Patent ID: 12244370

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present disclosure is further explained below with reference to the accompanying drawings.

In a satellite massive MIMO integrated sensing and communication method, a satellite end is equipped with a massive MIMO antenna array which simultaneously serves multiple users and detects multiple targets, as shown inFIG.1. Communication and sensing use the same spectrum resources and the same hardware platform, and integrated sensing and communication is implemented by transmitting a signal to focus on communication or sensing, where a communication process includes channel estimation and data transmission, and a sensing process includes target search by radar and beam forming. The satellite end estimates statistical status information of electromagnetic wave propagation according to received uplink and downlink pilot signals, where for the communication process, the statistical status information of electromagnetic wave propagation is a channel gain and a channel direction vector between the satellite end and user terminals; and for the sensing process, the statistical status information of electromagnetic wave propagation is angles of departure of the targets.

According to the statistical status information of electromagnetic wave propagation, the satellite end transmits a directional beam to a detection target and a downlink signal to each user terminal by means of integrated sensing and communication precoding, where the integrated sensing and communication precoding is a hybrid precoding scheme based on an energy efficiency maximization principle and a convex optimization algorithm. Each antenna unit of the massive MIMO antenna array sends signals independently by using a fully digital or analog or hybrid transmission manner. In the process of simultaneously implementing communication and sensing, the performance of communication and sensing is weighed by introduction of a weighting coefficient, so as to realize a flexible switch between wireless communication and target sensing functions. During the dynamic movement of the satellite and the user terminals as well as the targets, with the change in the statistical status information of electromagnetic wave propagation between the satellite and the user terminals as well as the targets, the integrated sensing and communication precoding is updated.

Specifically, as shown inFIG.2, the satellite end is equipped with a massive MIMO antenna array which includes more than hundreds of antenna units, where each antenna unit may be a unipolar or multipolar antenna. The array structure is a uniform surface array, where the numbers of antennas in the x and y directions are Ntxand Ntyrespectively, and then a total number of the antennas is Nt=Ntx×Nty; and a spacing between the antennas is r. Further, a hybrid analog/digital transmitter is used to serve K single antenna users, and each user terminal uses a fully digital receiver. Multiple targets are detected simultaneously, and the number of RF chains required by the transmitter is Mt, where K≤Mt≤Nt.

Considering frequency selectivity of a wideband massive MIMO low earth orbit satellite system, inter-symbol interference is reduced by means of Orthogonal Frequency Division Multiplexing (OFDM). That is, M sub-carriers are used in total for a signal bandwidth Bw, and then the spacing between the sub-carriers is Δb=Bw/M. Thus, the frequency of the mth sub-carrier is:

fm=(m-M+12)⁢ΔB,m=1,2,…,M.(1)
1. Communication Module
(1) Modeling of Statistical Properties of Multipath Channel Propagation that Considers Beam Squint

It is noted that the satellite altitude is much higher than the scatterers around the terrestrial user terminals. If there are in total Lkpropagation paths for the kth user, the propagation paths are set to have the same angle ϑk=(ϑkx, ϑky) of departure, where ϑkxand ϑkydenote angles of departure in the x and y directions respectively. If a propagation delay on the lth path is τk,l, a total delay τk,l,ny,nyto the (nx, ny)th element in the antenna array is:
τk,l,nx,ny=τk,l+nx,ny(ϑk),  (2)

The second term in the equation refers to a time delay from the (l,l)th element to the (nx, ny)th element in the antenna array for the kth user, namely:

τnx,ny(ϑk)=△r⁡((nx-1)⁢ϑkx+(ny-1)⁢ϑky)c,(3)
where nx∈{1,2, . . . , Ntx} and ny∈{1,2, . . . , Nty} denote antenna unit numbers in the x and y directions respectively, and c denotes the velocity of light.

Assuming that a channel gain of the lth path for the kth user is ak,land the Doppler gain is vk,l, a downlink channel space-frequency response hk,nx,ny(t, f) between the kth user and the (nx, ny)th element of the low earth orbit satellite-end antenna array at the time t and the frequency f is:

hk,nx,ny(t,f)=∑l=1Lkαk,l⁢exp⁢{𝒿2⁢π[tvk,l-f⁢τk,l]}⁢exp⁢{-𝒿2π⁡(fc+f)⁢γnx,ny(ϑk)},(4)
where exp {□} denotes an exponential operator, ø=√{square root over (−1)}, and fcdenotes the carrier frequency. The above equation is rearranged and vectorized to obtain the following baseband downlink channel space-frequency response vector after time-frequency synchronization:
hk(t,f)=vk(f)gk(t,f),  (5)
where the channel gain gk(t,f) follows the Rician distribution with a parameter being the Rician parameter κkand its energy meets E{|gk(t, f)|2}=γk, γkbeing the channel energy between the satellite and the kth user and E{┘} denoting an operator for evaluation of expectation; and vk(f) is an array response vector and meets the following formula:
vk(f)□v(f,ϑk)=vkx(f)⊗vky(f)=vx(f,ϑkx)⊗vy(f,ϑky)∈□Nt×1,  (6)
where □m×ndenotes a subspace with dimensions of m×n, and ⊗ denotes the Kronecker product; and in the case of d∈D□{x, y}, there is the following formula:

vkd(f)=△1Ntd[1⁢exp⁢{-𝒿⁢ϕ⁡(f,ϑkd)}⁢…⁢exp⁢{-𝒿ϕ⁡(f,ϑkd)⁢(Ntd-1)}]T,(7)
where

ϕ⁡(f,ϑkd)=△2⁢π⁢(fc+f)⁢rc⁢ϑkd
and the superscript T denotes a transpose operator; and v (f, ϑk) denotes an array response associated with the frequency and the angle of departure.

For ease of description, considering each coherent time interval, a time parameter t is omitted. In addition, at the mth sub-carrier with the frequency of fm, let hk[m]┘hk(fm), vk[m]┘vk(fm), and gk[m]┘gk(fm). Thus, a corresponding channel response vector may be expressed as follows:
hk[m]=vk[m]gk[m].(8)
(2) Consideration of Downlink Channel Transmission Signals

At the mth sub-carrier, a data vector is s[m]=[s1[m], s2[m], . . . , sK[m]]T∈□K×1, where sk[m] is a transmission symbol for the kth user. Then, a signal transmission vector is x[m]=B[m]s[m]∈□Nt×1, where B[m] is a hybrid precoding matrix including constant-modulus RF precoders V[m]∈□Nt×Mtand baseband precoders W[m]=[w1[m], w2[m], . . . , wK[m]]∈□Mt×K, where wk[m] is a baseband precoding vector for the kth user. Then, B[m]=V[m]W[m]=[b1[m], b2[m], . . . , bK[m]]∈□Nt×Kis obtained, where bk[m]=V[m]wk[m]∈□Nt×1is a precoding vector for the kth user.

The signal-to-interference-plus-noise ratio SINR, the rate Rk, and the energy efficiency EE between the satellite and the kth user are respectively defined as follows:

SINRk[m]=△❘"\[LeftBracketingBar]"bkH[m]⁢hk[m]❘"\[RightBracketingBar]"2∑ℓ≠k❘"\[LeftBracketingBar]"bℓH[m]⁢hk[m]❘"\[RightBracketingBar]"2+N0,(9)Rk=∑m=1MΔB⁢Rk[m]=∑m=1MΔB⁢𝔼⁢{log⁡(1+SINRk[m])},(10)EE=∑k=1KRkPtotal.(11)
where

Ptotal=∑k=1K∑m=1Mξ⁢bi[m]22+Pi
is a total transmit power,

1/ξ
being the effectiveness of an amplifier, Ptbeing the static power consumption, and ∥□∥2denoting the norm of vector 2; N0denotes the noise power; bl[m] denotes a precoding vector for the lth user; the superscript H is a matrix operator; SINRk[m] denotes the signal-to-interference-plus-noise ratio of the kth user at the mth sub-carrier; and Rk[m] denotes the rate of the kth user at the mth sub-carrier.
2. Sensing Module

A subarray MIMO radar designed in conjunction with a hybrid precoding architecture is considered, and at the mth sub-carrier, the mode of an omnidirectional beam sent by the radar is:
Qm(ϑ)=vmH(ϑ)X[m]vm(ϑ),∀ϑ,  (12)
where vmH(ϑ)□v(fm, ϑ) denotes an array response vector with the angle of departure of ϑ, v(fm, ϑ) denotes an array response associated with the frequency and the angle of departure, ϑ=(ϑx, ϑy) denotes the angle of departure, ϑxand ϑydenote the angles of departure in the x and y directions respectively, and the autocorrelation matrix X[m] is defined as follows:
X[m]=E{x[m]xH[m]}=V[m]W[m]WH[m]VH[m].(13)

