CN105071849B - A kind of method for realizing multi-flow beam forming in TD LTE Advanced - Google Patents

A kind of method for realizing multi-flow beam forming in TD LTE Advanced Download PDF

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Publication number
CN105071849B
CN105071849B CN201510297834.8A CN201510297834A CN105071849B CN 105071849 B CN105071849 B CN 105071849B CN 201510297834 A CN201510297834 A CN 201510297834A CN 105071849 B CN105071849 B CN 105071849B
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mrow
msubsup
matrix
sigma
matrixes
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CN105071849A (en
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王德胜
陈长帅
程荣涛
林宏志
熊磊
常成龙
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Huazhong University of Science and Technology
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Huazhong University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0891—Space-time diversity
    • H04B7/0897—Space-time diversity using beamforming per multi-path, e.g. to cope with different directions of arrival [DOA] at different multi-paths

Abstract

The invention discloses a kind of method for realizing multi-flow beam forming in TD LTE Advanced, including：4 × 8 channel matrix is obtained from the uplink detection reference signal of TD LTE Advanced base stations, by channel matrix A1Decomposed, to obtain two 4 × 4 sub-channel matrix, Household conversion is carried out to each sub-channel matrix, to generate upper Hessenberg matrixes, to upper Hessenberg matrix Js(1)Givens rotations are carried out, by the matrix J(1)It is transformed into diagonal matrix, above-mentioned computing is repeated to reach at least 5 times, the wherein last matrix being calculated can be used as the Hessenberg matrixes calculate next time used in again, the obtained right side is multiplied into Household transformation matrixs with the obtained right side multiply Givens matrixes to fold and multiply, to obtain 4*4 matrix.Processing is weighted to each row of the matrix V of generation using high specific transmission algorithm, to generate final wave beam forming weight vector.The present invention can overcome the shortcomings of existing EBB algorithms, calculate multi-flow beam forming weight vector exactly, and effectively reduce the bit error rate.

Description

A kind of method for realizing multi-flow beam forming in TD-LTE-Advanced
Technical field
The invention belongs to mobile communication technology field, and multithread in TD-LTE-Advanced is realized more particularly, to one kind The method of wave beam forming.
Background technology
Global communication cause is fast-developing in recent years, and the demand of radio communication is increasing, and radio communication cause obtains Flourish.But as people continue to increase to wireless communication needs, huge communication requirement amount and extremely limited frequency Contradiction between spectrum resource is more and more prominent.How limited frequency spectrum resource is efficiently utilized, and on the premise of quality is ensured The large-scale power system capacity that improves is into radio communication circle important topic urgently to be resolved hurrily, and the wave beam forming in smart antenna is Into an important directions to solve this problem.
Wave beam forming is the aerial array transmission technology applied to small spacing, the strong correlation of utilization space and the interference of ripple Principle produces the antenna pattern of directionality, the main lobe of antenna pattern is adaptively pointed to arrival bearing user, so as to carry High s/n ratio, power system capacity and coverage.
The algorithm of traditional calculating wave beam forming weight vector is the wave beam forming (Eigen-based that feature based decomposes Beamforming algorithm), although the algorithm is realized simply, two sides be present when calculating multi-flow beam forming weight vector The deficiency in face：(1) the selection dependence to initial vector is very high, if good primary iteration vector can not be selected, may lead Cause is difficult to restrain, it is impossible to tries to achieve wave beam forming weight vector；(2) in the case where channel matrix has same characteristic features value, can only obtain To the wave beam forming weight vector of single current, most cause the higher bit error rate at last.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the invention provides one kind to realize TD-LTE-Advanced The method of middle multi-flow beam forming weight vector, it is intended that overcoming the shortcomings of existing EBB algorithms, multithread ripple is calculated exactly Beam forming weight vector, and effectively reduce the bit error rate.
