CN116614165A - Intelligent reflection surface-assisted reflection coefficient optimization method for spatial modulation system - Google Patents

Intelligent reflection surface-assisted reflection coefficient optimization method for spatial modulation system Download PDF

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CN116614165A
CN116614165A CN202310610192.7A CN202310610192A CN116614165A CN 116614165 A CN116614165 A CN 116614165A CN 202310610192 A CN202310610192 A CN 202310610192A CN 116614165 A CN116614165 A CN 116614165A
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intelligent
signal
target
reflection
optimization
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吴亮
安博
张在琛
党建
朱秉诚
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Southeast University
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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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/90—Non-optical transmission systems, e.g. transmission systems employing non-photonic corpuscular radiation
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0602—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using antenna switching
    • H04B7/0608—Antenna selection according to transmission parameters
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
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Abstract

The invention discloses an intelligent reflection surface-assisted reflection coefficient optimization method for a spatial modulation system, which belongs to the field of wireless communication and comprises the steps of dividing information bits to be transmitted by a transmitting end into a plurality of information blocks with the same length, and selecting a corresponding active antenna to transmit a specific signal according to each information block; optimizing coefficients of reflection elements on the intelligent reflection surface, and maximizing Euclidean distances among different received signals; and adopting maximum likelihood detection decoding at a receiving end to recover the original information bits. The invention combines the intelligent reflecting surface with the spatial modulation scheme, utilizes the intelligent reflecting surface to reconstruct the wireless channel, increases the Euclidean distance between different received signals, improves the error code performance of the system, and can obtain better error code performance than the prior algorithm under the same condition.

Description

Intelligent reflection surface-assisted reflection coefficient optimization method for spatial modulation system
Technical Field
The invention relates to the technical field of wireless communication, in particular to an intelligent reflection surface-assisted reflection coefficient optimization method for a spatial modulation system.
Background
In the sixth Generation (6 g) wireless communication system in the future, how to improve the spectral efficiency (SE, spectral Efficiency) and energy efficiency (EE, energy Efficiency) of the system becomes more and more important, as the wireless network will use the Terahertz (THZ, terheretz) frequency band even higher. Index Modulation (IM) technology is one of the enabling technologies to meet these requirements of 6G. IM can provide higher spectral and energy efficiency by transmitting information bits through spatial, frequency, or polarization indexes. Spatial modulation has received increased attention as a technique in IM.
Spatial modulation is a modulation scheme based on a multi-antenna architecture. In each transmission, only one or a few antennas are activated to transmit signals, the activated antennas being called active antennas, their indices being used to transmit information bits. Compared with traditional constellation modulation, the spatial modulation technology introduces the spatial domain to transmit additional information bits, and the frequency spectrum efficiency of the system is greatly improved. Meanwhile, the number of radio frequency links in the space modulation system can be far less than the number of transmitting antennas, which effectively reduces the hardware cost and power loss of the system. In addition, in the space modulation system, only one or a plurality of antennas are activated to transmit signals in one transmission time slot, so that electromagnetic interference of adjacent antennas is effectively reduced, and the requirement on strict synchronization of the transmitted signals is reduced. With design flexibility and driving to achieve higher transmission rates, spatial modulation schemes are endless, with typical spatial modulation schemes including: a Spatial Modulation (SM) scheme, a Space shift keying (SSK, space Shift Keying) scheme, a quadrature spatial Modulation (QSM, quadrature Spatial Modulation) scheme, a progressive Coded Space shift keying (SC-SSK, progressive Coded-Space Shift Keying) scheme, and the like.
The intelligent reflective surface (RIS, reconfigurable Intelligent Surface) is a super surface consisting of a large number of low cost, low complexity and passive reflective elements, wherein the amplitude and phase response of the reflective elements can be controlled in real time by an external controller, thereby reconstructing the wireless transmission channel and improving the transmission quality. Unlike relay-assisted communication systems, RIS can reshape the incoming signal without the need for a Radio Frequency (RF) link and a power amplifier, without amplifying the ambient noise. Currently, in an RIS-assisted spatial modulation system, RIS reflection coefficient optimization is one of the hot spots of research, and many typical algorithms have been proposed in the academy, such as: semi-positive relaxation (SDR, semi-Definite Relaxation) algorithm and low complexity algorithm based on cosine similarity theorem. In the existing algorithm, the reflection coefficient on RIS is solved with the aim of maximizing the received signal-to-noise ratio. However, when the error code performance of the system is a main requirement index and the receiving end adopts maximum likelihood detection, the euclidean distance between different received signals is a key affecting the error code performance of the system, so that the existing algorithm has a great improvement space on the error code performance of the system. Based on the method, the invention aims at maximizing Euclidean distance among different received signals, and provides an intelligent reflection surface-assisted method for optimizing the reflection coefficient of a space modulation system.
