CN114629522B - Full duplex relay robust self-interference elimination method based on broadband millimeter wave system - Google Patents

Full duplex relay robust self-interference elimination method based on broadband millimeter wave system Download PDF

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CN114629522B
CN114629522B CN202210286692.5A CN202210286692A CN114629522B CN 114629522 B CN114629522 B CN 114629522B CN 202210286692 A CN202210286692 A CN 202210286692A CN 114629522 B CN114629522 B CN 114629522B
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罗臻
柳腾辉
刘宏清
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/38—Transceivers, i.e. devices in which transmitter and receiver form a structural unit and in which at least one part is used for functions of transmitting and receiving
    • H04B1/40—Circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B15/00—Suppression or limitation of noise or interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/14—Two-way operation using the same type of signal, i.e. duplex
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Abstract

The invention relates to a full duplex relay robust self-interference elimination method based on a broadband millimeter wave system, and belongs to the technical field of communication. First, a frequency selective fading channel is decomposed into a plurality of flat fading channels by an orthogonal frequency division multiplexing technology, and a self-interference elimination matrix is designed by utilizing the zero space property of the self-interference channel, so that the self-interference caused by full duplex relay is restrained. The full digital precoder of each subcarrier is then solved by alternating optimization using the upper bound of the capacity of the channel as an optimization objective, and the self-interference cancellation matrix is integrated into the full digital precoder of the relay. Finally, the all-digital transceiver is decomposed into a hybrid transceiver using an iterative decomposition method with a closed-form solution.

Description

Full duplex relay robust self-interference elimination method based on broadband millimeter wave system
Technical Field
The invention belongs to the technical field of communication, and relates to a full duplex relay robust self-interference elimination method based on a broadband millimeter wave system.
Background
Millimeter wave communication systems have widely adopted a hybrid architecture of analog and digital transceivers as a key technology for the next generation of mobile communication systems. Broadband is one of the main characteristics of millimeter waves, which makes it possible to meet the increasing frequency resource requirements of fifth-generation cellular networks, and is a promising technology. And under the participation of the full duplex relay system, the design of the hybrid transceiver can realize the expansion of the coverage area of the network and the improvement of the transmission rate.
In a wideband system, we use orthogonal frequency division multiplexing to split the wideband into multiple sub-carriers for data transmission. For a full duplex node, the signal sent by the transmitting antenna is received by its own receiving antenna to form a self-interference signal, and the key of the problem is to eliminate the self-interference signal from the transmitting end to the receiving end. The zero-space projection method is an effective self-interference elimination method, and can effectively eliminate the performance loss caused by self-interference by utilizing the zero-space characteristic of a self-interference channel.
However, most existing hybrid transceiver designs for wideband full duplex systems are based on perfect channel estimation, which is not possible in practical engineering applications. Few designs consider the case of imperfect channel estimation by performing an exhaustive search of the codebook, but this approach is relatively complex. Therefore, how to design a wideband full duplex transceiver system based on the related channel estimation error and make it possess a good transmission rate is a problem to be solved.
Disclosure of Invention
In view of the above, the present invention aims to provide a full duplex relay robust self-interference cancellation method based on a broadband millimeter wave system.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a full duplex relay robust self-interference elimination method based on a broadband millimeter wave system comprises the following steps:
s1: constructing a channel equivalent matrix to solve a self-interference elimination matrix C sic [l]；
S2: constructing an equivalent optimization problem by utilizing the upper bound of the channel capacity, and solving all-digital processing matrixes F [ l ], G [ l ] of a transmitting end and a relay;
s3: through C sic [l]All-digital receiver G with relay r [l]The self-interference signal is eliminated by combination;
s4: all-digital receiver using minimum mean square error criterion
Figure BDA0003558527320000011
S5: decomposing the all-digital processor by using the proposed alternative iterative optimization method, and solving the hybrid precoder;
s6: digital precoding matrix F for transmitting end bb [l]And a relay receiving end digital precoding matrix G bb [l]Normalizing to ensure that the power constraints of a transmitting end and a relay are respectively met:
