Patent ID: 12206469

DETAILED DESCRIPTION

In order to make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, it is a part of the embodiments of the present invention, but not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by a person of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Embodiment 1

Referring toFIG.1toFIG.3, this embodiment provides a near-field broadband uplink MIMO transmission method assisted by a dynamic metasurface antenna. In the method, the dynamic metasurface antenna is arranged on a base station side and configured to observe and capture signals from a channel. In the uplink transmission method, with system sum rate maximization as a criterion, based on methods such as MWMSE minimization, alternate optimization, matrix vectorization and MM, a baseband beamformer and a weight matrix of the dynamic metasurface antenna are determined, and formation of signal beams is completed, thereby improving transmission performance.

As channel state information in a communication system is changed, the base station side repeats the foregoing steps according to updated channel state information, to perform the near-field broadband uplink MIMO transmission method assisted by a dynamic metasurface antenna, thereby dynamically updating the transmission process, so as to ensure transmission performance.

Specifically, in this embodiment, the foregoing “MWMSE minimization” specifically includes:

A process of solving a sum rate expression of a near-field broadband uplink transmission system is relatively complex, so that in this embodiment, an original sum rate maximization problem is transformed into a mean square error sum minimization problem with MWMSE transformation, and a weighted auxiliary matrix is introduced based on original variables to reduce complexity of transmission optimization.

Specifically, in this embodiment, the foregoing “alternate optimization method” includes: for the weight matrix of the dynamic metasurface antenna and the weighted auxiliary matrix that are given, a baseband beamforming matrix is obtained with a closed-form solution; for the weight matrix of the dynamic metasurface antenna and the baseband beamforming matrix that are given, the weighted auxiliary matrix is obtained with a closed-form solution:

for the baseband beamforming matrix and the weighted auxiliary matrix that are given, the weight matrix of the dynamic metasurface antenna is designed with mean square error sum minimization as a criterion and with methods such as matrix vectorization and MM; and joint optimization of the baseband beamforming matrix and the weight matrix of the dynamic metasurface antenna is alternately implemented until a difference between two adjacent system sum rates is less than a given threshold.

More specifically, in this embodiment, the foregoing “designing the weight matrix of the dynamic metasurface antenna with mean square error sum minimization as a criterion and with methods such as matrix vectorization and MM” specifically includes the following steps:

Terms in the optimization problem that are unrelated to the weight matrix and that may be considered as constants are neglected, to obtain a simplified mean square error sum minimization problem:a target function is transformed into a matrix tracing form through MWMSE transformation, and the matrix tracing form may be transformed into a vector multiplication form with the matrix vectorization method, where the transformation may eliminate a block structure of the weight matrix of the dynamic metasurface antenna in the mean square error sum minimization problem, to reduce problem solving complexity; andsolving of a weight vector of the dynamic metasurface antenna in four weight feasible domains is considered, and the four feasible domains are an unconstrained (complex plane) weight, an amplitude weight, a binary amplitude weight and a Lorentzian phase constraint weight respectively, wherefor such two feasible domains as the unconstrained (complex plane) weight and the amplitude weight, the weight vector is solved with a common convex optimization algorithm;for such a feasible domain as the binary amplitude weight, the weight vector is solved with brute-force search; andfor such a feasible domain as the Lorentzian phase constraint weight, the weight vector is solved with an MM method.

More specifically, in this embodiment, the foregoing “solving the weight vector with an MM method” specifically includes:through the matrix vectorization method, an optimization variable is simplified from the weight matrix of the dynamic metasurface antenna into the weight vector, and the target function is simplified from matrix optimization into vector optimization;when a weighted auxiliary variable introduced by MWMSE transformation and the baseband beamforming matrix are considered as constants to solve the weight vector of the dynamic metasurface antenna, the target function is a non-convex function of the weight vector and iteratively solved with the MM method;in each time of iteration, a target function is replaced with its upper bounding function, a closed expression of an upper bounding problem is given, a target function in the next time of iteration is updated with this solution, a value of the original target function is calculated, and the iteration terminates when a difference between target functions in adjacent two times of iteration is less than a given threshold; and after the termination, the weight vector is changed again into a matrix as a solution to the mean square error sum minimization problem when the baseband beamforming matrix and the weighted auxiliary variable are given.