Disclosure of Invention
The invention provides an intelligent reflection surface assisted spatial modulation system reflection coefficient optimization method, which utilizes an RIS (reflection information system) to assist a spatial modulation system to optimize reflection coefficients on the RIS to maximize Euclidean distances among different received signals so as to solve the technical problem of limited system error code performance in the traditional optimization algorithm.
An embodiment of a first aspect of the present invention provides a reflection coefficient optimization method for an intelligent reflection surface-assisted spatial modulation system, where the spatial modulation system includes a transmitting end, an intelligent reflection surface, and a receiving end, and the reflection coefficient optimization method includes the following steps:
dividing information bits to be transmitted of the transmitting end into a plurality of information blocks with the same length, selecting active antennas for each information block to transmit modulation symbols based on a spatial modulation principle, transmitting the information bits through active antenna indexes and the modulation symbols, and performing spatial modulation of the transmitting end;
designing an optimal target receiving signal, maximizing Euclidean distance between the target receiving signals, taking minimized Euclidean distance between an actual receiving signal and the target receiving signal as an optimization target, taking all reflection coefficients of the intelligent reflecting surface as optimization variables, establishing an optimization problem, obtaining the optimal reflection coefficient of the intelligent reflecting surface by solving the optimization problem, changing the phase of an incident signal by utilizing the intelligent reflecting surface based on the optimal reflection coefficient, and reflecting the incident signal to the receiving end;
and according to the received signal of the receiving end, adopting a maximum likelihood detection algorithm, and decoding based on a space modulation scheme of the transmitting end to obtain the information bit to be transmitted.
Optionally, in one embodiment of the present invention, designing the target received signal includes:
and taking the average power of the received signals obtained based on the cosine similarity theorem optimization algorithm as the average power of the target received signals, and designing a normalized distribution form of the target received signals by taking the Euclidean distance between different received signals as a criterion to obtain the target received signals.
Optionally, in an embodiment of the present invention, taking a euclidean distance between a minimized actual received signal and the target received signal as an optimization target, all reflection coefficients of the intelligent reflection surface as optimization variables, and establishing the optimization problem includes:
the i-th actual received signal is:
y i ＝G·Θ i ·H·x i
wherein ,channel matrix from transmitting end to intelligent reflecting surface and from intelligent reflecting surface to receiving end respectively, N t Number of antennas provided for transmitting end, N r The number of antennae equipped for the receiving end, K is the number of reflecting elements of the intelligent reflecting surface, and Θ i ＝diag(θ i ) To correspond to x i Reflection matrix of intelligent reflecting surface of +.>Is->The j element in (2) is the coefficient of the j reflective element on the intelligent reflective surface, and has +.>x i Carrying bit information in an ith information block for an ith transmission signal;
taking the Euclidean distance between the minimum ith actual received signal and the ith target received signal as an optimization target, taking all reflection coefficients on the intelligent reflecting surface as optimization variables, and establishing an optimization problem as follows:
wherein ,(·)H To conjugate transpose the matrix, 1 represents an all 1 vector of dimension Kx1.
Alternatively, in one embodiment of the present invention, the method of solving the optimization problem is by a prime-dual interior point method.
Optionally, in an embodiment of the present invention, according to a received signal of the receiving end, a maximum likelihood detection algorithm is adopted, and decoding is performed based on a spatial modulation scheme of the transmitting end, so as to obtain the information bit to be transmitted, including:
the receiving signals of the noise-containing signals received by the receiving terminals are as follows:
wherein ,for a receiving signal of a noise-containing signal received by a receiving end, x is a transmitting signal of a transmitting end, and n is additive Gaussian white noise;
the maximum likelihood detection algorithm is as follows:
wherein I 2 The number of 2-norms is indicated,is x i Estimation under maximum likelihood detection.
