CN111988073A - Design method for semi-dynamic subarray mixed structure of broadband millimeter wave communication system - Google Patents

Design method for semi-dynamic subarray mixed structure of broadband millimeter wave communication system Download PDF

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CN111988073A
CN111988073A CN202010892498.2A CN202010892498A CN111988073A CN 111988073 A CN111988073 A CN 111988073A CN 202010892498 A CN202010892498 A CN 202010892498A CN 111988073 A CN111988073 A CN 111988073A
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王俊波
杨凡
张华�
常传文
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
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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

Design method for semi-dynamic subarray mixed structure of broadband millimeter wave communication system
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. This is achieved byIn 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, for the millimeter wave system based on the multi-subarray mixed structure, [5] an effective mixed precoding algorithm is proposed. 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: aiming at the broadband millimeter wave MIMO communication scene, the invention provides a new semi-dynamic subarray mixed structure and a corresponding subarray allocation and mixed pre-coding optimization algorithm, so as to overcome the defects of the existing mixed structure, reduce the hardware cost of a transmitting end and improve the communication performance of a system.
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 requirements
Figure BDA0002655495530000031
NsIs the number of data streams, E [ ·]Expecting to operate; the digital precoding matrix on the k sub-carrier is
Figure BDA0002655495530000032
The 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 the sub-array of the j-th RF chain connection as SjSince M sub-arrays are divided into NrfA subset of
Figure BDA0002655495530000033
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
Figure BDA0002655495530000034
Where n represents the intersection of the sets. At least one subarray may be selected for each RF chain, then
Figure BDA0002655495530000035
Wherein
Figure BDA0002655495530000036
Representing the empty set, the analog precoding matrix realized by the phase shifter is
Figure BDA0002655495530000037
Since the phase shifter only changes the phase of the signal and not the amplitude of the signal, the analog precoding matrix
Figure BDA0002655495530000038
There is a constant modulus constraint
Figure BDA0002655495530000039
Wherein v isijRepresenting the analog precoding matrix with the ith sub-matrix connected to the jth RF chain, | - |, representing the modulus of the vector,
Figure BDA00026554955300000310
is that the indication function is defined as
Figure BDA0002655495530000041
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
Figure BDA0002655495530000042
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
Figure BDA0002655495530000043
Wherein
Figure BDA0002655495530000044
φR，lAnd phiT，lRespectively representing parameters representing time delay, arrival angle, departure angle
Figure BDA0002655495530000045
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
Figure BDA0002655495530000046
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
Figure BDA0002655495530000047
Wherein
Figure BDA0002655495530000048
Is defined as
Figure BDA0002655495530000049
Wherein D is the pilot length.
Considering the effect of beam squint, the channel matrix on the k-th subcarrier is
Figure BDA0002655495530000051
Wherein
Figure BDA0002655495530000052
Wherein f iscRepresenting the center frequency, c the speed of light,
Figure BDA0002655495530000053
where B denotes bandwidth;
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
Figure BDA0002655495530000054
Where det (-) is the determinant of the matrix, 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 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
Figure BDA0002655495530000055
s.t. is a condition constrained to
In addition, the design of precoding by using instantaneous channel information has the problem of hybrid precoding
Figure BDA0002655495530000056
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 that the problem can be translated into
Figure BDA0002655495530000061
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) Wherein
Figure BDA0002655495530000062
Analog precoding representing the mth sub-array, with
am(i)＝1，m＝1，2，…，M，i＝1，2，…，NA (64)
Figure BDA0002655495530000063
Representing binary sub-array allocation matrices, having
Figure BDA0002655495530000064
The power constraint may be rewritten as
Figure BDA0002655495530000065
At this point an equivalent channel is introduced
Figure BDA0002655495530000066
The sub-array allocation problem may be equivalent to
Figure BDA0002655495530000067
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
Figure BDA0002655495530000068
Wherein
Figure BDA0002655495530000069
||·||1A 1-norm of the matrix is represented,
Figure BDA00026554955300000610
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,
Figure BDA0002655495530000071
solved by SVD decomposition, pair
Figure BDA0002655495530000072
Performing SVD to obtain
Figure BDA0002655495530000073
Suppose that
Figure BDA0002655495530000074
Comprises a
Figure BDA0002655495530000075
N of (A)rfA principal eigenvector, i.e.