In this embodiment, to describe the transmission method more clearly and in more detail, the transmission method is specifically described with a specific application scenario and includes:

(1) A sum rate maximization problem is constructed based on a broadband large-scale MIMO uplink single-cell system and a channel model that considers a near-field effect, frequency-selective fading, and a spatial broadband effect, and the problem is defined as a first optimization problem, where a dynamic metasurface antenna array is used on a base station side of the broadband large-scale MIMO uplink single-cell system, and the first optimization problem is solved in a manner of jointly designing a baseband beamforming matrix and a weight matrix of a dynamic metasurface antenna, to maximize a near-field broadband large-scale MIMO uplink sum rate, where the step specifically includes:

As shown inFIG.1, the method is based on a broadband large-scale MIMO uplink single-cell system, the system includes a plurality of single-antenna users and one base station, and a dynamic metasurface antenna array is used on a base station side as a signal receive antenna. The array is formed by M microwave transmission bands, and L metasurface units are mounted on each microwave transmission band. Therefore, the dynamic metasurface antenna array is formed by a total of NRML, a cell includes U single-antenna users, a set of user is{1, 2, ⋅ ⋅ ⋅ , U}, and Nuantennas are configured for each user.

Q∈M×NRrepresents a weight matrix of a dynamic metasurface antenna, whose expression is:

(Q)m1,(m2-1)⁢L+l={qm1.l,m1=m20,m1≠m2(1)

In the expression (1), m1∈{1, 2, ⋅ ⋅ ⋅ , M}, m2∈{1,2, ⋅ ⋅ ⋅ , M}, l∈{1, 2, ⋅ ⋅ ⋅ , L}, and qm1lrepresents a gain of a (l)thantenna unit on a (m)thmicrowave transmission band for a signal, that is, a change for a signal amplitude or phase. Specifically, metamaterial units may be considered as a resonance circuit, a change of the units for a signal may be modeled into a weight multiplier of an amplitude, a binary amplitude or a Lorentzian constraint phase, and a specific expression is:amplitude: q∈=[a,b],b>a>0; and binary amplitude: q∈=c·{0,1},c>0; and Lorentzian constraint phase:

q∈ℚ={𝒥+e𝒥ϕ2|ϕ∈[0,2⁢π]};
and whererepresents an imaginary unit.

Specifically, the near-field broadband uplink transmission system assisted by the dynamic metasurface antenna has characteristics such as large base station antenna array aperture, high signal carrier frequency, and large transmission bandwidth, these characteristics cause wireless communication to possibly occur in a near-field region of the base station, and meanwhile signal transmission is affected by frequency-selective fading and the spatial broadband effect. Therefore, the following channel model is introduced into this embodiment, and a specific expression is:

gu(f)=∑p=0Puau,p(f)⊙bu,p(f)(2)
in the expression (2),

au,p(f)=[ξ1,1,u,p⁢A1,1,u,p(f),ξ1,2,u,p⁢A1,2,u,p(f),…,ξM,L,u,p⁢AM,L,u,p(f)](3⁢a)bu,p(f)=[e-𝒥2π⁡(f+fc)⁢❘"\[LeftBracketingBar]"pu,p-p1,1❘"\[RightBracketingBar]"c,e-𝒥2π⁡(f+fc)⁢❘"\[LeftBracketingBar]"pu,p-p1,2❘"\[RightBracketingBar]"c,…,e-⁢2⁢π⁡(f+fc)⁢❘"\[LeftBracketingBar]"pu,p-pM,L❘"\[RightBracketingBar]"c](3⁢b)
where au,p(ƒ) and bu,p(ƒ) represent a channel gain that considers a near-field effect, frequency selectivity, and a spatial broadband effect and a response matrix of an antenna array respectively: ξm,l,u,pand Am,l,u,p(ƒ) represent a large-scale fading factor of a (p)thtransmission path between a (l)thmetamaterial on a (m)thmicrostrip of a base station antenna and a user u and a channel gain coefficient respectively, pu,pand Pm,lrepresent a scatterer position of the (p)thtransmission path between the user u and the base station and a position of the (l)thmetamaterial on the (m)thmicrostrip of the base station antenna respectively, ƒ and ƒcrepresent a frequency and a center frequency respectively, and c represents a signal transmission speed equal to 3×108;