According to the intelligent reflection surface-assisted spatial modulation system reflection coefficient optimization method, information bits to be transmitted by a transmitting end are divided into a plurality of information blocks with the same length, and corresponding active antennas are selected to transmit specific signals according to each information block; optimizing coefficients of reflection elements on the intelligent reflection surface, and maximizing Euclidean distances among different received signals; and adopting maximum likelihood detection decoding at a receiving end to recover the original information bits. The intelligent reflecting surface is combined with the spatial modulation scheme, the wireless channel is reconstructed by utilizing the intelligent reflecting surface, the Euclidean distance between different received signals is increased, and the error code performance of the system is improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a flowchart of an intelligent reflection surface assisted method for optimizing the reflection coefficient of a spatial modulation system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a reflection coefficient optimization structure of an intelligent reflection surface-assisted spatial modulation system according to an embodiment of the present invention;
FIG. 3 is a schematic block diagram of embodiment 1 according to the present invention;
FIG. 4 is a schematic block diagram of embodiment 2 according to the present invention;
FIG. 5 is a diagram of embodiment 1 according to the present invention, N t ＝5,N r Bit error rate simulation plots for the cases of =1, k=16, 32, r=4;
FIG. 6 is a schematic illustration of a system according to the present inventionIn example 2, N t ＝5,N r Error rate simulation plots for the case of = 2,K =16, 32, r=4.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
Fig. 1 is a flowchart of a method for optimizing a reflection coefficient of an intelligent reflection surface-assisted spatial modulation system according to an embodiment of the present invention.
The space modulation system comprises a transmitting end, an RIS and a receiving end, and the reflection coefficient optimization method comprises a transmitting end space modulation process, a target received signal design process, a reflection coefficient solving process on the RIS and a receiving end detection decoding process. Without loss of generality, the RIS can obtain ideal channel state information assuming that the direct paths of the transmitting end and the receiving end are blocked.
Based on the RIS advantages, the invention combines the RIS and the spatial modulation technology, reconstructs the wireless transmission channel by optimizing the coefficient of the reflection element on the RIS, and improves the error code performance of the spatial modulation system.
As shown in fig. 1, the reflection coefficient optimization method of the intelligent reflection surface assisted spatial modulation system comprises the following steps:
in step S101, the information bits to be transmitted of the transmitting end are divided into a plurality of information blocks with the same length, the information blocks are loaded on the transmitting end to be transmitted, an active antenna is selected for each information block to transmit a modulation symbol based on a spatial modulation principle, and the information bits are transmitted through an active antenna index and the modulation symbol to perform spatial modulation of the transmitting end.
As shown in fig. 2, the transmitting end is equipped with N t Root antenna, receiving end is equipped with N r The RIS has K reflection elements on the root antenna.Respectively from the transmitting end to the transmitting endRIS and channel matrix from RIS to receiving end, wherein each element obeys complex Gaussian distribution with mean value of 0 and variance of 1; the reflection matrix corresponding to RIS is Θ=diag (θ), whereθ j Is the j element in θ, represents the coefficient of the j reflective element on RIS, and has |θ j |＝1。
Transmitting signal vectorCan be expressed as:
wherein ,index indicating active antenna of transmitting end, +.>Representing the transmitting end n t Signals transmitted on the active antennas, respectively.
In step S102, an optimal target receiving signal is designed so that the euclidean distance between the target receiving signals is maximized, the euclidean distance between the minimized actual receiving signal and the target receiving signal is used as an optimization target, all reflection coefficients of the intelligent reflecting surface are used as optimization variables, an optimization problem is established, the optimal reflection coefficients of the intelligent reflecting surface are obtained by solving the optimization problem, the phase of the incident signal is changed by using the intelligent reflecting surface based on the optimal reflection coefficients, and the incident signal is reflected to the receiving end.
Optionally, in one embodiment of the present invention, the design target reception signal includes the following two steps: the method comprises the steps of determining the average power of a target received signal and designing a distribution form of the normalization of the target received signal. The method comprises the following steps: taking the average power of the received signal obtained based on the cosine similarity theorem optimization algorithm as the average power of the target received signal; designing a normalized distribution form of target received signals by taking the Euclidean distance between different maximized received signals as a criterion; finally, the target receiving signal is obtained.
The reflection coefficient on the RIS is optimized with the goal of maximizing the euclidean distance between the different received signals to obtain better error performance.
First, the average power of the received signal obtained based on the cosine similarity theorem optimization algorithm is taken as the target average power of the received signal.
The method is characterized in that a reflection coefficient on the RIS is optimized by maximizing a receiving signal-to-noise ratio as a target based on a cosine similarity theorem optimization algorithm, wherein a phase offset method is a special case of the algorithm, namely when a transmitting end and a receiving end are respectively activated to transmit and receive signals by only one antenna, each reflection element on the RIS can be used for achieving the purpose of maximizing the receiving signal-to-noise ratio by offsetting the phases of channel coefficients on two sides of the element, so that all reflection signals received by the receiving end are in phase. Under the condition that the parameter configuration is unchanged, the phase cancellation method can reach the theoretical upper bound of the received power, and the theoretical upper bound is taken as the average power of the target received signal.
