CN111988073B - Design method for semi-dynamic subarray mixed structure of broadband millimeter wave communication system - Google Patents
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Abstract
The invention provides a design method for a semi-dynamic subarray mixed structure of a broadband millimeter wave communication system. The method comprises the following steps: a semi-dynamic subarray (PDS) structure for allocating subarrays to the radio frequency link according to channel statistical information is provided, and compared with the existing full-dynamic subarray (FDS) structure, the PDS structure can greatly reduce the intensive deployment cost of the 5G base station; simplifying the sub-array design problem by using constant modulus constraint, and providing an alternative minimization-based sub-array design (AMD) algorithm for sub-array distribution; an optimization (HP) algorithm based on block coordinate descent is provided for effectively designing a hybrid precoding matrix of a broadband millimeter wave multiple-input multiple-output (MIMO) system so as to maximize the frequency efficiency of the system. The invention provides a PDS structure with lower hardware cost on the basis of an FDS structure and provides an AMD algorithm for designing a subarray structure according to channel statistical information and an HP algorithm for designing a system hybrid precoding matrix according to channel instantaneous information aiming at the PDS structure for a broadband millimeter wave MIMO system.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and relates to a novel semi-dynamic subarray mixed structure and a corresponding subarray allocation and mixed precoding optimization algorithm, which are provided in the field of broadband millimeter wave multiple-input multiple-output (MIMO).
Background
Wireless spectrum compaction promotes the integration of millimeter wave and massive multiple-input multiple-output, MIMO, technologies in next generation cellular systems. Millimeter wave signals operate in the 30-300GHz band and therefore may provide a wider bandwidth than current cellular systems. The wavelength of the radio signals in the millimeter wave band offers the possibility of equipping the transceiver with a large number of antennas, so that a high spectral efficiency can be achieved. In addition, massive MIMO can serve a group of users simultaneously through multiplexing and overcome severe path loss of millimeter wave channels through array gain provided by the transceiving end precoding technology.
However, it is impractical to apply the traditional all-digital FD precoding techniques in millimeter wave and massive MIMO systems. Since in this configuration a dedicated radio frequency RF chain is required for each antenna, resulting in high cost and high power consumption. In order to overcome the drawbacks of the FD structure, researchers have proposed and started to study the hybrid structure extensively. The goal of the hybrid architecture is to trade off between efficiency, hardware cost and power consumption. Furthermore, the hybrid structure reduces the number of RF chains by dividing the precoding process into two parts, analog precoding and digital precoding.
As shown in fig. 1, the existing hybrid structure schemes can be divided into two categories: fully connected hybrid structures and subarray connected hybrid structures. In a fully connected hybrid configuration, each RF chain is connected to all antennas through phase shifters, as shown in fig. 1 (a). In particular if the number of RF chains is NrfThe number of transmitting antennas is NtThen the number of phase shifters is NrfNt. In a subarray connected hybrid structure, each subarray is connected to only one RF chain. Thus, the number of phase shifters is equal to the number of transmit antennas, i.e., Nt. The sub-array connection hybrid structure can be divided into two types: fixed subarrays and fully dynamic subarrays, as shown in fig. 1(b) and 1 (c). In a fixed subarray, the antenna connected to each RF chain is fixed and does not vary with channel variations. Unlike the fixed subarray structure, the fully dynamic subarray FDS structure dynamically updates antenna allocation according to channel fluctuations to improve system transmission performance. In addition, the FDS architecture uses switches for antenna selection, the number of which is equal to the number of transmit antennas, i.e., Nt。
In recent years, fully connected hybrid structures have been intensively studied. Based on the sparsity of a millimeter wave channel, [1] a low-complexity hybrid precoding algorithm is provided, and the frequency efficiency of a millimeter wave MIMO system is improved to the maximum extent by using improved orthogonal matching pursuit OMP. In addition, the alternating minimization algorithm is also used to minimize the Frobenius norm [2] of the difference between FD and hybrid precoding matrix. Unlike the heuristic method, the hybrid precoding problem can be solved directly by using a penalty dual decomposition algorithm to obtain a KKT (Karush-Kuhn-Tucker) solution. However, in the fully-connected hybrid structure, the number of phase shifters linearly increases as the number of antennas increases, resulting in excessive hardware cost and power consumption.
