CN107786474A - A kind of channel estimation methods based on the models of Tucker 2 in MIMO relay system - Google Patents

A kind of channel estimation methods based on the models of Tucker 2 in MIMO relay system Download PDF

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CN107786474A
CN107786474A CN201711068383.6A CN201711068383A CN107786474A CN 107786474 A CN107786474 A CN 107786474A CN 201711068383 A CN201711068383 A CN 201711068383A CN 107786474 A CN107786474 A CN 107786474A
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杜建和
邓如意
王陈涛
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Communication University of China
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Communication University of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods

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Abstract

The present invention relates to a kind of channel estimation methods of the 3-dimensional encoding based on the models of Tucker 2 in multiple-input and multiple-output (MIMO) relay system.In this MIMO relay system, the problem of the defects of mainly solving the existing channel estimation methods based on PARAFAC needs elimination yardstick to obscure, while the number for needing to meet to send data flow makes calculating process complicate equal to the condition of the number of transmitting terminal antenna.Implementation step is：1) relay is transmitted a signal to from information source end；2) 3-dimensional encoding is carried out to the signal of reception in relay, and the signal after coding is sent to stay of two nights end；3) models of Tucker 2 are built to signal at stay of two nights end；4) model is fitted using ALS algorithms, realizes the estimation to information source trunk channel matrix and relaying stay of two nights channel matrix.The present invention can be in the case where or need not only need a small amount of CSI and encoder matrix, by being fitted constructed multi-dimensional matrix model, to realize good signal detection and channel estimation, while the estimated accuracy of information source trunk channel and relaying stay of two nights channel is independent of each other has stronger feasibility and validity.The viewpoint of the present invention can expand the channel estimation applied to multihop relay system.