Figure BDA0002655495530000076
The optimal solution is
B*＝UQQ (71)
Wherein
Figure BDA0002655495530000077
Is an arbitrary unitary matrix;
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
Figure BDA0002655495530000078
Where μ represents a set of unitary matrices, the problem is a stepwise solution, where the variable B is updated by solving the problem
Figure BDA0002655495530000079
The solution of the problem is
Figure BDA00026554955300000710
Where each i corresponds to j*Can be expressed as
Figure BDA00026554955300000711
The variable Q is updated by solving the following problem
Figure BDA00026554955300000712
The solution of the problem is
Figure BDA00026554955300000713
Wherein VZ，UZIs a pair of BHUQBy performing singular value decomposition, i.e.
Figure BDA00026554955300000714
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
Figure BDA0002655495530000081
To make a pair of constraints
Figure BDA0002655495530000082
Decoupling is carried out, and a new variable x is introducedk
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
Figure BDA0002655495530000083
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
Figure BDA0002655495530000084
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}
Figure BDA0002655495530000085
The optimal result is
Figure BDA0002655495530000086
Wherein C isk＝HkXkXkHk+σ2I
Updating the variable { W by solving the following problemk}
Figure BDA0002655495530000087
The optimal result is
Figure BDA0002655495530000088
Then, the variable A is updated by solving the following problem
Figure BDA0002655495530000091
The optimal solution is
Figure BDA0002655495530000092
Wherein
Figure BDA0002655495530000093
Update { F by solving the following problemk}
Figure BDA0002655495530000094
The optimal solution is
Figure BDA0002655495530000095
Wherein the content of the first and second substances,
Figure BDA0002655495530000096
representing the generalized inverse of the matrix.
Then, { x ] is updated by solving the following problemk}
Figure BDA0002655495530000097
The optimal solution is
Figure BDA0002655495530000098
Where μ ≧ 0 represents the Lagrangian multiplier,
Figure BDA0002655495530000099
the penalty factor ρ may be updated by the following formula
Figure BDA00026554955300000910
Wherein 0 < etan，c＜1，||·||∞Representing an infinite norm of the matrix. Multiplier variable VkThe updating can be done by the following formula
Figure BDA00026554955300000911
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.
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 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
A point-to-point broadband millimeter wave MIMO is considered, a broadband OFDM modulation mode is adopted, and 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
Figure BDA0002655495530000101
Wherein
Figure BDA0002655495530000102
φR，lAnd phiT，lObey [ -2 π, 2 π]Are uniformly distributed. Each cluster of beams consisting of R l6 rays and the AOAs/AODs follow a Laplacian distribution. Path delay at 0, DTs]Medium uniform distributionAnd T iss1. The cyclic prefix length is D-8.
Considering the effect of beam squint, the channel matrix on the k-th subcarrier is
Figure BDA0002655495530000111
Wherein the center frequency fcThe bandwidth is set to 400MHz to 2000MHz at 28GHz, and the intermediate frequency is 2 GHz.
The sum-rate expression of the millimeter wave MIMO system is
Figure BDA0002655495530000112
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
Figure BDA0002655495530000113
In addition, the design of precoding by using instantaneous channel information has the problem of hybrid precoding
Figure BDA0002655495530000114
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
Figure BDA0002655495530000115
For this problem, we define V ═ AB, where a is a block diagonal matrix, containing phase shifter information, i.e., a ═ diag (a)1，…，am，…，aM) Wherein
Figure BDA0002655495530000116
Analog precoding representing the mth sub-array, with
am(i)＝1，m＝1，2，…，M，i＝1，2，…，NA (99)
Figure BDA0002655495530000117
Representing binary sub-array allocation matrices, having
Figure BDA0002655495530000121
By using the property of matrix A elements modulo 1, the problem can be translated to only those related to matrix B, i.e.
Figure BDA0002655495530000122
Wherein
Figure BDA0002655495530000123
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.
Figure BDA0002655495530000124
The problem is a generalized eigenvalue problem that can be solved by SVD decomposition. To pair
Figure BDA0002655495530000125
Performing SVD to obtain
Figure BDA0002655495530000126
Suppose that
Figure BDA0002655495530000127
Comprises a
Figure BDA0002655495530000128
N of (A)rfA principal eigenvector, i.e.
