CN116094556A - Spatial multiplexing method based on IRS auxiliary terahertz MIMO communication system - Google Patents
Spatial multiplexing method based on IRS auxiliary terahertz MIMO communication system Download PDFInfo
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Abstract
The invention relates to a space multiplexing method based on an IRS auxiliary terahertz MIMO communication system, and belongs to the technical field of communication. The method comprises the following steps: the IRS multi-partition auxiliary receiving and transmitting terminal multi-subarray terahertz MIMO communication system architecture is proposed; under the proposed architecture, a channel model is built based on the kronecker product; constructing a non-convex objective function containing multivariable coupling and non-convex constraint according to the principle of maximizing the frequency spectrum efficiency; decoupling the optimization problem into two easily solved sub-problems, namely an IRS reflection coefficient matrix design problem and a mixed precoding/combining matrix design problem of a receiving/transmitting end; calculating an IRS reflection coefficient matrix based on a Riemann manifold optimization algorithm; based on mathematical derivation, a closed-form solution of the hybrid precoding matrix/combining matrix is obtained.
Description
Technical Field
The invention belongs to the technical field of communication, and relates to a spatial multiplexing method based on an IRS auxiliary terahertz MIMO communication system.
Background
In recent years, 5G construction work is expanding well in the global scope, at the same time, academia and industry explore new modes of 6G, preliminary imagination and research are made on the wish, demand, scene, key technology, system architecture and performance indexes of 6G networks, and full-coverage, full-spectrum, full-application and strong-safety development targets and overall prospects are proposed. Compared with 5G, the peak rate, the connection density, the spectrum efficiency and other performance indexes of 6G are improved by 10 to 100 times. Terahertz (THz) communication is favored by next-generation wireless communication systems because of having an ultra-large bandwidth, meeting the high data transmission rate requirements. However, the ultra-high path loss of the THz frequency band limits the communication distance of THz communication, and for this purpose, it is often combined with a massive multiple input multiple output (Multiple Input Multiple Output, MIMO) technology, and the path loss is compensated by means of the high array gain generated by the massive MIMO, and meanwhile, the multiplexing gain is provided, so that the spectral efficiency of the system is further improved. However, the high hardware cost and high energy consumption of massive MIMO technology presents challenges to the actual deployment of the network.
Emerging IRS (Intelligent Reflecting Surface, IRS) technologies provide a relay for effectively solving the network deployment problem. The IRS is incorporated into the key enabling technology of next-generation wireless communication due to the advantages of low cost, easy deployment, capability of actively and intelligently regulating the wireless propagation environment and the like. In particular, IRS is a reconfigurable plane made up of a large number of low cost passive reflective elements, each of which independently adjusts the phase shift and amplitude of the incident electromagnetic wave in a programmable manner to cooperatively implement reflected beam forming and reconfigure the propagation environment. Thus, the use of IRS in existing wireless communication systems may create a good propagation environment and provide more degrees of freedom for optimization. By reasonably regulating and controlling the physical characteristics of each reflection unit, the electromagnetic wave signals reflected by the IRS can form reflection beam forming, so that the energy of the reflection signals is gathered, the energy of the reflection signals is led to the receiving end, the strength of the received signals is improved, and the capacity of the system is improved.
Currently, the use of IRSs in wireless communications is widely studied. In many key technical studies, how to jointly optimize the RIS reflection coefficient and the transmitter beamforming matrix to maximize IRS performance gain is a critical issue. In this regard, most researches solve the hybrid precoding matrix of the IRS reflection coefficient matrix and the transmitting and receiving end in an alternative optimization manner, or alternatively optimize the precoding design of the transmitting and receiving end, alternatively optimize the inner and outer layers of the digital precoding and analog precoding, or alternatively optimize the IRS reflection phase shift matrix and the hybrid precoding matrix. However, the alternating optimization method has the problem of high computational complexity, so that improved optimization algorithms such as a block coordinate descent algorithm, a semi-definite relaxation algorithm, a truncated channel matrix singular value decomposition method and the like are generated to realize the balance between the system performance and the computational complexity. However, the above methods are all made on optimization algorithm, and the system is inherently based on half-wavelength antenna array architecture, and plane wave assumption is considered in information transmission, so that the spatial multiplexing gain of the system is limited by the number of resolvable paths. Particularly in high-frequency band communication such as THz communication, channels have extremely high propagation attenuation and scattering loss, the channels have sparsity, and the improvement of an algorithm to obtain spectrum efficiency and gain by means of a space multiplexing mode of a traditional architecture improves the space limited, so that the spectrum efficiency of an IRS auxiliary TH-MIMO system is improved. Therefore, the new architecture is proposed to improve spatial multiplexing gain and spectral efficiency of the IRS-assisted TH-MIMO system.