The number of phase shifters in a sub-array connected hybrid structure is significantly reduced compared to a fully connected hybrid structure. Therefore, the sub-array connection hybrid structure is considered as a promising candidate hybrid structure of the massive MIMO wireless communication system. [4] Aiming at a subarray connection mixed structure of a millimeter wave MIMO wireless communication system, a mixed precoding method based on continuous interference elimination is provided. In addition, an effective hybrid precoding algorithm is proposed [5] for the millimeter wave system based on the multi-subarray hybrid structure. Although most studies at present only consider narrow-band millimeter wave communication with a fixed sub-array mixed structure at the transmitter end, the sub-array connection structure mixed precoding technology in the Orthogonal Frequency Division Multiplexing (OFDM) -based broadband millimeter wave MIMO wireless communication system is considered [6 ]. In addition, in order to improve the system frequency efficiency, [6] an FDS hybrid structure is also proposed, and an algorithm for dynamically allocating antenna points is proposed, but the algorithm belongs to one of greedy algorithms. Therefore, [7] proposes a dynamic sub-array allocation (DSD) algorithm using an analog precoding matrix to solve this problem. However, the DSD algorithm is computationally complex due to the presence of the computation of the high-dimensional complex matrix.
Although the use of FDS hybrid architectures has been considered in prior research efforts to improve the spectral efficiency of the system, the architecture is difficult to implement in hardware. This is because the number of switches increases linearly with the number of transmit antennas in the FDS hybrid structure, resulting in higher hardware cost, insertion loss, and computational complexity. The present invention therefore proposes a more practical semi-dynamic sub-array connection (PDS) hybrid architecture. In this configuration, the set of antennas in each sub-array is fixed, but the sub-arrays connected to each RF chain are dynamically varied. The invention dynamically adjusts the sub-array distribution of each RF chain through the switch according to the statistical information of the channel, thereby improving the transmission performance of the communication system. The number of switches used in the PDS hybrid is the same as the number of sub-arrays and is significantly less than the number of switches in the FDS hybrid. Therefore, the PDS structure provided by the invention has more potential in the aspect of hardware implementation. Furthermore, most current research work on hybrid precoding in millimeter wave channels only considers narrowband communication scenarios. However, practical millimeter wave systems typically operate in a broadband millimeter wave scenario with frequency selectivity, and beam squint typically needs to be considered in this communication scenario. Therefore, it is necessary to consider the effect of beam squint in the wideband millimeter wave MIMO system, and an effective hybrid precoding algorithm is proposed for the PDS hybrid structure.
[1]O.E.Ayach,S.Rajagopal,S.Abu-Surra,Z.Pi,and R.W.Heath,“Spatially sparse precoding in millimeter wave MIMO systems,”IEEE Trans.Wireless Commun.,vol.13,no.3,pp.1499-1513,Mar.2014.
[2]X.Yu,J.Shen,J.Zhang,and K.B.Letaief,“Alternating minimization algorithms for hybrid precoding in millimeter wave MIMO systems,”IEEE J.Sel.Topics Signal Process.,vol.10,no.3,pp.485-500,Apr.2016.
[3]Q.Shi and M.Hong,“Spectral efficiency optimization for millimeter wave multiuser MIMO systems,”IEEE J.Sel.Topics Signal Process.,vol.12,no.3,pp.455-468,June 2018.
[4]X.Gao,L.Dai,S.Han,C.I,and R.W.Heath,“Energy-efficient hybrid analog and digital precoding for mmWave MIMO systems with large antenna arrays,”IEEE J.Sel.Areas Commun.,vol.34,no.4,pp.998-1009,Apr.2016.
[5]J.Zhang,Y.Huang,T.Yu,J.Wang,and M.Xiao,“Hybrid precoding for multi-subarray millimeter-wave communication systems,”IEEE Wireless Commun.Lett.,vol.7,no.3,pp.440-443,June 2018.
