CN106330276A - Large-scale MIMO linear detection method and device based on SOR algorithm - Google Patents

Large-scale MIMO linear detection method and device based on SOR algorithm Download PDF

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CN106330276A
CN106330276A CN201610929675.3A CN201610929675A CN106330276A CN 106330276 A CN106330276 A CN 106330276A CN 201610929675 A CN201610929675 A CN 201610929675A CN 106330276 A CN106330276 A CN 106330276A
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unit
matrix
algorithm
sor
realizing
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张川
俞安澜
尤肖虎
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Southeast University
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Southeast University
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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
    • H04B7/0413—MIMO systems
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • 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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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Power Engineering (AREA)
  • Radio Transmission System (AREA)

Abstract

The invention discloses a large-scale MIMO linear detection method and device based on the SOR algorithm. The method is based on the SOR algorithm, an improvement is made on the basis of the iterative formula of the SOR algorithm to improve precision, and accordingly the iterative formula of the algorithm is sorted. In the structure aspect of the device, a channel matrix and a receiving signal vector pass a preprocessing module and then enter an improved SOR algorithm module, wherein the preprocessing module conducts Gram matrix calculation, MMSE filter matrix calculation and matched filtering, the algorithm module obtains an MMSE filter matrix and matched filtering output to serve as a coefficient matrix and a constant vector respectively for iteration to solve a linear equation set, and a signal detection result is obtained. The algorithm is low in complexity, required iteration frequency is small, hardware loss is small, and precision is not interfered with by a correction factor omega.