Aiming at the THz-MIMO point-to-point communication system assisted by IRS, the architecture of the multi-subarray terahertz MIMO communication system of the IRS multi-subarea assisted receiving and transmitting terminal is provided; under the proposed architecture, a channel model is built based on the kronecker product; and constructing a non-convex optimization function by taking the maximization of the spectrum efficiency of the system as a target, and solving the original problem by decoupling the original problem into two sub-problems by utilizing the characteristic that the limiting conditions of the optimization function are not mutually coupled. The difference is that the traditional plane wave assumption is not considered any more, spherical wave propagation is considered among different subarrays of the receiving end and between different groups of IRS, and the hybrid precoding and the closed matrix of the combining matrix of the receiving end are deduced while the IRS reflection beam forming is optimized.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a spatial multiplexing method based on an IRS-assisted terahertz MIMO communication system.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the spatial multiplexing method based on the IRS auxiliary terahertz MIMO communication system comprises the following steps:
step one: the IRS multi-partition auxiliary receiving and transmitting terminal multi-subarray terahertz MIMO communication system architecture is proposed;
step two: under the proposed architecture, a channel model is built based on the kronecker product;
step three: constructing a non-convex objective function containing multivariable coupling and non-convex constraint under the proposed architecture according to the principle of maximizing the frequency spectrum efficiency;
step four: decoupling the optimization problem into two easily solved sub-problems, namely an IRS reflection coefficient matrix design problem and a mixed precoding/combining matrix design problem of a receiving/transmitting end;
step five: calculating an IRS reflection coefficient matrix based on a Riemann manifold optimization algorithm;
step six: based on mathematical derivation, a closed-form solution of the hybrid precoding matrix/combining matrix is obtained.
Optionally, in the first step, the architecture of the IRS multi-partition auxiliary transceiver multi-subarray terahertz MIMO communication system proposes that, for the IRS auxiliary terahertz MIMO system, it is assumed that the line-of-sight communication link between the transmitting end and the receiving end is blocked by an obstacle, and an effective communication link needs to be established depending on the IRS; in order to obtain richer space multiplexing gain, a wide-interval multi-subarray mixed precoding structure is adopted at a receiving and transmitting end, and a corresponding wide-interval multi-partition IRS architecture is designed.
Optionally, in the second step, under the proposed architecture, based on the kronecker product, the channel model is established, and the virtual line-of-sight communication channel constructed by the transmitting end and the receiving end through the IRS is obtained by combining the wide-space multi-subarray WSMS architecture channel model and the IRS cascade channel model, which is expressed as
H＝H r ΦH t
in the formula 
Channel H between transmitting end and IRS t Channel H between IRS and receiving end r Represented as
Optionally, in the third step, according to the spectrum efficiency maximization principle, a non-convex objective function containing multivariable coupling and non-convex constraint is constructed under the proposed architecture, and the limitation of a limited scattering path on multiplexing gain is broken through by deploying an antenna array at two ends of receiving and transmitting and elements on an IRS, so that the bottleneck of spectrum efficiency in the existing IRS-assisted terahertz MIMO communication system is broken through, and the maximization of the spectrum efficiency of the system is realized by jointly optimizing a reflection coefficient matrix on the IRS, a mixed precoding matrix at a transmitting end and a mixed merging matrix at a receiving end; the spectral efficiency of the system is
The optimization problem of maximizing the spectral efficiency of the system is expressed as
Optionally, in the fourth step, the optimization problem is decoupled into two easily solved sub-problems, namely, the IRS reflection coefficient matrix design problem and the mixed precoding/combining matrix design problem of the transmitting/receiving end, when solving each problem, we assume that the channel state information is completely known, and focus on joint beamforming on the transmitting/receiving end and the IRS under the proposed new architecture; firstly, assuming that a mixed precoding matrix of a receiving and transmitting end is all digital, optimizing a reflection coefficient matrix on IRS (inter-radio frequency standard) with the aim of maximizing the frequency spectrum efficiency of a system, and obtaining a first optimization subproblem