Assuming that there are Pr≤K detection targets, an optimal subarray radar precoder may be expressed as follows:
Brad[m]=blkdiag{u1[m], u2[m], . . . , uPt[m]}∈□Nt×Pr,  (14)
where up[m]∈□Nt/Pr×1denotes elements at corresponding positions in vp[m], blkdiag{□} denotes a block diagonal array, p∈{1,2, . . . , Pr}, vp[m] denotes an array response associated with the frequency and the angle of departure, and Prdenotes the number of the targets.
3. Design of a Hybrid Precoder Sensing Beam Squint

A hybrid precoder sensing beam squint is designed for the wideband downlink satellite massive MIMO integrated sensing and communication system, so as to ensure the radar sensing performance while seeking maximum energy efficiency of communication, where the following optimization problem P1is considered:

𝒫1:maximize{V❘m},W[m],U[m]}m=1M⁢∑k=1KRkPtotal(15)s.t.∑k=1K∑m=1MV[m]⁢wk[m]22≤P,V[m]∈𝒮,∀m,V[m]⁢W[m]-Brad[m]⁢U[m]F2≤ε,∀m,U[m]⁢UH[m]=IPr,∀m,

In the foregoing formula, P denotes the power budget; U[m] is an auxiliary unitary matrix introduced at the mth sub-carrier, which enables the optimal radar precoder and the hybrid precoder to match in dimensions, and this operation does not affect the beam mode of the radar; ε is an Euclidean distance tolerance term between the digital/analog hybrid precoder and the radar precoder (capable of rotation); IPris a unit matrix of the order Pr×Pr; and ∥_∥Fdenotes the Frobenius-norm of a matrix. In addition, S□{SFC, SPC} denotes the constraints the analog precoders need to satisfy, where specifically speaking, SFC, SPCrespectively denote the constraints which the analog precoders having fully connected and partially connected structures need to satisfy, that is:

𝒮PC=△{V❘❘"\[LeftBracketingBar]"[V]i,j❘"\[RightBracketingBar]"=1,∀i,j},(16)𝒮PC=△{V❘❘"\[LeftBracketingBar]"[V]i,j❘"\[RightBracketingBar]"=1,∀i,∀j=⌈iNg⌉},(17)
where Ng=Nt/Mtdenotes the number of groups.

Step 1: For the optimization problem P1, the product of the analog and digital precoders is regarded as a whole and irrelevant constraints are disregarded for the moment, to obtain a fully digital precoding problem P2:

𝒫2:maximize{B[m]}m=1M⁢∑k=1KRkPtotal(18)s.t.∑k=1K∑m=1Mbk[m]22≤P.

Step 2: Because it is difficult to estimate an accurate value of Rk[m], considering statistical properties of wave propagation, its tight bound is used as a replacement, namely:

Rk[m]≤R_k[m]=△log(1+γk⁢❘"\[LeftBracketingBar]"vkH[m]⁢bk[m]❘"\[RightBracketingBar]"2∑ℓ≠kγk⁢❘"\[LeftBracketingBar]"vkH[m]⁢bℓ[m]❘"\[RightBracketingBar]"2+N0).(19)

Step 3: Let B(i)={B(i)[m]}m=1Mbe a precoding matrix set of all the sub-carriers, and the problem P2is transformed into a series of sub-problems P3(i), i=1,2, . . . by means of the Dinkelbach algorithm, where i=1, 2, . . . :

P3(i):maximizeℬ(i)⁢F⁡(B(i),η(i))=∑k=1KR_k(B(i))-η(i)⁢Ptotal(B(i))(20)s.t.∑k=1K∑m=1Mbk(i)[m]22≤P.
where the auxiliary variable η(i)meets the following equation:

η(i)=∑k=1KR_k(B(i-1))Ptotal(B(i-1)).(21)

Step 4: The ith sub-problem is taken into consideration, and the serial number i is omitted for convenience. Let bk[m]=bk,mand vk[m]=vk,m, and then the problem P3(i)may be expressed as follows:

P3:maximizeℬ⁢F⁡(ℬ)=∑k=1K∑m=1Mlog(1+γk⁢❘"\[LeftBracketingBar]"vk,mH⁢bk,m❘"\[RightBracketingBar]"2∑ℓ=kγk⁢❘"\[LeftBracketingBar]"vk,mH⁢bk,m❘"\[RightBracketingBar]"2+N0)-η⁡(ξ⁢bk,m22+P1)(22)s.t.∑k=1K∑m=1Mbk,m22≤P.