Description

Extensive MIMO linearity test method and device based on SOR algorithm
Technical field
The invention belongs to computer communication field, relate to a kind of extensive mimo system uplink signal detection method and Device.
Background technology
Multiple-Input-Multiple-Output (MIMO) signal processing is transported because of the Matrix-Vector of its vast number Calculate device and become in MIMO-OFDM baseband receiver most difficulty and challenging part.All of MIMO technology is required for MIMO detection carries out accurate operational.But in extensive MIMO linearity test, due to the increase of antenna amount, channel matrix Dimension increases therewith, and then makes the calculating of Minimum mean square error (MMSE) filtered matrix become difficulty, less With saying the inverse matrix of MMSE filtered matrix, therefore, there has been the way using iterative method directly to invert.Have before this and pass through The test that Gauss-Seidel algorithm and SOR algorithm are iterated, but the relatively low degree of accuracy of complexity is general.The essence of SOR algorithm Exactness changes along with the change of modifying factor especially.
Summary of the invention
Goal of the invention: for the deficiencies in the prior art, it is an object of the present invention to provide a kind of based on SOR algorithm extensive MIMO linearity test method and device, optimizes on the basis of SOR algorithm advantage further, improves the degree of accuracy of algorithm, to the greatest extent may be used The exact value of matrix inversion can be reached.The degree of accuracy simultaneously avoiding algorithm changes with the change of modifying factor.
Technical scheme: for achieving the above object, the technical solution used in the present invention is as follows:
The present invention based on SOR iterative method, apply on the basis of SOR is iterative the definition of modifying factor ω substitute kth+ The result of 1 iteration, obtains the iterative of inventive algorithm.Particularly as follows: iterative (D+ ω L) X of SOR algorithmk+1=((1- ω)D-ωLH)Xk+ ω b, substitutes into the definition X of modifying factor ωk+1=Xk+ω(Xk+1-Xk), then can obtain changing of this algorithm For formula (D+ ω L) Xk+1=(-(1-ω) L-LH)Xk+b。
A kind of based on SOR algorithm the extensive MIMO linearity test method that the present invention provides, comprises the following steps:
(1) channel matrix H and reception signal y are carried out pretreatment, obtain matched filtering device output yMF=HHY and MMSE filters Ripple matrix W=G+ σ2IM, and W will be decomposed into W=D+L+LH, wherein Gram matrix G=HHH, σ2For noise variance, IMFor unit Battle array, (.)HFor conjugate transposition operation, D is diagonal matrix, and L is inferior triangular flap；
(2) matched filtering device is exported yMF, MMSE filtering matrix decomposition result D, L and LHAnd modifying factor ω is as defeated Enter, use the SOR algorithm improved to be iterated solving and obtain Signal estimation result to be detected, in the SOR algorithm wherein improved i-th Secondary iteration output siAccording to formula si=(D+ ω L)-1(ωL-LH-L)si-1+(D+ωL)-1yMF, i > 0 is calculated.
For ensureing iterative convergence, in described step (2), modifying factor ω span is 1 < ω < 2.
In a specific embodiment, s in described step (2)iInitial value s0For full 0 vector, modifying factor ω is constant 1.5, iterations is 3 times.
A kind of based on SOR algorithm the extensive MIMO linearity test device that the present invention provides, including pretreatment module and The SOR algoritic module improved；Wherein
Described pretreatment module, including: matched filter unit, Gram matrix calculation unit, MMSE filtering matrix calculates Unit, MMSE filtering matrix resolving cell and the first multiplication unit；
Described matched filter unit, for the channel matrix H conjugate transpose H according to inputHY is calculated with receiving signal yMF =HHY, exports yMF；
Described Gram matrix calculation unit, is used for calculating G=HHH, exports G；
Described MMSE filtering matrix computing unit, is connected with Gram matrix calculation unit, is used for calculating W=G+ σ2IM, output W；Wherein σ2For noise variance, IMFor unit battle array；
Described MMSE filtering matrix resolving cell, is connected with MMSE filtering matrix computing unit, for W is decomposed into W=D +L+LH, wherein D is diagonal matrix, and L is inferior triangular flap, exports D, L and L respectivelyH；
Described first multiplication unit, is connected with MMSE filtering matrix resolving cell, is used for realizing modifying factor ω and lower three Angle battle array L is multiplied；
The SOR algoritic module of described improvement, including: the first adder unit, the second adder unit, the 3rd adder unit, the Square law unit, the 3rd multiplication unit, the 4th multiplication unit, inversion unit and seek negative unit；
Described second multiplication unit, is connected with MMSE filtering matrix resolving cell, is used for realizing 1-ω and inferior triangular flap L phase Take advantage of；
Described first adder unit, is connected with MMSE filtering matrix resolving cell and the first multiplication unit respectively, for real Existing diagonal matrix D is added with inferior triangular flap ω L；
Described second adder unit, is connected with MMSE filtering matrix resolving cell and the second multiplication unit respectively, for real Existing inferior triangular flap (1-ω) L and upper triangular matrix LHIt is added；
Described inversion unit, is connected with the first adder unit, inverts for realizing the D+ ω L of inferior triangular flap；
Described seek negative unit, be connected with the second adder unit, be used for realizing matrix (1-ω) L+LHIntermediate value asks negative computing；
Described 3rd multiplication unit, is connected with asking negative unit and the 4th multiplication unit respectively, is used for realizing ω L-LH-L with On take turns iterative computation output si-1It is multiplied；
Described 3rd adder unit, is connected with the 3rd multiplication unit and matched filter unit respectively, is used for realizing (ω L- LH-L)si-1With yMFIt is added；
Described 4th multiplication unit, is connected with inversion unit and the 3rd adder unit respectively, is used for realizing both and exports phase Take advantage of, obtain epicycle iteration signal to be detected siEstimate.
Beneficial effect: compared with prior art, the advantage of the present invention: remain the advantage that SOR algorithm complex is low, in reality Now in the case of equal degree of accuracy, the iterations of inventive algorithm is fewer than the iterations of SOR algorithm, and complexity is more Low.It is capable of and MMSE algorithm degree of accuracy closely.In modifying factor change in the case of ceteris paribus, by Simulation result can be seen that the degree of accuracy of SOR algorithm presents the variation tendency of curve with the change of modifying factor.And the present invention Algorithm is almost unchanged with the change of modifying factor, close to the degree of accuracy of MMSE algorithm.