φ∈[0,2π)
Substituting the obtained IRS reflection coefficient matrix into a mixed precoding matrix (combining matrix) of an optimized transmitting (receiving) end, and obtaining a second optimized subproblem at the moment
Optionally, in the fifth step, based on the Riemann manifold optimization algorithm, the IRS reflection coefficient matrix is calculated, and since the precoding and combining matrix of the receiving and transmitting end are assumed to be all-digital optimal forms in P1, by further analyzing the structure of the cascade channel matrix, the optimization problem of simplifying P1 is as follows
φ∈[0,2π)
wherein 
and />
Respectively indicate->
and />
K row and k column of +.>
and />
Represents rounding up and down for x, < >>
A row vector representing all elements 1, 1 K ∈C K×1 A column vector representing all elements 1; order the
/>
φ∈[0,2π)
Considering the feasible search space of the transformed optimization problem as N irs_tot The product of the complex circles, namely:
and when the optimal phase shift is searched on the manifold M, constant mode constraint of the IRS reflection coefficient is always satisfied, P1 is converted into an unconstrained form, and a gradient descent algorithm is adopted for solving.
Optionally, in the sixth step, a closed-form solution of the mixed precoding matrix/combining matrix is obtained based on mathematical derivation, and SVD decomposition is performed on the cascade channels first
Wherein U is N r_tot xQ unitary matrix, Σq diagonal matrix, diagonal element singular value of cascade channel, V is N t_tot The unitary matrix of x Q,
q is the rank of the concatenated channel matrix H; by further parsing the structure of the concatenated channel matrix, the optimization problem of P2 is simplified, and the concatenated channel matrix is rewritten as follows
wherein ,
combining SVD decomposition of H to obtain closed type decomposition of the mixed precoding matrix of the transmitting end
wherein ,
front N representing right singular matrix s Column (S)/(S)>
Is a normalized water-filling power allocation matrix,/>
Representing the power allocated to the ith data stream, and i=1, 2, l, n s Epsilon is the water filling height, < >>
Rewriting the concatenated channel matrix as:
wherein ,
combining with SVD decomposition of H to obtain closed-form solution of receiving end mixed combined code matrix
wherein ,
front N representing left singular matrix s Columns.
The invention has the beneficial effects that:
1) The IRS multi-partition auxiliary receiving and transmitting end multi-subarray terahertz MIMO communication system architecture is provided, because the interval between the IRS and the subarray of the receiving and transmitting end is wider, the correlation between the subarray and the subarray is low, the resolvable phase difference brought by spherical wave transmission to each subarray is utilized, meanwhile, the multiplexing gain between paths and the multiplexing gain in the paths are obtained, and the limitation of the spatial multiplexing gain in the traditional architecture by the sparsity of a high-frequency band communication channel is broken;
2) Under the architecture of the IRS multi-partition auxiliary receiving and transmitting end multi-subarray terahertz MIMO communication system, a channel model based on Cronecker product is established by jointly analyzing a communication channel model under the wide subarray architecture and a cascade channel model of IRS auxiliary communication;
3) The method is characterized in that a non-convex optimization function is constructed by taking the maximization of the spectrum efficiency of the system as a target, the original problem is decoupled into two sub-problems to solve by utilizing the characteristic that the limiting conditions of the optimization function are not coupled with each other, an IRS reflection coefficient matrix is calculated by adopting a Riemann manifold optimization algorithm through an anatomic channel structure, and a closed solution of a mixed precoding matrix/combination matrix is obtained through mathematical derivation, so that a good compromise is obtained between the calculation complexity and the spectrum efficiency of the system.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
Drawings
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a process for designing a spatial multiplexing scheme for an IRS-assisted terahertz MIMO communication system;
fig. 2 is a diagram of an IRS multi-partition auxiliary transceiver multi-subarray terahertz MIMO communication system;
fig. 3 is a schematic diagram of a geometric diagram of the Riemann manifold optimization.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
As shown in fig. 1, the present invention provides a spatial multiplexing scheme design based on an IRS-assisted terahertz MIMO communication system.