To achieve the above object, according to one aspect of the present invention, there is provided one kind is realized more in TD-LTE-Advanced The method of wave beam forming is flowed, is comprised the following steps：
(1) 4 × 8 channel matrix A is obtained from the uplink detection reference signal of TD-LTE-Advanced base stations1；
(2) by channel matrix A1Decomposed, to obtain two 4 × 4 sub-channel matrix A(p,1), it corresponds respectively to two Sub-antenna array, wherein p represent the sequence number of sub-antenna array；
(3) to each sub-channel matrix A(p,1)Household conversion is carried out, to generate upper Hessenberg matrix Js(1)；
(4) to upper Hessenberg matrix Js(1)Givens rotations are carried out, by the matrix J(1)It is transformed into diagonal matrix；
(5) computing of (4) of repeating the above steps reaches at least 5 times, wherein the last matrix being calculated can be used as down again Upper Hessenberg matrix Js used in once calculating(1)；
(6) right side obtained in step (3) is multiplied to the right side obtained in Household transformation matrixs and step (4) and multiplies Givens Matrix is folded to be multiplied, to obtain 4*4 matrix V, i.e.,Each row of the matrix V are designated as v1, v2,v3,v4, wherein, R(i)Represent that the right side multiplies Household matrixes, Q(i)Represent that the right side multiplies Givens matrixes；
(7) each row v of the matrix V generated using high specific transmission algorithm to step (6)1,v2,v3,v4It is weighted place Reason, to generate final wave beam forming weight vector v'1,v'2,v'3,v'4：
v′1=p1v1
v′2=p2v2
v′3=p3v3
v′4=p4v4
Wherein, p1、p2、p3And p4For weighted factor.
Preferably, step (3) includes following sub-step：
(3-1) sets counter k=1；
(3-2) constructs premultiplication Household matrix Ls(k), using the matrix to A(p,k)Premultiplication is carried out, to obtain matrix A(p ,k+1/2)=L(k)A(p,k)；
(3-3) determines whether that k+1=4 is set up, if it is matrix A(p,1)As upper Hessenberg matrix Js(1), mistake Journey terminates, otherwise into step (3-4)；
(3-4) construction right side multiplies Household matrixes R(k), multiply Household matrixes R using the right side(k)To A(p,k+1/2)Carry out right Multiply, to obtain matrix A(p,k+1)=A(p,k+1/2)R(k)；
(3-5) sets k=k+1, and return to step (3-2)；
Preferably, premultiplication Household matrixes are constructed in the following ways：
(3-2-1) first calculates zoom factor Kx, orderExpression is transformed matrix A(p,k)In the i-th row jth row element：
(3-2-2) construction column vector { xtemp }k：
(3-2-3) is by { xtemp }kIt is converted into unit vector { x }(k)：
(3-2-4) is according to { x }(k)Construct premultiplication Household matrix Ls(k)：
L(k)=I-2 { x }(k){x}(k)*, wherein I is 4*4 unit matrix.
Preferably, the construction right side multiplies Household matrixes in the following ways：
(3-4-1) first calculates zoom factor Ky, orderExpression is transformed matrix A(p,k+1/2)In row k i-th arrange member Element
(3-4-2) construction column vector { ytemp }k：
(3-4-3) is by { ytemp }kTurn to unit vector { y }(k)：
(3-4-4) is according to { y }(k)Construct R(k)
R(k)=I-2 { y }(k){y}(k)*, wherein I is 4*4 unit matrix, wherein, R(k)Represent that the right side multiplies Household squares Battle array.
Preferably, step (4) includes following sub-step：
(4-1) sets counter m=1；
(4-2) construction right side multiplies Givens matrixes Q(m), to J(m)Carry out the right side to multiply, to obtain J(m+1/2).I.e.：J(m+1/2)=J(m)Q(m)；
(4-3) construction premultiplication Givens matrixes P(m), to J(m+1/2)Premultiplication is carried out, obtains J(m+1).I.e.：J(m+1)=P(m)J(m +1/2)；
(4-4) sets counter m=m+1；
(4-5) determines whether m=4, if process terminates, otherwise return to step (4-2).