Step 5: By introducing the auxiliary variable λ={λk,m}k=1,m=1K,Mand by means of Lagrangian dual transformation, the foregoing problem is transformed into P4:

P4:maximizeℬ,λ⁢F⁡(ℬ,λ)=∑k=1K∑m=1Mlog⁡(1+λk,m)+(1+λk,m)⁢γk⁢❘"\[LeftBracketingBar]"vk,mH⁢bk,m❘"\[RightBracketingBar]"2∑ℓ=1Kγk⁢❘"\[LeftBracketingBar]"vk,mH⁢bℓ,m❘"\[RightBracketingBar]"2+N0-λk,m-η⁡(ξ⁢bk,m22+P1)(23)s.t.∑k=1K∑m=1Mbk,m22≤P.

It should be noted that, when B is fixed, F (B, λ) is a concave function for the variable λk,m; and let ϑF/ϑλk,m=0, to obtain:

λk,mopt=γk⁢❘"\[LeftBracketingBar]"vk,mH⁢bk,m❘"\[RightBracketingBar]"2∑ℓ≠kγk⁢❘"\[LeftBracketingBar]"vk,mH⁢bℓ,m❘"\[RightBracketingBar]"2+N0.(24)

Step 6: By introducing the auxiliary variable ρ={ρk,m}k=1,m=1K,Mand by means of quadratic transformation, the problem P4is transformed into:

P5:maximizeB,λ,ρ⁢F⁡(B,λ,ρ)(25)s.t.∑k=1K∑m=1Mbk,m22≤P.where:(26)F⁡(B,λ,ρ)=∑k=1K∑m=1Mlog⁡(1+λk,m)-λk,m+2⁢(1+λk,m)⁢γk⁢ℜ⁢{bk,mH⁢vk,m⁢ρk,m}-❘"\[LeftBracketingBar]"ρk,m❘"\[RightBracketingBar]"2⁢(∑ℓ=1Kγk⁢❘"\[LeftBracketingBar]"vk,mH⁢bℓ,m❘"\[RightBracketingBar]"2+N0)-η⁡(ξ⁢bk,m22+P1).Let⁢∂F/∂ρk,m=0,to⁢obtain:(27)ρk,mopt=(1+λk,m)⁢γk⁢vk,mH⁢bk,m∑ℓ=1Kγk⁢❘"\[LeftBracketingBar]"vk,mH⁢bℓ,m❘"\[RightBracketingBar]"2+N0.

Step 7: It is noted that when (η, λ, ρ) is fixed, the target function of the problem P5is convex for the variable bk,m; and then the Lagrangian operator method may be used for evaluation. Specifically, the Lagrange multiplier t is introduced, and then the Lagrange function of the problem P5may be expressed as follows:

L⁡(B,λ,ρ,t)=F⁡(B,λ,ρ)+t⁡(∑k=1K∑m=1Mbk,m22-P).(28)

From KKT conditions, the following formulas can be obtained:

bk,mopt=(∑ℓ=1K❘"\[LeftBracketingBar]"ρℓ,m❘"\[RightBracketingBar]"2⁢γℓ⁢vℓ,m⁢vℓ,mH+(ηξ+t)⁢I)-1⁢(1+λk,m)⁢γk⁢ρk,m⁢vk,m,(29)t=argmint≥0∑k=1K∑m=1Mbk,mopt22≤P.(30)

Step 8: For the mth sub-carrier, after an equivalent fully digital pre-coding matrix Bcom[m] is obtained, a weighting coefficient ζ is introduced to weigh the performance of communication and sensing modules, where a corresponding minimization problem for a weighted sum is:

Qim:minimizeV[m],W[m],U[m]⁢f⁡(V[m],W[m],U[m])=ζ⁢V[m]⁢W[m]-Bcom[m]F2+(1-ζ)⁢V[m]⁢W[m]-Brad[m]⁢U[m]F2(31)s.t.V[m]∈S,∀m,Bcom[m]F2=V[m]⁢W[m]F2,U[m]⁢UH[m]=IPr,∀m,
where ζ denotes the weight. For any sub-carrier m, analog and digital precoding vectors can be obtained by means of iterative solution, and the mark number m is omitted in the following description.

Step 9: For the analog precoders having the fully connected structure: (4) for the fixed V and W, the problem Q1is transformed into:

Q2:minimizeU⁢VW-Brad⁢UF2(32)s.t.UUH=IPr,
A solution to the foregoing problem can be obtained by means of singular value decomposition, namely:
U=QIPr×KR,  (33)
where Q and R are results after singular value decomposition is performed for BradHVW, that is, QΣR=BradHVW, Q and R being unitary matrixes and Σ being a diagonal matrix; and IPr×K=[IPr,0] is a sparse matrix.

