CN102545986A - Multicast beamforming method based on two-dimensional iteration - Google Patents

Abstract

The invention discloses a multicast beamforming method based on two-dimensional iteration, and is characterized by utilizing pruning search based two-antenna beamforming method to solve the multicast beamforming problem of more than two transmitting antenna in an iterative solution manner, constructing and continuously expanding a bottleneck user set in the iteration process, and designing an orthogonal guide vector to accelerate the iterative convergence speed. Compared with the existing SDR (semi-definite relaxation) randomized method and one-dimensional iteration method, the single-group physical layer multicast beamforming method based on the two-dimensional iteration, provided by the invention, can not only acquire higher multicast transmission rate, but also have lower computation complexity, thus the method is suitable for multicast scenes with more user numbers and is easy to implement in the new generation broadband wireless and mobile communication systems, such as 802.11n, TD-HSPA+ (time division-high speed packet access), TD-LTE (time division-long term evolution) and TD-LTE-Advanced and the like.

Description

A kind of multicast beam form-endowing method based on two-dimentional iteration

Technical field

The invention belongs to multiple-input and multiple-output (MIMO) broadband wireless and mobile communication technology field, be specifically related to be applicable to new generation broadband wireless and the bigger single beam form-endowing methods of organizing under the physical layer multicast scene of GSM number of transmit antennas such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced.

Background technology

Sending under the limited situation of signal power, how base station end adopts transmission beam form-endowing method transmission public information to give one group of user to obtain maximum multicast transmission speed, is the research hot issue of current MIMO broadband wireless and GSM.At " international IEEE-signal processing transactions " (IEEE Transactions on Signal Processing; Vol.54; No.6; Pp.2239-2251, June 2006) point out in " physical layer multicast wave beam forming " (Transmit beamforming for physical-layer multicasting) literary composition, belong to a nondeterministic polynomial difficult problem (NP-hard) on this question essence; And proposed a kind of based on semidefinite method of relaxation (SDR) and combine wave beam forming vector method for designing, i.e. the SDR method of randomization of randomization (Randomization).When two transmitting antennas of base station end configuration; Beta pruning search and algebraically method for solving based on the performance bottleneck user of design has multicast transmission speed that is superior to the SDR method of randomization and the computational complexity that is lower than the SDR method of randomization in " a kind of two antenna beam shaping methods based on the beta pruning search " of one Chinese patent application number 201110313794.3 propositions, is specially adapted to the more multicast scene of number of users.Yet; When base station end configuration number of transmit antennas surpasses two; The optimal solution of seeking former problem becomes very complicated; Be difficult to obtain definite performance bottleneck number of users and implement beta pruning search and algebraic manipulation on the one hand,, adopt the SDR method of randomization to be prone to cause that performance is seriously depleted on the other hand along with the increase of antenna number and number of users based on the bottleneck user." a kind of multiple-input and multiple-output beam form-endowing method " that one Chinese patent application 201110099222.x proposes adopts one dimension Iterative Design wave beam forming vector, though be applicable to number of transmit antennas greater than 2 scenes, its performance and theoretical limits still have big gap.Therefore, when base station end configuration number of transmit antennas surpasses two, existing method be difficult to be effectively applied in real time Wideband wireless with GSM in, press for the multicast beam form-endowing method that design has high-performance low complex degree characteristic.

Summary of the invention

The objective of the invention is to propose a kind of multicast beam form-endowing method based on two-dimentional iteration; To be applicable to that number of transmit antennas surpasses two physical layer multicast scene; And improve big, the poor-performing of existing SDR method of randomization existing operand in obtaining the wave beam forming vector process, can't effectively be applied to the problem of practical communication system in real time.