Preferably, the construction right side multiplies Givens matrixes in the following ways：
(4-2-1) sets the first initial vectorWhereinFor J(m)In the i-th row J column elements；
(4-2-2) is by [f(m),g(m)] calculate the right side multiply Givens matrixes Q(m), for Q(m)Element on middle diagonal And l ≠ m and l ≠ m+1；
(4-2-3) makes Q(m)Middle matrix-block
Wherein r be the first initial vector mould, RfFor f(m)Mould；
(4-2-4) takes 0 for remaining element.
Preferably, premultiplication Givens matrixes are constructed in the following ways：
(4-3-1) sets the second initial vector
WhereinFor J(m+1/2)In the i-th row jth row member Element；
(4-3-2) is by [f(m+1/2),g(m+1/2)]TCalculate premultiplication Givens matrixes P(m), for the element on diagonal And l ≠ m and l ≠ m+1；
(4-3-3) makes P(m)Middle matrix-block
Wherein r is the second initial vector Mould, RfFor f(m+1/2)Mould；
(4-3-4) takes 0 for remaining element.
Preferably, weighted factor is tried to achieve by equation below：
Wherein σ1,σ2,σ3,σ4Respectively sub-channel matrix A(p,1)Singular value.
In general, by the contemplated above technical scheme of the present invention compared with prior art, it can obtain down and show Beneficial effect：
1st, the problem of present invention can overcome the selection dependence present in existing method to initial vector very high：Due to The present invention is no to use initial vector, therefore selection of the present invention independent of initial vector；
2nd, because the singular value that channel matrix is realized present invention employs Householder transformation and Givens rotation is divided Solution.Therefore, the present invention can also obtain the wave beam forming weight vector of multithread in the case where channel matrix has same characteristic features value, This reduces the bit error rate.
Brief description of the drawings
Fig. 1 is the aerial array schematic diagram that the present invention uses.
Fig. 2 is the flow chart that the present invention realizes the method for multi-flow beam forming in TD-LTE-Advanced.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below Conflict can is not formed each other to be mutually combined.
The basic ideas of the present invention are, are converted into channel matrix by carrying out Householder transformation to channel matrix Upper Hessenberg matrix, Givens rotation is carried out to upper Hessenberg matrix afterwards, diagonal matrix is translated into, thus realizes The singular value decomposition of channel matrix, each row that will obtain the right singular value matrix of channel matrix are sweared as the power of wave beam forming Amount uses.
The present invention uses 4 × 4 cross polarised antenna arrays in Fig. 1, and the aerial array is made up of two subarrays, and 1,2, 3,4 composition subarrays 1, using -45.Polarization, 5,6,7,8 composition subarrays 2, using+45.Polarization.
The aerial array pattern supports 2.6GHz carrier frequency, and base station side of the present invention configures eight antennas, and user side configures four antennas.
As shown in Fig. 2 the method that the present invention realizes multi-flow beam forming in TD-LTE-Advanced, comprises the following steps：
(1) from the uplink detection reference signals of TD-LTE-Advanced base stations (sounding referencesignal, Abbreviation SRS) obtain 4 × 8 channel matrix A1；
(2) by channel matrix A1Decomposed, to obtain two 4 × 4 sub-channel matrix A(p,1), it corresponds respectively to two Sub-antenna array, wherein p represent the sequence number of sub-antenna array；
(3) to each sub-channel matrix A(p,1)Household conversion is carried out, to generate upper Hessenberg matrix Js(1), this Step includes following sub-step：
(3-1) sets counter k=1；
(3-2) constructs premultiplication Household matrix Ls(k), using the matrix to A(p,k)Premultiplication is carried out, to obtain matrix A(p ,k+1/2), i.e.,：A(p,k+1/2)=L(k)A(p,k)；Wherein construct premultiplication Household matrixes in the following ways：