Description

A kind of channel estimation methods based on Tucker-2 models in MIMO relay system
Technical field
It is a kind of more particularly in MIMO relay system to be based on Tucker-2 models the present invention relates to wireless communication technology field 3-dimensional encoding channel estimation methods.
Background technology
Relay system, because of the characteristics of its covering is wide, transmission rate is high and transmission is reliable, is considered as mesh in wireless channel It is preceding that there is a promising technology.On the other hand, mimo system can improve the speed and reliability of transmission, therefore wide It is applied to research and practice generally.Relay system and MIMO technology combine, and can make full use of the specific structure of Spatial Dimension, enter one Walk to improve the performance of system.Generally, in the known whole accurate channel condition information of link (CSI), in MIMO Advantage after network will be embodied well.
Repetition policy is broadly divided into amplification forwarding (AF) and decoding forwarding (DF) two schemes.Under AF schemes, pass through letter The signal that easy AF processing operations receive to via node carries out linear transformation, so as to which the signal of amplification is sent into the stay of two nights End.AF schemes can reduce computing cost in the case where relay signal handling capacity is limited.
, it is necessary to the CSI of known whole information source-trunk channel and relaying-stay of two nights channel for the optimization of communication system. And from the perspective of wireless signal processing, the algebraic model of some matrix operations is used for signal sending end and/or output end. Multidimensional symbol data and statistics can be retained by multilinear algebra model.At this stage, based on multidimensional processiug technology Novel wireless communication system learnt always by numerous scholars, researcher in past ten years, tensor algebra or multi-thread Property algebraically be beneficial to multidimensional processiug is suitably incorporated into those processing strategy uses in unsupervised and/or blind (half-blindness) signal Domain existing for redundancy symbol in estimation.Due to the dimensions such as code domain-Spatial-Temporal special construction and decompose uniqueness, Multidimensional processiug technology can be constructed in the case where or need not only need a small amount of CSI and encoder matrix by fitting Multi-dimensional matrix model, to realize signal detection and channel estimation.It is more in communication system compared to traditional technology based on matrix Dimensional signal treatment technology can benefit from the diversity of two or more forms simultaneously, be easy under the conditions of model can recognize more easily control real Existing channel estimation and Signal separator.
Method based on PARAFAC can realize effective estimation to allied signal and channel, but these sides Method is all based on PARAFAC and obscured, it is necessary to eliminate yardstick, while the number for needing to meet to send data flow is equal to transmission The condition of the number of antenna is held, therefore there is also certain limitation for the method for utilization PARAFAC.
The content of the invention
Goal of the invention：The present invention is applied to the limitation in MIMO relay system for PARAFAC, proposes a kind of The channel estimation methods of 3-dimensional encoding based on Tucker-2 models, realize to information source-trunk channel matrix and relaying-stay of two nights letter The estimation of road matrix.
Technical scheme：A kind of letter of the 3-dimensional encoding based on Tucker-2 models in MIMO relay system of the present invention Channel estimation method.Including：
Channel training signals are sent to relay from information source end；
Three-dimensional matrice extended coding is carried out to the signal of reception in relay, and the signal after coding is forwarded to the stay of two nights End；
Tucker-2 models are built to signal at stay of two nights end；
The model is fitted using ALS algorithms, realized to information source-trunk channel matrix and relaying-stay of two nights channel square The estimation of battle array.
Further, relay is transmitted a signal to from information source end, specifically included：
In information source end, identical orthogonal channel training signal is sentTo relay.
The signal of reception is at via node：
Further, three-dimensional matrice extended coding is carried out to the signal of reception in relay, and the signal after coding is turned Stay of two nights end is sent to, including：
P-th of chip of three-dimensional spreading code matrix is utilized at relayingTo the letter received Number encoded.
Stay of two nights end receive p-th of slice signal be：
Peer-to-peer both ends are multiplied by S simultaneouslyH, then have
Further, Tucker-2 models are built to signal at stay of two nights end, including：
Matrix section collection is stacked in column direction, madeAnd Y2=[Y..1, Y..2..., Y..P ]T, can obtain：
Order
Matrix section collection is stacked by line direction, makes Y3=[vec (Y..1), vec (Y..2) ..., vec (Y..P)], then Have：
Make F3=[vec (C..1), vec (C.2) ..., vec (C..P)] and V3=[vec (V..1), vec (V..2) ..., vec (V.P)].Have：
Further, the model is fitted using ALS algorithms, realized to information source-trunk channel matrix and relaying-letter The estimation of place channel matrix, including：