The present invention is based on the multicast beam form-endowing method of two-dimentional iteration, establish base station configuration number of transmit antennas M＞2, the multicast users group contains K user, and k user wherein disposes N _kThe root reception antenna, corresponding channel matrix does

And known in base station end, wave beam forming vector w ∈ ￡ ^MIt is characterized in that the concrete operations step is:

The first step: signaling channel power and matrix Q satisfy relational expression

It is carried out singular value decomposition, obtain the corresponding right singular vector v of its maximum right singular value _Max, initialization wave beam forming vector w=v _Max, initialization iteration thresholding δ ₀=-100dB, initialization iterations m=1, establishing current bottleneck number of users is C=3, maximum bottleneck number of users is L=min{2M-2, K} and bottleneck signal to noise ratio λ ₀=-∞;

Second step: in the m time iterative process, according to the signal to noise ratio ρ of user k _kCalculating formula

K=1, L, K, a calculating K user's signal to noise ratio is successively selected C minimum user of signal to noise ratio wherein as current bottleneck user, and is stored each bottleneck user index b _kIn bottleneck user set B={ b ₁, L, b _CIn;

The 3rd step: w calculates extended matrix according to the wave beam forming vector $W={\left[\begin{array}{cc}\mathrm{Re}\left\{w^T\right\}& \mathrm{Im}\left\{w^T\right\}\\ -\mathrm{Im}\left\{w^T\right\}& \mathrm{Re}\left\{w^T\right\}\end{array}\right]}^T$ And computing differential matrix $R=\left[\begin{array}{ccc}\mathrm{Re}\left\{H_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000131173910000011.png,HDA0000131173910000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_1}^{*}{H}_{b_1}w\right\}& L& \mathrm{Re}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\\ -\mathrm{Im}\left\{H_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000131173910000011.png,HDA0000131173910000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_1}^{*}{H}_{b_1}w\right\}& L& -\mathrm{Im}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\end{array}\right],$ And according to quadrature boot vector equation $\left[\begin{array}{c}{R}^T\\ W^T\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\left\{v^{\&perp;}\right\}\\ \mathrm{Im}\left\{v^{\&perp;}\right\}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$ Calculate quadrature boot vector v ^⊥, and carry out $v^{\&perp;}=\frac{v^{\&perp;}}{\left|\right|v^{\&perp;}\left|\right|}$ Normalization is handled, and wherein 1 is the current bottleneck number of users C dimensional vector of element complete 1, and 0 is 2 dimensional vectors of element complete 0;

The 4th step: calculate equivalent channel matrix P _k=H _k[w, v ^⊥], utilize two antenna multicast beam form-endowing methods to calculate two antenna optimal beam figurations vector u based on the beta pruning search, and according to wave beam forming vector renewal equation w=[w, v ^⊥] u upgrades wave beam forming vector w;

The 5th step: according to the poorest user's snr computation formula ${\mathrm{\&lambda;}}_{\mathrm{Min}}=\underset{1\&le;k\&le;K}{\mathrm{<figure-callout\; id="1"\; label="Min"\; filenames="HDA0000131173910000011.png,HDA0000131173910000021.png"\; state="\{\{state\}\}">Min</figure-callout>}}{w}^H{H}_k^H{H}_{k}w$ Calculate the poorest user's signal to noise ratio λ _Min, according to bottleneck Error Calculation formula δ=10log (λ _Min-λ ₀) the current bottleneck error delta of calculating;

The 6th step: judge bottleneck error relational expression δ≤δ ₀Whether set up,, then original iterations m is upgraded replacing with m+1, bottleneck signal to noise ratio λ if this formula is false ₀Renewal replaces with λ _Min, current bottleneck number of users C upgrades and replaces with min{C+1, L}, and return the second step repetition above-mentioned steps; If this formula is set up, then export optimum beam figuration vector w _Opt=w.

Compare with existing SDR method of randomization; The present invention is based on the multicast beam form-endowing method of two-dimentional iteration; Its essence is the multicast wave beam forming vector w that utilizes based on two antenna beam shaping method Iterative Design M＞2 antennas of beta pruning search, and based on gradient design quadrature boot vector v ^⊥Promote the convergence rate of wave beam forming vector w.Its characteristics are that on the one hand be two-dimensional case with the primary antenna number greater than many antennas maximization multicast speed problem dimensionality reductions of 2, utilize two antenna multicast beam form-endowing methods based on the beta pruning search to carry out iterative; In order to reduce iterations and to reduce computational complexity, in each step iterative process, utilize gradient and linear algebraic equation design quadrature boot vector on the other hand, lead beam figuration vector upgrades to optimum orientation.Because two antenna multicast beam form-endowing methods based on the beta pruning search all are being superior to existing SDR method of randomization aspect performance and the computational complexity; Therefore the inventive method can converge to optimum beam figuration vector fast with lower computational complexity; Thereby obtain to be superior to the multicast transmission speed of SDR method of randomization, be applicable to such as new generation broadband wireless and GSMs such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced.

