CN102130709B - Multiple-input multiple-output (MIMO) multicasting beamforming method - Google Patents

Abstract

The invention discloses a multiple-input multiple-output (MIMO) multicasting beamforming method, which is characterized by comprising the following steps of: adopting iterative search with adjustable step length; decomposing a channel matrix corresponding to a user with the worst signal to noise ratio in a group by utilizing singular value decomposition (SVD) in the process of each step of iteration, and acquiring a maximum right singular vector of the channel matrix; and approaching a beamforming vector to the direction of the maximum right singular vector gradually. Compared with the conventional single data rate (SDR) randomization method, the method has the advantages that: the beamforming vector acquired by the method can increase channel capacity effectively and have lower operation complexity simultaneously. Moreover, as the number of transmitting antennae configured in a base station end is increased and the number of the users in the group is increased, the method provided by the invention has the more obvious performance advantages and is applicable for implementation in new generation MIMO broadband wireless and mobile communication systems of 802.11n, time division high speed packet access + (TD-HSPA+) and time division long term evolution (TD-LTE).

Description

A kind of multiple-input and multiple-output multicast beamforming method

Technical field

The invention belongs to multiple-input and multiple-output (MIMO) broadband wireless and mobile communication technology field, the beam form-endowing method that is specifically related to alone family group MIMO multicast down link, is applicable to new generation broadband wireless and mobile communication system such as 802.11n, TD-HSPA+ and TD-LTE.

Background technology

The omnidirectional antenna adopting from tradition or fixed beam antenna transmission mode are different, how in MIMO multicast service, effectively to design wave beam forming vector and have caused industry extensive concern to improve radio spectrum resources utilance.Particularly design and find effective MIMO multicast transmission strategy to guarantee that the fairness of multicast users is the main research of association area all the time.MIMO multicast service can be understood as in the base station range of a configuration M root transmitting antenna, at least exists one to receive user's combination, and this base station all users wherein provide same data flow at one time.In this sense, for MIMO multicast service, in group, between user, generally there is not phase mutual interference, only need to consider to disturb between different user groups.

In recent years, multi-user organizes MIMO multicasting technology and sole user and organizes MIMO multicasting technology and all in many documents, inquired into.Its major technique challenge is, for the limited base station of transmitted power, optimal design transmitting terminal wave beam forming vector how, can maximize promote user organize in SNR or the channel capacity of the poorest signal to noise ratio (SNR) institute respective user.This problem is called in the industry the minimum SNR transmitting terminal wave beam forming problem that maximizes.International IEEE-the signal of < < is processed < < physical layer multicast wave beam forming > > (the Transmit beamformingfor physical-layer multicasting.IEEE Transactions on Signal Processing of transactions > > publication in 2006, vol.54, pp.2239-2251, June2006) in, point out, the problems referred to above are in fact nondeterministic polynomial difficult problems (NP-hard).Solve this non-protruding optimization problem, extensively adopt at present approximate evaluation method was, the method is derived from Cambridge University Press and within 2004, publishes the protruding optimization of document < < > > (Convex Optimization.Cambridge University Press, 2004) semidefinite method of relaxation (SDR),, the all non-protruding constraints of lax former non-protruding optimization problem, is converted into new protruding optimization problem by former problem and solves.Obviously, for former problem, this behave must cause the solution of new optimization problem in fact unreachable, often becomes the performance upper bound of former problem.In order to make the solution of new optimization problem meet former non-protruding constraints, conventionally also should be in conjunction with randomized technique to guarantee that wave beam forming covariance matrix is order 1.

Analyze knownly, existing conventional SDR method of randomization is obtained wave beam forming vector and is had some limitations and weak point.First, the method is continued to use in fact interior point method, and its efficiency of algorithm and the speed of service are slower, thereby is difficult to effectively realize on existing communication system or specialized hardware platform.Secondly, the wave beam forming vector obtaining based on SDR method of randomization is larger with optimal solution performance gap in many scenes, and its design performance still has greater room for improvement.In order effectively to improve above-mentioned present situation, meet the actual demand of the wireless and mobile communication system of Wideband, be necessary that design obtains MIMO multicast wave beam forming vector new method.

