CN102545986B - 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 beamforming method based on two-dimensional 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 the new generation broadband wireless such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced and the larger single beam form-endowing method of organizing under physical layer multicast scene of mobile communication system number of transmit antennas.

Background technology

The in the situation that of transmitted signal power limited, base station end how to adopt send beam form-endowing method transmission public information to one group of user to obtain maximum multicast transmission speed, be the study hotspot problem of current MIMO broadband wireless and mobile communication system.At " international IEEE-signal is processed transactions " (IEEE Transactions on Signal Processing, vol.54, no.6, pp.2239 – 2251, June2006) " physical layer multicast wave beam forming " (Transmit beamforming for physical-layer multicasting) the article pointed out, on this question essence, belong to a nondeterministic polynomial difficult problem (NP-hard), and propose a kind of based on semidefinite method of relaxation (SDR) and in conjunction with the wave beam forming vector method for designing of randomization (Randomization), it is SDR method of randomization.In the time of two transmitting antennas of base station end configuration, in " a kind of two antenna beam shaping methods based on pruning search " that Chinese Patent Application No. 201110313794.3 proposes, pruning search based on performance bottleneck user of design and Algebraic Method have and are better than the multicast transmission speed of SDR method of randomization and the computational complexity lower than SDR method of randomization, are specially adapted to the more multicast scene of number of users.But, in the time that base station end configuration number of transmit antennas exceedes two, the optimal solution of seeking former problem becomes very complicated, be difficult to obtain definite performance bottleneck number of users and implement pruning search and algebraic manipulation based on bottleneck user on the one hand, along with the increase of antenna number and number of users, adopt SDR method of randomization easily to cause the serious exhaustion of performance on the other hand." a kind of multiple-input and multiple-output beam form-endowing method " that Chinese Patent Application No. 201110099222.x proposes, adopts one dimension Iterative Design wave beam forming vector, is greater than 2 scenes although be applicable to number of transmit antennas, and its performance still has larger gap with theoretical limit.Therefore,, in the time that base station end configuration number of transmit antennas exceedes two, existing method is difficult to be effectively applied in real time, in the wireless and mobile communication system of Wideband, to have the multicast beamforming method of high-performance low complex degree feature in the urgent need to design.

Summary of the invention

The object of the invention is to propose a kind of multicast beamforming method based on two-dimensional iteration, exceed the physical layer multicast scene of two to be applicable to number of transmit antennas, and existing operand is large, poor-performing obtaining in wave beam forming vector process to improve existing SDR method of randomization, cannot effectively be applied in real time the problem of practical communication system.

The present invention is based on the multicast beamforming method of two-dimensional iteration, establish 2 of base station configuration number of transmit antennas M >, multicast users group is containing K user, and k user wherein configures N _kroot reception antenna, corresponding channel matrix is

and known at base station end, wave beam forming vector

; It is characterized in that concrete operation step is:

The first step: signaling channel combinatorial matrix Q meets relational expression

it is carried out to singular value decomposition, obtain right singular vector v corresponding to 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=log (0);

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

k=1 ..., K, a calculating K user's signal to noise ratio successively, selects C user of signal to noise ratio minimum wherein as current bottleneck user, and stores each bottleneck user index b _kgather in bottleneck user

in;

The 3rd step: w calculates extended matrix according to 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 $R=\left[\begin{array}{ccc}\mathrm{Re}\left\{H_{b_1}^{*}{H}_{b_1}W\right\}& ...& \mathrm{Re}\left\{H_{b_C}^{*}{H}_{b_C}W\right\}\\ -\mathrm{Im}\left\{H_{b_1}^{*}{H}_{b_1}w\right\}& ...& -\mathrm{Im}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\end{array}\right],$ And according to orthogonal boot vector equation $\left[\begin{array}{c}{R}^T\\ W^T\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\left\{v^{\⊥}\right\}\\ \mathrm{Im}\left\{v^{\⊥}\right\}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$ Calculate orthogonal boot vector v ^⊥, and carry out

normalized, wherein 1 is the current bottleneck number of users C dimensional vector of element complete 1,0 is 2 dimensional vectors of element full 0;

The 4th step: calculate equivalent channel matrix P _k=H _k[w, v ^⊥], utilize the Chinese invention patent application number 201110313794.3 a kind of two antenna beam shaping methods based on pruning search that propose to calculate two antenna optimal beam figuration vector u, 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 calculating formula δ=10log (λ _min-λ ₀) calculate current bottleneck error delta;

The 6th step: judge bottleneck error relationship formula δ≤δ ₀whether set up, if this formula is false, original iterations m is upgraded and replaces with m+1, bottleneck signal to noise ratio λ ₀renewal replaces with λ _min, current bottleneck number of users C upgrades and replaces with min{C+1, L}, and return to second step and repeat above-mentioned steps; If this formula is set up, export optimum beam figuration vector w _opt=w.