Description of drawings

Fig. 1 is the MIMO down link signal processing procedure sketch map of user k.

Fig. 2 obtains the flow process theory diagram of wave beam forming vector for adopting the multicast beam form-endowing method that the present invention is based on two-dimentional iteration.

Fig. 3 is the constringency performance curve when the inventive method is applied in embodiment 1.

Fig. 4 is the minimum signal to noise ratio curve when the inventive method is applied in embodiment 2.

Embodiment

Embodiment 1: the MIMO multicast beam form-endowing method with 4 transmitting antennas

Present embodiment is to be example with situation with 4 transmitting antennas, 8 users, specifies the operating process of adopting the MIMO multicast beam form-endowing method that the present invention is based on two-dimentional iteration.

Fig. 1 has provided wherein k user's MIMO down link signal processing procedure sketch map: in the information source forwarding step A1 of base station end, source symbol be s and satisfy power be 1 (E [| s| ²]=1), wherein symbol E represents expectation operator, and after power division steps A 2, transmitted power is P, in wave beam forming steps A 3, calculates wave beam forming vector w, and carries out the transmission wave beam forming of signal, sends signal and does

To k user's channel,, make and send the channel matrix H of signal through user k through Channel Transmission steps A 4 _kTransmission, again through noise stack steps A 5, the multiple Gaussian noise z of stack circulation symmetry _k, the reception signal of user k does in the signal receiving step A6 of user k receiving terminal at last $y_k=\sqrt{P}{H}_k\mathrm{Ws}+z_k.$

Establish base station configuration number of transmit antennas M=4 in the present embodiment, transmitted power P=1, multicast users group number of users K=8, and be the single antenna user, promptly reception antenna is counted N _k=1, k=1 ..., 8.The noise variance of each subscriber channel is 1.Known each the subscriber channel matrix of base station end

$\left[\begin{array}{c}{H}_1\\ H_2\\ M\\ H_8\end{array}\right]=\left[\begin{array}{cccc}-0.5744-0.0550i& -0.4130-1.0722i& -1.1945+0.7649i& -0.4388+0.7935i\\ -0.5150-1.1803i& -0.6315+0.6730i& 0.7465+0.3024i& 0.2881+0.8472i\\ 0.3223+0.6540i& -1.0868+0.0466i& -0.6945+1.1022i& 0.5520+0.7706i\\ -0.4783+0.1882i& -0.9992+0.8533i& -0.1345-0.7043i& -0.4953+0.6416i\\ 0.9362+0.1754i& -0.7962+0.3120i& -1.2178-0.9924i& 0.4551-0.0886i\\ -1.4435+0.4226i& 0.2272-0.1433i& -1.3409-0.6466i& -0.7397-0.2242i\\ 0.5485+0.7094i& -1.3368+0.5258i& -0.4047+0.1457i& -1.0059-0.4848i\\ -0.5710-0.3166i& 0.5084+0.2744i& -0.2103+0.2791i& -0.8491+0.3331i\end{array}\right]$

Fig. 2 has provided and has adopted the multicast beam form-endowing method that the present invention is based on two-dimentional iteration to obtain the flow process theory diagram of wave beam forming vector.The concrete operations step is following:

Parameter initialization step B1: signaling channel power and matrix Q satisfy relational expression

it are carried out singular value decomposition, calculate to obtain channel power and matrix

$Q=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{H}_k^{*}{H}_k=\left[\begin{array}{cccc}7.1871& -1.6708+1.7905i& 0.5927+2.3174i& 0.9575-0.4387i\\ -1.6708-1.7905i& 8.2821& 0.7802-1.5883i& 0.4286-1.2547i\\ 0.5927-2.3174i& 0.7802+1.5883i& 9.8631& 2.9737-0.7639i\\ 0.9575+0.4387i& 0.4286+1.2547i& 2.9737+0.7639i& 6.0606\end{array}\right]$

