CN111865379B - Safe precoding method based on alternating direction multiplier method - Google Patents

Safe precoding method based on alternating direction multiplier method Download PDF

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CN111865379B
CN111865379B CN202010678686.5A CN202010678686A CN111865379B CN 111865379 B CN111865379 B CN 111865379B CN 202010678686 A CN202010678686 A CN 202010678686A CN 111865379 B CN111865379 B CN 111865379B
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CN111865379A (en
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束锋
蒋昕怡
刘笑语
刘林
滕殷
邹骏
桂林卿
李逸凡
史柏华
俞娴
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Nanjing University of Science and Technology
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Abstract

The invention provides a safe precoding method based on an alternating direction multiplier method. The method designs digital precoding and analog precoding respectively to improve the safety performance of the system. Firstly, the fact that a transmitter only activates one antenna subarray to send information at a time is utilized, the overall precoding matrix is cut, and the consistency optimization problem is established. Secondly, introducing new matrix variables and dual variables changes the problem from non-convex to convex. And updating the overall precoding matrix by an alternating direction multiplier method, and calculating the Euclidean distance of the overall precoding matrix before and after updating until a termination condition is met. Finally, the overall pre-coding is used to obtain the analog and digital pre-coding respectively. The invention is different from the traditional full digital-based spatial modulation system, and the circuit cost is obviously reduced by adopting a partially connected hybrid structure at the transmitter; and through the design of safe pre-coding, the mixed space modulation has good safety performance.

Description

Safe precoding method based on alternating direction multiplier method
Technical Field
The invention relates to the technical field of wireless communication, in particular to a safe precoding method based on an alternating direction multiplier method.
Background
With the rapid development of 5G communication networks, the number of network devices is dramatically increased, and wireless communication faces greater and greater challenges. The demand of wireless resources for future wireless communication systems is also increasing, including ultra-high capacity, ultra-low delay, and a large number of connections. Researchers are constantly working on developing new transmission technologies, and among various technologies, spatial modulation transfers information by activating one transmitting antenna, has the advantages of higher energy efficiency, lower detection complexity, compatibility with large-scale MIMO and the like, and is considered to be the digital modulation technology with the greatest development prospect.
To meet the situation that the amount of data is rapidly increasing with the advent of the 5G era, massive MIMO is being widely studied in modern wireless communication. However, as the number of antennas increases, it is impractical to install one rf chain for each antenna, which results in a significant increase in power consumption, and hardware cost. Therefore, a spatial modulation system with a hybrid analog and digital structure can be considered, and the system can achieve better performance only by using radio frequency chains far less than the number of antennas through hybrid beam forming or hybrid precoding design. In addition, since the wireless communication channel is open and broadcast, and is very vulnerable to eavesdropping and interference by a third party, it is very important to improve the security of the hybrid spatial modulation system. Aiming at the hybrid space modulation system, the invention provides a safe precoding design method based on an alternative direction multiplier method, which cuts and simplifies the overall precoding matrix, channel and the like by utilizing the fact that the hybrid space modulation system only activates one antenna subarray to send useful information each time, and constructs a consistency optimization problem; then, the problem is converted from non-convex to convex by introducing matrix variables, dual variables and the like; finally, updating the matrix variable, the dual variable and the overall precoding matrix by using an alternating direction multiplier method, and calculating the Euclidean distance of the overall precoding matrix before and after updating until a termination condition is met; after the total pre-coding matrix is obtained, analog pre-coding and digital pre-coding are respectively obtained through calculation, and the safety rate of the system is improved.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a safe precoding method based on an alternating direction multiplier method. Firstly, cutting a total pre-coding matrix according to the activation condition of an antenna subarray, and simplifying channels and the like; secondly, introducing a matrix variable and a dual variable, and establishing a convex consistency optimization problem; then, designing an overall precoding matrix by using an alternating direction multiplier method; and finally, designing digital precoding and analog precoding respectively according to the relation between the overall precoding and the digital precoding and the analog precoding.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps: cutting a total pre-coding matrix and simplifying a channel, a modulation bit and the like by utilizing the fact that each time slot in a hybrid space modulation system only activates one antenna subarray to send useful information, re-expressing a safety rate and establishing a consistency optimization problem; introducing a matrix variable and a dual variable, and converting the optimization problem from non-convex to convex; designing an overall safety pre-coding matrix by an alternative direction multiplier method; and designing a digital and analog precoding matrix after obtaining the total precoding matrix by utilizing the relation between the total precoding and the digital and analog precoding.