(5) For the fixed V and U, the problem Q1is transformed into:

Q3:minimizeW⁢ζ⁢VW-BcomF2+(1-ζ)⁢VW-Brad⁢UF2(34)s.t.BcomF2=VWF2,

It is noted that, for the problem Q3, its target function is expressed as a weighted sum of two F norms. Let the auxiliary matrixes A=[√{square root over (ζ)}VT, √{square root over (1−ζ)}VT]T∈□2Nt×Mtand C=[√{square root over (ζ)}BcomT, √{square root over (1−ζ)}UTBradT]T∈□2Nt×K, AHA=VHV can be easily deduced. Thus, the problem Q3can be transformed into:

Q4:minimizeW⁢AW-CF2(35)s.t.BcomF2=AWF2,
Then, the digital precoder W can be updated as follows:

W=(AH⁢A)-1⁢AH⁢C=(VH⁢V)-1⁢AH⁢C,(36)W=BcomFVWF⁢W.(37)

(6) Let G=[√{square root over (ζ)}W, √{square root over (−1ζ)}W]∈□M1×2Kand T=[√{square root over (ζ)}Bcom, √{square root over (1−ζ)}BradU]∈□Nt×2Kbe auxiliary matrixes, and for the fixed W and U, the problem Q1is transformed into:

Q5:minimizeV⁢VG-TF2(38)s.t.V∈𝒮FC,

Let the auxiliary matrix Y=GGH, where its maximum characteristic value is λmax(Y); and then the problem Q5is transformed into:
V=exp{−ø∠ZT},  (39)
where Z=GTH−(Y−λmax(Y)IMt)VHis an auxiliary matrix, and ∠ denotes an operator for evaluation of an angle.

Steps (1) to (3) are repeated till the target function f converges.

Step 10: For the analog precoders having the partially connected structure, the (i,j)th element thereof is [V]i,j=exp{øϕi,j}, and ∀i, j=┌i/Ng┐, where ┌□┐ denotes an operator for evaluation of an upper bound, ϕi,jis an angle of the (i,j)th element in the matrix, and a corresponding analog precoding matrix meets

VWF2=Ng⁢WF2=BcomF2.

(4) For the fixed V and W, the problem Q1is transformed into:

Q6:minimizeU⁢VW-Brad⁢UF2(40)s.t.UUH=IPr,
A solution to the foregoing problem can be obtained by means of singular value decomposition, namely:
U=QIPr×KR,  (41)
where Q and R are results after singular value decomposition is performed for BradHVW, that is, QΣR=BradHVW, Q and R being unitary matrixes and Σ being a diagonal matrix; and IPr×k=[Ipr,0] is a sparse matrix.

(5) Let A=[√{square root over (ζ)}VT, √{square root over (1−ζ)}VT]T∈□2Nt×Mtand C=[√{square root over (ζ)}BcomT, √{square root over (1−ζ)}UTBradT]T∈□2Nt×Kbe auxiliary matrixes, and for the fixed V and U, the problem Q1may be transformed into:

Q7:minimizeW⁢AH⁢C-WF2(42)s.t.WF=BcomFNg,
Then, the digital precoder W can be updated as follows:

W=BcomFNg⁢AH⁢CAH⁢CF.(43)

(6) Let the auxiliary matrixes a=[√{square root over (ζ)}[Bcom]i,:, √{square root over (1−ζ)}[BradU]i,:] and p=[√{square root over (ζ)}[W]j,:, √{square root over (1−ζ)}[W]j,:], where [□]i,:denotes the ith row of the matrix and [□]j,:denotes the jth row of the matrix; and for the fixed W and U, the problem Q1is transformed into:

Q8:minimizev⁢a-exp⁢{⌀ϕi,j}⁢p22(44)s.t.V∈SPC,
Then, a solution to this problem may be expressed as follows:

[V]i,j=exp⁢{⌀∠⁡(apH)},∀i,∀j=⌈iNg⌉.(45)
Steps (1) to (3) are repeated till the target function f converges.

During the dynamic movement of the satellite and the user terminals as well as the targets, with the change in the statistical properties of wave propagation between the satellite and the user terminals as well as the targets, the foregoing integrated sensing and communication hybrid precoding process is dynamically implemented, to form an updated integrated sensing and communication hybrid precoding method.

The above merely describes preferred embodiments of the present disclosure. It should be noted that, several improvements and modifications may be made by those of ordinary skill in the art without departing from the principle of the present disclosure, and these improvements and modifications should also be construed as falling within the protection scope of the present disclosure.