[6]S.Park,A.Alkhateeb,and R.W.Heath,“Dynamic subarrays for hybrid precoding in wideband mmWave MIMO systems,”IEEE Trans.Wireless Commun.,vol.16,n0.5,pp.2907-2920,May 2017.
[7]J.Jin,C.Xiao,W.Chen,andY.Wu,“Channel-statistics-based hybrid precoding for millimeter-wave MIMO systems with dynamic subarrays,”IEEE Trans.Commun.,vol.67,no.6,pp.3991-4003,June 2019.
[8]G.Li,H.Zhao,and H.Hui,“Beam squint compensation for hybrid precoding in millimetre-wave communication systems,”Electron.Lett.,vol.54,no.14,pp.905-907,Jul.2018.
Disclosure of Invention
The technical problem is as follows: in order to overcome the defects of the existing mixed structure, the invention provides a novel semi-dynamic subarray mixed structure and a corresponding subarray allocation and mixed pre-coding optimization algorithm aiming at a broadband millimeter wave MIMO communication scene, so that the hardware cost of a transmitting end is reduced, and the communication performance of a system is improved.
The technical scheme is as follows: the invention relates to a design method for a semi-dynamic subarray mixed structure of a broadband millimeter wave communication system, which comprises the following steps:
step 1: a semi-dynamic sub-array PDS mixed structure is provided, a system model and a channel model are established for a broadband millimeter wave multiple-input multiple-output MIMO communication scene, an optimization target for maximizing the system frequency effect is provided, and an optimization problem is established;
step 2: analyzing the optimization problem in the step 1, and providing an alternative minimization AMD algorithm for dynamically allocating the subarrays according to channel statistical information to obtain a subarray allocation matrix;
and step 3: on the basis of obtaining the sub-array distribution matrix in the step 2, a hybrid precoding algorithm according to the channel instantaneous information is further provided, and the hybrid precoding matrix is compensated in a digital domain by considering the influence of beam squint.
Wherein:
the establishing of the system model and the channel model in the step 1 specifically comprises the following steps:
step 1.1: establishing a broadband millimeter wave MIMO system model aiming at a semi-dynamic subarray PDS mixed structure:
as shown in fig. 2, a point-to-point broadband millimeter wave MIMO is considered, a modulation mode of broadband orthogonal frequency division multiplexing OFDM is adopted, and the total number of subcarriers is K; let the transmitted symbol vector on the k sub-carrier be skSatisfy the following requirementsNsIs the number of data streams, E [ ·]Expecting to operate; the digital precoding matrix on the k sub-carrier isThe number of RF chains is Nrf(ii) a Count total number of antennasIs Nt,NtEach antenna is divided into M sub-arrays, and each sub-array is Na=Nta/M antenna; recording the set of the sub-array of the j-th RF chain connection as SjSince M sub-arrays are divided into NrfA subset of
Where, U represents the union of sets. In addition, each subarray can only be connected with one RF chain, namely the subarray set connected with the ith RF chain is not intersected with the subarray set connected with the jth RF chain, then
Where n represents the intersection of the sets. At least one subarray may be selected for each RF chain, then
WhereinRepresenting the empty set, the analog precoding matrix realized by the phase shifter isSince the phase shifter only changes the phase of the signal and not the amplitude of the signal, the analog precoding matrixThere is a constant modulus constraint
Wherein v isijAnalog precoding representing the connection of the ith sub-array to the jth RF chainThe matrix, |, represents the modulus of the vector,is that the indication function is defined as
Wherein 1 represents a matrix in which all elements are 1; 0 denotes a matrix in which all elements are 0.
The transmitting end thus transmits symbols expressed as
xk=VFksk,k∈{1,2,…,K} (52)
In addition, there is a transmit power constraint
Wherein P istotRepresenting the total transmit power, | · | | non-woven phosphorFIs the F norm of the matrix;
step 1.2: establishing a millimeter wave MIMO channel model:
the geometric channel model has L beam clusters, and the first (L is more than or equal to 1 and less than or equal to L) cluster has RlA scattering path, under the model, the channel matrix of the d-th time delay is
WhereinφR,lAnd phiT,lRespectively representing parameters representing time delay, arrival angle, departure angleDenotes complex path gain, relative time delay, r-th cluster in the l-th clusterlRelative arrival and departure angles of the scattering paths, p (τ)With a presentation period of TsOf the pulse shaping function at τ, and, in addition, aR(. and a)TDenotes the transmit and receive array response vector, denoted as
Wherein N is the number of corresponding antennas, λ is the carrier wavelength, and d' is the distance between the antennas; based on the channel model, when the influence of beam skew is not considered, the channel matrix on the k sub-carrier is
Wherein D is the pilot length.
