)}{{\&PartialD;x}_k}$ ；x _k+1＝x _k+α _kδ _k；α _k+1＝0.75α _k；

End

Step 6: make w _j=x _K+1

Step 7: with w _jSubstitution step 2 generates the subspace of upgrading, and so circulation is until satisfying the convergence precision requirement.

Wherein, () ^HThe conjugate transpose of-matrix or vector; Diag ()-get diagonal element constitutes a diagonal matrix; I _kThe unit matrix of-K * K, K are the relaying number; ∑ ()-summation operation; -function f (x) is asked local derviation to independent variable x; ‖ ‖ _F-get the Frobenius norm of matrix; Max ()-maximizing.

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