Compare with existing SDR method of randomization, the present invention is based on the multicast beamforming method of two-dimensional iteration, its essence, be the multicast wave beam forming vector w that utilizes 2 antennas of two antenna beam shaping method Iterative Design M > based on pruning search, and design orthogonal boot vector v based on gradient ^⊥promote the convergence rate of wave beam forming vector w.Its feature is on the one hand primary antenna number to be greater than many antennas of 2, and to maximize multicast speed problem dimensionality reductions be two-dimensional case, utilizes the two antenna multicast beamforming methods based on 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 to design orthogonal boot vector on the other hand, lead beam figuration vector upgrades to optimum orientation.Because the two antenna multicast beamforming methods based on pruning search are all being better than existing SDR method of randomization aspect performance and computational complexity, therefore the inventive method can be with lower computational complexity Fast Convergent to optimum beam figuration vector, thereby obtain the multicast transmission speed that is better than SDR method of randomization, be applicable to new generation broadband wireless and mobile communication system such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced.

Accompanying drawing explanation

Fig. 1 is the MIMO down link signal processing procedure schematic diagram of user k.

Fig. 2 adopts the multicast beamforming method that the present invention is based on two-dimensional iteration to obtain the flow process theory diagram of wave beam forming vector.

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

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

Embodiment

Embodiment 1: the MIMO multicast beamforming method with 4 transmitting antennas

The present embodiment be the situation with 4 transmitting antennas, 8 users be example, illustrate the operating process that adopts the MIMO multicast beamforming method that the present invention is based on two-dimensional iteration.

Fig. 1 has provided wherein k user's MIMO down link signal processing procedure schematic diagram: in the information source forwarding step A1 of base station end, source symbol is s and to meet power be 1 (E[|s| ²]=1), wherein symbol E represents expectation operator, and after power division steps A 2, transmitted power is P, calculates wave beam forming vector w in wave beam forming steps A 3, and carries out the transmission wave beam forming of signal, and transmitted signal is to k user's channel, through transmission steps A 4, make the channel matrix H of transmitted signal through user k _ktransmission, then through noise stack steps A 5, the multiple Gaussian noise z of stack Cyclic Symmetry _k, finally in the signal receiving step A6 of user k receiving terminal, the reception signal of user k is

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

$\left[\begin{array}{c}{H}_1\\ H_2\\ .\\ .\\ .\\ H_8\end{array}\right]=\left[\begin{array}{cccc}-0.5744-0.0550i& -0.4130-1.0722i& -1.1945+0.7649i& -0.4388+0.7935i\\ -0.5150-1.1803i& -0.6315+0.6730i& 0.7465+0.3024i& 0.2881+0.8472i\\ 0.3223+0.6540i& -1.0868+0.0466i& -0.6945+1.1022i& 0.5520+0.7706i\\ -0.4783+0.1882i& -0.9992+0.8533i& -0.1345-0.7043i& -0.4953+0.6416i\\ 0.9362+.1754i& -0.7962+0.3120i& -1.2178-0.9924i& 0.4451-0.0886i\\ -1.4435+0.4226i& 0.2272-0.1433i& -1.3409-0.6466i& -0.7397-0.2242i\\ 0.5485+0.7094i& -1.3368+0.5258i& -0.4047+0.1457i& -1.0059-0.4848i\\ -0.5710-0.3166i& 0.5084+0.2744i& -0.2103+0.2791i& -0.8491+0.3331i\end{array}\right]$

Fig. 2 has provided the flow process theory diagram that adopts the multicast beamforming method that the present invention is based on two-dimensional iteration to obtain wave beam forming vector.Concrete operation step is as follows:

Parameter initialization step B1: signaling channel combinatorial matrix Q meets relational expression it is carried out to singular value decomposition, calculate and obtain channel combinatorial matrix

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

This matrix is carried out to singular value decomposition, obtain right singular vector corresponding to 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=log (0);

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

k=1 ..., K calculates all user's signal to noise ratios successively, selects C current bottleneck user of signal to noise ratio minimum wherein and stores each bottleneck user index b _kgather in bottleneck user

in.