Considering the effect of beam squint, the channel matrix on the k-th subcarrier is
Wherein
step 1.3: an optimization target for maximizing the system frequency effect is provided, and an optimization problem is established
The sum-rate expression of the millimeter wave MIMO system is
Where det (·) is the determinant for matrix calculation, and I is the unit matrix. To maximize the sum rate of the system, dynamic subarray junctions are implemented
Joint design of the structure and precoding matrix, σ2Is the noise variance;
because the channel change is fast, the dynamic subarray structure design is carried out by utilizing statistical channel information, and the subarray distribution problem exists
s.t. is a condition constrained to
In addition, the design of precoding by using instantaneous channel information has the problem of hybrid precoding
Where det (-) is the determinant of the matrix. Therefore, the optimization problem with the maximum system resultant rate can be split into the above two sub-problems
The problem is solved.
The step 2 comprises the following steps:
step 2.1: analyzing and converting an optimization problem:
for the first sub-problem, note { S }jDenotes the position of the non-zero entries of the analog precoding matrix V, so the problem can be translated into
Define V ═ AB, where a is a block diagonal matrix containing phase shifter information, and the diagonal block matrix is a1,…,am,…,aMI.e. a ═ diag (a)1,…,am,…,aM) WhereinAnalog precoding representing the mth sub-array, with
am(i)=1,m=1,2,…,M,i=1,2,…,NA (64)
The power constraint may be rewritten as
At this point an equivalent channel is introduced
The sub-array allocation problem can be equated with
Where tr (-) denotes the trace of the matrix. By using the property of matrix a elements modulo 1, it is possible to transform the matrix B only in relation to it,
namely, it is
step 2.2: and (3) proposing an AMD algorithm of subarray design:
firstly, solving the unconstrained optimal solution, then projecting the solved solution into a constrained space to obtain a subarray distribution matrix B,
solved by SVD decomposition, pairPerforming SVD to obtainSuppose thatComprises aN of (2)rfA principal eigenvector, i.e.The optimal solution is
B*=UQQ (71)
then considering the constraints of the original problem, Q needs to be updated to minimize B and B*F norm of (1) then obtainingTo as follows
Where μ represents a set of unitary matrices, the problem is a stepwise solution, where the variable B is updated by solving the problem
The solution to this problem is
The variable Q is updated by solving the following problem
The solution of the problem is
Updating the variables B and Q through alternate minimization to obtain a solution of the subarray connection matrix B; the AMD algorithm is designed for the subarrays corresponding to the semi-dynamic subarray mixed structure.
