CN105847194B

CN105847194B - A QRD Structure Based on MGS

Info

Publication number: CN105847194B
Application number: CN201610172198.0A
Authority: CN
Inventors: 邢座程; 危乐; 刘苍; 唐川; 原略超; 张洋; 王庆林; 王�锋; 吕朝; 董永旺; 刘丹; 陈礼锐
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2016-03-24
Filing date: 2016-03-24
Publication date: 2019-05-03
Anticipated expiration: 2036-03-24
Also published as: CN105847194A

Abstract

An MGS-based QRD structure, including a first module CORE_GEQRT and a second module CORE_TTQRT, the first module CORE_GEQRT is used to perform QR decomposition on an input 2×2 matrix [a ₁ , a ₂ ] through MGS algorithm to output q ₁ ,r ₁₁ ,r ₂₂ ,sign(f(A)),r ₁₂ ,q ₂ , where [q ₁ ,q ₂ ] is a Q matrix, r ₁₁ ,r ₁₂ ,r ₂₂ form an upper triangular matrix R, sign(f (A))=(a ₂₁ a ₁₂ ‑a ₁₁ a ₂₂ )/r ₁₁ ; the two obtained R matrices are used as the input of the second module CORE_TTQRT and [1,0; 01], [0,0; 0, 0] together form a matrix [a ₁₁ , a ₁₂ , 1, 0; 0, a ₂₂ , 0, 1; a ₃₁ , a ₃₂ , 0, 0; 0, a ₄₂ , 0, 0], and finally get 4 × 2 matrix. The present invention has the advantages of simple structure, capable of improving overall performance and the like.

Description

A kind of QRD structure based on MGS

Technical field

Present invention relates generally to extensive multi-antenna technology fields, refer in particular to a kind of novel 2 × 2 tile QRD based on MGS Structure.

Background technique

Extensive multi-antenna technology (multiple input multiple output, MIMO) is next generation communication technology One of the key technology of (5G).In extensive mimo system, base station end can service tens equipped with up to a hundred antennas simultaneously User's (for the sake of simplicity, each user only has 1 antenna).This and 4 foundation station antennas in traditional mimo system service 4 The case where single-antenna subscriber (referred to as 4 × 4MIMO system), is compared, and more antennas provide more spatial multiplexing gain and diversity increases Benefit.Moreover, simple linear signal processing process can reach near-optimization performance in extensive mimo system.

In extensive mimo system, by being accommodated more in a large amount of antenna of base station equipment with providing bigger freedom degree More information.Therefore, extensive MIMO can preferably improve the availability of frequency spectrum, channel capacity and company compared to traditional mimo system Connect reliability.Compared with traditional mimo system, several times of the matrix dimension of the base band signal process algorithm of extensive MIMO is even Tens times.Especially when algorithm is related to matrix inversion operation and QR decomposition etc..In order to overcome extensive matrix complex degree bottleneck, need The new structure of one kind is designed to accelerate crucial matrix algorithm unit.

QRD matrix decomposition algorithm obtains extensive utilization in mimo systems, and in some known work, QRD Become an essential component in transmitting terminal.In general, QRD is used to decompose channel response matrix H as one A unitary matrice Q and upper triangular matrix R.In extensive MIMO, the number of user and the antenna number of base station are very big at one Variation in range.The dimension of H changes in a very big range, it needs QRD hardware configuration to decompose the square of this multidimensional Battle array.For now, already present QRD hardware configuration is concentrated mainly on one or several fixed dimensions in the field of wireless communication Matrix.Therefore, flexible QRD hardware configuration has very great meaning to wireless communication system in future.