Summary of the invention

The object of the invention is to propose a kind of multiple-input and multiple-output (MIMO) multicast beamforming method, to improve, existing SDR method of randomization existing operand in obtaining wave beam forming vector process is large, poor-performing, cannot effectively be applied to the problem of practical communication system.

Multiple-input and multiple-output multicast beamforming method of the present invention, establishes center base station end configuration M root transmitting antenna, only comprises sole user's group in its coverage cell, and in group, number of users is K, and user k disposes N _kroot reception antenna, corresponding channel matrix

base station end source signal x, transmitted power P; It is characterized in that comprising successively following steps:

Step 1, initial setting up iterations n and the highest iterations n thereof _max, make n ∈ [0, n _max], its initial value is made as 0; The higher limit λ of initial setting up iteration step length λ _maxwith lower limit λ _min, make λ ∈ [λ _min, λ _max], its initial value is made as λ _min; Initial setting up wave beam forming vector w ₀, produce at random and make its satisfied constraint formula || w ₀||=1;

Step 2, in the n time iterative process, first for group in K user, make Customs Assigned Number k=1 ..., K, calculates each user's signal to noise ratio successively select wherein minimum value, remember that its reference numeral is the n time iteration user sequence number k _n;

Step 3, with the n-1 time iteration user sequence number k _n-1compare, judge iteration user sequence number k the n time _nwhether change: if change, make iteration step length λ=λ _min; Otherwise, according to regular min (2* λ, λ _max) adjustment iteration step length λ;

Step 4, choose iteration user sequence number k the n time _nsubscriber channel matrix carry out singular value decomposition (SVD), find out the right singular vector of the corresponding maximum of its maximum singular value

as the n time iteration reference vector, and utilize angle computing formula

calculate iteration reference vector the n time with the n time iteration wave beam forming vector w _nbetween angle

Step 5, first utilize the n time iteration wave beam forming vector w _ncalculate and obtain relational expression numerical value, then gives this numerical value iteration wave beam forming vector w the n+1 time _n+1, then calculate and obtain normalization numerical value w _n+1/ || w _n+1||, then give iteration wave beam forming vector w the n+1 time by this numerical value _n+1;

Step 6, judge whether iterations n has reached the highest iterations n _maxif: n>n _maxbe false, by the n+1 time iteration wave beam forming vector w _n+1as new wave beam forming vector, iterations n is updated to n+1 and repeats above-mentioned steps two to step 6; If n>n _maxset up, stop iterative process;

Step 7, by n _maxinferior wave beam forming vector

give optimum beam figuration vector w _opt, then according to transmitted power P and according to relational expression

to base station, end source signal x realizes MIMO multicast wave beam forming.

Be different from existing method, the inventive method does not rely in fact SDR method, but adopt the adjustable iterative search thinking of step-length, in each step, utilize in the SVD minute system of solutions the poorest signal to noise ratio user's institute's respective channels matrix in iterative process and obtain its maximum right singular vector, progressively wave beam forming vector being approached to this vector direction.Process transactions > > 2006 annual published articles with the international IEEE-signal of < < and offer < < physical layer multicast wave beam forming > > (Transmit beamforming for physical-layer multicasting.IEEE Transactions on Signal Processing, vol.54, pp.2239-2251, June2006) the SDR method of randomization adopting is compared, the inventive method can effectively reduce computational complexity, improve design performance, its channel capacity obtaining is all the time higher than existing SDR method of randomization.Therefore, the inventive method is a kind of alone family group MIMO multicast wave beam forming vector approach that effectively obtains, and its advantage is mainly reflected in than existing SDR method of randomization has higher channel capacity, has lower computational complexity simultaneously.And along with base station end transmitting antenna configured number increases, the interior number of users of group promotes, the inventive method can show more significant performance advantage, is adapted at implementing in MIMO broadband wireless of new generation and mobile communication system.