Specifically, a specific expression of the channel gain coefficient is:

Am,l,u,p(f)=❘"\[LeftBracketingBar]"Γu,p(f)❘"\[RightBracketingBar]"⁢F⁡(Θm,l,u,p)⁢c4⁢π⁡(f+fc)⁢pu,p-pm,lF(4)in the expression (4), Θm,l,u,p=(θm,l,u,pϕm,l,u,p) represents height-azimuth of a signal reflected from the user u by a (p)threflector and reaching a (l)thantenna unit on the (m)thmicrostrip of the base station antenna, and a specific expression of F(Θm,l,u,p) is:

F⁡(Θm,l,u,p)={6⁢cos2(θm,l,u,p),θm,l,u,p∈[0,π2]0,otherwise(5)Γu,p(ƒ) refers to a reflection coefficient of a reflector on a (p)thpath of the user u, and a specific expression thereof is:

Γu,p(f)={cos⁢ϕi,u,p-nt⁢cos⁢ϕt,u,pcos⁢ϕi,u,p+nt⁢cos⁢ϕt,u,p⁢e-(8⁢π2(f+fc)2⁢σrough2⁢cos2⁢ϕi,u,pc2),p=1,2,…,P1,p=0(6)in the expression (6), ntis a refractive index, σrough2is a roughness coefficient of a reflection surface, and cos ϕi,u,pand cos ϕt,u,pare an incident angle and a reflection angle of the signal of the user u on a (p)threflection object respectively.

To sum up, the sum rate of the system may be expressed as:

RS=∑s=0S-1ΔB⁢log⁢❘"\[LeftBracketingBar]"IU+PtΔB⁢σ2⁢WsH⁢Q⁢Hs⁢Gs⁢GsH⁢HsH⁢QH⁢Ws(WsH⁢Q⁢Hs⁢HsH⁢QH⁢Ws)-1❘"\[RightBracketingBar]"(7)in the expression (7), S represents a quantity of subcarriers, and ΔBrepresents a subcarrier spacing and is expressed as a ratio of a bandwidth B to the quantity of subcarriers S, that is,

ΔB=BS;IU
is an identity matrix of U×U, σ2is a variance of noise, Ptrepresents a transmit power, and U is a quantity of users in a cell; Gs=[g1,s,g2,s, . . . , gU,s]∈NR×Urepresents a channel matrix of an (s)thsubcarrier, Ws∈M×Urepresents a baseband beamformer of the (s)thsubcarrier, Hs∈NR×NRdescribes a frequency-selective effect of a signal propagated on a microwave transmission band, and Q∈M×NRrepresents a weight matrix of a dynamic metasurface antenna; and log is a logarithm operation, and |⋅| is a matrix determinant obtaining operation.

Specifically, a baseband beamforming matrix and a weight matrix of a dynamic metasurface antenna are jointly designed, to maximize a near-field broadband large-scale MIMO uplink sum rate, and a specific expression of the foregoing first optimization problem is:

𝒫1:minQ,Ws,∀s∈{1,2,…,S}RS⁢s.t.(Q)m1,(m2-1)⁢L+l={qm1,l,m1=m20,m1≠m2,qm1,l∈ℚ,∀m1,l(8)

In this problem, calculation complexity of the target function is very high, constraints are complex, and a plurality of target matrices need to be jointly optimized.

Therefore, this embodiment proposes a near-field broadband uplink MIMO transmission method assisted by a dynamic metasurface antenna, including methods such as MWMSE transformation, alternate optimization, matrix vectorization, and MM. Involved algorithms are described in detail below with reference to the foregoing optimization problem model.