Figure BDA0003558527320000021
optionally, the S1 specifically is:
the built relay processor makes the self-interference item zero, meets the following requirements
Figure BDA0003558527320000022
Constructing an equivalent matrix:
Figure BDA0003558527320000023
wherein,,
Figure BDA0003558527320000024
is a self-interference channel matrix with estimation error, and is formed by R los [l]And->
Figure BDA0003558527320000025
Constructing;
order the
Figure BDA0003558527320000026
Figure BDA0003558527320000027
Channel for sender to relay->
Figure BDA0003558527320000028
A left unitary matrix of SVD decomposition of (2); constructing an equivalent matrix and carrying out singular value decomposition on the equivalent matrix:
Figure BDA0003558527320000029
matrix array
Figure BDA00035585273200000210
The vectors in (a) constitute an equivalent matrix +.>
Figure BDA00035585273200000211
Zero space of (i.e.)>
Figure BDA00035585273200000212
By->
Figure BDA00035585273200000213
Vector construction self-interference cancellation matrix C in (3) sic [l]So that->
Figure BDA00035585273200000214
Optionally, the S2 specifically is:
the mean square error MSE matrix is expressed as:
Figure BDA00035585273200000215
wherein,,
Figure BDA00035585273200000216
according to the MSE matrix, the channel capacity-based optimization problem is constructed as follows:
Figure BDA00035585273200000217
Figure BDA00035585273200000218
Figure BDA00035585273200000219
introducing auxiliary variables: v [ l ]]＝E -1 [l]；
Converting the original optimization problem into an optimization problem I:
Figure BDA0003558527320000031
Figure BDA0003558527320000032
Figure BDA0003558527320000033
the optimization problem is solved by solving the KKT condition, wherein the Lagrangian is calculated by a binary search algorithm, thereby obtaining the full-digital F [ l ] and G [ l ].
Optionally, the S3 specifically is:
by C sic [l]To correct the relay precoding matrix G [ l ]]；
Known G r [l]Order-making
Figure BDA0003558527320000034
Figure BDA0003558527320000035
Updating G [ l ] again so that it satisfies the power constraint:
Figure BDA0003558527320000036
optionally, the S4 specifically is:
updating the receiver of the last receiver using all-digital fl, gl:
Figure BDA0003558527320000037
all the all digital transceivers are solved.
Optionally, the step S5 specifically includes:
in the relay, the optimization problem of the relay all-digital processor decomposed into hybrid transceivers is represented as two:
Figure BDA0003558527320000038
Figure BDA0003558527320000039
|G t，rf |＝|G r，rf |＝F g .
wherein the method comprises the steps of
Figure BDA00035585273200000310
Decomposing the optimization problem into three sub-problems:
Figure BDA0003558527320000041
Figure BDA0003558527320000042
Figure BDA0003558527320000043
Figure BDA0003558527320000044
Figure BDA0003558527320000045
according to the alternating optimization algorithm, the closed-form solution is expressed as:
Figure BDA0003558527320000046
Figure BDA0003558527320000047
Figure BDA0003558527320000048
where k represents the kth iterative process, iterating the three closed-form solutions above until the termination condition is met.
The invention has the beneficial effects that: firstly, the invention combines the situation in the actual engineering to design the transceiver aiming at the imperfect estimation channel, and has better robustness; secondly, the invention is designed aiming at a broadband channel, and compared with a narrowband system, the broadband system has better transmission performance; then, aiming at the self-interference signal brought by the full duplex mode, the invention uses the zero space of the self-interference channel to carry out interference elimination, and the result shows that the invention can effectively inhibit self-interference and greatly improve the channel capacity; and then constructing an optimization problem by using the upper bound of the channel capacity, solving a corresponding all-digital transceiver, and finally obtaining a mixed transceiver by using an iterative decomposition method with a closed solution.
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.
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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 comparison of the transmission rates of the present invention with the full digital half duplex method at different INR (ratio of self-interference signal to noise).
Fig. 2 is a comparison of the transmission rates of the present invention with the schemes in document [1] and document [2] at different SNRs (ratio of signal to noise).
Fig. 3 is a comparison of transmission rates of the relay decomposition scheme proposed by the present invention with the conventional decomposition scheme, the decomposition scheme in document [3], at different SNRs.
FIG. 4 is a diagram of
Figure BDA0003558527320000051
Is a value of (2).
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.
Fig. 1 is a transmission rate comparison of the proposed hybrid design with a full digital half duplex scheme at different INR (ratio of self-interference signal to noise). The mixed design scheme provided by the invention has no self-interference in the four different scenes of INR from 10dB to 40 dB.