Further, the specific process comprises the following steps: s1, cutting data of an optimization problem by utilizing the characteristic that the overall mixed pre-coding matrix only activates pre-coding corresponding to one antenna subarray at a time, and decomposing an objective function into a plurality of sub objective functions. Firstly, cutting and initializing the total precoding matrix according to the activated antenna subarrays, and simultaneously simplifying the transmitted modulation bits, channels and decoding matrix. Secondly, rewriting an expression of the safe rate by using the variables obtained by cutting and simplifying, and establishing a consistency optimization problem by using the Jersen inequality; s2, the objective function obtained in S1 is still a non-convex problem, so that a new matrix variable and a dual variable are introduced, an expression for processing a fusion center is written, and the non-convex problem is converted into a convex optimization problem. Meanwhile, initializing a matrix variable and a dual variable; s3, obtaining matrix variables and dual variables corresponding to all possibly activated antenna subarrays through iterative calculation of an alternating direction multiplier method; further calculating a fusion center, and calculating Euclidean distances of the overall pre-coding matrixes before and after updating until a condition of terminating iteration is met; and S4, after the total pre-coding matrix is obtained according to the steps, respectively designing a digital pre-coding matrix and an analog pre-coding matrix according to the relation between the total pre-coding matrix and the digital pre-coding matrix and the analog pre-coding matrix.
Has the advantages that: the safe precoding method based on the alternative direction multiplier method provided by the invention has the following advantages: 1. compared with the traditional full-digital spatial modulation system, the method has the advantages that the transmitter adopts a mixed structure of partial connection and combination of digital pre-coding and analog pre-coding, so that the number of radio frequency links can be reduced, and the hardware cost and the power consumption are reduced; 2. compared with the existing hybrid precoding designed based on the semidefinite relaxation iteration minimization algorithm, the hybrid precoding in the safe spatial modulation system designed by the method has the advantage that the performance of the hybrid spatial modulation system in the aspect of the safe rate is improved considerably in the medium and high signal-to-noise ratio areas.
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
Fig. 1 is a flowchart of a secure precoding method based on an alternating direction multiplier method.
Detailed Description
The present invention is further illustrated by the following figures and specific examples, which are to be construed as merely illustrative and not limitative of the remainder of the disclosure, and all changes and modifications that would be obvious to those skilled in the art are intended to be included within the scope of the present invention and the appended claims are intended to be embraced therein.
The invention provides a spatial modulation system model based on a hybrid structure, wherein a transmitter adopts a partially connected hybrid structure and is provided with NRFA radio frequency chain, each radio frequency chain is connected with NAAA transmitting antenna. Both the expected user and the eavesdropping user are all digital structures, and each has NbAnd NeThe root receives the antenna. In most cases, the number of transmit antenna subarrays N of the transmitterRFNot necessarily to the power of 2. According to the basic principle of spatial modulation, antenna numbers are mapped to bit information, so that only an exponential power of 2 number of antennas is used, so we are at NRFSelection among sub-arrays of transmit antennas
Figure GDA0003356746560000031
And each antenna subarray. Total sum of all
Figure GDA0003356746560000032
An alternative antenna set
Figure GDA0003356746560000033
For a selected set of antenna subarrays, where liFrom the set of all antenna subarrays {1,2RFAnd (6) selecting. After the antenna selection subarray is obtained by using the relevant antenna subarray selection algorithm, the transmission signal of Alice can be represented as
Figure GDA0003356746560000034
Wherein, bjIs the jth symbol in the M-ary constellation diagram and satisfies
Figure GDA0003356746560000035
Matrix array
Figure GDA0003356746560000036
i∈IAASIs a block diagonal matrix, and only the ith sub-block is an identity matrix, and the rest sub-blocks are all zero matrices. This means that the ith antenna sub-array is activated, i.e. satisfies Ei＝diag[0,…,0,ei,0,…,0]Wherein
Figure GDA0003356746560000037
T is like EiA form of antenna sub-array selection matrix,
Figure GDA0003356746560000038
for all I ∈ IAASSatisfy the following requirements
Figure GDA0003356746560000039
The other sub-blocks are all zero matrixes, which indicate that I is selectedAASN in (1)tOne dayAnd (5) linear subarrays.