Assuming that the mth antenna of the transmitting end is selected as an active antenna, a signal s is transmitted, wherein E (s H ·s)＝1。The channel coefficients respectively representing the m-th antenna of the transmitting end to the k-th reflecting element on the RIS and the k-th reflecting element on the RIS to the n-th antenna of the receiving end are subjected to complex Gaussian distribution with 0 mean and 1 variance. Thus, alpha mk and βkn Is an independent random variable and all obeys the mean value +.>Variance is->Rayleigh distribution of (2).
The signal received by the nth antenna of the receiving end is:
wherein ,y(n) Representing the nth element in y.
According to the phase cancellation method, letThe above-mentioned rewrites as:
the average power of the received signal on the nth antenna may be expressed as:
when k is 1 ＝k 2 In the time-course of which the first and second contact surfaces,
when k is 1 ≠k 2 In the time-course of which the first and second contact surfaces,
the average power of the received signal on the nth antenna may be rewritten as:
the receiving end has N r When the antenna is root, the average received power is:
thus, P y Can be used as the average power of the target received signal.
Secondly, a target received signal normalized distribution form is designed based on the minimum Euclidean distance between different received signals as a standard.
Under the constraint of average power normalization of the received signals, the distribution form of the target received signals is designed so as to maximize the minimum Euclidean distance between different received signals.
1) When N is r When the number of the codes is =1,
the received signal is a complex number and can be considered as a constellation point in the constellation. At this time, the QAM scheme may be directly used as a design method of the target reception signal.
For example, when N r When the system transmission rate is Rbits/transmission, m=2 can be performed R The average power of M constellation points generated by the order QAM modulation is normalized, and the normalized average power can be used as a target receiving signal.
2) When N is r When not less than 2
The received signal is N r 1, each component being a complex number comprising a real part and an imaginary part, then the complex-valued vector contains N in total r Sum of real parts N r And imaginary parts. Thus, one N r X 1 received signal vector and 2N r One point in the dimensional space corresponds. When the transmission rate of the system is Rbits/transmission, M=2 is designed R N number r The x 1 received signal vector can be equivalently expressed as at 2N r Find M points in the dimensional space and maximize the minimum euclidean distance between the M points.
When N is r When not less than 2, 2N r The dimensional space is a high-dimensional space. Finding M points in the high-dimensional space and maximizing the minimum euclidean distance between the M points is a very complex problem, here we give a sub-optimal approach by observing the characteristics of the low-dimensional space.
In two dimensions, 2 can be found 2 =4 points, and the euclidean distance between these 4 points is made as large as possible. The coordinates of these 4 points are: (1,1), (1, -1), (-1,1), (-1, -1). They are the 4 vertices of a unit square centered at the origin of coordinates.
In three dimensions, 2 can be found 3 =8 points, and the euclidean distance between these 8 points is made as large as possible. The coordinates of these 8 points are: (1,1,1), (1,1, -1), (1, -1,1), (1, -1, -1), (-1,1,1), (-1,1, -1), (-1, -1,1), (-1, -1, -1). They are 8 vertices of a unit cube centered at the origin of coordinates.
At 2N r In dimensional space, one can findAnd the euclidean distance between the P points is made as large as possible. These P points may be determined by letting 2N r Each dimension in the dimension space is traversed in the set s= {1, -1 }.
For example, when N r When=2, 2 can be found in four-dimensional space using the method described above 4 =16 points, and the euclidean distance between these 16 points is made as large as possible. The coordinates of these 16 points are: (1,1,1,1), (1,1,1, -1), (1,1, -1,1), (1,1, -1, -1), (1, -1,1,1), (1, -1,1, -1), (1, -1, -1,1), (1, -1, -1, -1), (-1,1,1,1), (-1,1,1, -1), (-1,1, -1,1), (-1,1, -1, -1), (-1, -1,1,1), (-1, -1,1, -1), (-1, -1, -1,1), (-1, -1, -1, -1).
To sum up, when N r Not less than 2, when the system transmission rate is Rbits/transmission, finding M=2 R N number r The method of x 1 complex value vector is summarized as follows:
1. when r=2n r When, m=2 can be found directly using the above method R Complex value vectors and make the euclidean distance between them as large as possible. The average power of the M complex value vectors is normalized, so that the M complex value vectors can be used as a normalized target received signal.