Fig. 2 is a comparison of the transmission rates of the present invention with the schemes in document [1] and document [2] at different SNRs (ratio of signal to noise). Wherein scene one is in the case of broadband; in the case of the second scenario, which is narrowband, and the receiving end has only one antenna, the scheme in document [2] is only applicable to this case.
Fig. 3 is a comparison of transmission rates of the relay decomposition scheme proposed by the present invention with the conventional decomposition scheme, the decomposition scheme in document [3], at different SNRs. The relay decomposition of the present invention is to decompose the relay node into an analog-digital-analog structure, whereas the conventional decomposition scheme is an analog-digital-analog structure.
FIG. 4 is a diagram illustrating
Figure BDA0003558527320000061
It can be seen that this value is small enough and stable.
The implementation mode of the full duplex relay robust self-interference elimination design algorithm based on the broadband millimeter wave system is as follows:
(1) Wideband millimeter wave channel model
Millimeter wave channel model H 1 [l](sender-to-relay) and H 2 [l](relayed to the receiving end) can be expressed as:
Figure BDA0003558527320000062
wherein,,
Figure BDA0003558527320000063
N t and N r Respectively representing the number of antennas at a transmitting end and the number of antennas at a receiving end, N p Representing the total propagation path number; l represents the total number of subcarriers, L represents the first subcarrier; a, a r And a t Receiving and transmitting array response vectors, alpha, respectively p For transmission gain, p (·) is a raised cosine pulse shaping function with signal spacing T s Time delay of tau p ，(·) H Representing the conjugate transpose matrix. The antenna array is a uniform linear array.
The self-interference channel can be expressed as:
Figure BDA0003558527320000064
H los a (line of) LoS portion representing the channel, and is related to the position and angle of the transmit and receive antenna arrays of the relay; h nlos [l]Representing the reflected portion of the channel, again following the wideband millimeter wave channel model described above.
The proposed correlation channel estimation error model is expressed as:
Figure BDA0003558527320000065
here, the
Figure BDA0003558527320000066
Representing the relative actual channel H [ l ]]N [ l ]]Representing the matrix of errors and,
Figure BDA0003558527320000067
for error handling matrix, XL]Is a pilot signal sequence. Channel estimation error model suitable for H 1 [l]、H 2 [l]And a reflection part H of self-interference channel nlos [l]While the signal is in the LoS part H of the self-interfering channel los Is stable and there is no estimation error.
(2) System model
According to the full duplex relay strategy, the estimated signal at the receiving end can be expressed as:
Figure BDA0003558527320000068
wherein F [ l ]]＝F rf F bb [l]For the mixed processing matrix of the transmitting end, F rf And F bb [l]Respectively analog and digital precoders. In a wideband system, all subcarriers share the same analog precoder, and each subcarrier needs to be designed separately by a digital precoder; g t [l]＝G t，rf G t，bb [l]And G r [l]＝G r，rf G r，bb [l]Hybrid precoder and hybrid receiver, respectively, for relay]＝W bb [l]W rf Is a hybrid receiver at the receiving end.
(3) Robust hybrid transceiver design
In the case of completely eliminated errors, the second term in the above equation should be zero, so that the relay processor we wish to build can satisfy
Figure BDA0003558527320000071
Then construct an equivalent matrix:
Figure BDA0003558527320000072
wherein,,
Figure BDA0003558527320000073
is a self-interference channel matrix with estimation error, and is formed by H los [l]And->
Figure BDA0003558527320000074
The composition is formed. Order the
Figure BDA0003558527320000075
Here->
Figure BDA0003558527320000076
Channel for sender to relay->
Figure BDA0003558527320000077
Left unitary matrix of SVD decomposition of (c). The null space of the equivalent matrix can be obtained by singular value decomposition:
Figure BDA0003558527320000078
here matrix
Figure BDA0003558527320000079
The vectors in (a) constitute the equivalent matrix +.>
Figure BDA00035585273200000710
Zero space of (i.e.)>
Figure BDA00035585273200000711
Then use->
Figure BDA00035585273200000712
Vector construction self-interference cancellation matrix C in (3) sic [l]So that->
Figure BDA00035585273200000713
Because we have eliminated self-interference, the self-interference term can be temporarily removed, the system can be simplified to a traditional half-duplex relay system, i.e. the received signal can be approximated as