Accompanying drawing explanation

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

Fig. 2 is the flow process theory diagram that the present invention obtains MIMO multicast wave beam forming vector approach.

Fig. 3 applies the inventive method and the channel capacity correlation curve that adopts existing SDR method and SDR method of randomization to obtain in embodiment 2.

Embodiment

Embodiment 1: the MIMO multicast beamforming method with 8 transmitting antennas and 16 user's scenes

The present embodiment is with 8 transmitting antennas of base station end configuration, single multicast users group, and in group, to comprise 16 user's scenes be example, introduces the specific embodiment of the present invention.

Fig. 1 has provided the MIMO down link signal processing procedure schematic diagram about user k.In the end information source forwarding step A1 of base station, making source signal is x and satisfied

through power division steps A 2, distribute power P to user k, then the wave beam forming providing in wave beam forming steps A 3 vector w completes base station end MIMO and send wave beam forming, end transmitted signal in base station can be expressed as

this signal carries out physical transfer through user k transmission environment: channel transmitting step A4 wherein, makes transmitted signal channel matrix transmission, and through noise stack steps A 5, stack interchannel noise z _k, this interchannel noise is for meeting

the multiple Gaussian noise signal of Cyclic Symmetry; This user can obtain reception signal in its receiving end signal receiving step A6

In the present embodiment, establish base station end transmitting antenna configurable number M=8, transmitted power P=1, in MIMO multicast users group, each user's reception antenna configurable number is N _k=1, in group, number of users is K=16.For user k, the channel matrix that it is corresponding

make each user's subchannel noise variance be

and transmitting terminal is mimo channel matrix corresponding to known each user accurately,

${[H_1,H_2,{\mathrm{<figure-callout\; id="3"\; label="H"\; filenames="HDA0000056361480000021.png"\; state="\{\{state\}\}">H</figure-callout>}}_3,H_4]}^T=\left[\begin{array}{cccc}-0.9707+j0.7794& -0.2341-j0.9182& -0.1728+j1.0292& 0.0393+j0.1005\\ -0.9098-j0.6327& 0.6778+j0.2406& -0.7361-j0.7857& -0.2118+j0.9501\\ 0.5231-j0.0789& 0.4587-j0.3237& -0.0153+j0.1097& -0.1286-j0.5060\\ -0.3303+j0.0315& 0.0134-j0.6127& 0.4096+j0.2217& 0.2470-j0.7131\\ 0.0778+j1.2285& 1.0039-j0.6645& -1.1480+j0.4210& 0.1965+j1.0263\\ 1.0756-j1.5563& -0.2861+j0.6925& 0.3920+j0.9665& -0.3151-j0.5915\\ -0.9206-j1.1757& 0.3361+j0.5004& -0.2537+j0.4268& 0.0154-j0.2856\\ 0.2301+j0.4086& -0.2342-j0.0160& -0.4928+j0.4704& 1.0839-j0.2821\end{array}\right]$

${[H_5,H_6,H_7,H_8]}^T=\left[\begin{array}{cccc}1.5524+j0.9795& 0.7435+j1.2078& -0.5452+j0.2972& 0.0500-j0.1332\\ -0.4826-j0.9282& 0.2177-j0.2853& -0.1669-j0.7797& 0.7004-j0.8659\\ -0.0442-j0.1473& -0.4677-j0.3839& 1.2513-j0.3316& 0.8792+j0.5401\\ 0.6127-j0.2044& 0.5891+j1.5037& 0.6672+j0.0069& -0.0721-j0.6603\\ -0.7321-j0.2302& -0.1252-j0.1793& 0.6272-j0.1764& 0.2542-j0.6998\\ -0.7018-j0.0408& -0.4289+j0.0718& -0.0743+j0.1994& -0.1584+j0.1872\\ -0.1537-j0.3577& -1.1245-j1.6196& 0.5852+j1.1821& -1.6104-j0.3161\\ -0.3494-j0.2876& -0.1785-j0.1596& 0.5892+j0.1963& 0.4251-j0.5572\end{array}\right]$

Wherein, (.) ^trepresent matrix transpose operation.