2. When R > 2N r When we can increase 2N r The traversal range of each dimension in the dimension space, that is, each dimension may carry more than one bit of information and the number of information bits carried by each dimension is made equal as much as possible. Order theV 1 ＝R-2N r ·U 1, wherein />Representing a rounding down operation.
For 2N r Front V in dimensional space 1 Dimension space, where each dimension carries (U 1 +1) bit information. Let S 1 Before representing V 1 A set of traversals for each dimension in a dimension space, comprisingElements, S 1 Can be expressed as:
for 2N r Remaining (2N) in dimensional space r -V 1 ) Dimension space, where each dimension carries a U 1 Bit information. Let S 2 Indicating the remainder (2N r -V 1 ) A set of traversals for each dimension in a dimension space, comprisingElements, S 2 Can be expressed as:
3. when R < 2N r When the method is used, the dimension reduction operation can be utilized to reduce the number of 2N r The dimension space is reduced to the R dimension space and then scheme 1 can be used. The strategy for dimension reduction is to reduce the 2N r The dimensions are divided into R groups, and each group is regarded as a generalized dimension, wherein the values of all the dimensions in each group are consistent. The strategy for grouping is to make the dimensions contained in each group as equal as possible.
Order theV 2 ＝2N r -R·(U 2 -1) wherein>Representing a rounding up operation. 2N r Front U in dimensional space 2 V 2 The dimensions are divided into V 2 Groups, each group comprising U 2 And a dimension. Then, the remaining (2N 2 -U 2 V 2 ) The dimensions are divided into (R-V 2 ) Groups, each group comprising (U) 2 -1) dimensions, 2N 2 -U 2 V 2 ＝(R-V 2 )·(U 2 -1). In this way, 2N r The dimensional space is reduced to an equivalent R-dimensional space and scheme 1 can be used directly to produce a normalized target received signal.
4. Combining step 2 and step 3, the target received signal can be obtained.
When the transmission rate of the system is R bits/transmission, m=2 R The number of transmitted signal vectors may be denoted as x 1 ,x 2 ,…,x M The method comprises the steps of carrying out a first treatment on the surface of the The M target received signals may be expressed as
The i-th actual received signal is:
y i ＝G·Θ i ·H·x i
wherein ,channel matrix from transmitting end to intelligent reflecting surface and from intelligent reflecting surface to receiving end respectively, N t Number of antennas provided for transmitting end, N r The number of antennae equipped for the receiving end, K is the number of reflecting elements of the intelligent reflecting surface, and Θ i ＝diag(θ i ) To correspond to x i Reflection matrix of intelligent reflecting surface of +.>Is->The j element in (2) is the coefficient of the j reflective element on the intelligent reflective surface, and has +.>x i And carrying bit information in the ith information block for the ith transmission signal.
Taking the Euclidean distance between the minimum ith actual received signal and the ith target received signal as an optimization target, taking all reflection coefficients on the intelligent reflecting surface as optimization variables, and establishing an optimization problem as follows:
wherein ,(·)H Representing the conjugate transpose of the matrix, 1 represents an all 1 vector of dimension K x 1.
As a specific embodiment, the optimization problem is solved by a prime-dual interior point method.
Specifically, the optimization problem is solved by adopting the fmincon function in Matlab, and the solution of the optimization problem is the reflection coefficient of RIS.
Solving the optimization problem, wherein the solution of the optimization problem is the coefficient of the reflection element on the RIS. The RIS changes the phase of the incident signal according to the obtained reflection coefficient and reflects the incident signal to the receiving end.
In step S103, according to the received signal of the receiving end, a maximum likelihood detection algorithm is adopted, and decoding is performed based on the spatial modulation scheme of the transmitting end, so as to obtain the information bits to be transmitted.
The received signal of the noise-containing signal received by the receiving end is:
wherein ,is the noise-containing signal vector received by the receiving end, and the dimension is N r X 1; x is a signal vector sent by a sending end, and the dimension is N t X 1; n is an additive white gaussian noise vector with a dimension N r X 1, wherein each component obeys a mean of zero, variance of +.>Complex gaussian distribution of (a);
the maximum likelihood detection algorithm is as follows:
wherein I 2 Representing a 2-norm; x is x i Representing an ith transmission signal vector carrying bit information in an ith information block; theta (theta) i Representation and x i A corresponding RIS reflection matrix;is x i Estimation under maximum likelihood detection.
After maximum likelihood detection at the receiving end, based on the decoding principle of the corresponding spatial modulation scheme, according to the estimated parametersThe original information bits are recovered.
The reflection coefficient optimization method of the intelligent reflection surface-assisted spatial modulation system is described in detail below through specific embodiments.