Accompanying drawing explanation
Fig. 1 is apparatus of the present invention structural representation；
Fig. 2 is 16 for launching antenna number, when reception antenna number is 128, uses signal detection algorithm of the present invention and other inspections The ber curve figure of method of determining and calculating；
Fig. 3 is 8 for launching antenna number, when reception antenna number is 64, uses signal detection algorithm of the present invention and other detections The ber curve figure of algorithm；
Fig. 4 be iterations be 3, when signal to noise ratio is 4, use the mistake of signal detection algorithm of the present invention and other detection algorithms Code check is with modifying factor ω change curve.
Detailed description of the invention
Below in conjunction with specific embodiment, it is further elucidated with the present invention, it should be understood that these embodiments are merely to illustrate the present invention Rather than restriction the scope of the present invention, after having read the present invention, the those skilled in the art's various equivalences to the present invention The amendment of form all falls within the application claims limited range.
The present embodiment is set up an extensive mimo channel model and is simulated operation.In extensive mimo system, Typically there is N ＞ ＞ M (antenna for base station number N is much larger than launching antenna number, i.e. number of users M).Allow s=[s1,s2,s3,…,sM]TRepresent Signal vector, contains the transmission symbol produced respectively from M user in s, use 16-QAM mode to map.H represents that dimension is N × M channel matrix, therefore the received signal vector y of uplink base station end can be expressed as
Y=Hs+n
Wherein the dimension of y is N × 1, and n is the additive white noise vector of N × 1 dimension.Uplink multiuser signal detection is appointed Business is exactly to receive vector y=[y from receiver1,y2,y3,…,yN]TEstimate transmission signal code s.Assume H it is known that its yuan of white clothing From average be 0 variance be the independent same distribution of 1, use least mean-square error (MMSE) linearity test theoretical, to transmission signal to The estimation of amount is expressed as
s ^ = ( H H H + &sigma; 2 I M ) - 1 H H y = W - 1 y M F
Owing to matrix W is Hermitian positive definite, and
W=D+L+LH
Wherein D, L and LHIt is respectively triangular component on the diagonal of W, lower trigonometric sum.Linear equation is solved according to SOR method Group
W s ^ = y M F
Can arrange according to SOR algorithm iterative and obtain the testing result of ith iteration gained and be
si=(D+ ω L)-1(ωL-LH-L)si-1+(D+ωL)-1yMF, i=1,2 ...,
If iteration initial value s0For full 0 vector, i.e. s0=[01,02,…,0M]T, iteration terminates for 3 times.Initial value ω is constant 1.5.Then iterative process can be expressed as
s1=(D+ ω L)-1(ωL-LH-L)s0+(D+ωL)-1yMF,
s2=(D+ ω L)-1(ωL-LH-L)s1+(D+ωL)-1yMF,
s3=(D+ ω L)-1(ωL-LH-L)s2+(D+ωL)-1yMF。
The most just the estimated value through 3 iteration can be obtained
For the extensive mimo system that antenna configurations is 128 × 16 and 64 × 8, use 3/4 speed Turbo code and 16-QAM maps, and the simulation result of extensive MIMO detection method based on above-mentioned algorithm is shown in Fig. 2 and Fig. 3.
Inventive algorithm 1 < ω < restrain when 2, and SOR algorithm 0 < ω < restrain when 2, thus its public interval of convergence be 1 < Curve such as Fig. 4 that ω < 2, inventive algorithm and other algorithms change with modifying factor ω.
Hardware structure aspect, the device knot of based on SOR algorithm the extensive MIMO detection method used in the present embodiment Fig. 1 is shown in by structure schematic diagram, including pretreatment module and algoritic module.
Specifically, in pretreatment module, comprise:
1) matched filter unit: the systolic arrays being made up of M complex multiplier accumulator (MAC), is used for calculating yMF= HHY, exports yMF；
2) Gram matrix calculation unit: the lower triangle systolic arrays being made up of (1+M) M/2 MAC, is used for calculating G= HHH, exports G；
3) MMSE filtering matrix computing unit: by M2Individual complex adder forms, and is connected with Gram matrix calculation unit, uses In calculating W=G+ σ2IM, export W；
4) MMSE filtering matrix resolving cell: be connected with Gram matrix calculation unit, W is decomposed into W=D+L+LH, wherein D is diagonal matrix, and L is inferior triangular flap, exports D, L, L respectivelyH；
5) the first multiplication unit: be connected with MMSE filtering matrix resolving cell, exports ω L；
In algoritic module, described algoritic module mainly comprises a systolic arrays inv solving triangle battle array inverse matrix, and two Individual Matrix-Vector multiplication array, a vector addition array, two addition of matrices arrays and one group of depositor, eventually pass through The signal of detection will be in write depositor, it is simple to the operation such as decoding carrying out next step comprises:
1) 2 Matrix-Vector multiplication arrays (the 3rd multiplication unit and the 4th multiplication unit): the pulsation being made up of M MAC Array；
2) 1 systolic arrays inv (inversion unit) solving triangle battle array inverse matrix: use 2 kinds of PE, comprises 6M and deposits Device, 4M multiplier and 4M adder, and 1 reciprocal unit, be used for calculating the inverse matrix of inferior triangular flap (D+ ω L)；
3) 1 vector addition array (the 3rd adder unit): the systolic arrays being made up of M complex adder；
4) 2 addition of matrices arrays (the first adder unit and the second adder unit): by M2Individual complex adder composition Systolic arrays.
Complexity aspect, when iterations is 2, number of multipliers used by the algorithm that the present invention proposes is 3M2+ 3M, adds Musical instruments used in a Buddhist or Taoist mass quantity is 3M2+M；When iterations is 3, number of multipliers used by the algorithm that the present invention proposes isAdder number Amount isContrast as shown in table 1 with the complexity of SOR algorithm.
The carried algorithm of table 1 present invention and SOR algorithm complex contrast table
From simulation result, the algorithm that the present invention proposes is that degree of accuracy when 2 is changing higher than SOR algorithm at iterations Generation number is degree of accuracy when 3.So, on the premise of completing same performance, the algorithm complex that the present invention proposes is less than SOR The complexity of algorithm.