Figure GDA00033567465600000310
Is the artificial noise, P is the total power of the transmitted signal, and β is the power division factor of the modulated signal and the artificial noise. FBBIs a digital precoding matrix of the transmitted useful signal
Figure GDA00033567465600000311
Matrix in formula (1)
Figure GDA00033567465600000312
Is a digital precoding matrix of artificial noise. Since only N is presenttThe antenna subarrays are selected such that the artificial noise is projected only to NtA sub-array of antennas, hence TBBOnly corresponding NtThe behavior is a non-zero vector and the rest are zero vectors. After passing through the corresponding radio frequency chain, the signal is sent to an analog phase shifting network consisting of phase shifters for analog precoding, and the process can use the dimension NAANRF×NRFAnalog precoding matrix FRFTo represent
Figure GDA00033567465600000313
Wherein,
Figure GDA00033567465600000314
i＝1,2,…,NRFis the ith analog weight vector, each element in the vector having the same magnitude
Figure GDA00033567465600000315
And a different phase, phase modulating the signal. Let P be FRFFBBRepresents the overall precoding matrix of the useful signal, and thus
Figure GDA00033567465600000316
And is
Figure GDA00033567465600000317
＝1,2,…,NRF. Similarly, PAN＝FRFTBBRepresenting the total precoding matrix of the artificial noise.
Assuming a desired channel
Figure GDA0003356746560000041
And eavesdropping on the channel
Figure GDA0003356746560000042
Are all flat Rayleigh fading channels, and the eavesdropper knows the precoding matrix of the transmitter, and the received signals respectively decoded at the desired user and the eavesdropped user are
Figure GDA0003356746560000043
Figure GDA0003356746560000044
Wherein,
Figure GDA0003356746560000045
and
Figure GDA0003356746560000046
all-digital decoding matrices for the intended user and the eavesdropping user, respectively.
Assuming that the receiver employs the ML detection method, the detection of a legitimate receiver is as follows
Figure GDA0003356746560000047
In the hybrid pre-coding SM system, the average safe rate can be expressed as
Figure GDA0003356746560000048
Wherein, I (x; y)b) And I (x; y ise) The mutual information amount of the signals received by the expected user and the eavesdropping user respectively is expressed as the following formula
Figure GDA0003356746560000049
Figure GDA00033567465600000410
Wherein omegaBAnd ΩECovariance matrices of interference and noise signals of desired and eavesdropped users, respectively
Figure GDA00033567465600000411
Figure GDA00033567465600000412
ΩBAnd ΩEIt can be regarded as a whitening filter for the desired user and the eavesdropping user, and whitens the interference and noise of the two receiving ends into white gaussian noise with the mean value of 0 and the variance of 1. In the formulae (9) and (10),
Figure GDA00033567465600000413
and is
Figure GDA00033567465600000414
And is
Figure GDA00033567465600000415
Since the above-mentioned safe rate expression is too complicated, it is not favorable for the design of the following precoding. The present invention extends the cut-off rate in a conventional MIMO system to derive an approximate safe rate, which is expressed as follows
Figure GDA00033567465600000416
Wherein
Figure GDA00033567465600000417
And
Figure GDA00033567465600000418
is the cutoff rate of the desired user
Figure GDA00033567465600000419
Figure GDA00033567465600000420
For the convenience of the subsequent design of the precoding matrix, the approximate safe rate is expressed as
Figure GDA0003356746560000051
Wherein,
Figure GDA0003356746560000052
Figure GDA0003356746560000053
considering the approximate safe rate of equation (16), the hybrid precoding design problem can be expressed as follows
Figure GDA0003356746560000054
Due to mixingUnder the spatial modulation system, the approximate safe rate is still a very complicated expression, and in order to simplify the optimization problem, we first find P ═ FRFFBBTotal precoding matrix, and then according to P ═ FRFFBBThe digital precoding matrix and the analog precoding matrix are obtained respectively according to the relationship.
S1: cutting and initializing the obtained precoding matrix P to select the precoding corresponding to the currently activated antenna subarray to obtain qm,m'. Meanwhile, corresponding to the cutting of the pre-coding matrix P, the transmitted modulation bit, the channel and the decoding matrix are simplified to obtain
Figure GDA0003356746560000055
And
Figure GDA0003356746560000056
q obtained by cutting and simplifying as described abovem,m'、
Figure GDA0003356746560000057
And
Figure GDA0003356746560000058
re-expressing the safety rate, deducing an approximate safety rate by using a Jersen inequality, and establishing a consistency optimization problem; for all m, m' epsilon IAASComputing
Figure GDA0003356746560000059
And
Figure GDA00033567465600000510
in the actual communication process, the mixed precoding matrix P requiring solution only activates the precoding P of one antenna subarray at a timeiThis is equivalent to P being sparse during each safe rate solution in practice. Therefore, the data of the optimization problem can be considered to be cut, converted into global variable consistency optimization, and solved by an alternating direction multiplier method. The specific process is as follows, the objective function
Figure GDA00033567465600000511
According to NRFPrecoding p of antenna sub-arraysiDecomposition into NRFSub-objective functions, each sub-objective function obtaining a sub-precoding piBut the global solution has only one P.