Example 1
As shown in fig. 3, the transmitting end is equipped with N t =5 antennas, and the receiving end is equipped with N r =1 antenna, with k=32 reflective elements on RIS.Channel matrix representing sender to RIS, < >>Representing the channel matrix of the RIS to the receiving end. H and G 1 Each element in (a) obeys a complex gaussian distribution with a mean of 0 and a variance of 1. It is assumed that the direct path from the transmitting end to the receiving end is blocked. The transmitting end carries out SC-SSK modulation, and in each transmission, two antennas are selected as active antennas to respectively transmit signals s 1 ,s 2, wherein ,s1 ≠s 2 。
The intelligent reflection surface-assisted reflection coefficient optimization method for the spatial modulation system can be implemented through the following four processes:
(1) Transmitting-side spatial modulation process
The transmitting end divides the information bit to be transmitted into a plurality of information blocks with the same length. According to the information bit in the information block, based on the SC-SSK modulation principle, the transmitting end selects two active antennas to transmit s respectively 1 ,s 2 。
According to the SC-SSK modulation principle, the transmitting end modulation comprises two steps, and in each step, the transmitting end selects one antenna from 4 antennas as an active antenna. Therefore, there are a total of 4×4=16 transmission patterns, each of which is mapped with 4-bit information, and the mapping relationship is shown in table 1.
Table 1 mapping relationship between information bits and transmission patterns
2) Target received signal design process
The average power of the target received signal is:
when N is r When=1, the QAM scheme can be targeted for receptionA signal design method. At this time, r=4, m=2 4 =16, normalize the average power of 16 constellation points obtained after 16-QAM modulation, where the normalized 16 constellation points can be used as the target received signal normalized by the current system. Normalized target received signal set S 3 This can be expressed as:
S 3 ＝{c 1 ,c 2 ,c 3 ,c 4 ,c 5 ,c 6 ,c 7 ,c 8 ,c 9 ,c 10 ,c 11 ,c 12 ,c 13 ,c 14 ,c 15 ,c 16 }
wherein ,ci And the ith constellation point obtained by the average power normalization of the 16-QAM modulation is represented.
The average power of the target received signal and the normalized target received signal are combined and the target received signal of the current system is shown in table 2.
Table 2 target received signal in example 1
(3) Reflection coefficient solving process on RIS
When the information bit in the information block is 0000, it can be seen from Table 1 that the signal vector is transmittedCan be expressed as:
x 1 ＝[s 1 ,s 2 ,0,0,0] T
actually received signalCan be expressed as:
y 1 ＝G 1 ·Θ 1 ·H·x 1
wherein ,Θ1 ＝diag(θ 1 )，
As can be seen from Table 2, the target received signalCan be expressed as: />
Taking the Euclidean distance between the minimized actual received signal and the target received signal as an optimization target and taking all reflection coefficients on RIS as optimization variables, the following optimization problem can be established:
wherein ,(·)H Representing the conjugate transpose of the matrix, 1 represents an all 1 vector with dimensions 32 x 1.
And solving the optimization problem by using an fmincon function in Matlab, wherein the solution of the optimization problem is the coefficient of the reflection element on the RIS. The RIS changes the phase of the incident signal according to the obtained reflection coefficient and reflects the signal to the receiving end.
(4) Receiving end detecting and decoding process
Noise-containing signal vector received by receiving endCan be expressed as:
the maximum likelihood detection algorithm may be expressed as follows:
wherein ：is x i Estimation under maximum likelihood detection. />
After the maximum likelihood detection is carried out at the receiving end, the decoding principle based on the SC-SSK scheme is adopted, and the estimated parameters are used forThe original information bits are recovered.
Example 2
As shown in fig. 4, the receiving end is equipped with N r The number of antennas is =2,the channel matrix from RIS to receiving end is represented, wherein each element obeys complex Gaussian distribution with mean 0 and variance 1. The remaining parameter configurations are identical to those of example 1.
The intelligent reflection surface-assisted reflection coefficient optimization method for the spatial modulation system can be implemented through the following four processes:
(1) Transmitting-side spatial modulation process
The transmitting end divides the information bit to be transmitted into a plurality of information blocks with the same length. According to the information bit in the information block, based on the SC-SSK modulation principle, the transmitting end selects two active antennas to transmit s respectively 1 ,s 2 . The mapping relation between the transmission pattern and the information bit is shown in table 1.
According to the SC-SSK modulation principle, the transmitting end modulation comprises two steps, and in each step, the transmitting end selects one antenna from 4 antennas as an active antenna. Therefore, there are a total of 4×4=16 transmission patterns, each of which is mapped with 4-bit information, and the mapping relationship is shown in table 1.