This matrix is carried out singular value decomposition, obtain the corresponding right singular vector of its maximum right singular value

v _Max=[0.4215,0.2928+0.3647i ,-0.2766+0.6322i ,-0.2546+0.2503i] ^T, initialization wave beam forming vector w=v _Max, initialization iterations m=1, initialization iteration thresholding δ ₀=-100dB, establishing current bottleneck number of users is C=3, maximum bottleneck number of users is L=min{2M-2, K}=6 and bottleneck signal to noise ratio λ ₀=-∞;

Structure bottleneck user gathers step B2: in the m time iterative process, according to the snr computation formula of user k

K=1, L, K calculate all user's signal to noise ratios successively, select the minimum C of a signal to noise ratio wherein current bottleneck user and store each bottleneck user index b _kIn bottleneck user set B={ b ₁, L, b _CIn.

Calculate quadrature boot vector step B3: w calculates extended matrix according to the wave beam forming vector

$W={\left[\begin{array}{cc}\mathrm{Re}\left\{w^T\right\}& \mathrm{Im}\left\{w^T\right\}\\ -\mathrm{Im}\left\{w^T\right\}& \mathrm{Re}\left\{w^T\right\}\end{array}\right]}^T,$

The computing differential matrix $R=\left[\begin{array}{ccc}\mathrm{Re}\left\{H_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000131173910000011.png,HDA0000131173910000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_1}^{*}{H}_{b_1}w\right\}& L& \mathrm{Re}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\\ -\mathrm{Im}\left\{H_{b_1}^{*}{H}_{b_1}w\right\}& L& -\mathrm{Im}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\end{array}\right],$

And according to quadrature boot vector equation $\left[\begin{array}{c}{R}^T\\ W^T\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\left\{v^{\&perp;}\right\}\\ \mathrm{Im}\left\{v^{\&perp;}\right\}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$ Calculate quadrature boot vector v ^⊥, and carry out $v^{\&perp;}=\frac{v^{\&perp;}}{\left|\right|v^{\&perp;}\left|\right|}$ Normalization is handled;

Compute beam figuration vector step B4: calculate equivalent channel matrix P _k=H _k[w, v ^⊥], utilize two antenna multicast beam form-endowing methods to calculate two antenna optimal beam figurations vector u based on the beta pruning search, and according to wave beam forming vector renewal equation w=[w, v ^⊥] u renewal wave beam forming vector w;

Calculate iteration error step B5: according to the poorest user's snr computation formula

Calculate the poorest user's signal to noise ratio λ _Min, according to bottleneck Error Calculation formula δ=10log (λ _Min-λ ₀) the current bottleneck error delta of calculating;

Judge iterated conditional step B6: judge bottleneck error relational expression δ≤δ ₀Whether set up,, then original iterations m is upgraded replacing with m+1, bottleneck signal to noise ratio λ if this formula is false ₀Renewal replaces with λ _Min, current bottleneck number of users C upgrades and replaces with min{C+1, L}, and return structure bottleneck user and gather step B2 repetition above-mentioned steps until this formula establishment, output optimal beam figuration vector

w _opt＝[0.2555-0.2832i，-0.4183+0.7799i，0.0584-0.1038i，0.2391+0.0004i] ^T。

It is λ that employing the present invention is based on the bottleneck signal to noise ratio that the resulting optimal beam figuration of the multicast beam form-endowing method vector of two-dimentional iteration can reach ₀=0.9496, corresponding multicast transmission speed is R _Opt=0.9632bps/Hz.And adopt " international IEEE-signal processing transactions " (IEEE Transactions on Signal Processing, vol.54, no.6; Pp.2239-2251; June 2006) the SDR method of randomization (RandA wherein, RandB, the RandC each 100 times that propose in " physical layer multicast wave beam forming " (Transmit beamforming for physical-layer multicasting) literary composition of publication; Totally 300 times), the SDR wave beam forming vector that it obtained does