FIG. 2 is a system model diagram of the present invention, and is described below with reference to the accompanying drawings:
the IRS-assisted terahertz MIMO communication system model considered in the present invention is shown in fig. 2. The system consists of a transmitting end, an IRS and a receiving end. The transmitting terminal comprises N t_tot Root RF chain and N t_tot The root antenna uniformly divides the transmitting end into K t At uniform intervals of d wid_t Each sub-array is configured with N RF_t Root radio frequency RF chain and N t Root spacing is d=λ/2 antennas; IRS comprises N irs_tot A plurality of reflecting elements uniformly dividing the elements into K irs A group with a group spacing d wid_irs Each group of IRSs contains N irs A uniform spacing of d=λ/2 reflective elements; the receiving end comprises N r_tot Root RF chain and N r_tot The root antenna uniformly divides the receiving end into K r At uniform intervals of d wid_r Each sub-array is configured with N RF_r Root radio frequency RF chain and N r The root spacing is d=λ/2 antennas.
Transmitting end transmits N S Stripe parallel data streams, denoted as
And have->
E represents the desire, (A) H Representing the conjugate transpose of the matrix +.>
Is N s ×N s Is a unit matrix of (a). The number of transmission data streams, the number of RF chains at a receiving end and the number of antennas at a receiving end have the following relationship: n (N) s ≤N RFt_tot ≤N t_tot ，N s ≤N RFr_tot ≤N r_tot ，1≤N RF_t ≤N t ，1≤N RF_r ≤N r . The transmission signal s is first passed through a digital precoder +.>
Mapping to the radio frequency domain via an RF link, then via an analog precoder->
Is radiated by a transmitting end antenna to obtain a transmitting signal as
Where ρ represents the signal transmission power. The analog precoding matrix F is due to the independence of the RF chains between the sub-arrays RF Is a block diagonal structure, which is a block diagonal structure,
analog precoding matrix for each subarray
θ i,n Is a subarray F RF,i N-th column vector of>
n＝1,2,3,L,N RF_t Non-zero elements in the analog precoding matrix all meet the constant modulus constraint, namely +.>
Hybrid precoder satisfies the power constraint +.>
Wherein I II F Indicating the Frobenius norm.
Defining a channel matrix between a transmitting end and an IRS as
The channel between IRS and receiving end is
The phase shift matrix on IRS is +.>
In IRS auxiliary communication, when receiving endWhen the pitch between subarrays and the group pitch of IRSs are large, the plane wave transmission approximation is no longer applicable and spherical waves need to be considered. Therefore, combining the wide-space multi-subarray (WSMS) architecture channel model and the IRS cascade channel model, the virtual line-of-sight communication channel constructed by the transmitting end and the receiving end through the IRS can be expressed as
H＝H r ΦH t
wherein ,
wherein ,
representing Cronecker product, metropolyl>
and />
Is the complex gain of the channel, L t and Lr The number of propagation paths between the transmitting end and the IRS, and between the IRS and the receiving end are respectively represented. />
and />
Respectively, signal arrival (departure) of IRS t (l r ) Azimuth and pitch angle of the strip path, +.>
For a uniform planar subarray response vector on IRS, < >>
and />
Respectively represent the first of the signal leaving (arriving) transmitting (receiving) end t (l r ) Azimuth and pitch angle of the strip path, +.>
The response vector is uniformly planar for the transmitting (receiving) end.
and />
Respectively represent the first between the transmitting end and IRS under spherical wave transmission t Complex phase shift matrix between subarrays on a plurality of paths and first between IRS and receiving end r Complex phase shift matrices between subarrays on a plurality of paths, and has
wherein />
K represents the transmitting end t The subarray is on path l t In the direction and on IRS kth irs Distance between groups, ++>
Represents the kth of the receiving end r The subarray is on path l r In the direction and on IRS kth irs Distance between groups.