According to the thought, the obtained precoding matrix P is cut, and the precoding corresponding to the currently activated antenna subarray is selected
Figure GDA00033567465600000512
At the same time, the transmitted modulation bits, channels and decoding matrix, etc. are simplified
Figure GDA00033567465600000513
Wherein Hm,m'＝[hm hm']Representing the channel corresponding to the selected antenna subarray which is currently activated;
Figure GDA0003356746560000061
Figure GDA0003356746560000062
representing a mapping of modulation symbols.
Similarly, modulation bit, channel and decoding matrix can be simplified for eavesdropping user terminal
Figure GDA0003356746560000063
Gm,m'＝[gm gm'] (23)
Thus, κ in formulae (17) and (18)BAnd kappaEBy using the characteristics of the traces of the matrix, namely, for the matrix A and the matrix B, tr (AB) ═ tr (BA), the trace can be respectively converted into
Figure GDA0003356746560000064
Figure GDA0003356746560000065
Due to log2exp (x) is a concave function, and using the Jackson inequality, the approximate safe rate can be derived as
Figure GDA0003356746560000066
Thus, the optimization problem in equation (19) is transformed into a global variable consistency optimization problem as shown below
Figure GDA0003356746560000067
Wherein,
Figure GDA0003356746560000068
and p ism,m'＝Lm,m'P,
Figure GDA0003356746560000071
And mapping the obtained precoding of each subarray to a corresponding position in the P.
Figure GDA0003356746560000072
l＝(m-1)NAA+1 and
Figure GDA0003356746560000073
l'＝(m'-1)NAA+1，Lm,m'the remaining elements of (a) are zero.
S2: in the non-convex consistency optimization problem (27) established in S1, a new matrix variable is introduced
Figure GDA0003356746560000074
And dual variable Ym,m'Expressing the optimization problem again (27), and establishing a fusion center for processing the global variable P; according to the total precoding matrix P initialized in S10For all m, m' epsilon IAASComputing
Figure GDA0003356746560000075
And
Figure GDA0003356746560000076
the optimization problem (27) is a general form of consistency optimization problem that remains a non-convex problem, thus introducing a new matrix variable
Figure GDA0003356746560000077
To obtain
Figure GDA0003356746560000078
Let the above formula be pmAnd pm'And introducing a dual variable Ym,m'Finally, the optimization problem (27) is re-expressed as the following formula
Figure GDA0003356746560000079
Wherein
Figure GDA00033567465600000710
Figure GDA00033567465600000711
Figure GDA00033567465600000712
In the formula (30), the third term
Figure GDA00033567465600000717
For the penalty term, equation (31) that handles the global variable P is also called the fusion center.
S3: the optimization problem is solved iteratively using an Alternating Direction Multiplier Method (ADMM).
For all m, m' epsilon IAASThe equations (30) and (32) are iteratively calculated to find all
Figure GDA00033567465600000713
And
Figure GDA00033567465600000714
further, all the partitions of the precoding matrix are obtained
Figure GDA00033567465600000715
Will be provided with
Figure GDA00033567465600000716
Substituting into fusion center formula (31) to obtain Pt+1(ii) a Judging termination condition Pt+1-Pt||2If < 0.01 is true, if true, the iteration is ended, and the output mixed precoding matrix P is equal to Pt+1Otherwise, the iterative calculation of S3 is continued.
S4: and respectively designing and solving an analog precoding matrix and a digital precoding matrix according to the obtained total precoding matrix P.
Since the required total precoding matrix P has been found as described above, we naturally pass P ═ FRFFBBSeparately solving the analog precoding matrix FRFAnd a digital precoding matrix FBB. According to an analog precoding matrix FRFProperty of (1) to
Figure GDA0003356746560000081
As an analog precoding for the ith antenna sub-array,
pi＝||pi|| (34)
as the ith antenna sub-arrayDigital precoding, wherein p is known from equation (4)iIs the precoding corresponding to the ith antenna subarray, thereby determining FRFAnd FBB. Thus, the design of the spatial modulation hybrid precoding based on the alternating direction multiplier method is completed.