Using following condition least square (LS) criterion of alternating minimization come Combined estimator H2With
Estimate is represented by：
Wherein i represents iterations,H is represented respectively2WithThe estimate of ith.
The cost function of ith iteration is represented by
Beneficial effect：Compared with prior art, its major advantage is：The present invention need not eliminate yardstick and obscure, and also be not required to Meet that the number for sending data flow is equal to the condition of the number of transmitting terminal antenna.The characteristic of Tucker-2 models can be utilized, Without or in the case of only needing a small amount of CSI and encoder matrix, by being fitted constructed multi-dimensional matrix model, come realize compared with Good signal detection and channel estimation.
Brief description of the drawings
Fig. 1 is the channel estimation methods flow chart of the present invention；
Fig. 2 is the node M IMO relay system structural representations of double bounce three of the present invention；
Fig. 3 is channel estimating performance figure of the present invention under different channels training sequence number P；
Fig. 4 is channel estimating performance figure of the present invention under different channels training sequence length L；
Fig. 5 is the present invention in various information source number MSWith relay antenna number MRUnder channel estimating performance figure；
Fig. 6 is that the present invention in systematic parameter is MS=MR=3, MDDuring=L=4, with existing methods channel estimating performance ratio Compared with figure；
Embodiment
To make the features of the present invention and advantage more obvious understandable, the present invention is described in detail below in conjunction with the accompanying drawings.
Fig. 2 be the present invention the node M IMO relay system structural representations of double bounce three, the node of double bounce three as shown in Figure 2 M is respectively configured in MIMO communication system, transmitting terminal and receiving terminalSAnd MDRoot antenna, the receiving terminal and transmitting terminal of via node are matched somebody with somebody respectively PutWithRoot antenna.In information source end, identical orthogonal channel training signal is sent to relay, three dimensional expansions are utilized in relay Code matrix is transmitted to stay of two nights end after being encoded to the signal of reception.
Embodiment one
Fig. 3 is referred to, Fig. 3 is channel estimating performance figure of the present invention under different channels training sequence number P.System is joined Number is：MS=MR=L=2, MD=4.Fig. 3 shows, estimates channel H1And H2NMSE values with SNR increase and be gradually reduced.Together When, the increase of channel training sequence number can to estimate that performance gets a promotion.Under different P values, estimate parallel due to using Meter method, H1And H2NMSE values it is very close.
Embodiment two
Fig. 4 is referred to, Fig. 4 is channel estimating performance figure of the present invention under different channels training sequence length L.System is joined Number is：MS=MR=2, MD=4, P=8.Fig. 4 shows, with the increase of channel training sequence length, estimates channel H1And H2's NMSE values are gradually reduced, and the estimation performance for carrying algorithm improves.And under shorter channel training sequence length, carried Algorithm still has higher estimation precision.
Embodiment three
Fig. 5 is referred to, Fig. 5 is the present invention in various information source number MSWith relay antenna number MRUnder channel estimating performance Figure.Systematic parameter is：MD=L=4, P=8.Fig. 5 shows, with the increase of information source end or relay number of antennas, estimates channel H1And H2NMSE values gradually increase.Due in the case where other conditions are constant, increasing information source end or relay number of antennas, The channel parameter that carried algorithm needs to estimate becomes more, thus causes channel estimating performance to reduce.
Understood with reference to Fig. 3 and Fig. 4, if wanting in the case of information source end or relay number of antennas are increased, keep or improve The estimated accuracy of channel, it can suitably increase channel training sequence number or length.
Embodiment four
Refer to Fig. 6, Fig. 6 is that the present invention in systematic parameter is MS=MR=3, MDDuring=L=4, with existing methods channel Estimate performance comparision figure；Compared to existing program, suggest plans in H1Channel estimation in terms of there is higher estimated accuracy, but To H2Precision of channel estimation be less than existing program.Because existing program is to H1And H2Two stage estimation has been respectively adopted, And carried algorithm is to H1And H2Using the scheme of Combined estimator.
To sum up, the present invention has a preferable channel estimating performance, while information source-trunk channel and relaying-stay of two nights channel Estimated accuracy is independent of each other, and simulation result shows the feasibility and validity of the present invention.The viewpoint of the present invention can expand application In the channel estimation of multihop relay system.
The explanation of above example is only to help to understand the method and its main thought of the present invention.The content of this specification is not The interest field of the present invention can be limited with this, therefore, protection scope of the present invention should be determined by the appended claims.