(2) The first optimization problem in step (1) is equivalent to a mean square error sum minimization problem, the problem is defined as a second optimization problem, and then the second optimization problem is solved with the alternate optimization method where system sum rate maximization is used as a criterion, where when the second optimization problem is solved, a weighted auxiliary matrix is introduced based on an original variable to reduce complexity of transmission optimization; and the step (2) specifically includes:the first optimization problemposed in the step (1) is a typical sum rate maximization problem and is equivalent to a matrix-weighted mean square error sum minimization problem, the problem is defined as the second optimization problemin this embodiment, and a specific expression thereof is:

𝒫2:minMs,Q,Ws,∀s∈{1,2,…,S}∑s=0S-1tr⁢{Ms⁢Es(Q,Ws)}-log2⁢❘"\[LeftBracketingBar]"Ms❘"\[RightBracketingBar]"(9⁢a)s.t.(Q)m1,(m2-1)⁢L+l={qm1,l,m1=m20,m1≠m2(9⁢b)qm1,l∈ℚ,∀m1,l(9⁢c)

In the foregoing expression, Msis a weighted auxiliary matrix, and Es(Q,Ws) is a mean square error sum matrix, whose specific expression is:

Es(Q,Ws)=Pt(WsH⁢QHs⁢Gs-IU)⁢(WsH⁢QHs⁢Gs-IU)H+ΔB⁢σ2⁢WsH⁢QHs⁢HsH⁢QH⁢Ws(10)

Specifically, In this embodiment, the second optimization problemis solved through alternate optimization, specifically including:

When Q and Wsare given, where ∀s∈{1, 2, . . . , S}, Msmay be obtained from the following expression, where ∀s∈{1, 2, . . . , S}:

Msopt=Es(Q,Ws)-1(11)

When Q and Msare given, where ∀s∈{1, 2, . . . , S}, Wsmay be given by the following expression, where ∀s∈{1, 2, . . . , S}:

Wsopt=(Pt⁢QHs⁢Gs⁢GsH⁢HsH⁢QH+ΔB⁢σ2⁢QHs⁢HsH⁢QH)-1⁢QHs⁢Gs(12)

When Wsand Msare given, where ∀s∈{1, 2, . . . , S}, Q may be obtained by solving a third optimization problem, and a specific expression of the third optimization problemis:

𝒫3:∑s=0S-1tr⁢{Pt⁢Ms⁢WsH⁢QHs⁢Gs⁢GsH⁢HsH⁢QH⁢Ws}-tr⁢{Pt⁢Ms⁢WsH⁢QHs⁢Gs}-tr⁢{Pt⁢Ms⁢GsH⁢HsH⁢QH⁢Ws}+tr⁢{ΔB⁢σ2⁢Ms⁢WsH⁢QHs⁢HsH⁢QH⁢Ws}(13⁢a)s.t.(Q)m1,(m2-1)⁢L+1={qm1,l,m1=m20,m1≠m2,(13⁢b)qm1,l∈ℚ,∀m1,l(13⁢c)

The third optimization problemis obtained by substituting Es(Q,Ws) into the second optimization problem, where ∀s∈{1, 2, . . . , S} and leaving out terms unrelated to Q.

Specifically, as shown inFIG.2, this embodiment gives a flow of an algorithm of near-field broadband uplink transmission assisted by a dynamic metasurface antenna based on an alternate optimization method and with system sum rate maximization as a criterion, and a detailed process of the algorithm is as follows:

Step 1, initialize a baseband beamforming matrix Ws(0), where ∀s∈{1, 2, . . . , S}, a weight matrix Q(0)of the dynamic metasurface antenna, a weighted auxiliary matrix M(0), and a system sum rate RS(0), where a quantity of iteration times is2=0, and a threshold is ξ2.

Step 2, give a weight matrixof the dynamic metasurface antenna, and solve a baseband beamforming matrixaccording to the expression (12), where ∀s∈{1, 2, . . . , S}.

Step 3, giveand the baseband beamforming matrix, where ∀s∈{1, 2, . . . , S}, and calculate a mean square error sum matrix Es(Q,Wsaccording to the expression (10), where ∀s∈{1, 2, . . . , S}.

Step 4, give the mean square error sum matrix Es(Q,Ws, where ∀s∈{1, 2, . . . , S}, and solve a weighted auxiliary matrixaccording to the expression (11), where ∀s∈{1, 2, . . . , S}.