w _Sdr=[0.0674+0.3312i ,-0.5595-0.1121i ,-0.3911+0.0340i ,-0.6122-0.1766i] ^T, can calculate w _SdrPairing SDR bottleneck signal to noise ratio is snr _Sdr=0.5938, corresponding SDR multicast transmission speed is R _Sdr=0.6725bps/Hz.The obtainable 1-D wave beam forming of the one dimension alternative manner vector that adopts Chinese invention patent " a kind of multiple-input and multiple-output multicast beam form-endowing method " literary composition to propose does

w _1-D=[0.2742+0.0805i ,-0.1399+0.2066i ,-0.1642-0.3090i ,-0.8321+0.2033i] ^T, the 1-D bottleneck signal to noise ratio that can reach is snr _1-D=0.7394, corresponding 1-D multicast transmission speed is R _1-D=0.7986bps/Hz.

Fig. 3 has provided the constringency performance curve that adopts the multicast beam form-endowing method that the present invention is based on two-dimentional iteration in the present embodiment.As can be seen from Figure 3, along with iterations increases, bottleneck signal to noise ratio convergence curve C1 monotonic increase, and after 14 step iteration, converge to stationary value 0.9496.

This shows; The multicast beam form-endowing method that the present invention is based on two-dimentional iteration is than the have an appointment performance gain of 0.29bps/Hz of SDR method of randomization; Than the have an appointment performance gain of 0.16bps/Hz of one dimension alternative manner; And can reach the stable convergence state through less iterations, therefore adopt the performance of the inventive method to be better than SDR method of randomization and one dimension alternative manner.

Embodiment 2: the MIMO multicast beam form-endowing method with 8 transmitting antennas

Present embodiment is an example with 8 transmitting antennas and user variable number, and the multicast beam form-endowing method that employing the present invention is based on two-dimentional iteration compares with the performance that adopts SDR method of randomization and employing one dimension alternative manner.

In the present embodiment, base station configuration number of transmit antennas M=8, transmitted power P=1, multicast users group number of users satisfies K ∈ [4,32], and is two reception antenna users, and promptly reception antenna is counted N _k=2, k=1 ..., K.The noise variance of each subscriber channel is 1.Known each the subscriber channel matrix of base station end is standard independent same distribution Rayleigh channel.

To each fixing number of users K; The multicast beam form-endowing method that employing the present invention is based on two-dimentional iteration with adopt SDR method of randomization and one dimension alternative manner the bottleneck signal to noise ratio that can obtain compare; Carry out 1000 Monte Carlos (Monte Carlo) emulation experiment altogether, to compare the performance difference between them.

Fig. 4 has provided the correlation curve that adopts multicast beam form-endowing method that the present invention is based on two-dimentional iteration and the bottleneck signal to noise ratio that adopts SDR method of randomization, employing one dimension alternative manner to be obtained in the present embodiment.As can be seen from Figure 4; In number of users (like K≤6) more after a little while; The SDR bottleneck signal to noise ratio curve D 1 that adopts the SDR method of randomization to be reached; With the 1-D bottleneck signal to noise ratio curve D 2 that adopts the one dimension alternative manner to be reached, overlap basically with adopting the 2-D bottleneck signal to noise ratio curve D 3 that the inventive method reached.Yet along with number of users increases, the performance gain when adopting the inventive method increases gradually.Particularly when number of users reaches 32, the high about 1.76dB of bottleneck signal to noise ratio that adopts bottleneck signal to noise ratio that the inventive method obtained to adopt the SDR method of randomization to be obtained, the about 0.69dB of bottleneck signal to noise ratio height that adopts the one dimension alternative manner to be obtained.

This shows; When number of transmit antennas is big; The multicast beam form-endowing method that employing the present invention is based on two-dimentional iteration is superior to adopting the SDR method of randomization and adopts the one dimension alternative manner on performance; Particularly in the more scene of multicast users number, therefore be adapted at such as implementing in new generation broadband wireless such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced and the GSM.