The alone family of the design group MIMO down link multicast wave beam forming vector w proposing in the present invention, it is basic with being intended to: under power limited constraints, how base station end maximizes system channel capacity C.And theoretical research shows, this system channel capacity is subject to user to organize interior Minimum mutual information amount I (y _k, x) determine.Therefore this problem is equivalent to following optimization problem:

$\underset{w\&Element;C^M}{\max }\underset{1\&le;k\&le;K}{\min }{w}^H{H}_k^H{H}_{k}w$

s.t. ||w||=1

Wherein, (.) ^hrepresent conjugate transpose operation.For solving of this optimization problem, the basic ideas of the inventive method are to utilize Iterative Design thought constantly along certain reference vector adjustment in direction wave beam forming vector, to promote user, organize interior Minimum mutual information amount I (y _k, x).

Fig. 2 is the flow process theory diagram that the present invention obtains MIMO multicast wave beam forming vector approach.It is as follows that the present invention obtains the concrete operation step of MIMO multicast wave beam forming vector approach:

1, initialization step B1, comprises and establishes n _max=500, λ _min=0.03, λ _max=0.4; In order to arrange, meet constraints || w ₀||=1 initial beam figuration vector w ₀, can be first to each user's subchannel H _kcarry out respectively SVD decomposition, find out the right singular vector v of the corresponding maximum of maximum singular value separately _k, then calculate

thereby can obtain l ₀=3, so order:

$w_0={\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA0000056361480000021.png"\; state="\{\{state\}\}">v</figure-callout>}}_3=\left[\begin{array}{c}-0.4344\\ 0.2718+j0.3564\\ -0.0461-j0.0013\\ -0.0628-j0.1834\\ -0.2520+j0.4422\\ -0.3698-j0.2275\\ -0.1927+j0.0747\\ -0.2271+j0.1699\end{array}\right];$

2, choose the poorest user steps B2,, in the n time iterative process, first user, organize the poorest SNR user of interior foundation and select formula

carry out iteration user sequence number k the n time _nselect;

3, adjust iteration step length step B3, by with the n-1 time iteration user sequence number k _n-1compare, judge iteration user sequence number k the n time _nwhether equal iteration user sequence number k the n-1 time _n-1if this sequence number changes, make iteration step length λ=λ _min, otherwise, according to iteration step length selective rule min (2* λ, λ _max) adjustment iteration step length λ;

4, select reference vector step B4, for the n time iteration user sequence number k _n, choose this subscriber channel matrix

the right singular vector of the corresponding maximum of maximum singular value

as the n time iteration reference vector, and utilize angle computing formula

calculate iteration reference vector the n time

with the n time iteration wave beam forming vector w _nbetween angle

5, upgrade figuration vector step B5, first utilize iteration wave beam forming vector w the n time _ncalculate and obtain relational expression

numerical value, then gives this numerical value iteration wave beam forming vector w the n+1 time _n+1, then calculate and obtain normalization numerical value w _n+1/ || w _n+1||, then give iteration wave beam forming vector w the n+1 time by this numerical value _n+1, to guarantee that this wave beam forming vector meets constraints || w _n-1||=1;

6, decision steps B6, by judging whether iterations n has reached the highest iterations n _maxdecide iterative process whether to stop, if relational expression n>n _maxbe false, upgrading iterations n is n+1, by the n+1 time iteration wave beam forming vector w _n+1as new wave beam forming vector, repeat above-mentioned 2-5 step; If relational expression n>n _maxset up, stop iterative process;

7, design output step B7, through above-mentioned 1-6 step, by n _maxinferior wave beam forming vector

give optimum beam figuration vector w _opt, can obtain

$w_{\mathrm{opt}}=\left[\begin{array}{c}-0.4813-j0.0284\\ 0.5220+j0.1355\\ 0.5104-j0.0045\\ 0.0555-j0.1486\\ -0.1712+j0.2005\\ -0.1186-j0.1973\\ 0.0005-j0.0450\\ -0.2043+0.1569\end{array}\right]$

This is according to the designed optimum beam figuration vector going out of the inventive method, then can be according to transmitted power P and according to relational expression

to base station, end source signal x realizes MIMO multicast wave beam forming.