Claims (5)

  1. A kind of channel estimation methods of the 3-dimensional encoding based on Tucker-2 models in 1.MIMO relay systems, it is characterised in that should Method includes：
    Channel training signals are sent to relay from information source end；
    Three-dimensional matrice extended coding is carried out to the signal of reception in relay, and the signal after coding is forwarded to stay of two nights end；
    Tucker-2 models are built to signal at stay of two nights end；
    The model is fitted using ALS algorithms, realized to information source-trunk channel matrix and relaying-stay of two nights channel matrix Estimation.
  2. 2. a kind of channel of the 3-dimensional encoding based on Tucker-2 models is estimated in the MIMO relay system according to requiring right 1 Meter method, it is characterised in that：Relay is transmitted a signal to from information source end first, is specifically included：
    In information source end, identical orthogonal channel training signal is sentTo relay.Have：Y(R)=H1S+V(R)
    Wherein,For a sign matrix,For information source and the channel matrix of relay well, For the noise matrix at via node.For the signal received at via node.
  3. 3. a kind of channel of the 3-dimensional encoding based on Tucker-2 models is estimated in the MIMO relay system according to requiring right 2 Meter method, it is characterised in that three-dimensional Space-Time coding is carried out to the signal of reception in relay, and the signal after coding is sent To stay of two nights end, including：
    P-th of chip of three-dimensional spreading code matrix is utilized at relayingThe signal received is entered Row coding.Then have：
    <mrow> <msubsup> <mi>Y</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> </msub> <msup> <mi>Y</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <msubsup> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </msubsup> </mrow>
    Wherein,P-th of section that stay of two nights end receives is represented,Represent the channel square between relaying and the stay of two nights Battle array,Represent p-th of section of stay of two nights end noise tensor.Again due to the signal Y received at via node(R)= H1S+V(R), you can obtain：
    <mrow> <msubsup> <mi>Y</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> </msub> <msub> <mi>H</mi> <mn>1</mn> </msub> <mi>S</mi> <mo>+</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> </msub> <msup> <mi>V</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <msubsup> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </msubsup> </mrow>
    Peer-to-peer both ends are multiplied by S simultaneouslyH, can obtain：
    <mrow> <msubsup> <mi>Y</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </msubsup> <msup> <mi>S</mi> <mi>H</mi> </msup> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> </msub> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> </msub> <msup> <mi>V</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <msubsup> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>p</mi> </mrow> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <msup> <mi>S</mi> <mi>H</mi> </msup> </mrow>
  4. 4. a kind of channel of the 3-dimensional encoding based on Tucker-2 models is estimated in the MIMO relay system according to requiring right 3 Meter method, it is characterised in that Tucker-2 models are built to signal at stay of two nights end, including：
    OrderWith
    Cut into slices collection { Y to matrix in column direction··1, Y·2..., Y··PAndStacked, madeAnd Y2=[Y··1, Y··2..., Y··P]T, you can：
    <mrow> <msub> <mi>Y</mi> <mn>1</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>P</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>P</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <msub> <mi>Y</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>&amp;CircleTimes;</mo> <msubsup> <mi>H</mi> <mn>1</mn> <mi>T</mi> </msubsup> <mo>)</mo> </mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>P</mi> </mrow> <mi>T</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>H</mi> <mn>2</mn> <mi>T</mi> </msubsup> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>P</mi> </mrow> <mi>T</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Make F1=[C··1 T, C··2 T..., C··P T]T, V1=[V··1 T, V··2 T..., V··P T]T, F2=[C··1, C··2..., C··P]TAnd V2=[V··1, V··2..., V··P]T, then can obtain：
    <mrow> <msub> <mi>Y</mi> <mn>1</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>V</mi> <mn>1</mn> </msub> </mrow>
    <mrow> <msub> <mi>Y</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>&amp;CircleTimes;</mo> <msubsup> <mi>H</mi> <mn>1</mn> <mi>T</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> <msubsup> <mi>H</mi> <mn>2</mn> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>V</mi> <mn>2</mn> </msub> </mrow>
    Matrix is cut into slices by line direction and collects { vec (Y··1), vec (Y··2) ..., vec (Y··P) stacked, make
    Y3=[vec (Y··1), vec (Y··2) ..., vec (Y··P)]
    Have：
    <mrow> <msub> <mi>Y</mi> <mn>3</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>H</mi> <mn>1</mn> <mi>T</mi> </msubsup> <mo>&amp;CircleTimes;</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>P</mi> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mo>(</mo> <msub> <mi>V</mi> <mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mi>P</mi> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>
    Make F3=[vec (C··1), vec (C··2) ..., vec (C··P)] and V3=[vec (V··1), vec (V··2) ..., vec (V··P)], Y3It is represented by：
    <mrow> <msub> <mi>Y</mi> <mn>3</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>H</mi> <mn>1</mn> <mi>T</mi> </msubsup> <mo>&amp;CircleTimes;</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>V</mi> <mn>3</mn> </msub> </mrow>
  5. 5. a kind of channel of the 3-dimensional encoding based on Tucker-2 models is estimated in the MIMO relay system according to requiring right 4 Meter method, it is characterised in that the model is fitted using ALS algorithms, realize to information source-trunk channel matrix and relaying- The estimation of stay of two nights channel matrix, including：
    ALS algorithms are simple and easy, and have higher fitting precision, and the present invention has used a kind of ALS receiving algorithms of iteration to structure The Tucker-2 models built are fitted.Its thought is to be combined using following condition least square (LS) criterion of alternating minimization Estimate H2WithIts estimate can be write as
    <mrow> <msub> <mover> <mi>H</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>min</mi> </mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> </munder> <mo>|</mo> <mo>|</mo> <msub> <mi>Y</mi> <mn>1</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>&amp;CircleTimes;</mo> <msub> <mi>H</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> </mrow>
    <mrow> <msub> <mover> <mi>H</mi> <mo>^</mo> </mover> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>min</mi> </mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> </munder> <mo>|</mo> <mo>|</mo> <msub> <mi>Y</mi> <mn>2</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>&amp;CircleTimes;</mo> <msubsup> <mi>H</mi> <mrow> <mn>1</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> </mrow>
    Wherein i represents iterations,WithH is represented respectively2WithThe estimate of ith.The cost function of ith iteration It is represented byThe step of carried ALS algorithms, is as follows：Step 1) initializesIf i=1 and φ(0)=∞；Step 2) is according to Y1Value, calculate H1Estimate：Step 3) is according to Y2Value, calculate H2Estimate：If step 4) | φ(i)-φ(i-1)|/φ(i)≤ ε (ε=10-5), iteration is completed； Otherwise i=i+1, repeat step 2 are made) continue iteration to step 4).
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