The method comprises the following steps in step 3:
step 3.1: on the basis of the subarray distribution matrix, the optimization problem is converted:
upon obtaining the sub-matrix allocation matrix, for the second sub-problem
xk=ABFk,k=1,2,…,K (78)
An enhanced Lagrange punishment method is utilized, and K multiplier variables V are introducedkAnd the penalty coefficient rho, the original problem can be restated as
Wherein { WkDenotes weights, { U }kDenotes the merging matrix at the receiving end, tr (-) denotes the trace of the matrix, Ek(Uk,xk) Representing mean square error MSE matrix
Step 3.2: a hybrid precoding HP algorithm is proposed:
note that the constraint variables of the problem are separable, and we use the block coordinate descent BCD algorithm to pair the block variables { U }k},{Wk},A,{FkAnd { x }kThe solution is carried out, and the solution is carried out,
first, the variable { U } is updated by solving the following problemk}
The optimal result is
Wherein C isk=HkXkXkHk+σ2I
Updating the variable { W by solving the following problemk}
The optimal result is
Then, the variable A is updated by solving the following problem
The optimal solution is
Update { F by solving the following problemk}
The optimal solution is
Then, { x ] is updated by solving the following problemk}
The optimal solution is
the penalty factor ρ can be updated by the following formula
Wherein 0 < etan,c<1,||·||∞Representing an infinite norm of the matrix. Multiplier variable VkThe updating can be done by the following formula
Wherein Vdec=max{||xk-ABFk||∞|1≤k≤K}
Step 3.3: the precoding matrix is compensated for considering the effect of beam squint:
in addition, due to the influence of beam squint, the same analog precoder is shared in all frequency bands for OFDM millimeter wave communicationIs a challenging task; the reason is that the phase shifter varies with frequency, which means that for phase shifter-based analog precoding in OFDM millimeter wave systems, the actual analog precoder is not the same for all subcarriers; to compensate for the effects of beam squint, the actual analog precoding is the analog precoding V obtained from the above algorithm, and the actual digital precoding is FBB[k]=Fc[k]FkIn which F iskIs the number precoding obtained by the above algorithm, Fc[k]Is that the compensation matrix can pass through document [8 ]]The algorithm in (1) is obtained.
Has the advantages that: compared with the conventional subarray design algorithm, the AMD algorithm provided by the invention has the advantages that the calculation complexity is obviously reduced under the condition of approaching frequency-effect performance; compared with the existing hybrid pre-coding algorithm, the frequency efficiency performance of the HP algorithm is obviously improved; compared with the existing hybrid structure and the corresponding design algorithm thereof, the semi-dynamic hybrid structure and the corresponding design algorithm thereof provided by the invention can not only improve the frequency efficiency and the energy efficiency of a communication system, but also reduce the cost of hardware. Therefore, the semi-dynamic subarray mixed structure and the corresponding design algorithm thereof provided by the invention are more suitable for the requirement of large-scale deployment of the base station in the current 5G communication scene.
Drawings
Fig. 1(a) is a fully connected hybrid structure.
Fig. 1(b) shows a fixed subarray hybrid structure.
Fig. 1(c) is a fully dynamic subarray hybrid structure.
Fig. 2 is a PDS hybrid structure in a wideband MIMO-OFDM system.
Fig. 3 calculates the time versus the number of transmit antennas. Here, (a, b) denotes a parameter, where a and b denote the number of RF chains, respectively
The destination and the number of subarrays.
FIG. 4: the frequency effect in the HP algorithm is related to the signal-to-noise ratio.
FIG. 5: and (4) comparing the frequency efficiency performance of the PDS structure with that of the FDS structure.
Detailed Description
Considering a point-to-point broadband millimeter wave MIMO, adopting broadband OIn the FDM modulation scheme, the total number of subcarriers is 32. The transmitting end adopts a PDS structure, as shown in FIG. 1. The number of the RF chains is 4, the total number of the antennas is 64, the 64 antennas are divided into 8 sub-arrays, and each sub-array has 8 antennas. Total transmission power PtotIs 1W. The number of receiving antennas is Nr=4。
Considering the geometric channel model, there are 8 beam clusters. Based on the above channel model, when the influence of beam skew is not considered, the channel matrix on the k-th subcarrier is
WhereinφR,lAnd phiT,lObey [ -2 π, 2 π]Are uniformly distributed. Each cluster consisting of R l6 rays and AOAs/AODs follow a Laplacian distribution. Path delay at 0, DTs]In a medium to uniform distribution, and T s1. The cyclic prefix length is D-8.
Considering the effect of beam squint, the channel matrix on the k-th subcarrier is
Wherein the center frequency fcThe bandwidth is set to be 400MHz to 2000MHz, and the intermediate frequency is 2 GHz.
The sum-rate expression of the millimeter wave MIMO system is
In order to maximize the sum rate of the system, a dynamic subarray structure and a precoding matrix are designed jointly.
Because the channel change is fast, the dynamic subarray structure design is designed by using statistical channel information, and the subarray allocation problem exists
In addition, the design of precoding by using instantaneous channel information has the problem of hybrid precoding
Therefore, the optimization problem with the maximum system resultant rate can be split into the above two sub-problems to be solved.