The present invention is based on the multicast beam form-endowing method of two-dimentional iteration, is the multicast wave beam forming vector w that utilizes based on two antenna beam shaping method Iterative Design M＞2 antennas of beta pruning search, and based on gradient design quadrature boot vector v ^⊥Promote the convergence rate of wave beam forming vector w.Its characteristics are that on the one hand be two-dimensional case with the primary antenna number greater than many antennas maximization multicast speed problem dimensionality reductions of 2, utilize two antenna multicast beam form-endowing methods based on the beta pruning search to carry out iterative; In order to reduce iterations and to reduce computational complexity, in each step iterative process, utilize gradient and linear algebraic equation design quadrature boot vector on the other hand, lead beam figuration vector upgrades to optimum orientation.Because two antenna multicast beam form-endowing methods based on the beta pruning search all are being superior to existing SDR method of randomization aspect performance and the computational complexity; Therefore the inventive method can converge to optimum beam figuration vector fast with lower computational complexity; Thereby obtain to be superior to the multicast transmission speed of SDR method of randomization, be applicable to such as new generation broadband wireless and GSMs such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced.

Claims (1)

1. multicast beam form-endowing method based on two-dimentional iteration is established base station configuration number of transmit antennas M＞2, and the multicast users group contains K user, and k user wherein disposes N _kThe root reception antenna, corresponding channel matrix does

And known in base station end, wave beam forming vector w ∈ ￡ ^MIt is characterized in that the concrete operations step is:

The first step: signaling channel power and matrix Q satisfy relational expression

It is carried out singular value decomposition, obtain the corresponding right singular vector v of its maximum right singular value _Max, initialization wave beam forming vector w=v _Max, initialization iteration thresholding δ ₀=-100dB, initialization iterations m=1, establishing current bottleneck number of users is C=3, maximum bottleneck number of users is L=min{2M-2, K} and bottleneck signal to noise ratio λ ₀=-∞;

Second step: in the m time iterative process, according to the signal to noise ratio ρ of user k _kCalculating formula K=1, L, K, a calculating K user's signal to noise ratio is successively selected C minimum user of signal to noise ratio wherein as current bottleneck user, and is stored each bottleneck user index b _kIn bottleneck user set B={ b ₁, L, b _CIn;

The 3rd step: w calculates extended matrix according to the wave beam forming vector $W={\left[\begin{array}{cc}\mathrm{Re}\left\{w^T\right\}& \mathrm{Im}\left\{w^T\right\}\\ -\mathrm{Im}\left\{w^T\right\}& \mathrm{Re}\left\{w^T\right\}\end{array}\right]}^T$ And computing differential matrix $R=\left[\begin{array}{ccc}\mathrm{Re}\left\{H_{b_1}^{*}{H}_{b_1}w\right\}& L& \mathrm{Re}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\\ -\mathrm{Im}\left\{H_{b_1}^{*}{H}_{b_1}w\right\}& L& -\mathrm{Im}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\end{array}\right],$ And according to quadrature boot vector equation $\left[\begin{array}{c}{R}^T\\ W^T\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\left\{v^{\&perp;}\right\}\\ \mathrm{Im}\left\{v^{\&perp;}\right\}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$ Calculate quadrature boot vector v ^⊥, and carry out $v^{\&perp;}=\frac{v^{\&perp;}}{\left|\right|v^{\&perp;}\left|\right|}$ Normalization is handled, and wherein 1 is the current bottleneck number of users C dimensional vector of element complete 1, and 0 is 2 dimensional vectors of element complete 0;

The 4th step: calculate equivalent channel matrix P _k=H _k[w, v ^⊥], utilize two antenna multicast beam form-endowing methods to calculate two antenna optimal beam figurations vector u based on the beta pruning search, and according to wave beam forming vector renewal equation w=[w, v ^⊥] u upgrades wave beam forming vector w;

The 5th step: according to the poorest user's snr computation formula

Calculate the poorest user's signal to noise ratio λ _Min, according to bottleneck Error Calculation formula δ=10log (λ _Min-λ ₀) the current bottleneck error delta of calculating;

The 6th step: judge bottleneck error relational expression δ≤δ ₀Whether set up,, then original iterations m is upgraded replacing with m+1, bottleneck signal to noise ratio λ if this formula is false ₀Renewal replaces with λ _Min, current bottleneck number of users C upgrades and replaces with min{C+1, L}, and return the second step repetition above-mentioned steps; If this formula is set up, then export optimum beam figuration vector w _Opt=w.

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