y[l]＝W[l]H 2 [l]G[l]H 1 [l]F[l]s[l]+W[l]H 2 [l]G[l]n1[l]+W[l]n 2 [l]
Wherein,,
Figure BDA00035585273200000714
for a half duplex relay system, constructing (minimum mean squared error) an MMSE receiver:
Figure BDA00035585273200000715
wherein,,
Figure BDA00035585273200000716
Figure BDA00035585273200000717
Figure BDA00035585273200000718
and->
Figure BDA00035585273200000719
Are respectively->
Figure BDA00035585273200000720
Is a noise variance of (1); />
Figure BDA00035585273200000721
And->
Figure BDA00035585273200000722
Respectively->
Figure BDA00035585273200000723
Is used for the channel estimation error of (a). Its corresponding Mean Square Error (MSE) matrix can be expressed as:
Figure BDA00035585273200000724
wherein,,
Figure BDA00035585273200000725
according to the MSE matrix, the optimization problem based on the channel capacity upper bound is constructed as follows:
Figure BDA0003558527320000081
Figure BDA0003558527320000082
Figure BDA0003558527320000083
solving the above problem directly becomes very complex. By introducing the following auxiliary variables: v [ l ]]＝E -1 [l]. Thus, the original optimization problem can be converted into the following optimization problem:
Figure BDA0003558527320000084
Figure BDA0003558527320000085
Figure BDA0003558527320000086
the optimization problem described above can be solved by solving the KKT condition, wherein the Lagrangian operator can be obtained by a binary search algorithm, thereby obtaining fully numerical Fl and Gl.
Figure BDA0003558527320000087
Wherein,,
Figure BDA0003558527320000088
Figure BDA0003558527320000089
Figure BDA00035585273200000810
and
Figure BDA00035585273200000811
wherein the method comprises the steps of
Figure BDA00035585273200000812
Figure BDA00035585273200000813
At this time we need to use C sic [l]To correct the relay precoding matrix G [ l ]]. By the previous knowledge of G r [l]Order-making
Figure BDA00035585273200000814
Figure BDA00035585273200000815
At this point we update G [ l ] again and let it meet the power constraint:
Figure BDA00035585273200000816
thus, all numbers F [ l ], G [ l ] are obtained. The receiver of the final receiving end can be obtained by the MMSE criterion:
Figure BDA00035585273200000817
all digital transceivers are now solved.
The use of an all-digital transceiver in a millimeter wave system requires significant hardware costs, while a hybrid form of analog and digital saves hardware costs and has near-all-digital performance. The hybrid transceiver can be implemented by minimizing the euclidean distance between the all-digital processor and its corresponding hybrid processor, taking the precoder at the transmitting end as an example, and creating an optimization problem:
Figure BDA0003558527320000091
Figure BDA0003558527320000092
Figure BDA0003558527320000093
wherein F is rf And F bb [l]The precoders of the analog and digital parts, respectively. The first constraint is the power constraint of the transmitting end, F rf Because of the analog processor constituted by the phase shifter, there is a constant modulus constraint (amplitude of each element of the matrix is 1), the second constraint of the above problem. There is literature [4]]Prove that if there is no power constraint for the mixed solution F rf F bb [l]Is close enough to an all-digital solution fl]Then the corresponding constrained mixed solution is combined with F [ l ]]The same euclidean distance can be used. The power constraint can be temporarily ignored and the above problem can be split into two sub-problems by an alternate optimization approach:
Figure BDA0003558527320000094
Figure BDA0003558527320000095
and
Figure BDA0003558527320000096
by least squares solution, its solution can be expressed as:
Figure BDA0003558527320000097
Figure BDA0003558527320000098
wherein the method comprises the steps of
Figure BDA0003558527320000099
k represents the kth iterative process. By solving alternately two Euclidean distance minimization problems, i.e. one variable is fixed to solve the other, F is finally calculated rf And F bb [l]. Finally, the digital pre-coder is normalized fully
Figure BDA00035585273200000910
And (5) enabling the power constraint to be met, and obtaining the hybrid precoder of the transmitting end.
Since the receiver and the transmitting end are the same hybrid structure, for the receiver W MMSE [l]The same decomposition method can be adopted. In addition, for the transceiver design of the relay processor, we propose a new decomposition method: the precoding matrix digital part and the receiver digital part of the hybrid relay are regarded as one entity, and then they are decomposed into an analog-digital-analog hybrid structure instead of the conventional analog-digital oneWord-analog structure and solved by alternate iteration.