Fig. 1 is a flow chart showing a design of a secure precoding algorithm based on an alternating direction multiplier method in a hybrid spatial modulation system.

Claims (5)

1. A safety pre-coding method based on an alternative direction multiplier method is characterized in that: the base station adopts a partially connected hybrid structure, so that the hardware cost and the power consumption are greatly reduced; in order to perform safe precoding in a hybrid spatial modulation system, firstly, a total precoding matrix is required to be cut according to an activated antenna subarray, transmitted modulation bits, channels and decoding matrixes are simplified, an approximate safe rate is deduced by using a Jersen inequality, and a consistency optimization problem is established; then, converting the non-convex problem into a convex optimization problem by introducing a matrix variable and a dual variable; then, iterative computation is carried out through an alternating direction multiplier method to obtain updated matrix variables and dual variables, and meanwhile Euclidean distances of the pre-coding matrixes before and after updating need to be computed until a termination condition is met; finally, respectively designing a digital pre-coding matrix and an analog pre-coding matrix according to the relation between the total pre-coding matrix and the digital pre-coding matrix and the analog pre-coding matrix; the specific process comprises the following steps:
s1, cutting data of an optimization problem by utilizing the characteristic that a total mixed pre-coding matrix only activates pre-coding corresponding to one antenna subarray at a time, and decomposing an objective function into a plurality of sub objective functions; firstly, cutting and initializing a total pre-coding matrix according to an activated antenna subarray, and simplifying a transmitted modulation bit, a channel and a decoding matrix; secondly, rewriting an expression of the safe rate by using the variables obtained by cutting and simplifying, and establishing a consistency optimization problem by using the Jersen inequality;
s2. the objective function obtained in S1 remains a non-convex problem, and therefore a new matrix variable Q is introducedm,m'And dual variable Ym,m'M represents the activated antenna subarray to obtain the precoding loss function f corresponding to the activated antenna subarraym,m'(Qm,m') And writing an expression of the global variable P and an updating formula of the dual variable, so as to re-express the original non-convex problem as a convex optimization problem, which is as follows:
Figure FDA0003356746550000011
Figure FDA0003356746550000012
Figure FDA0003356746550000016
Figure FDA0003356746550000013
wherein
Figure FDA0003356746550000014
In order to be a penalty term,
Figure FDA0003356746550000015
pm,m'＝Lm,m'P，Lm,m'mapping the obtained precoding of each sub-array to a matrix of a corresponding position in the global variable, wherein t represents the updating times; the formula that handles global variables is called the fusion center; meanwhile, calculating initial values of a matrix variable and a dual variable according to the total precoding matrix initialized in the S1;
s3, obtaining matrix variables and dual variables corresponding to all possibly activated antenna subarrays through iterative calculation of an alternating direction multiplier method; further calculating a fusion center, and calculating Euclidean distances of the overall pre-coding matrixes before and after updating until a condition of terminating iteration is met;
and S4, after the total pre-coding matrix is obtained according to the steps, respectively designing a digital pre-coding matrix and an analog pre-coding matrix according to the relation between the total pre-coding matrix and the digital pre-coding matrix and the analog pre-coding matrix.
2. The secure precoding method according to claim 1, wherein: in the hybrid spatial modulation system, only one antenna subarray is activated to send useful information each time, that is, only a matrix block corresponding to one antenna subarray is activated each time in the overall precoding matrix; by utilizing the characteristic, the cutting and simplification of the total pre-coding matrix, the modulation bit, the channel and the decoding matrix corresponding to the antenna subarrays are carried out; and rewriting an expression of the safe rate, wherein the optimization problem is converted into a global variable consistency optimization problem due to the cutting of data in the optimization problem and can be further expressed by a Jersen inequality.
3. The secure precoding method according to claim 1, wherein: the optimization problem is changed from a non-convex optimization problem to a convex optimization problem by introducing a new matrix variable and a dual variable and writing an expression of a processing fusion center; when initializing the variables, the activation of each possible antenna subarray needs to be calculated one by one.
4. The secure precoding method according to claim 1, wherein: performing iterative computation by an alternating direction multiplier method to obtain updated matrix variables and dual variables; and comparing the total pre-coding matrixes before and after updating until a termination condition is met by calculating a new fusion center to obtain a mixed total pre-coding matrix for realizing the optimal safe rate performance.
5. The secure precoding method according to claim 1, wherein: designing an overall precoding matrix, and respectively designing a post-digital precoding matrix and an analog precoding matrix according to the relation between the overall precoding matrix and the digital and analog precoding matrices.
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