wherein ,
and />
Respectively indicate the inclusion of +.>
Array response vector sum representing a Uniform Linear Array (ULA) of individual array elements comprising +.>
Array response vectors for Uniform Linear Arrays (ULA) of individual array elements. For the array of receiving terminals there is +.>
Array response vector of receiving end if each array element
In addition, IRS normalized subarray response vector
Can be expressed as
Wherein x and y represent the index of elements in the subarray on the IRS, and there are
Likewise, by transformation->
The upper and lower marks of the formula (I) can be obtained>
Transmitting a signalx via channel H t Reaching the IRS, under the control of the FPGA controller, the IRS applies phase shift phi to the received signal, and the IRS reflected signal passes through H r Reaching the receiving end. Thus, the signal received by the receiving end is
wherein ,
is additive white gaussian noise in the channel and n:>
since the reflection coefficients of the elements on the IRS are independent of each other, the reflection coefficients of the elements of the groups on the IRS are also independent of each other, the phase shift matrix on the IRS is a block diagonal matrix, +.>
Reflection coefficient matrix of each IRS group
The reflection coefficient of each element is->
k＝1,2,L,K irs ，l＝1,2,L,N irs ，γ k,l and φk,l The reflection amplitude and phase shift of the first element on the kth IRS, respectively, are typically the amplitude gamma of the passive IRS k,l =1, reflection phase shift Φ k,l E [0,2 pi). The signal received by the receiving end antenna passes through the analog combiner
And digital combiner->
The signal obtained is
Similar to the analog precoder at the transmitting end, W RF Is also block diagonalized and meets constant modulus constraints, i.e
Under the proposed system framework, the main objective is to maximize the spectral efficiency of the system by jointly optimizing the hybrid precoding matrix/combining moment of the transmit/receive end and the reflection phase matrix of the IRS end. First, the system spectral efficiency is
in the formula ,
representing the covariance matrix of the noise. Thus, the optimization problem of maximizing the spectral efficiency of the system can be expressed as
φ∈[0,2π)
The optimization problem is decoupled into two sub-problems which are easy to solve, namely an IRS reflection coefficient matrix design problem and a mixed pre-coding/combination matrix design problem of a receiving end and a transmitting end, when each problem is solved, the channel state information is assumed to be completely known, and the joint beamforming on the receiving end and the IRS under a new architecture is mainly researched. Specifically, it is first assumed that the hybrid precoding matrix (combining matrix) at the transmitting and receiving end is all digital, and the reflection coefficient matrix on the IRS is optimized with the goal of maximizing the spectral efficiency of the system, and the first optimization sub-problem is obtained
φ∈[0,2π)
Substituting the obtained IRS reflection coefficient matrix into a mixed precoding matrix (combining matrix) of an optimized transmitting (receiving) end, and obtaining a second optimized subproblem at the moment
Fig. 3 is a schematic diagram for explaining the geometry of the method of the risman manifold optimization. The following description is made with reference to the accompanying drawings:
based on Riemann manifold optimization algorithm, IRS reflection coefficient matrix is calculated, because in P1, the precoding and combination matrix of the receiving and transmitting end are assumed to be all-digital optimal form, and by further analyzing the structure of cascade channel matrix, the optimization problem of P1 is simplified, and cascade channel matrix is rewritten into the following form
wherein 
and />
Respectively represent K r ×K r and Kt ×K t Identity matrix of dimension>
And is also provided with
wherein 
When the antenna array of the receiving and transmitting end is large enough, A R and AT Can be considered as orthonormal matrix, the column vectors of the two matrices respectively form respective orthogonal sets, known as +.>
And
is also a standard orthogonal matrix. If the reflection coefficient on the IRS is reasonably designed, the element on the main diagonal of the matrix DThe element is far greater than the element on the non-principal diagonal, then +.>
The SVD decomposition of the concatenated channel matrix H can be considered approximately. The optimization problem P1 can thus be converted into the following form
φ∈[0,2π)
wherein 
and />
Respectively indicate->
and />
K row and k column of +.>
and />
Represents rounding up and down for x, < >>
A row vector representing all elements 1, 1 K ∈C K×1 A column vector representing all 1's elements. Order the
φ∈[0,2π)
The feasible search space of the transformed optimization problem can be regarded as N irs_tot The product of the complex circles, namely:
when searching the optimal phase shift on the manifold M, the constant mode constraint of the IRS reflection coefficient is always satisfied, so that P1 can be converted into an unconstrained form, and the solution is carried out by adopting a gradient descent algorithm, wherein the optimized objective function is that
In the Riemann manifold, the fastest descent direction of the objective function is the direction associated with the negative Riemann gradient, which may be passed through the Euclidean ladderAnd obtaining the degree mapping. Thus, first, the objective function f (v) is calculated at v k Euclidean gradient at
The euclidean gradient is then applied using the orthogonal projection operator Proj ()
Projection into tangential space->
And calculate f (v) at v k Riemann gradient at
Then, according to step mu k Updating v in negative Riemann degree direction k
wherein ,μk Represents Armijo step size. Updated
In cut space, the updated points need to be remapped back to the manifold using a contraction operator in order to continue using the negative Riemann gradient for further updating. />
V mapping onto manifold k+1 The position of the part
And obtaining the optimal solution of the IRS reflection coefficient matrix according to the steps.