As depicted in figs. 1 and 2, traditional MGS (Modified Gram-Schmidt) hardware algorithm structure is broadly divided into Two modules of DP, TP.Wherein DP module is mainly used to generate q_jAnd r_jj, TP module be mainly used to generate update matrixWith r_ji, DMP is mainly used to generate q_j, r_jj,r_ji。

To the matrix column vector a of input in DP module_j, firstly, by each of which element be separately input to squaring module M1, Squaring module M2, squaring module M3, in squaring module M4, obtained result deposit Buffer1.Then, by obtained result point It is not input in adder M1, adder M2, obtained result is separately input in adder M3, the result that adder M3 is obtained It is stored in Buffer2.Result r is obtained as a result, being input to and opening in more number module M1 obtained in Buffer2_jj.In Buffer3 The result arrived is as divisor, a_jAs dividend each of which element be separately input to divider M1, divider M2, divider M3, Result q is obtained in divider M4_jIt is stored in Buffer4.

To the matrix column vector a of input in TP module_iAnd q_j, wherein (<=3 i) incremented by successively i and each q_jIt is corresponding a₀、a₁、a₂、a₃, a_iSuccessively as input, with q_jIt is separately input to multiplier M1, multiplier M2, multiplier M3, multiplier M4, is obtained To result deposit Buffer1 in.The knot that result is deposited into adder M4 respectively, adder M5 is obtained is read from Buffer1 Fruit deposit is input to adder M6, in obtained result deposit Buffer2.The column of result and input obtained in the Buffer2 Vector q_jIn each element be separately input to multiplier M5, multiplier M6, multiplier M7, multiplier M8, obtained result is deposited Enter into Buffer3.Using result obtained in Buffer3 as subtrahend a_iSubtracter M1 is separately input to as minuend, is subtracted Musical instruments used in a Buddhist or Taoist mass M2, subtracter M3, subtracter M4, obtain result

In above-mentioned traditional structure, extensive MIMO matrix dimension is larger, causes to be related to significantly increase when QRD algorithm The computational complexity of base station,

Summary of the invention

The technical problem to be solved in the present invention is that, for technical problem of the existing technology, the present invention provides one Kind structure is simple, can be improved the QRD structure based on MGS of overall performance.

In order to solve the above technical problems, the invention adopts the following technical scheme:

A kind of QRD structure based on MGS, including the first module CORE_GEQRT and the second module CORE_TTQRT, it is described First module CORE_GEQRT is used to 2 × 2 matrix [a to input₁,a₂] pass through MGS algorithm progress QR decomposition output q₁,r₁₁, r₂₂,sign(f(A)),r₁₂,q₂, wherein [q₁,q₂] it is Q matrix, r₁₁,r₁₂,r₂₂Composition upper triangular matrix R, sign (f (A))= (a₂₁a₁₂-a₁₁a₂₂)/r₁₁；Using obtain two R matrixes as the input and [1,0 of the second module CORE_TTQRT；01],[0, 0；0,0] matrix [a is collectively constituted₁₁,a₁₂,1,0；0,a₂₂,0,1；a₃₁,a₃₂,0,0；0,a₄₂, 0,0], finally obtain 4 × 2 square Battle array.

As a further improvement of the present invention: the first module CORE_GEQRT includes:

2 × 2 matrixes of input are stored in buffer1, the matrix-vector a being stored by selector first₁Element a₁₁ Two inputs, a as multiplier 1₂₁Two inputs as multiplier 2.Obtain two are exportedWithAs addition The input terminal of device 1, adder 1 obtain resultIt is stored in buffer2；The result that adder 1 obtains is read from buffer2 defeated Enter to carry out out radical sign module 1, result radical sign operation will be opened obtainedIt is stored in buffer4.It will Vector a₁Make dividend, the r of divider₁₁It is separately input in divider 1 and divider 2 as divisor, obtained result q₁It deposits Enter buffer5；