For the first sub-problem, note { S }jDenotes the position of the non-zero entries of the analog precoding matrix V, so that the problem can be translated into
For this problem, we define V ═ AB, where a is a block diagonal matrix, which contains phase shifter information, i.e., a ═ diag (a)1,…,am,…,aM) WhereinAnalogue precoding to represent the m-th sub-array, with
am(i)=1,m=1,2,…,M,i=1,2,…,NA (99)
By using the property of matrix A elements modulo 1, the problem can be translated to only those related to matrix B, i.e.
For the problem, an unconstrained optimal solution is solved firstly, and then the solved solution is projected into a constrained space, so that a subarray distribution matrix B is obtained.
The problem is a generalized eigenvalue problem that can be solved by SVD decomposition. To pairPerforming SVD to obtainSuppose thatComprises aN of (2)rfA principal eigenvector, i.e.The optimal solution to the problem is
B*=UQQ (103)
Then, considering the constraints of the original problem, we need to update Q to minimize B and B*F norm of (d). Then the following problems were obtained
WhereinRepresenting a set of unitary matrices. It was observed that the problem was solved in steps, where the variable B could be updated by solving the following problem
The solution of the problem is
Where each i corresponds to j*Can be expressed asThe variable Q can be updated by solving the following problem
The solution of the problem is
We can obtain a solution for the subarray connection matrix B by updating the variables B and Q with an alternating minimization-based design (AMD).
On the basis of obtaining the sub-matrix allocation matrix, for the second sub-problem
xk=ABFk,k=1,2,…,K (110)
{WkDenotes weights, { U }kDenotes a combining matrix at the receiving end, Ek(Uk,xk) Representing MSE matrices
An enhanced Lagrange punishment method is utilized, and K multiplier variables V are introducedkAnd the penalty coefficient rho, the original problem can be restated as
Note that the constraint variables of the problem are separable, and we use the block coordinate reduction (BCD) algorithm to match the block variables { U }k},{Wk},A,{FkAnd { x }kThe solution is carried out.
First, the variable { U } is updated by solving the following problemk}
The optimal result is
Wherein C isk=HkXkXkHk+σ2I。
Updating the variable { W by solving the following problemk}
The optimal result is
Then, the variable A is updated by solving the following problem
The optimal solution is
Then, { F ] is updated by solving the following problemk}
The optimal solution is
Then, { x ] is updated by solving the following problemk}
The optimal solution is
the penalty factor ρ may be updated by the following formula
Wherein 0 < etanAnd c is less than 1. Multiplier variable VkThe updating can be done by the following formula
Wherein Vdec=max{||Xk-ABFk||∞|1≤k≤K}。
In addition, sharing the same analog precoder in all frequency bands is a challenging task for OFDM millimeter wave communications due to the effects of beam squint. The reason is that the phase shifter followsFrequency variation, which means that for phase shifter based analog precoding in OFDM-mmWave systems, the actual analog precoder is not the same for all subcarriers. To compensate for the effects of beam squint, the actual analog precoding is the analog precoding V obtained from the above algorithm, and the actual digital precoding is FBB[k]=Fc[k]FkIn which F iskIs the number precoding obtained by the above algorithm, Fc[k]Is that the compensation matrix can be passed through document [7]]The algorithm in (1) to obtain.
FIG. 3 shows that compared with the conventional subarray design algorithm, the AMD algorithm provided by the invention has significantly reduced computational complexity under the condition of approximate frequency-efficiency performance; FIG. 4 shows that compared with the existing hybrid pre-coding algorithm, the frequency efficiency performance of the HP algorithm provided by the invention is significantly improved; fig. 5 shows that compared with the existing hybrid structure and the corresponding design algorithm thereof, the semi-dynamic hybrid structure and the corresponding design algorithm thereof provided by the invention can not only improve the frequency efficiency and energy efficiency of the communication system, but also reduce the cost of hardware. Therefore, the semi-dynamic subarray mixed structure and the corresponding design algorithm thereof provided by the invention are more suitable for the requirement of large-scale deployment of the base station in the current 5G communication scene.
It should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.