Step 5, giveand, where ∀s∈{1, 2, . . . , S}, and solve a problemto obtain a weight matrixof a dynamic metasurface antenna.

Step 6, calculate a system sum rate, and if |−|≤ξ2holds, jump out of the loop, and using (,), where ∀s∈{1, 2, . . . , S}, as a solution meeting the baseband beamforming matrix under the system sum rate maximization criterion and the weight matrix of the dynamic metasurface antenna: otherwise2=2+1, and perform step 2 to step 6 again.

(3) Solve the weight matrix of the dynamic metasurface antenna based on the matrix vectorization method

Specifically, in this embodiment, for the third optimization problem, the following method is taken:

For the block structure (13b) of the matrix Q, with the matrix vectorization method, a matrix tracing form in the target function is transformed into a vector multiplication form. Specifically, the matrix Q is pulled into q=[q1,1,q1,2, . . . ,qm,(m−1)L+l, . . . ,qM,ML]T, where qm,(m−1)L+lrepresents an element of a (m)throw and a (l)thcolumn of the matrix Q. Moreover, a matrix vectorization rule is used for obtaining:

tr⁢{QCs}=qT⁢cs,and⁢tr⁢{QH⁢CsH}=csH⁢q(14⁢a)tr⁢{QH⁢Bs⁢QAs=qH(Bs⊗NL)⊙AsT⁢q(14⁢b)tr⁢{QH⁢Bs⁢QDs=qH(Bs⊗IL)⊙Ds⁢q(14⁢c)where As=HsGsGsHHsH, Bs=WsMsWsH, Cs=HsGsMsWsH, and Ds=HsHsH;L represents a quantity of metasurface units on each microwave transmission band, NLis an all 1's matrix of L×L, ILis an identity matrix of L×L, {tilde over (B)}sis a diagonal matrix, and ({tilde over (B)}s)m,m=(Bs)m,m; and
cs=[(Cs)1,1,(Cs)2,1, . . . ,(Cs)(m−1)L+l,m, . . . ,(Cs)ML,M]T.

The expression (14) is substituted into the target function of the problem, to obtain:

f⁡(q)=∑s=0S-1qH[Pt(Bs⊗NL)⊙AsT+ΔB⁢σ2(B~s⊗IL)⊙Ds]⁢q-2⁢Re⁢{Pt⁢qH⁢cs*}

Therefore, a problem of optimizing a weight vector of the dynamic metasurface antenna to maximize the system sum rate may be expressed as:

𝒫4:minq⁢qH⁢Sq-2⁢Re⁢{qH⁢c*}(15⁢a)s.t.qm1,l∈ℚ,∀m1,l(15⁢b)where⁢S=∑s=0S-1Pt(Bs⊗NL)⊙AsT+ΔB⁢σ2(B~s⊗IL)⊙Ds,c=∑s=0S-1Pt⁢cs.

For the constraint (15b), four weight feasible domains are considered, are an unconstrained feasible domain, an amplitude feasible domain, a binary amplitude feasible domain and a Lorentzian constraint phase feasible domain respectively, and are specifically as follows:a. For the unconstrained feasible domain, a problem of optimizing a weight vector of the dynamic metasurface antenna to maximize the system sum rate may be expressed as, whose specific expression is:

𝒫5:minqqH⁢Sq-2⁢Re⁢{cT⁢q}(16)is a convex problem, and can be solved with a conventional convex optimization method.b. For the amplitude feasible domain, a problem of optimizing a weight vector of the dynamic metasurface antenna to maximize the system sum rate may be expressed as, whose specific expression is:

𝒫6:minqqT⁢Sq-2⁢Re⁢{cT}⁢q(17⁢a)s.t.qm1,l∈[a,b],b>a>0,∀m1,l(17⁢b)

Similarly,is a convex problem, and can be solved with a conventional convex optimization method.c. For the binary amplitude feasible domain, a problem of optimizing a weight vector of the dynamic metasurface antenna to maximize the system sum rate may be expressed as, whose specific expression is:

𝒫7:minqqT⁢Sq-2⁢Re⁢{cT}⁢q(18⁢a)s.t.qm1,l∈c·{0,1},c>0,∀m1,l(18⁢b)can be solved with a brute-force search method.d. For the Lorentzian constraint phase weight, a problem of optimizing a weight vector of the dynamic metasurface antenna to maximize the system sum rate may be expressed as, whose specific expression is:

𝒫8:minqqH⁢Sq-2⁢Re⁢{cT⁢q}(19⁢a)s.t.qm1,l∈{𝒿+e𝒿ϕ2|ϕ∈[0,2⁢π]},∀m1,l(19⁢b)
whererepresents an imaginary unit.