After vector is input to buffer1, vector a is read from buffer1₁While read vector a₂, first by a₁₁Become For-a₁₁, then by data-a₁₁, a₁₂, a₂₁, a₂₂It is stored in buffer2；WhenWhen being input to out radical sign module 1, a₁₂, a₂₁As multiplying The input of musical instruments used in a Buddhist or Taoist mass 1, a₂₂,-a₁₁As the input of multiplier 2, the input that obtain two are exported as adder 1 finally will In obtained output f (A) deposit buffer3；F (A) is read from buffer3 and carries out the operation that takes absolute value, obtained value is defeated Enter into buffer4；Meanwhile taking the symbol of f (A) as output Sig_nValue, will | f (A) | with r₁₁It is read from buffer4 defeated Enter in dividing module 3, by operation result r₂₂It is stored in buffer5；

After the completion of f (A) calculating, by element a₁₁, a₁₂It is input to multiplier 1, by element a₂₁, a₂₂Multiplier 2 is inputted, it will Input of the obtained output as adder 1, the result that adder 1 obtains are stored in buffer4；The result that adder 1 is obtained It is taken out from buffer4 and r₁₁It is linked into the input terminal of dividing module 4 jointly, obtains result r₁₂It is stored in buffer5；

When obtaining q₁It after Sign (f (A)), is entered into and is input in selector 2, wherein Sign (f (A)) is used as item Part signal.When Sign (f (A)) is timing q₂₁=q₁₂, q₂₂=-q₁₁, the q when Sign (f (A)) is negative₂₁=-q₁₂, q₂₂=q₁₁。 Obtained q₂As output.

As a further improvement of the present invention: the second module CORE_TTQRT includes: including third module QR and Four module Column update；The third module QR is fully pipelined architecture, in first clock cycle first to its input matrix A_1=[a₁₁,1；a₃₁, 0] and QR operation is carried out, in second clock cycle to its input matrix A_2=[a₂₂,1；a₄₂, 0] and it carries out QR operation；Firstly, 2 × 2 matrixes of input are stored in buffer1, the matrix-vector a being stored by selector₁Element a₁₁ Two inputs, a as multiplier 3₂₁As two inputs of multiplier 4, meanwhile, take a₂₁Symbol as output Sign；It will Two obtained outputsWithAs the input terminal of adder 2, adder 1 obtains resultIt is stored in buffer2；By addition The input of result that device 2 obtains carries out out radical sign module 2, the result that will be opened radical sign operation and obtain As output；By vector a₁Make dividend, the r of divider 5₁₁It is input to divider 6 as divisor, obtained result q₁As defeated Out.Wherein r₁₂=q₁₁, r₂₂=q₁₂；

Obtain Sign and q₁Afterwards, by Sign and q₁The alternatively input of device, wherein Sign alternatively signal.Work as Sign It is q for timing output₂₁=q₁₂, q₂₂=-q₁₁, when Sign is negative, output is q₂₁=-q₁₂, q₂₂=q₁₁；Obtained q₂As defeated Out；

After obtaining the Q matrix of A_1, to a₁₂, a₃₂Column, which are carried out, by Column update updates operation；By a₁₁, q₁₂As The input a of multiplier 5₂₁, q₂₂Multiplier 6 is inputted, by a₁₁, q₁₁Multiplier 7 is inputted, by a₂₁, q₂₁Input multiplier 8；Multiplier 5 The result input summer 3 obtained with multiplier 6 obtains resultThe result input summer that multiplier 7 and multiplier 8 obtain 2 obtain resultObtain matrixTake matrixMiddle submatrixProgress is similarly operated with A_1 Afterwards, to vectorIt is updated operation, obtains 2 × 2 R matrix.

Compared with the prior art, the advantages of the present invention are as follows:

QRD structure based on MGS of the invention, structure is simple, can be improved overall performance, solves extensive MIMO square Battle array dimension is larger, causes to be related to significantly increase this problem of the computational complexity of base station when QRD algorithm.Due to QRD tile Algorithm is very suitable for future broadband wireless communication systems, and its bottleneck is the calculating of 2 × 2 tiles, therefore, proposed by the invention 2 × 2 tile structures are very meaningful.