Substituting the obtained IRS reflection coefficient matrix into the original optimization problem, and performing SVD decomposition on the cascade channel
Wherein U is N r_tot xQ unitary matrix, Σq diagonal matrix, diagonal element singular value of cascade channel, V is N t_tot The unitary matrix of x Q,
q is the rank of the concatenated channel matrix H. By further parsing the structure of the concatenated channel matrix, the optimization problem of P2 is simplified, and the concatenated channel matrix is rewritten as follows
wherein ,
combining SVD decomposition of H to obtain closed type decomposition of the mixed precoding matrix of the transmitting end
wherein ,
front N representing right singular matrix s Column (S)/(S)>
Is a normalized water-filling power allocation matrix,/>
Representing the power allocated to the ith data stream, and i=1, 2, l, n s Epsilon is the water filling height，/>
Similarly, the concatenated channel matrix is rewritten as
wherein ,
combining with SVD decomposition of H to obtain closed-form solution of receiving end mixed combined code matrix
wherein ,
front N representing left singular matrix s Columns.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (7)
1. The spatial multiplexing method based on the IRS auxiliary terahertz MIMO communication system is characterized by comprising the following steps of: the method comprises the following steps:
step one: the IRS multi-partition auxiliary receiving and transmitting terminal multi-subarray terahertz MIMO communication system architecture is proposed;
step two: under the proposed architecture, a channel model is built based on the kronecker product;
step three: constructing a non-convex objective function containing multivariable coupling and non-convex constraint under the proposed architecture according to the principle of maximizing the frequency spectrum efficiency;
step four: decoupling the optimization problem into two easily solved sub-problems, namely an IRS reflection coefficient matrix design problem and a mixed precoding/combining matrix design problem of a receiving/transmitting end;
step five: calculating an IRS reflection coefficient matrix based on a Riemann manifold optimization algorithm;
step six: based on mathematical derivation, a closed-form solution of the hybrid precoding matrix/combining matrix is obtained.
2. The spatial multiplexing method based on the IRS-assisted terahertz MIMO communication system according to claim 1, wherein: in the first step, the architecture of the multi-subarea terahertz MIMO communication system of the IRS multi-subarea auxiliary receiving and transmitting end proposes that for the IRS auxiliary terahertz MIMO system, an effective communication link needs to be established depending on the IRS on the assumption that the line-of-sight communication link between the transmitting end and the receiving end is blocked by an obstacle; in order to obtain richer space multiplexing gain, a wide-interval multi-subarray mixed precoding structure is adopted at a receiving and transmitting end, and a corresponding wide-interval multi-partition IRS architecture is designed.