Claims (4)

1. an extensive MIMO linearity test method based on SOR algorithm, it is characterised in that: comprise the following steps:
(1) channel matrix H and reception signal y are carried out pretreatment, obtain matched filtering device output yMF=HHY and MMSE filters square Battle array W=G+ σ2IM, and W will be decomposed into W=D+L+LH, wherein Gram matrix G=HHH, σ2For noise variance, IMFor unit battle array, (. )HFor conjugate transposition operation, D is diagonal matrix, and L is inferior triangular flap；
(2) matched filtering device is exported yMF, MMSE filtering matrix decomposition result D, L and LHAnd modifying factor ω is as input, The SOR algorithm using improvement is iterated solving and obtains Signal estimation result to be detected, i & lt in the SOR algorithm wherein improved Iteration output siAccording to formula si=(D+ ω L)-1(ωL-LH-L)si-1+(D+ωL)-1yMF, i > 0 is calculated.
Extensive MIMO linearity test method based on SOR algorithm the most according to claim 1, it is characterised in that: described In step (2), modifying factor ω span is 1 < ω < 2.
Extensive MIMO linearity test method based on SOR algorithm the most according to claim 2, it is characterised in that: described S in step (2)iInitial value s0For full 0 vector, modifying factor ω is constant 1.5, and iterations is 3 times.
4. an extensive MIMO linearity test device based on SOR algorithm, it is characterised in that: include pretreatment module and improvement SOR algoritic module；
Described pretreatment module, including: matched filter unit, Gram matrix calculation unit, MMSE filtering matrix computing unit, MMSE filtering matrix resolving cell and the first multiplication unit；
Described matched filter unit, for the channel matrix H conjugate transpose H according to inputHY is calculated with receiving signal yMF= HHY, exports yMF；
Described Gram matrix calculation unit, is used for calculating G=HHH, exports G；
Described MMSE filtering matrix computing unit, is connected with Gram matrix calculation unit, is used for calculating W=G+ σ2IM, export W；Its Middle σ2For noise variance, IMFor unit battle array；
Described MMSE filtering matrix resolving cell, is connected with MMSE filtering matrix computing unit, for W is decomposed into W=D+L+ LH, wherein D is diagonal matrix, and L is inferior triangular flap, exports D, L and L respectivelyH；
Described first multiplication unit, is connected with MMSE filtering matrix resolving cell, is used for realizing modifying factor ω and inferior triangular flap L It is multiplied；
The SOR algoritic module of described improvement, including: the first adder unit, the second adder unit, the 3rd adder unit, second takes advantage of Method unit, the 3rd multiplication unit, the 4th multiplication unit, inversion unit and seek negative unit；
Described second multiplication unit, is connected with MMSE filtering matrix resolving cell, is used for realizing 1-ω and is multiplied with inferior triangular flap L；
Described first adder unit, is connected with MMSE filtering matrix resolving cell and the first multiplication unit respectively, and it is right to be used for realizing Angle battle array D is added with inferior triangular flap ω L；
Described second adder unit, is connected with MMSE filtering matrix resolving cell and the second multiplication unit respectively, under realizing Triangle battle array (1-ω) L and upper triangular matrix LHIt is added；
Described inversion unit, is connected with the first adder unit, inverts for realizing the D+ ω L of inferior triangular flap；
Described seek negative unit, be connected with the second adder unit, be used for realizing matrix (1-ω) L+LHIntermediate value asks negative computing；
Described 3rd multiplication unit, is connected with asking negative unit and the 4th multiplication unit respectively, is used for realizing ω L-LH-L with on take turns repeatedly In generation, calculates output si-1It is multiplied；
Described 3rd adder unit, is connected with the 3rd multiplication unit and matched filter unit respectively, is used for realizing (ω L-LH-L) si-1With yMFIt is added；
Described 4th multiplication unit, is connected with inversion unit and the 3rd adder unit respectively, is used for realizing both outputs and is multiplied, To epicycle iteration signal to be detected siEstimate.
CN201610929675.3A 2016-10-31 2016-10-31 Large-scale MIMO linear detection method and device based on SOR algorithm Pending CN106330276A (en)