Claims (1)
1. A design method for a semi-dynamic subarray mixed structure of a broadband millimeter wave communication system is characterized by comprising the following steps:
step 1: a semi-dynamic sub-array PDS mixed structure is provided, a system model and a channel model are established for a broadband millimeter wave multiple-input multiple-output MIMO communication scene, an optimization target for maximizing the system frequency effect is provided, and an optimization problem is established;
step 2: analyzing the optimization problem in the step 1, and providing an alternative minimization AMD algorithm for dynamically allocating the subarrays according to channel statistical information to obtain a subarray allocation matrix;
and step 3: on the basis of obtaining the sub-array distribution matrix in the step 2, a mixed pre-coding algorithm according to the channel instantaneous information is further provided, the influence of beam skew is considered, and the mixed pre-coding matrix is compensated in a digital domain;
wherein:
the establishing of the system model and the channel model in the step 1 specifically comprises the following steps:
step 1.1: establishing a broadband millimeter wave MIMO system model aiming at a semi-dynamic subarray PDS mixed structure:
considering a point-to-point broadband millimeter wave MIMO, adopting a modulation mode of broadband orthogonal frequency division multiplexing OFDM, wherein the total number of subcarriers is K; let the transmitted symbol vector on the k sub-carrier be skSatisfy the following requirementsNsIs the number of data streams, E [.]Expecting to operate; the digital precoding matrix on the k sub-carrier isThe number of RF chains is Nrf(ii) a Count the total number of antennas as Nt,NtEach antenna is divided into M sub-arrays, and each sub-array is Na=Nta/M antenna; recording the set of subarrays connected by the jth RF chain as SjSince M sub-arrays are divided into NrfA subset of
Wherein, U represents union of sets, and in addition, each subarray can only be connected with one RF chain, i.e. subarray set S connected with ith RF chainiThe subarray set connected with the jth RF chain has no intersection, then
Where n represents the intersection of the sets, and each RF chain can select at least one subarray, then
WhereinRepresenting the empty set, the analog precoding matrix realized by the phase shifter isSince the phase shifter only changes the phase of the signal and not the amplitude of the signal, the analog precoding matrixThere is a constant modulus constraint
Wherein v isijRepresenting the analog precoding matrix with the ith sub-matrix connected to the jth RF chain, | - |, representing the modulus of the vector,is that the indication function is defined as
Wherein 1 represents a matrix in which all elements are 1; 0 denotes a matrix in which all elements are 0,
the transmitting end thus transmits symbols expressed as
xk=VFksk,k∈{1,2,…,K} (6)
In addition, there is a transmit power constraint
Wherein P istotRepresenting the total transmit power, | · | | non-woven phosphorFIs the F norm of the matrix;
step 1.2: establishing a millimeter wave MIMO channel model:
the geometric channel model has L beam clusters, and the first (L is more than or equal to 1 and less than or equal to L) cluster has RlA scattering path, under the model, the channel matrix of the d-th time delay is
WhereinφR,lAnd phiT,lRespectively representing time delay, arrival angle, departure angle, parameters Denotes complex path gain, relative delay, r-th in the l-th clusterlThe relative arrival and departure angles of the scattering paths, p (τ) representing a period TsOf the pulse shaping function at τ, and, in addition, aR(. and a)TDenotes the transmit and receive array response vector, denoted as
Wherein N is the number of corresponding antennas, λ is the carrier wavelength, and d' is the distance between the antennas; based on the above channel model, when the influence of beam skew is not considered, the channel matrix on the k-th subcarrier is
Wherein D is the pilot frequency length;
considering the effect of beam squint, the channel matrix on the k-th subcarrier is
Wherein
step 1.3: an optimization target for maximizing the system frequency effect is provided, and an optimization problem is established
The sum-rate expression of the millimeter wave MIMO system is
Wherein detFor solving determinant of matrix, I is unit matrix, and for maximizing sum rate of system, joint design of dynamic subarray structure and precoding matrix is carried out, sigma2Is the variance of the noise;
because the channel change is fast, the dynamic subarray structure design is carried out by utilizing statistical channel information, and the subarray distribution problem exists
s.t. is a condition that is constrained to follow;
in addition, the design of precoding by using instantaneous channel information has the problem of hybrid precoding
The det is a determinant for solving the matrix, so that the optimization problem with the maximum system synthesis rate can be divided into the two sub-problems for solving;
the step 2 comprises the following steps:
step 2.1: analyzing and converting an optimization problem:
for the first sub-problem, note { S }jDenotes the position of the non-zero entries of the analog precoding matrix V, so that the problem can be translated into
Define V ═ AB, where a is a block diagonal matrix containing phase shifter information, and the diagonal block matrix is a1,…,am,…,aMI.e. a ═ diag (a)1,…,am,…,aM) WhereinAnalog precoding representing mth sub-arrayAt the same time have
am(i)=1,m=1,2,…,M,i=1,2,…,NA (18)
The power constraint may be rewritten as
At this point an equivalent channel is introduced
The sub-array allocation problem may be equivalent to
Where tr denotes the trace of the matrix, and the property of the matrix A element modulo 1 is used to transform the trace only associated with matrix B, i.e.