Detailed description of the invention

Fig. 1 is the hardware structural diagram of DP in traditional MGS algorithm.

Fig. 2 is the hardware structural diagram of TP in traditional MGS algorithm.

Fig. 3 is the hardware structural diagram of present invention CORE_GEQRT in specific application example.

Fig. 4 is the hardware structural diagram of present invention CORE_TTQRT in specific application example.

Specific embodiment:

The present invention is described in further details below with reference to Figure of description and specific embodiment.

MGS structure of the invention includes: CORE_GEQRT and CORE_TTQRT, and wherein CORE_GEQRT is used to input 2 × 2 matrix [a₁,a₂] pass through MGS algorithm progress QR decomposition output q₁,r₁₁,r₂₂,sign(f(A)),r₁₂,q₂, wherein [q₁,q₂] For Q matrix, r₁₁,r₁₂,r₂₂Form upper triangular matrix R, sign (f (A))=(a₂₁a₁₂-a₁₁a₂₂)/r₁₁.By obtain two R squares Input and [1,0 of the battle array as CORE_TTQRT；01],[0,0；0,0] matrix [a is collectively constituted₁₁,a₁₂,1,0；0,a₂₂,0,1； a₃₁,a₃₂,0,0；0,a₄₂, 0,0], finally obtain 4 × 2 matrix.

In specific application example, as shown in figure 3, the hardware of CORE_GEQRT forms are as follows:

2 × 2 matrixes of input are stored in buffer1, the matrix-vector a being stored by selector first₁Element a₁₁ Two inputs, a as multiplier 1₂₁Two inputs as multiplier 2.Obtain two are exportedWithAs adding The input terminal of musical instruments used in a Buddhist or Taoist mass 1, adder 1 obtain resultIt is stored in buffer2.The result that adder 1 obtains is read from buffer2 Input carries out out radical sign module 1, the result that will be opened radical sign operation and obtainIt is stored in buffer4. By vector a₁Make dividend, the r of divider₁₁It is separately input in divider 1 and divider 2 as divisor, obtained result q₁ It is stored in buffer5.

After vector is input to buffer1, vector a is read from buffer1₁While read vector a₂, first by a₁₁Become For-a₁₁, then by data-a₁₁, a₁₂, a₂₁, a₂₂It is stored in buffer2.WhenWhen being input to out radical sign module 1, a₁₂, a₂₁As multiplying The input of musical instruments used in a Buddhist or Taoist mass 1, a₂₂,-a₁₁As the input of multiplier 2, the input that obtain two are exported as adder 1 finally will In obtained output f (A) deposit buffer3.F (A) is read from buffer3 and carries out the operation that takes absolute value, obtained value is defeated Enter into buffer4；Meanwhile taking the symbol of f (A) as the value of output Sign, and incite somebody to action | f (A) | with r₁₁It is read from buffer4 defeated Enter in dividing module 3, by operation result r₂₂It is stored in buffer5.

After the completion of f (A) calculating, by element a₁₁, a₁₂It is input to multiplier 1, by element a₂₁, a₂₂Multiplier 2 is inputted, it will Input of the obtained output as adder 1, the result that adder 1 obtains are stored in buffer4.The result that adder 1 is obtained It is taken out from buffer4 and r₁₁It is linked into the input terminal of dividing module 4 jointly, obtains result r₁₂It is stored in buffer5.

As shown in figure 4, CORE_TTQRT includes two modules of QR and Column update in specific application example.QR Module is fully pipelined architecture, in first clock cycle first to its input matrix A_1=[a₁₁,1；a₃₁, 0] and QR operation is carried out, Second clock cycle is to its input matrix A_2=[a₂₂,1；a₄₂, 0] and carry out QR operation.Firstly, 2 × 2 matrixes of input are deposited Enter buffer1, the matrix-vector a being stored by selector₁Element a₁₁Two inputs, a as multiplier 3₂₁As multiplying Two inputs of musical instruments used in a Buddhist or Taoist mass 4, meanwhile, take a₂₁Symbol as output Sign.Obtain two are exportedWithAs adder 2 input terminal, adder 1 obtain resultIt is stored in buffer2.The result input that adder 2 obtains is subjected to out radical sign module 2, result radical sign operation will be opened obtainedAs output.By vector a₁Make the quilt of divider 5 Divisor, r₁₁It is input to divider 6 as divisor, obtained result q₁As output.Wherein r₁₂=q₁₁, r₂₂=q₁₂。