According to above-mentioned design process, the MIMO multicast optimum beam figuration vector w that the inventive method is obtained _optcan make this system channel capacity reach 0.9846bps.Adopt the international IEEE-signal of < < to process transactions > > 2006 annual published articles and offer < < physical layer multicast wave beam forming > > (Transmit beamforming for physical-layer multicasting.IEEE Transactions on Signal Processing, vol.54, pp.2239-2251, June2006) the SDR-RANDC method of pointing out in, can calculate the optimum beam figuration vector for this embodiment

for:

$w_{\mathrm{opt}}^{\mathrm{SDR}-\mathrm{RANDC}}=\left[\begin{array}{c}0.5269+j0.2690\\ 0.2306+j0.1406\\ 0.2408-j0.0434\\ -0.2910-j0.2174\\ 0.2264+j0.3824\\ 0.0121-j0.1491\\ 0.0483-j0.5064\\ 0.1280+j0.1645\end{array}\right];$

Thereby can calculate the system channel capacity that adopts the method to reach is 0.8408bps.And only adopt the designed wave beam forming vector going out of SDR method can obtain the channel capacity upper bound, be 1.3702bps.Obviously, the wave beam forming vector that the inventive method is obtained has the performance more superior compared with SDR-RANDC method, and in the present embodiment, its performance boost for MIMO Multicast Channel capacity can reach about 0.14bps.For MIMO multicast service, the designed wave beam forming vector of the inventive method can further approach channel capacity performance bound, that is, the designed wave beam forming vector going out of the inventive method is better than adopting the design output of existing conventional SDR method of randomization.On the other hand, the computational complexity of analyzing the inventive method is known, number of users K and the highest iterations n in the algorithm complex of the method and transmitting antenna configurable number M, multicast group _maxrelated, be O (2n _maxkM ²+ 12KM ³).This point, than generally acknowledged in the industry SDR algorithm complex O ((K+M ²) ^3.5) be much smaller.Hence one can see that, the inventive method be specially adapted to transmitting antenna configured number more, group in larger broadband wireless and the mobile communication system of number of users.

Embodiment 2: have the MIMO multicast beamforming method that 16 transmitting antennas and user variable are counted scene

The present embodiment is with 16 transmitting antennas of base station given below end configuration, single multicast users group, and in group, comprising user variable, to count scene be example, introduces the specific embodiment of the present invention.

If base station end transmitting antenna configurable number M=16, transmitted power P=1, in MIMO multicast users group, each user's reception antenna configurable number is N _k=1, in group, number of users K is variable, and excursion is K ∈ [2,32].Adopt Rayleigh flat fading channel, each user's subchannel noise variance is

and suppose accurately mimo channel state information (CSI) corresponding to known each user of transmitting terminal.

For number of users K in each definite group, adopt the inventive method design MIMO multicast wave beam forming vector, can adopt the implementation step identical with embodiment 1, both difference is only embodied in:

1, for comprehensive assessment with weigh the performance that the inventive method is obtained optimum beam figuration vector, for number of users K in each definite group, adopt 500 Monte Carlos (Monte Carlo) emulation experiment, verify in accidental channel environment the validity of the inventive method and performance thereof.

2, performance for ease of comparative analysis the inventive method, for number of users K in each definite group, adopt international IEEE-signal to process transactions > > 2006 annual published articles simultaneously and offer < < physical layer multicast wave beam forming > > (Transmit beamforming for physical-layer multicasting.IEEE Transactions on Signal Processing, vol.54, pp.2239-2251, June2006) SDR-RANDA pointing out in, tri-kinds of SDR method of randomization of SDR-RANDB and SDR-RANDC, and select the wave beam forming vector of its performance the best as the design output of SDR method of randomization.