(3-2-1) first calculates zoom factor Kx, orderExpression is transformed matrix A(p,k)In the i-th row jth row element：
(3-2-2) construction column vector { xtemp }k：
(3-2-3) is by { xtemp }kIt is converted into unit vector { x }(k)：
(3-2-4) is according to { x }(k)Construct premultiplication Household matrix Ls(k)：
L(k)=I-2 { x }(k){x}(k)*；Wherein I is 4*4 unit matrix；
(3-3) determines whether that k+1=4 is set up, if it is matrix A(p,1)As upper Hessenberg matrix Js(1), mistake Journey terminates, otherwise into step (3-4)；
(3-4) construction right side multiplies Household matrixes R(k), multiply Household matrixes R using the right side(k)To A(p,k+1/2)Carry out right Multiply, to obtain matrix A(p,k+1), i.e.,：A(p,k+1)=A(p,k+1/2)R(k)；Wherein the construction right side multiplies Household matrixes and used with lower section Formula：
(3-4-1) first calculates zoom factor Ky, orderExpression is transformed matrix A(p,k+1/2)In row k i-th arrange Element
(3-4-2) construction column vector { ytemp }k：
(3-4-3) is by { ytemp }kTurn to unit vector { y }(k)：
(3-4-4) is according to { y }(k)Construct R(k), I is 4*4 unit matrix, R(k)Represent that the right side multiplies Household matrixes：
R(k)=I-2 { y }(k){y}(k)*
(3-5) sets k=k+1, and return to step (3-2)；
(4) to upper Hessenberg matrix Js(1)Robin Givens (Givens) rotation is carried out, by the matrix J(1)It is transformed into pair Angular moment battle array, this step include following sub-step：
(4-1) sets counter m=1；
(4-2) construction right side multiplies Givens matrixes Q(m), to J(m)Carry out the right side to multiply, to obtain J(m+1/2).I.e.：J(m+1/2)=J(m)Q(m)；Wherein construct premultiplication Givens matrixes in the following ways：
(4-2-1) sets the first initial vectorWhereinFor J(m)In the i-th row J column elements；
(4-2-2) is by [f(m),g(m)] calculate the right side multiply Givens matrixes Q(m), for Q(m)Element on middle diagonal And l ≠ m and l ≠ m+1
(4-2-3) makes Q(m)Middle matrix-block
Wherein r be the first initial vector mould, RfFor f(m)Mould.
(4-2-4) takes 0 for remaining element.
(4-3) construction premultiplication Givens matrixes P(m), to J(m+1/2)Premultiplication is carried out, obtains J(m+1).I.e.：J(m+1)=P(m)J(m +1/2)；Wherein construct premultiplication Givens matrixes in the following ways：
(4-3-1) sets the second initial vector
For J(m+1/2)In the i-th row jth row element.
(4-3-2) is by [f(m+1/2),g(m+1/2)]TCalculate premultiplication Givens matrixes P(m), for the element on diagonal And l ≠ m and l ≠ m+1
(4-3-3) makes P(m)Middle matrix-block
Wherein r is the second initial vector Mould, RfFor f(m+1/2)Mould.
(4-3-4) takes 0 for remaining element.
(4-4) sets counter m=m+1；
(4-5) determines whether m=4, if process terminates, otherwise return to step (4-2).
(5) computing of (4) of repeating the above steps reaches at least 5 times, wherein the last matrix being calculated can be used as down again Upper Hessenberg matrix Js used in once calculating(1)；
(6) right side obtained in step (3) is multiplied to the right side obtained in Household transformation matrixs and step (4) and multiplies Givens Matrix is folded to be multiplied, to obtain 4*4 matrix V, i.e.,Each row of the matrix V are designated as v1, v2,v3,v4, wherein, R(i)Represent that the right side multiplies Household matrixes, Q(i)Represent that the right side multiplies Givens matrixes；
(7) it is raw to step (6) using high specific transmission algorithm (Maximum Ratio Transmission, abbreviation MRT) Into matrix V each row v1,v2,v3,v4Processing is weighted, to generate final wave beam forming weight vector v'1,v'2,v'3, v'4：
v′1=p1v1
v′2=p2v2
v′3=p3v3
v′4=p4v4
Wherein p is weighted factor, and it is tried to achieve by equation below：
Wherein σ1,σ2,σ3,σ4Respectively sub-channel matrix A(p,1)Singular value.