Obtain Sign and q₁Afterwards, by Sign and q₁The alternatively input of device, wherein Sign alternatively signal.Work as Sign It is q for timing output₂₁=q₁₂, q₂₂=-q₁₁, when Sign is negative, output is q₂₁=-q₁₂, q₂₂=q₁₁.Obtained q₂As defeated Out.

After obtaining the Q matrix of A_1, to a₁₂, a₃₂Column, which are carried out, by Column update updates operation.By a₁₁, q₁₂As The input a of multiplier 5₂₁, q₂₂Multiplier 6 is inputted, by a₁₁, q₁₁Multiplier 7 is inputted, by a₂₁, q₂₁Input multiplier 8.Multiplier 5 The result input summer 3 obtained with multiplier 6 obtains resultThe result input summer that multiplier 7 and multiplier 8 obtain 2 obtain resultObtain matrixTake matrixMiddle submatrixProgress is similarly operated with A_1 Afterwards, to vectorIt is updated operation.Obtain 2 × 2 R matrix.

The above is only the preferred embodiment of the present invention, protection scope of the present invention is not limited merely to above-described embodiment, All technical solutions belonged under thinking of the present invention all belong to the scope of protection of the present invention.It should be pointed out that for the art For those of ordinary skill, several improvements and modifications without departing from the principles of the present invention should be regarded as protection of the invention Range.

Claims

1. A MGS-based QRD device, characterized in that it comprises a first module CORE_GEQRT and a second module CORE_TTQRT, and the first module CORE_GEQRT is used for inputting a 2×2 matrix QR decomposition through MGS algorithm outputs q ₁ , r ₁₁ , r ₂₂ , sign(f(A)), r ₁₂ , q ₂ , where [q ₁ , q ₂ ] is the Q matrix, r ₁₁ , r ₁₂ , r ₂₂ Form an upper triangular matrix R, sign(f(A))=(a ₂₁ a ₁₂ -a ₁₁ a ₂₂ )/r ₁₁ , a ₁ =[a ₁₁ ,a ₂₁ ] ^T ,a ₂ =[a ₁₂ ,a ₂₂ ] ^T , q ₁ =[q ₁₁ , q ₂₁ ] ^T , q ₂ =[q ₁₂ , q ₂₂ ] ^T ; two R matrices obtained by QR decomposition of two continuous matrices A are used as the input of the second module CORE_TTQRT Together with [1,0; 01], [0,0; 0,0] form a matrix [a ₁₁ ,a ₁₂ ,1,0;0,a ₂₂ ,0,1;a ₃₁ ,a ₃₂ ,0,0 ; 0,a ₄₂ ,0,0], the final matrix is obtained after QR decomposition;

The first module CORE_GEQRT includes:

First convert the input 2x2 matrix Store in buffer1, use the element a ₁₁ of the stored matrix vector a ₁ as the two inputs of the multiplier 1 and a ₂₁ as the two inputs of the multiplier 2 through the selector, and the obtained two outputs and As the input to adder 1, adder 1 gets the result Stored in buffer2; read the result obtained by adder 1 from buffer2 and input the root number module 1, and the result obtained by the root number operation Stored in buffer4, the vector a ₁ is used as the dividend of the divider, and r ₁₁ is input into the divider 1 and the divider 2 as the divisor respectively, and the obtained result q ₁ is stored in buffer5;