step 2.2: and (3) proposing an AMD algorithm of subarray design:
firstly, solving the unconstrained optimal solution, then projecting the solved solution into a constrained space to obtain a subarray distribution matrix B,
solved by SVD decomposition, pairPerforming SVD to obtainSuppose thatComprises aN of (A)rfA principal eigenvector, i.e.The optimal solution is
B*=UQQ (25)
then considering the constraints of the original problem, Q needs to be updated to minimize B and B*Then the F norm of (1) is obtained as follows
WhereinRepresenting a set of unitary matrices, the problem being a stepwise solution, in which the variable B is updated by solving a problem
The solution of the problem is
The variable Q is updated by solving the following problem
The solution of the problem is
Updating the variables B and Q through alternate minimization to obtain a solution of the subarray connection matrix B; the AMD algorithm is designed for the subarrays corresponding to the semi-dynamic subarray mixed structure;
the method comprises the following steps in step 3:
step 3.1: on the basis of the subarray distribution matrix, the optimization problem is converted:
on the basis of obtaining the sub-matrix allocation matrix, for the second sub-problem
Xk=ABFk,k=1,2,…,K (32)
An enhanced Lagrange punishment method is utilized, and K multiplier variables V are introducedkAnd the penalty coefficient rho, the original problem can be restated as
Wherein { WkDenotes weights, { U }kDenotes a combining matrix at the receiving end, Ek(Uk,Xk) Representing mean square error MSE matrix
Step 3.2: a hybrid precoding HP algorithm is proposed:
note that the constraint variables of the problem are separable, and we use the block coordinate descent BCD algorithm to pair the block variables { U }k},{Wk},A,{FkAnd { X }kThe solution is carried out, and the solution is carried out,
first, the variable { U } is updated by solving the following problemk}
The optimal result is
Wherein C isk=HkXkXkHk+σ2I
Updating the variable { W by solving the following problemk}
The optimal result is
Then, the variable A is updated by solving the following problem
The optimal solution is
Update { F by solving the following problemk}
The optimal solution is
then, { X ] is updated by solving the following problemk}
The optimal solution is
Where μ ≧ 0 represents the Lagrangian multiplier,the penalty factor ρ may be updated by the following formula
Wherein 0 < etan,c<1,||·||∞Infinite norm, multiplier variable V representing a matrixkThe updating can be done by the following formula
Wherein Vdec=max{||Xk-ABFk||∞|1≤k≤K}
Step 3.3: the precoding matrix is compensated for considering the effect of beam squint:
in addition, due to the influence of beam squint, sharing the same analog precoder in all frequency bands is a challenging task for OFDM millimeter wave communication; the reason is that the phase shifter varies with frequency, which means that for phase shifter-based analog precoding in OFDM millimeter wave systems, the actual analog precoder is not the same for all subcarriers; to compensate for the effects of beam squint, the actual analog precoding is the analog precoding V obtained from the above algorithm, and the actual digital precoding is FBB[k]=Fc[k]FkIn which F iskIs the number precoding obtained by the above algorithm, Fc[k]Is that the compensation matrix can pass through document [8 ]]The algorithm in (1) to obtain.
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