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

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

Computing differential matrix $R=\left[\begin{array}{ccc}\mathrm{Re}\left\{H_{b_1}^{*}{H}_{b_1}W\right\}& ...& \mathrm{Re}\left\{H_{b_C}^{*}{H}_{b_C}W\right\}\\ -\mathrm{Im}\left\{H_{b_1}^{*}{H}_{b_1}w\right\}& ...& -\mathrm{Im}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\end{array}\right],$

And according to orthogonal boot vector equation $\left[\begin{array}{c}{R}^T\\ W^T\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\left\{v^{\⊥}\right\}\\ \mathrm{Im}\left\{v^{\⊥}\right\}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$ Calculate orthogonal boot vector v ^⊥, and carry out

normalized;

Compute beam figuration vector step B4: calculate equivalent channel matrix P _k=H _k[w, v ^⊥], utilize the Chinese invention patent application number 201110313794.3 a kind of two antenna beam shaping methods based on pruning search that propose to calculate two antenna optimal beam figuration vector u, 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 calculating formula δ=10log (λ _min-λ ₀) calculate current bottleneck error delta;

Judge iterated conditional step B6: judge bottleneck error relationship formula δ≤δ ₀whether set up, if this formula is false, original iterations m is upgraded and replaces with m+1, bottleneck signal to noise ratio λ ₀renewal replaces with λ _min, current bottleneck number of users C upgrades and replaces with min{C+1, L}, and return to structure bottleneck user and gather step B2 repetition above-mentioned steps until this formula is set up, 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 optimal beam figuration vector that the multicast beamforming method of two-dimensional iteration obtains can reach ₀=0.9496, corresponding multicast transmission speed is R _opt=0.9632bps/Hz.And adopt " international IEEE-signal process transactions " (IEEE Transactions on Signal Processing, vol.54, no.6, pp.2239 – 2251, June2006) SDR method of randomization (the wherein RandA proposing in " physical layer multicast wave beam forming " (the Transmit beamforming for physical-layer multicasting) literary composition publishing, RandB, each 100 times of RandC, totally 300 times), the SDR wave beam forming vector that it obtains is

W _sdr=[0.0674+0.3312i ,-0.5595-0.1121i ,-0.3911+0.0340i ,-0.6122-0.1766i] ^t, can calculate w _sdrcorresponding 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 beamforming method " literary composition to propose is

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 beamforming method that the present invention is based on two-dimensional 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 converge to stationary value 0.9496 after 14 step iteration.

This shows, the multicast beamforming method that the present invention is based on two-dimensional iteration is compared with the have an appointment performance gain of 0.29bps/Hz of SDR method of randomization, compared with the have an appointment performance gain of 0.16bps/Hz of one dimension alternative manner, and can reach 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 beamforming method with 8 transmitting antennas

The present embodiment, take 8 transmitting antennas and user variable number as example, the present invention is based on the multicast beamforming method of two-dimensional iteration and adopts SDR method of randomization and adopt the performance of one dimension alternative manner to compare adopting.

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

For each fixing number of users K, the bottleneck signal to noise ratio that employing be the present invention is based on to the multicast beamforming method of two-dimensional iteration and adopts SDR method of randomization and one dimension alternative manner to obtain contrasts, carry out altogether 1000 Monte Carlos (Monte Carlo) emulation experiment, to compare the performance difference between them.

Fig. 4 has provided to adopt in the present embodiment and the present invention is based on the multicast beamforming method of two-dimensional iteration and the correlation curve of the bottleneck signal to noise ratio that employing SDR method of randomization, employing one dimension alternative manner obtain.As can be seen from Figure 4, in the time that number of users is less (as K≤6), the SDR bottleneck signal to noise ratio curve D 1 that adopts SDR method of randomization to reach, with the 1-D bottleneck signal to noise ratio curve D 2 that adopts one dimension alternative manner to reach, substantially overlap with the 2-D bottleneck signal to noise ratio curve D 3 that adopts the inventive method to reach.But along with number of users increases, the performance gain while adopting the inventive method increases gradually.Particularly in the time that number of users reaches 32, the high about 1.76dB of bottleneck signal to noise ratio that the bottleneck signal to noise ratio that adopts the inventive method to obtain adopts SDR method of randomization to obtain, the high about 0.69dB of bottleneck signal to noise ratio that adopts one dimension alternative manner to obtain.