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CN106941393A (en) * 2017-03-03 2017-07-11 东南大学 LDPC interpretation methods and system based on SOR
CN107070514A (en) * 2017-01-20 2017-08-18 南京邮电大学 A kind of extensive MIMO signal detection method of optimization
CN107222246A (en) * 2017-05-27 2017-09-29 东南大学 The efficient extensive MIMO detection method and system of a kind of approximated MMSE-based performance
CN109257076A (en) * 2018-09-20 2019-01-22 东南大学 Compression Landweber detection method and framework based on extensive MIMO
CN109379116A (en) * 2018-10-30 2019-02-22 东南大学 Extensive MIMO linear detection algorithm based on Chebyshev acceleration Yu SOR algorithm
CN111310370A (en) * 2020-01-17 2020-06-19 湖北汽车工业学院 Mechanical part fuzzy reliability calculation method based on random finite element of ultra-relaxation iterative method

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Cited By (12)

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Publication number Priority date Publication date Assignee Title
CN107070514A (en) * 2017-01-20 2017-08-18 南京邮电大学 A kind of extensive MIMO signal detection method of optimization
CN107070514B (en) * 2017-01-20 2020-07-14 南京邮电大学 Optimized large-scale MIMO signal detection method
CN106941393A (en) * 2017-03-03 2017-07-11 东南大学 LDPC interpretation methods and system based on SOR
CN106941393B (en) * 2017-03-03 2019-11-12 东南大学 LDPC interpretation method and system based on SOR
CN107222246A (en) * 2017-05-27 2017-09-29 东南大学 The efficient extensive MIMO detection method and system of a kind of approximated MMSE-based performance
CN107222246B (en) * 2017-05-27 2020-06-16 东南大学 Efficient large-scale MIMO detection method and system with approximate MMSE performance
CN109257076A (en) * 2018-09-20 2019-01-22 东南大学 Compression Landweber detection method and framework based on extensive MIMO
CN109257076B (en) * 2018-09-20 2020-06-30 东南大学 Large-scale MIMO-based compressed Landweber detection method and system
CN109379116A (en) * 2018-10-30 2019-02-22 东南大学 Extensive MIMO linear detection algorithm based on Chebyshev acceleration Yu SOR algorithm
CN109379116B (en) * 2018-10-30 2021-04-27 东南大学 Large-scale MIMO linear detection algorithm based on Chebyshev acceleration method and SOR algorithm
CN111310370A (en) * 2020-01-17 2020-06-19 湖北汽车工业学院 Mechanical part fuzzy reliability calculation method based on random finite element of ultra-relaxation iterative method
CN111310370B (en) * 2020-01-17 2022-06-10 湖北汽车工业学院 Mechanical part fuzzy reliability calculation method based on random finite element

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