The problem of the optimization of the relay all-digital processor into a hybrid transceiver can be expressed as:
Figure BDA0003558527320000101
Figure BDA0003558527320000102
Figure BDA0003558527320000103
wherein the method comprises the steps of
Figure BDA0003558527320000104
Let G bb [l]＝bG′ bb [l]Wherein G' bb [l]In order for the digital processor portion to meet the power constraints,
Figure BDA0003558527320000105
then
Figure BDA0003558527320000106
Figure BDA0003558527320000107
The values of (2) are given in fig. 4, which can be seen to be sufficiently small and stable. So we can also get the best of the literature [4]]Also, it is concluded that the power constraint can be temporarily removed in this optimization problem. This optimization problem is then decomposed into three sub-problems:
Figure BDA0003558527320000108
Figure BDA0003558527320000109
Figure BDA0003558527320000111
Figure BDA0003558527320000112
Figure BDA0003558527320000113
according to the same alternating optimization algorithm, the closed-form solution can be expressed as:
Figure BDA0003558527320000114
Figure BDA0003558527320000115
Figure BDA0003558527320000116
first fix G bb [l]And G r，rf Update G t，rf The method comprises the steps of carrying out a first treatment on the surface of the Then fix G bb [l]And G t，rf Update G r，rf Finally, update G bb [l]And exiting the alternating iteration process until the termination condition is met.
Finally, for G bb [l]Normalizing to enable the power to meet the transmission power of the relay terminal:
Figure BDA0003558527320000117
to this end, the full duplex robust hybrid transceiver is solved, and the whole algorithm flow can be expressed as follows:
a) Interference elimination matrix G constructed based on zero space projection method sic [l]。
b) And constructing an optimization problem equivalent to the upper bound of the channel capacity, and solving all-digital processing matrixes F [ l ] and G [ l ] of the transmitting end and the relay.
c) Will G sic [l]Is combined into a relay all-digital processing matrix and normalized.
d) Finding an all-digital receiver W using MMSE criterion MMSE [l]。
e) Fixing
Figure BDA0003558527320000118
Use->
Figure BDA0003558527320000119
Update->
Figure BDA00035585273200001110
f) Fixing
Figure BDA00035585273200001111
Use->
Figure BDA00035585273200001112
Update->
Figure BDA00035585273200001113
g) Iterating steps f) and g) until an iteration termination condition is met. And to F bb [l]Normalizing to meet the power constraint of the transmitting end,
Figure BDA00035585273200001114
h) Fixing
Figure BDA00035585273200001115
By using
Figure BDA0003558527320000121
Update->
Figure BDA0003558527320000129
i) Fixing
Figure BDA0003558527320000122
By using
Figure BDA0003558527320000123
Update->
Figure BDA0003558527320000124
j) Fixing
Figure BDA0003558527320000125
By using
Figure BDA0003558527320000126
Update->
Figure BDA0003558527320000127
k) Iterating the steps h), i) and j) until the iteration termination condition is satisfied. And to G bb [l]Normalization is performed so that it meets the transmit power constraints of the relay,
Figure BDA0003558527320000128
l) solving for W by the same iterative method MMSE [l]A corresponding hybrid receiver.
The document [1] is: S.Park, A.Alkhateeb and R.W. Heath, "Dynamic Subarrays for Hybrid Precoding in Wideband mmWave MIMO Systems," in IEEE Transactions on Wireless Communications, vol.16, no.5, pp.2907-2920, may 2017.
Document [2] is: Y.Cai, Y.Xu, Q.Shi, B.Champagne, and L.Hanzo, "Robust joint hybrid transceiver design for millimeter wave full-duplex MIMO relay systems," IEEE Trans.Wireless Commun., vol.18, no.2, pp.1199-1215, 2019.
Document [3] is: X.Yu, J.Shen, J.Zhang and K.B. Letaief, "Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems," in IEEE Journal of Selected Topics in Signal Processing, vol.10, no.3, pp.485-500, april 2016.
Document [4] is: Z.Luo, L.Zhao, H.Liu, and Y.Li, "Robust hybrid beamforming in millimeter wave systems with closed-form less-square solutions," IEEE Wireless Commun.Lett., early Access ".