(2) Target received signal design process
The average power of the target received signal is:
when N is r ＝2，R＝2N r When=4, the proposed sub-optimization method can be used to obtain normalized target received signal profileFormula (I). In four-dimensional space, 2 can be found 4 =16 points, and the euclidean distance between these 16 points is made as large as possible. The coordinates of these 16 points are: (1,1,1,1), (1,1,1, -1), (1,1, -1,1), (1,1, -1, -1), (1, -1,1,1), (1, -1,1, -1), (1, -1, -1,1), (1, -1, -1, -1), (-1,1,1,1), (-1,1,1, -1), (-1,1, -1,1), (-1,1, -1, -1), (-1, -1,1,1), (-1, -1,1, -1), (-1, -1, -1,1), (-1, -1, -1, -1). The 16 points are converted into 16 complex value vectors with 2 multiplied by 1 dimensions, and the average power is normalized, so that 16 normalized target received signals can be obtained.
The average power of the target received signal and the normalized target received signal are combined and the target received signal of the current system is shown in table 3.
Table 3 target received signal in example 2
(3) Reflection coefficient solving process on RIS
When the information bit in the information block is 0001, it can be seen from Table 1 that the signal vector is transmittedCan be expressed as:
x 2 ＝[s 1 ,0,s 2 ,0,0] T
actually received signalCan be expressed as:
y 2 ＝G 2 ·Θ 2 ·H·x 2
wherein ,Θ2 ＝diag(θ 2 )，
As can be seen from Table 3, the target received signalCan be expressed as: />
Taking the Euclidean distance between the minimized actual received signal and the target received signal as an optimization target and taking all reflection coefficients on RIS as optimization variables, the following optimization problem can be established:
wherein ,(·)H Representing the conjugate transpose of the matrix, 1 represents an all 1 vector with dimensions 32 x 1.
And solving the optimization problem by using an fmincon function in Matlab, wherein the solution of the optimization problem is the coefficient of the reflection element on the RIS. The RIS changes the phase of the incident signal according to the obtained reflection coefficient and reflects the signal to the receiving end.
(4) Receiving end detecting and decoding process
Noise-containing signal vector received by receiving endCan be expressed as:
the maximum likelihood detection algorithm may be expressed as follows:
/>
wherein ：is x i Estimation under maximum likelihood detection.
After the maximum likelihood detection is carried out at the receiving end, the decoding principle based on the SC-SSK scheme is adopted, and the estimated parameters are used forThe original information bits are recovered.
Fig. 5 and 6 show simulated comparison diagrams of the proposed algorithm with the existing SDR algorithm and the algorithm based on cosine similarity theorem in terms of error code performance in embodiment 1 and embodiment 2, respectively. It can be seen from the figure that in the case of the same system transmission rate, no matter what N r =1 or N r The proposed algorithm has a lower error rate than the other two existing algorithms, i.e., = 2,K =16 or k=32. For example, as shown in FIG. 6, when N r ＝2，K＝32，BER＝10 -3 When the algorithm is compared with an SDR algorithm and a cosine similarity theorem-based algorithm, the signal-to-noise ratio gain of 9dB and the signal-to-noise ratio gain of 18dB can be obtained respectively. The method is characterized in that the method optimizes RIS coefficients by taking the Euclidean distance between different received signals as a target, and not only considers the power of the received signals, but also considers the distribution of the received signals, so that the Euclidean distance between the received signals is as large as possible; the other two algorithms are to optimize RIS coefficient with the maximum received signal-to-noise ratio as the target, and the distribution of the received signals is not considered, so that the Euclidean distance between the received signals is smaller, the noise resistance is poor, and the error code performance is reduced. Meanwhile, as can be seen from the observation of fig. 5 and 6, the error performance of all algorithms is gradually improved as the number of reflective elements on the RIS is increased or the number of receiving antennas is increased.
According to the intelligent reflection surface-assisted spatial modulation system reflection coefficient optimization method provided by the embodiment of the invention, information bits to be transmitted by a transmitting end are divided into a plurality of information blocks with the same length, and a corresponding active antenna is selected to transmit a specific signal according to each information block; optimizing coefficients of reflection elements on the intelligent reflection surface, and maximizing Euclidean distances among different received signals; and adopting maximum likelihood detection decoding at a receiving end to recover the original information bits. The invention combines the intelligent reflecting surface with the spatial modulation scheme, utilizes the intelligent reflecting surface to reconstruct the wireless channel, increases the Euclidean distance between different received signals, improves the error code performance of the system, and can obtain better error code performance than the prior algorithm under the same condition.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or N embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "N" means at least two, for example, two, three, etc., unless specifically defined otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and additional implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order from that shown or discussed, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present invention.