3. The spatial multiplexing method based on the IRS-assisted terahertz MIMO communication system according to claim 1, wherein: in the second step, under the proposed architecture, based on the Cronecker product, the channel model is established, and the virtual line-of-sight communication channel constructed by the transmitting end and the receiving end through IRS is obtained by combining the wide-space multi-subarray WSMS architecture channel model and the IRS cascade channel model
H＝H r ΦH t
in the formula 
Channel H between transmitting end and IRS t Channel H between IRS and receiving end r Represented as
4. The spatial multiplexing method based on the IRS-assisted terahertz MIMO communication system according to claim 1, wherein: in the third step, according to the spectrum efficiency maximization principle, a non-convex objective function containing multivariable coupling and non-convex constraint is constructed under the proposed architecture, the limitation of a limited scattering path on multiplexing gain is broken through by deploying an antenna array at two ends of receiving and transmitting and elements on an IRS, the spectrum efficiency bottleneck in the existing IRS-assisted terahertz MIMO communication system is broken through, and the maximization of the spectrum efficiency of the system is realized by jointly optimizing a reflection coefficient matrix on the IRS, a mixed precoding matrix at a transmitting end and a mixed merging matrix at a receiving end; the spectral efficiency of the system is
The optimization problem of maximizing the spectral efficiency of the system is expressed as
5. The spatial multiplexing method based on the IRS-assisted terahertz MIMO communication system according to claim 1, wherein: in the fourth step, the optimization problem is decoupled into two sub-problems which are easy to solve, namely, an IRS reflection coefficient matrix design problem and a mixed precoding/combining matrix design problem of a receiving/transmitting end, when each problem is solved, we assume that channel state information is completely known, and the joint beamforming on the receiving/transmitting end and the IRS under a new architecture is mainly researched and proposed; firstly, assuming that a mixed precoding matrix of a receiving and transmitting end is all digital, optimizing a reflection coefficient matrix on IRS (inter-radio frequency standard) with the aim of maximizing the frequency spectrum efficiency of a system, and obtaining a first optimization subproblem
P1:
φ∈[0,2π)
Substituting the obtained IRS reflection coefficient matrix into a mixed precoding matrix (combining matrix) of an optimized transmitting (receiving) end, and obtaining a second optimized subproblem at the moment
P2:
6. The spatial multiplexing method based on the IRS-assisted terahertz MIMO communication system according to claim 1, wherein: in the fifth step, based on the Riemann manifold optimization algorithm, the IRS reflection coefficient matrix is calculated, and since the precoding and combining matrix of the receiving and transmitting end are assumed to be all-digital optimal forms in P1, the optimization problem of simplifying P1 is as follows by further analyzing the structure of the cascade channel matrix
φ∈[0,2π)
wherein 
and />
Respectively indicate->
and />
K row and k column of +.>
and />
Represents rounding up and down for x, < >>
A row vector representing all elements 1, 1 K ∈C K×1 A column vector representing all elements 1; order the
/>
φ∈[0,2π)
Considering the feasible search space of the transformed optimization problem as N irs_tot The product of the complex circles, namely:
and when the optimal phase shift is searched on the manifold M, constant mode constraint of the IRS reflection coefficient is always satisfied, P1 is converted into an unconstrained form, and a gradient descent algorithm is adopted for solving.
7. The spatial multiplexing method based on the IRS-assisted terahertz MIMO communication system according to claim 1, wherein: in the sixth step, based on mathematical derivation, a closed solution of a mixed precoding matrix/combining matrix is obtained, and SVD decomposition is performed on the cascade channels first
Wherein U is N r_tot xQ unitary matrix, Σq diagonal matrix, diagonal element singular value of cascade channel, V is N t_tot The unitary matrix of x Q,
q is the rank of the concatenated channel matrix H; by further parsing the structure of the concatenated channel matrix, the optimization problem of P2 is simplified, and the concatenated channel matrix is rewritten as follows
wherein ,
combining SVD decomposition of H to obtain closed type decomposition of the mixed precoding matrix of the transmitting end
wherein ,
front N representing right singular matrix s Column (S)/(S)>
Is a normalized water-filling power allocation matrix,/>
Representing the power allocated to the ith data stream, an
i＝1,2,L,N s Epsilon is the water injection height,
rewriting the concatenated channel matrix as:
wherein ,
combining with SVD decomposition of H to obtain closed solution of mixed combined code matrix of receiving end>
wherein ,
front N representing left singular matrix s Columns. />
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