As can be seen here, in the time that number of transmit antennas is larger, the multicast beamforming method that employing the present invention is based on two-dimensional iteration is better than adopting SDR method of randomization and adopts one dimension alternative manner in performance, particularly, in the more scene of multicast users number, be therefore adapted at implementing new generation broadband wireless such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced with in mobile communication system.

The present invention is based on the multicast beamforming method of two-dimensional iteration, be the multicast wave beam forming vector w that utilizes 2 antennas of two antenna beam shaping method Iterative Design M > based on pruning search, and design orthogonal boot vector v based on gradient ^⊥promote the convergence rate of wave beam forming vector w.Its feature is on the one hand primary antenna number to be greater than many antennas of 2, and to maximize multicast speed problem dimensionality reductions be two-dimensional case, utilizes the two antenna multicast beamforming methods based on 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 to design orthogonal boot vector on the other hand, lead beam figuration vector upgrades to optimum orientation.Because the two antenna multicast beamforming methods based on pruning search are all being better than existing SDR method of randomization aspect performance and computational complexity, therefore the inventive method can be with lower computational complexity Fast Convergent to optimum beam figuration vector, thereby obtain the multicast transmission speed that is better than SDR method of randomization, be applicable to new generation broadband wireless and mobile communication system such as 802.11n, TD-HSPA+, TD-LTE and TD-LTE-Advanced.

Claims (1)

1. the multicast beamforming method based on two-dimensional iteration, establishes 2 of base station configuration number of transmit antennas M >, and multicast users group is containing K user, and k user wherein configures N _kroot reception antenna, corresponding channel matrix is

and known at base station end, wave beam forming vector

; It is characterized in that concrete operation step is:

The first step: signaling channel combinatorial matrix Q meets relational expression

it is carried out to singular value decomposition, obtain right singular vector v corresponding to 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=log (0);

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

k=1 ..., K, a calculating K user's signal to noise ratio successively, selects C user of signal to noise ratio minimum wherein as current bottleneck user, and stores each bottleneck user index b _kgather in bottleneck user

in;

The 3rd step: w calculates extended matrix according to 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 $R=\left[\begin{array}{ccc}\mathrm{Re}\left\{H_{b_1}^{*}{H}_{b_1}W\right\}& ...& \mathrm{Re}\left\{H_{b_C}^{*}{H}_{b_C}W\right\}\\ -\mathrm{Im}\left\{H_{b_1}^{*}{H}_{b_1}w\right\}& ...& -\mathrm{Im}\left\{H_{b_C}^{*}{H}_{b_C}w\right\}\end{array}\right],$ And according to orthogonal boot vector equation $\left[\begin{array}{c}{R}^T\\ W^T\end{array}\right]\left[\begin{array}{c}\mathrm{Re}\left\{v^{\⊥}\right\}\\ \mathrm{Im}\left\{v^{\⊥}\right\}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]$ Calculate orthogonal boot vector v ^⊥, and carry out

normalized, wherein 1 is the current bottleneck number of users C dimensional vector of element complete 1,0 is 2 dimensional vectors of element full 0;

The 4th step: calculate equivalent channel matrix P _k=H _k[w, v ^⊥], utilize the Chinese invention patent application number 201110313794.3 a kind of two antenna beam shaping methods based on pruning search that propose to calculate two antenna optimal beam figuration vector u, 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 calculating formula δ=10log (λ _min-λ ₀) calculate current bottleneck error delta;

The 6th step: judge bottleneck error relationship formula δ≤δ ₀whether set up, if this formula is false, original iterations m is upgraded and replaces with m+1, bottleneck signal to noise ratio λ ₀renewal replaces with λ _min, current bottleneck number of users C upgrades and replaces with min{C+1, L}, and return to second step and repeat above-mentioned steps; If this formula is set up, export optimum beam figuration vector w _opt=w.

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