Sum it up, the present invention has following beneficial effect：
1st, the problem of present invention can overcome the selection dependence present in existing method to initial vector very high：Due to The present invention is no to use initial vector, therefore selection of the present invention independent of initial vector；
2nd, because the singular value that channel matrix is realized present invention employs Householder transformation and Givens rotation is divided Solution, therefore, the present invention can also obtain the wave beam forming weight vector of multithread in the case where channel matrix has same characteristic features value, This reduces the bit error rate.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles of the invention etc., all should be included Within protection scope of the present invention.

Claims (1)

  1. A kind of 1. method for realizing multi-flow beam forming in TD-LTE-Advanced, it is characterised in that comprise the following steps：
    (1) 4 × 8 channel matrix A is obtained from the uplink detection reference signal of TD-LTE-Advanced base stations1；
    (2) by channel matrix A1Decomposed, to obtain two 4 × 4 sub-channel matrix A(p,1), it corresponds respectively to two sub- days Linear array, wherein p represent the sequence number of sub-antenna array；
    (3) to each sub-channel matrix A(p,1)Household conversion is carried out, to generate upper Hessenberg matrix Js(1)；
    Wherein, step (3) includes following sub-step：
    (3-1) sets counter k=1；
    (3-2) constructs premultiplication Household matrix Ls(k), using the matrix to A(p,k)Premultiplication is carried out, to obtain matrix A(p,k+1/2) =L(k)A(p,k)；
    Wherein, premultiplication Household matrixes are constructed in the following ways：
    (3-2-1) first calculates zoom factor Kx, orderExpression is transformed matrix A(p,k)In the i-th row jth row element：
    <mrow> <msub> <mi>K</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msqrt> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>k</mi> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>*</mo> </mrow> </msubsup> </mrow> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>*</mo> </mrow> </msubsup> </mrow> </mfrac> </msqrt> </mrow>
    (3-2-2) construction column vector { xtemp }k：
    (3-2-3) is by { xtemp }kIt is converted into unit vector { x }(k)：
    <mrow> <msup> <mrow> <mo>{</mo> <mi>x</mi> <mo>}</mo> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>k</mi> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>xtemp</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>xtemp</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>*</mo> </mrow> </msubsup> </mrow> </msqrt> </mfrac> <msup> <mrow> <mo>{</mo> <mi>x</mi> <mi>t</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <mo>}</mo> </mrow> <mi>k</mi> </msup> </mrow>
    (3-2-4) is according to { x }(k)Construct premultiplication Household matrix Ls(k)：
    L(k)=I-2 { x }(k){x}(k)*, wherein I is 4*4 unit matrix；
    (3-3) determines whether that k+1=4 is set up, if it is matrix A(p,1)As upper Hessenberg matrix Js(1), process knot Beam, otherwise into step (3-4)；
    (3-4) construction right side multiplies Household matrixes R(k), multiply Household matrixes R using the right side(k)To A(p,k+1/2)The right side is carried out to multiply, To obtain matrix A(p,k+1)=A(p,k+1/2)R(k)；
    Wherein, the construction right side multiplies Household matrixes in the following ways：
    (3-4-1) first calculates zoom factor Ky, orderExpression is transformed matrix A(p,k+1/2)In row k i-th arrange element, Wherein
    <mrow> <msub> <mi>K</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msqrt> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>)</mo> <mo>*</mo> </mrow> </msubsup> </mrow> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>)</mo> <mo>*</mo> </mrow> </msubsup> </mrow> </mfrac> </msqrt> </mrow>
    (3-4-2) construction column vector { ytemp }k：
    (3-4-3) is by { ytemp }kTurn to unit vector { y }(k)：
    <mrow> <msup> <mrow> <mo>{</mo> <mi>y</mi> <mo>}</mo> </mrow> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>ytemp</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <msubsup> <mi>ytemp</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>*</mo> </mrow> </msubsup> </mrow> </msqrt> </mfrac> <msup> <mrow> <mo>{</mo> <mi>y</mi> <mi>t</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <mo>}</mo> </mrow> <mi>k</mi> </msup> </mrow>