Figure BDA0002655495530000129
The optimal solution to the problem is
B*＝UQQ (103)
Wherein
Figure BDA00026554955300001210
Is an arbitrary unitary matrix.
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 are obtained
Figure BDA00026554955300001211
Wherein
Figure BDA00026554955300001212
Representing 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
Figure BDA00026554955300001213
The solution of the problem is
Figure BDA00026554955300001214
Where each i corresponds to j*Can be expressed as
Figure BDA00026554955300001215
The variable Q can be updated by solving the following problem
Figure BDA00026554955300001216
The solution of the problem is
Figure BDA0002655495530000131
Wherein VZ，UZIs a pair of BHUQBy performing singular value decomposition, i.e.
Figure BDA0002655495530000132
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
Figure BDA0002655495530000133
To make a pair of constraints
Figure BDA0002655495530000134
To decouple, we introduce a new variable xk
xk＝ABFk，k＝1，2，…，K (110)
Thus, the total power constraint is constrained
Figure BDA0002655495530000135
Can be written as
Figure BDA0002655495530000136
{WkDenotes weights, { U }kDenotes a combining matrix at the receiving end, Ek(Uk，xk) Representing MSE matrices
Figure BDA0002655495530000137
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
Figure BDA0002655495530000138
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}
Figure BDA0002655495530000139
The optimal result is
Figure BDA00026554955300001310
Wherein C isk＝HkXkXkHk+σ2I。
Updating the variable { W by solving the following problemk}
Figure BDA0002655495530000141
The optimal result is
Figure BDA0002655495530000142
Then, the variable A is updated by solving the following problem
Figure BDA0002655495530000143
The optimal solution is
Figure BDA0002655495530000144
Wherein
Figure BDA0002655495530000145
Then, { F ] is updated by solving the following problemk}
Figure BDA0002655495530000146
The optimal solution is
Figure BDA0002655495530000147
Then, { x ] is updated by solving the following problemk}
Figure BDA0002655495530000148
The optimal solution is
Figure BDA0002655495530000149
Where μ ≧ 0 represents the Lagrangian multiplier,
Figure BDA00026554955300001410
the penalty factor ρ may be updated by the following formula
Figure BDA00026554955300001411
Wherein 0 < etanAnd c is less than 1. Multiplier variable VkThe updating can be done by the following formula
Figure BDA00026554955300001412
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 shifters vary with frequency, 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 AMD algorithm of the prior art, the AMD algorithm of the present invention has significantly reduced computational complexity under the condition of approaching 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 (4)

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 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.
2. The semi-dynamic subarray hybrid structure for a wideband millimeter wave MIMO communication system according to claim 1, 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 requirements
Figure FDA0002655495520000011
NsIs the number of data streams, E [.]Expecting to operate; the digital precoding matrix on the k sub-carrier is
Figure FDA0002655495520000012
The 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 the sub-array of the j-th RF chain connection as SjSince M sub-arrays are divided into NrfA subset of
Figure FDA0002655495520000013
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
Figure FDA0002655495520000014
Where n represents the intersection of the sets, and each RF chain can select at least one subarray, then
Figure FDA0002655495520000015
Wherein
Figure FDA0002655495520000016
Representing the empty set, the analog precoding matrix realized by the phase shifter is
Figure FDA0002655495520000017
Since the phase shifter only changes the phase of the signal and not the amplitude of the signal, the analog precoding matrix
Figure FDA0002655495520000018
There is a constant modulus constraint
Figure FDA0002655495520000019
Wherein v isijRepresenting the analog precoding matrix with the ith sub-matrix connected to the jth RF chain, | - |, representing the modulus of the vector,
Figure FDA0002655495520000021
is that the indication function is defined as
Figure FDA0002655495520000022
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
Figure FDA0002655495520000023
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
Figure FDA0002655495520000024
Wherein
Figure FDA0002655495520000025
φR，lAnd phiT，lRespectively representing parameters representing time delay, arrival angle, departure angle
Figure FDA0002655495520000029
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
Figure FDA0002655495520000026
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
Figure FDA0002655495520000027
Wherein
Figure FDA0002655495520000028
Is defined as
Figure FDA0002655495520000031
Wherein D is the pilot frequency length;
considering the effect of beam squint, the channel matrix on the k-th subcarrier is
Figure FDA0002655495520000032
Wherein
Figure FDA0002655495520000033
Wherein f iscRepresenting the center frequency, c the speed of light,
Figure FDA0002655495520000034
where B denotes bandwidth;
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
Figure FDA0002655495520000035
Where det (-) is determinant of matrix, I is unit matrix, and in order to maximize 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
Figure FDA0002655495520000036
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
Figure FDA0002655495520000037
And det (-) is a determinant for solving the matrix, so that the optimization problem with the maximum system total rate can be divided into the two sub-problems for solving.