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 (1)

1. A full duplex relay robust self-interference elimination method based on a broadband millimeter wave system is characterized in that: the method comprises the following steps:
s1: constructing a channel equivalent matrix to solve a self-interference elimination matrix C sic [l]；
S2: constructing an equivalent optimization problem by utilizing the upper bound of the channel capacity, and solving all-digital processing matrixes F [ l ], G [ l ] of a transmitting end and a relay;
s3: through C sic [l]All-digital receiver G with relay r [l]The self-interference signal is eliminated by combination;
s4: all-digital receiver using minimum mean square error criterion
Figure FDA0004262085140000011
S5: decomposing the all-digital processor by using the proposed alternative iterative optimization method, and solving the hybrid precoder;
s6: digital precoding matrix F for transmitting end bb [l]And a relay receiving end digital precoding matrix G bb [l]Normalizing to ensure that the power constraints of a transmitting end and a relay are respectively met:
Figure FDA0004262085140000012
Figure FDA0004262085140000013
the S1 specifically comprises the following steps:
the built relay processor makes the self-interference item zero, meets the following requirements
Figure FDA0004262085140000014
Constructing an equivalent matrix:
Figure FDA0004262085140000015
wherein,,
Figure FDA0004262085140000016
is a self-interference channel matrix with estimation error, and is formed by H los [l]And->
Figure FDA0004262085140000017
Constructing;
order the
Figure FDA0004262085140000018
Figure FDA0004262085140000019
Channel for sender to relay->
Figure FDA00042620851400000110
A left unitary matrix of SVD decomposition of (2); constructing an equivalent matrix and carrying out singular value decomposition on the equivalent matrix:
Figure FDA00042620851400000111
matrix array
Figure FDA00042620851400000112
The vectors in (a) constitute an equivalent matrix +.>
Figure FDA00042620851400000113
Zero space of (i.e.)>
Figure FDA00042620851400000114
By->
Figure FDA00042620851400000115
Vector construction self-interference cancellation matrix C in (3) sic [l]So that->
Figure FDA00042620851400000116
The step S2 is specifically as follows:
the mean square error MSE matrix is expressed as:
Figure FDA00042620851400000117
wherein,,
Figure FDA00042620851400000118
according to the MSE matrix, the channel capacity-based optimization problem is constructed as follows:
Figure FDA0004262085140000021
Figure FDA0004262085140000022
Figure FDA0004262085140000023
introducing auxiliary variables: v [ l ]]＝E -1 [l]；
Converting the original optimization problem into an optimization problem I:
Figure FDA0004262085140000024
Figure FDA0004262085140000025
Figure FDA0004262085140000026
the optimization problem is solved by solving the KKT condition, wherein the Lagrangian operator is obtained by a binary search algorithm, thereby obtaining full-digital F [ l ] and G [ l ];
the step S3 is specifically as follows:
by C sic [l]To correct the relay precoding matrix G [ l ]]；
Known G r [l]Order-making
Figure FDA0004262085140000027
Figure FDA0004262085140000028
Updating G [ l ] again so that it satisfies the power constraint:
Figure FDA0004262085140000029
the step S4 specifically comprises the following steps:
updating the receiver of the last receiver using all-digital fl, gl:
Figure FDA00042620851400000210
wherein,,
Figure FDA00042620851400000211
Figure FDA00042620851400000212
Figure FDA00042620851400000213
and->
Figure FDA00042620851400000214
Are respectively->
Figure FDA00042620851400000215
Is a noise variance of (1); />
Figure FDA00042620851400000216
And->
Figure FDA00042620851400000217
Respectively->
Figure FDA00042620851400000218
Channel estimation error of (a); phi 1 [l]And phi is 2 [l]Respectively->
Figure FDA00042620851400000219
A channel estimation error processing matrix of (a);
all the digital transceivers are solved;
the step S5 specifically comprises the following steps:
in the relay, the optimization problem of the relay all-digital processor decomposed into hybrid transceivers is represented as two:
Figure FDA0004262085140000031
Figure FDA0004262085140000032
|G t，rf |＝|G r，rf |＝F g
wherein the method comprises the steps of
Figure FDA0004262085140000033
Decomposing the optimization problem into three sub-problems:
Figure FDA0004262085140000034
Figure FDA0004262085140000035
Figure FDA0004262085140000036
Figure FDA0004262085140000037
Figure FDA0004262085140000038
according to the alternating optimization algorithm, the closed-form solution is expressed as:
Figure FDA0004262085140000039
Figure FDA00042620851400000310
Figure FDA00042620851400000311
where k represents the kth iterative process, iterating the three closed-form solutions above until the termination condition is met.
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