    (3-4-4) is according to { y }(k)Construct R(k)：
    R(k)=I-2 { y }(k){y}(k)*, wherein I is 4*4 unit matrix；
    (3-5) sets k=k+1, and return to step (3-2)；
    (4) to upper Hessenberg matrix Js(1)Givens rotations are carried out, by the matrix J(1)It is transformed into diagonal matrix；
    Wherein, step (4) includes following sub-step：
    (4-1) sets counter m=1；
    (4-2) construction right side multiplies Givens matrixes Q(m), to J(m)Carry out the right side to multiply, to obtain J(m+1/2), i.e.,：J(m+1/2)=J(m)Q(m)；
    Wherein, the construction right side multiplies Givens matrixes in the following ways：
    (4-2-1) sets the first initial vectorWhereinFor J(m)In the i-th row jth row Element；
    (4-2-2) is by [f(m),g(m)] calculate the right side multiply Givens matrixes Q(m), for Q(m)Element on middle diagonalAnd l ≠ m and l ≠ m+1；
    (4-2-3) makes Q(m)Middle matrix-block
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>q</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> </mtd> <mtd> <msubsup> <mi>q</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>q</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> </mtd> <mtd> <msubsup> <mi>q</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> <mo>*</mo> </mrow> </msup> <mo>/</mo> <mi>r</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msup> <mi>g</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msup> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> <mo>*</mo> </mrow> </msup> <mo>/</mo> <mrow> <mo>(</mo> <mi>r</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>R</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>g</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> <mo>*</mo> </mrow> </msup> <mo>/</mo> <mi>r</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>f</mi> </msub> <mo>/</mo> <mi>r</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
    Wherein r be the first initial vector mould, RfFor f(m)Mould；
    (4-2-4) takes 0 for remaining element；
    (4-3) construction premultiplication Givens matrixes P(m), to J(m+1/2)Premultiplication is carried out, obtains J(m+1), i.e.,：J(m+1)=P(m)J(m+1/2)；
    Wherein, premultiplication Givens matrixes are constructed in the following ways：
    (4-3-1) sets the second initial vector
    WhereinFor J(m+1/2)In the i-th row jth row element；
    (4-3-2) is by [f(m+1/2),g(m+1/2)]TCalculate premultiplication Givens matrixes P(m), for the element on diagonalAnd l ≠ m and l ≠ m+1；
    (4-3-3) makes P(m)Middle matrix-block
    Wherein r is the mould of the second initial vector, RfFor f(m+1/2)Mould；
    (4-3-4) takes 0 for remaining element；
    (4-4) sets counter m=m+1；
    (4-5) determines whether m=4, if process terminates, otherwise return to step (4-2)；
    (5) computing of (4) of repeating the above steps reaches at least 5 times, wherein the last matrix being calculated again can be as next time Upper Hessenberg matrix Js used in calculating(1)；
    (6) right side obtained in step (3) is multiplied to the right side obtained in Household matrixes and step (4) and multiplies that Givens matrixes are folded to be multiplied, To obtain 4*4 matrix V, i.e.,Wherein, R(i)Represent that the right side multiplies Household matrixes, Q(i)Represent that the right side multiplies Givens matrixes, each row of the matrix V are designated as v1,v2,v3,v4；
    (7) each row v of the matrix V generated using high specific transmission algorithm to step (6)1,v2,v3,v4Processing is weighted, with Generate final wave beam forming weight vector v'1,v'2,v'3,v'4：
    v′1=p1v1
    v′2=p2v2
    v′3=p3v3
    v′4=p4v4
    Wherein, p is weighted factor, and weighted factor is tried to achieve by equation below：
    <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>4</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>4</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>3</mn> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>4</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>4</mn> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mn>4</mn> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mn>4</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow>
    Wherein σ1,σ2,σ3,σ4Respectively sub-channel matrix A(p,1)Singular value.
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