Claims (5)

1. The reflection coefficient optimization method of the intelligent reflection surface-assisted spatial modulation system comprises a transmitting end, an intelligent reflection surface and a receiving end, and is characterized by comprising the following steps of:
dividing information bits to be transmitted of the transmitting end into a plurality of information blocks with the same length, selecting active antennas for each information block to transmit modulation symbols based on a spatial modulation principle, transmitting the information bits through active antenna indexes and the modulation symbols, and performing spatial modulation of the transmitting end;
designing an optimal target receiving signal, maximizing Euclidean distance between the target receiving signals, taking minimized Euclidean distance between an actual receiving signal and the target receiving signal as an optimization target, taking all reflection coefficients of the intelligent reflecting surface as optimization variables, establishing an optimization problem, obtaining the optimal reflection coefficient of the intelligent reflecting surface by solving the optimization problem, changing the phase of an incident signal by utilizing the intelligent reflecting surface based on the optimal reflection coefficient, and reflecting the incident signal to the receiving end;
and according to the received signal of the receiving end, adopting a maximum likelihood detection algorithm, and decoding based on a space modulation scheme of the transmitting end to obtain the information bit to be transmitted.
2. The method of claim 1, wherein designing the target received signal comprises:
and taking the average power of the received signals obtained based on the cosine similarity theorem optimization algorithm as the average power of the target received signals, and designing a normalized distribution form of the target received signals by taking the Euclidean distance between different received signals as a criterion to obtain the target received signals.
3. The method of claim 1, wherein establishing an optimization problem with respect to minimizing the euclidean distance between the actual received signal and the target received signal as an optimization objective, and wherein all reflection coefficients of the intelligent reflecting surface as optimization variables comprises:
the i-th actual received signal is:
y i ＝G·Θ i ·H·x i
wherein ,channel matrix from transmitting end to intelligent reflecting surface and from intelligent reflecting surface to receiving end respectively, N t Number of antennas provided for transmitting end, N r The number of antennae equipped for the receiving end, K is the number of reflecting elements of the intelligent reflecting surface, and Θ i ＝diag(θ i ) To correspond to x i Reflection matrix of intelligent reflecting surface of +.>Is->The j element in (2) is the coefficient of the j reflective element on the intelligent reflective surface, and has +.>x i Carrying bit information in an ith information block for an ith transmission signal;
taking the Euclidean distance between the minimum ith actual received signal and the ith target received signal as an optimization target, taking all reflection coefficients on the intelligent reflecting surface as optimization variables, and establishing an optimization problem as follows:
s.t.diag(θ i ·θ i H )＝1
wherein ,(·)H To conjugate transpose the matrix, 1 represents an all 1 vector of dimension Kx1.
4. A method according to claim 1 or 3, characterized in that the method of solving the optimization problem is by a prime pair interior point method.
5. The method of claim 3, wherein decoding based on a spatial modulation scheme of a transmitting end to obtain the information bits to be transmitted by using a maximum likelihood detection algorithm according to the received signal of the receiving end, comprises:
the receiving signals of the noise-containing signals received by the receiving terminals are as follows:
wherein ,for a receiving signal of a noise-containing signal received by a receiving end, x is a transmitting signal of a transmitting end, and n is additive Gaussian white noise;
the maximum likelihood detection algorithm is as follows:
wherein I 2 The number of 2-norms is indicated,is x i Estimation under maximum likelihood detection.
CN202310610192.7A 2023-05-26 2023-05-26 Intelligent reflection surface-assisted reflection coefficient optimization method for spatial modulation system Pending CN116614165A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118101007A (en) * 2024-04-26 2024-05-28 南京派格测控科技有限公司 Multi-user-oriented intelligent reflection surface auxiliary step-by-step coding space shift keying method and system
CN118101007B (en) * 2024-04-26 2024-08-02 南京派格测控科技有限公司 Multi-user-oriented intelligent reflection surface auxiliary step-by-step coding space shift keying method and system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118101007A (en) * 2024-04-26 2024-05-28 南京派格测控科技有限公司 Multi-user-oriented intelligent reflection surface auxiliary step-by-step coding space shift keying method and system
CN118101007B (en) * 2024-04-26 2024-08-02 南京派格测控科技有限公司 Multi-user-oriented intelligent reflection surface auxiliary step-by-step coding space shift keying method and system

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