3. The semi-dynamic subarray hybrid structure for a wideband millimeter wave MIMO communication system according to claim 2, wherein: 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
Figure FDA0002655495520000041
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) Wherein
Figure FDA0002655495520000042
Analog precoding representing the mth sub-array, with
am(i)＝1，m＝1，2，…，M，i＝1，2，…，NA (18)
Figure FDA0002655495520000043
Representing binary sub-array allocation matrices, having
Figure FDA0002655495520000044
The power constraint may be rewritten as
Figure FDA0002655495520000045
At this point an equivalent channel is introduced
Figure FDA0002655495520000046
The sub-array allocation problem may be equivalent to
Figure FDA0002655495520000047
Wherein tr (-) represents the trace of the matrix, and the property that the modulus of the element of the matrix A is 1 is utilized to convert the trace only related to the matrix B,
namely, it is
Figure FDA0002655495520000051
Wherein
Figure FDA0002655495520000052
||·||1A 1-norm of the matrix is represented,
Figure FDA0002655495520000053
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,
Figure FDA0002655495520000054
solved by SVD decomposition, pair
Figure FDA00026554955200000516
Performing SVD to obtain
Figure FDA0002655495520000055
Suppose that
Figure FDA0002655495520000056
Comprises a
Figure FDA00026554955200000517
N of (A)rfA principal eigenvector, i.e.
Figure FDA0002655495520000057
The optimal solution is
B*＝UQQ (25)
Wherein
Figure FDA0002655495520000058
Is an arbitrary unitary matrix;
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
Figure FDA0002655495520000059
Wherein
Figure FDA00026554955200000518
Representing a set of unitary matrices, the problem being a stepwise solution, in which the variable B is updated by solving a problem
Figure FDA00026554955200000510
The solution of the problem is
Figure FDA00026554955200000511
Where each i corresponds to j*Can be expressed as
Figure FDA00026554955200000512
The variable Q is updated by solving the following problem
Figure FDA00026554955200000513
The solution of the problem is
Figure FDA00026554955200000514
Wherein VZ，UZIs a pair of BHUQBy performing singular value decomposition, i.e.
Figure FDA00026554955200000515
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.
4. The semi-dynamic subarray hybrid structure for a wideband millimeter wave MIMO communication system according to claim 3, wherein: 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
Figure FDA0002655495520000061
To make a pair of constraints
Figure FDA0002655495520000062
Decoupling is carried out, and a new variable x is introducedk
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
Figure FDA0002655495520000063
Wherein { WkDenotes weights, { U }kDenotes a combining matrix at the receiving end, Ek(Uk，Xk) Representing mean square error MSE matrix
Figure FDA0002655495520000064
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}
Figure FDA0002655495520000065
The optimal result is
Figure FDA0002655495520000066
Wherein C isk＝HkXkXkHk+σ2I
Updating the variable { W by solving the following problemk}
Figure FDA0002655495520000071
The optimal result is
Figure FDA0002655495520000072
Then, the variable A is updated by solving the following problem
Figure FDA0002655495520000073
The optimal solution is
Figure FDA0002655495520000074
Wherein
Figure FDA0002655495520000075
Update { F by solving the following problemk}
Figure FDA0002655495520000076
The optimal solution is
Figure FDA00026554955200000711
Wherein the content of the first and second substances,
Figure FDA00026554955200000712
a generalized inverse of the matrix is represented,
then, { X ] is updated by solving the following problemk}
Figure FDA0002655495520000077
The optimal solution is
Figure FDA0002655495520000078
Where μ ≧ 0 represents the Lagrangian multiplier,
Figure FDA0002655495520000079
the penalty factor ρ may be updated by the following formula
Figure FDA00026554955200000710
Wherein 0 < etan，c＜1，||·||∞Infinite norm, multiplier variable V representing a matrixkThe updating can be done by the following formula
Figure FDA0002655495520000081
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 beReference is made to [8 ]]The algorithm in (1) to obtain.
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