Specifically, in this embodiment,can be solved with an MM method (an ordered convex optimization method), specifically including: First, a tractable valid upper bound is found, the problemis replaced with a problem about an upper bound replacement function, and then a weight vector of a dynamic metasurface antenna is obtained with an alternate optimization method. An algorithm of solving a Lorentzian constraint phase weight with an MM method is described in detail below.

More specifically, the foregoing solving a Lorentzian constraint phase weight with an MM method specifically includes the following steps:

First, the weight vector of the dynamic metasurface antenna is expressed as

q=12⁢(𝒿INR+p),
where 1NRis an all 1's vector, and

p=[e𝒿⁢ϕ1,e𝒥ϕ2,…,e𝒥⁢ϕNR]T.
Therefore, the Lorentzian constraint phase is simplified into a modulo-1 constraint phase.

In this case, the expression (19a) may be written as:

f⁡(p)=14⁢pH⁢Sp+Re⁢{𝒥2⁢pH⁢S⁢1NR-pH⁢c*}+Re⁢{𝒥1NRT⁢c*}+14⁢1NRT⁢S⁢1NR

The function f(p) is a non-convex quadratic function about P, and with the MM method that is a sequential convex optimization method, a compact upper bounding function of f(p) may be obtained. First, a tractable compact upper bounding function is found and expressed as:

pH⁢Sp≤pH⁢Tp-2⁢Re⁢{pH(T-S)⁢p(ℓ)}+(p(ℓ))H)⁢(T-S)⁢p(ℓ)(20)

T=λmaxI, λmaxis a maximum eigenvalue of S, and the expression (20) is substituted into the problemto obtain a problem, whose specific expression is:

𝒫9(ℓ)maxpRe⁢{pH⁢a(ℓ)}(21⁢a)s.t.pn∈{e𝒥ϕ|ϕ∈[0,2⁢π]},∀n(21⁢b)where=(λmaxINR−S)+2c*−. Additionally, in the target function of the problem, terms unrelated to the variable p are left out. The problem, can be solved by alternately optimizing the vectors a and p. Moreover, in each time of iteration, the vectors a and p may be obtained through a closed-form solution.

FIG.3gives a flow of an algorithm of solving a Lorentzian constraint phase weight based on an MM method, and a detailed process of the algorithm is specifically:

Step 1, initializeand, and set an iteration index1=0 and a threshold ξ1.

Step 2, give, and calculate=and ∀n.

Step 3, give, and calculate=(λmaxINR−S)+2c*−.

Step 4, calculate the system sum rate, and if a difference between the (1)thsystem sum rateand the (1+1)thsystem sum rateis less than the given threshold ξ1, jump out of the loop, usingas a solution meeting the Lorentzian constraint phase weight under the system sum rate maximization criterion when the baseband beamforming matrix is given: otherwise1=1+1, and perform steps 2 to 4 again.

As channel state information in a communication system is changed, the base station side dynamically implements, according to updated channel state information, near-field broadband large-scale MIMO uplink transmission assisted by a dynamic metasurface antenna with system sum rate maximization as a criterion, thereby dynamically updating transmission, to ensure transmission performance.

Any content not described in detail in the present invention is a technology publicly known by a person skilled in the art. The specific exemplary embodiments of the present invention are described in detail above. It should be understood that, a person of ordinary skill in the art may make many modifications and changes according to the idea of the present invention without creative effort. Therefore, any technical solution that may be obtained by a person skilled in the art through logic analysis, reasoning or limited experiments based on the existing technology according to the idea of the present invention should fall within the protection scope determining by the claims.