When the vector is input to buffer1, the vector a ₁ is read out from buffer1 and the vector a ₂ is read at the same time. First, a ₁₁ is changed to -a ₁₁ , and then the data -a ₁₁ , a ₁₂ , a ₂₁ , a ₂₂ are stored in buffer2 ;when When input to the square root module 1, a ₁₂ , a ₂₁ are used as the input of the multiplier 1, a ₂₂ , -a ₁₁ are used as the input of the multiplier 2, and the obtained two outputs are used as the input of the adder 1, and finally we will get The output f(A) is stored in buffer3; f(A) is read out from buffer3 for absolute value operation, and the obtained value is input into buffer4; at the same time, the symbol of f(A) is taken as the value of the output Sign, Read |f(A)| and r ₁₁ from buffer4 and input into division module 3, and store the operation result r ₂₂ in buffer5;

When f(A) is calculated, input elements a ₁₁ , a ₁₂ to multiplier 1, input elements a ₂₁ , a ₂₂ to multiplier 2, and use the obtained output as the input of adder 1, and the result obtained by adder 1 The result is stored in buffer4; the result obtained by the adder 1 is taken out from buffer4 and connected to the input end of the division module ₄ together with r11, and the result r12 is obtained and stored in _buffer5 ;

When q ₁ and Sign(f(A)) are obtained, they are input into selector 2, where Sign(f(A)) is used as the condition signal, and when Sign(f(A)) is positive, q ₂₁ =q ₁₂ , q ₂₂ =-q ₁₁ , when Sign(f(A)) is negative, q ₂₁ =-q ₁₂ , q ₂₂ =q ₁₁ , and q ₂ is obtained as output.

2. The MGS-based QRD device according to claim 1, wherein the second module CORE_TTQRT comprises: a third module QR and a fourth module Column update; the third module QR is a full pipeline structure, In the first clock cycle, QR operation is performed on its input matrix A_1=[a ₁₁ ,1;a ₃₁ ,0], and in the second clock cycle its input matrix A_2=[a ₂₂ ,1;a ₄₂ ,0] ] to perform QR operation; first, store the input 2×2 matrix A_1=[a ₁₁ ,1;a ₃₁ ,0] into buffer1, and use the element a ₁₁ of the stored matrix vector a ₁ as multiplier 3 through the selector The two inputs of a ₂₁ are used as the two inputs of the multiplier 4, and at the same time, the sign of a ₂₁ is taken as the output Sign; the obtained two outputs and As the input to adder 2, adder 1 gets the result Store in buffer2; input the result obtained by the adder 2 into the square root module 2, and the result obtained by the square root operation As output; input the vector a ₁ as the dividend of the divider 5, and r ₁₁ as the divisor and input it to the divider 6, and obtain the result q ₁ as the output, wherein r ₁₂ =q ₁₁ , r ₂₂ =q ₁₂ ;

After getting Sign and q ₁ , use Sign and q ₁ as the input of the selector, where Sign is used as the selection signal, when the Sign is positive, the output is q ₂₁ =q ₁₂ , q ₂₂ =-q ₁₁ , and when the Sign is negative, the output is For q ₂₁ =-q ₁₂ , q ₂₂ =q ₁₁ , the obtained q ₂ is used as the output;

get A_1's After matrix, perform column update operation on a ₁₂ and a ₃₂ through Column update; use a ₁₁ and q ₁₂ as the input of multiplier 5, input a ₂₁ and q ₂₂ into multiplier 6, and input a ₁₁ and q ₁₁ into the multiplier 7. Input a ₂₁ and q ₂₁ into multiplier 8; the results obtained by multiplier 5 and multiplier 6 are input into adder 3 to obtain the result The result of multiplier 7 and multiplier 8 is input to adder 2 to get the result get the matrix in Calculated by QR operation for A_1, Calculated by QR operation for matrix A_2, take the matrix Neutron matrix After performing the same operation as A_1, the vector Perform an update operation to get a 2×2 R matrix.