Fig. 3 has provided in the present embodiment and has adopted the inventive method to offer < < physical layer multicast wave beam forming > > (Transmit beamforming for physical-layer multicasting.IEEE Transactions on Signal Processing with adopting international IEEE-signal processing transactions > > 2006 annuals published articles, vol.54, pp.2239-2251, June2006) the channel capacity correlation curve that the SDR method of pointing out in and SDR method of randomization obtain.As can be seen from Figure 3, as existing conventional design method, the channel capacity curve C l that SDR method of randomization reflects, when in group, number of users is lower, the channel capacity curve C 2 corresponding with the inventive method overlaps substantially, and all very approaching with employing SDR method acquisition performance upper bound curve C 3, even overlap.Yet, along with number of users increases, the inventive method has embodied the design performance better compared with SDR method of randomization, its channel capacity obtaining is all the time higher than SDR method of randomization, and along with number of users increases, and performance advantage is more and more obvious, particularly in group during number of users K=32, the inventive method performance advantage is extended to about 0.3bps.Visible, method for designing provided by the present invention is a kind of effective alone family group MIMO multicast beamforming method, not only can improve the channel capacity of this system, simultaneously the lower computational complexity of more existing SDR method of randomization also.And along with base station end transmitting antenna configured number increases, the interior number of users of group promotes, the performance advantage of the inventive method is more remarkable, is adapted at implementing in MIMO broadband wireless of new generation and mobile communication system.

Claims (1)

1. a multiple-input and multiple-output multicast beamforming method, establishes center base station end configuration M root transmitting antenna, only comprises sole user's group in its coverage cell, and in group, number of users is K, and user k disposes N _kroot reception antenna, corresponding channel matrix

base station end source signal x, transmitted power P; It is characterized in that comprising successively following steps:

Step 1, initial setting up iterations n and the highest iterations n thereof _max, make n ∈ [0, n _max], its initial value is made as 0; The higher limit λ of initial setting up iteration step length λ _maxwith lower limit λ _min, make λ ∈ [λ _min, λ _max], its initial value is made as λ _min; Initial setting up wave beam forming vector w ₀, produce at random and make its satisfied constraint formula || w ₀||=1;

Step 2, in the n time iterative process, first for group in K user, make Customs Assigned Number k=1 ..., K, calculates each user's signal to noise ratio successively

select wherein minimum value, remember that its reference numeral is the n time iteration user sequence number k _n;

Step 3, with the n-1 time iteration user sequence number k _n-1compare, judge iteration user sequence number k the n time _nwhether change: if change, make iteration step length λ=λ _min; Otherwise, according to regular min (2* λ, λ _max) adjustment iteration step length λ;

Step 4, choose iteration user sequence number k the n time _nsubscriber channel matrix

carry out singular value decomposition, find out the right singular vector of the corresponding maximum of its maximum singular value

as the n time iteration reference vector, and utilize angle computing formula

calculate iteration reference vector the n time

with the n time iteration wave beam forming vector w _nbetween angle

Step 5, first utilize the n time iteration wave beam forming vector w _ncalculate and obtain relational expression

numerical value, then gives this numerical value iteration wave beam forming vector w the n+1 time _n+1, then calculate and obtain normalization numerical value w _n+1/ || w _n+1||, then give iteration wave beam forming vector w the n+1 time by this numerical value _n+1;

Step 6, judge whether iterations n has reached the highest iterations n _maxif: n>n _maxbe false, by the n+1 time iteration wave beam forming vector w _n+1as new wave beam forming vector, iterations n is updated to n+1 and repeats above-mentioned steps two to step 6; If n>n _maxset up, stop iterative process;

Step 7, by n _maxinferior wave beam forming vector give optimum beam figuration vector w _opt, then according to transmitted power P and according to relational expression

to base station, end source signal x realizes MIMO multicast wave beam forming.

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