CN113872912A - Low-complexity reduction method for peak-to-average power ratio of MIMO-OFDM system - Google Patents

Low-complexity reduction method for peak-to-average power ratio of MIMO-OFDM system Download PDF

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CN113872912A
CN113872912A CN202111208504.9A CN202111208504A CN113872912A CN 113872912 A CN113872912 A CN 113872912A CN 202111208504 A CN202111208504 A CN 202111208504A CN 113872912 A CN113872912 A CN 113872912A
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signal
ofdm
mimo
optimization problem
convex optimization
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王亚军
陈蕊
卢璐
许铭扬
孙静海
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Jiangsu University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2614—Peak power aspects
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting

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Abstract

The invention discloses a low-complexity reduction method of a peak-to-average power ratio of an MIMO-OFDM system, which comprises the following steps: s1: setting base station configuration data, defining subcarrier set for data transmission and subcarrier set for band guard, generating signal vector sn(ii) a S2: for signal vector snPrecoding to obtain a precoded signal wn(ii) a To wnReordering to obtain frequency domain transmission signal an(ii) a S3: OFDM: by transmitting the signal a in the frequency domainnIFFT is carried out to obtain a time domain transmitting signal xn(ii) a S4: calculating a time-domain signal xnThe PAPR of (1); s5: the method is characterized in that interference among multiple users is eliminated, PAPR is reduced, OFDM modulation is combined into a convex optimization problem, the convex optimization problem is solved by adopting a linear alternating direction multiplier method, and complexity reduction is achieved. The invention utilizesRedundant freedom degrees provided by a large number of antennas in an MMU-MIMO-OFDM system combine MU precoding, PAPR reduction and transmitted signal power constraint into a convex optimization problem, and a linear alternating direction multiplier method is designed to solve the convex optimization problem.

Description

Low-complexity reduction method for peak-to-average power ratio of MIMO-OFDM system
Technical Field
The invention relates to the technical field of wireless communication, in particular to a low-complexity reduction method for a peak-to-average power ratio of an MIMO-OFDM system.
Background
The large-scale multi-user multiple-input multiple-output (MIMO) technology is considered as one of the key technologies in 5G, and the large-scale antenna array technology can be adapted to the MIMO system, so that the spatial freedom of a wireless channel is improved, and higher data rate and transmission reliability are brought. Orthogonal Frequency Division Multiplexing (OFDM) is an important multi-carrier modulation technique, and can well solve the frequency selective fading problem by decomposing a wideband channel into several independent narrowband channels. The combination of OFDM and MIMO systems can achieve the advantages of both, and achieve faster communication rate and higher spectrum utilization, and such systems have been identified as reliable technologies in future generations of wireless communication.
However, OFDM, a multi-carrier technology, tends to cause the envelope fluctuation of a signal to be large when the frequency spectrums of the carriers are the same or close to each other, and further causes the peak-to-average power ratio (PAPR) of the signal to be high. High peak-to-average ratio signals usually require power amplifiers with large feedback, which increases the complexity of the analog-to-digital converter and the digital-to-analog converter, and also puts high demands on the linearity of the amplifier in the transmitter, thereby possibly causing signal distortion, causing the frequency spectrum of the signal to change, and causing serious deterioration of the system performance. When a large-scale multi-user MIMO (MMU-MIMO) technology is applied to engineering practice, a base station must be required to use a low-power-consumption radio frequency link and a low-power-consumption power-efficient radio frequency power amplifier, which requires a low PAPR of a transmission signal. In order to satisfy the requirements of using a power amplifier with low power consumption and high power efficiency and reducing interference among multiple users in the MMU-MIMO technology, it is highly desirable to use a more efficient method to reduce the PAPR of the system.
Disclosure of Invention
The invention provides a low-complexity reduction method for the peak-to-average power ratio of an MIMO-OFDM system, which aims to solve the problem that the average power of the peak value of a transmitted signal is higher in the prior art.
The invention provides a low-complexity reduction method of a peak-to-average power ratio of an MIMO-OFDM system, which comprises the following steps:
s1: setting base station configuration data, defining subcarrier set for data transmission and subcarrier set for band guard, generating signal vector sn；
S2: for signal vector snPrecoding to obtain a precoded signal wn(ii) a To wnReordering to obtain frequency domain transmission signal an；
S3: OFDM: by transmitting the signal a in the frequency domainnIFFT is carried out to obtain a time domain transmitting signal xn；
S4: calculating a time-domain signal xnThe PAPR of (1);
s5: the method is characterized in that interference among multiple users is eliminated, PAPR is reduced, OFDM modulation is combined into a convex optimization problem, the convex optimization problem is solved by adopting a linear alternating direction multiplier method, and complexity reduction is achieved.
Further, the S1 specifically includes: setting a base station to be configured with M transmitting antennas to serve K single-antenna mobile users, and satisfying K < M, the number of OFDM subcarriers is N, and a signal vector sn∈ΘKContains information transmitted to K users, N is 1,2, N is the carrier index of OFDM, Θ is the complex constellation set, s is the complex constellation setn，kE theta represents a symbol sent to user k on carrier n; the set of subcarriers used for data transmission is defined as Γ, the complementary set of which ΓcUsed as band guard, i.e. when n ∈ ΓcWhen there is a signal vector sn＝0K×1。
Further, the S2 specifically includes: signal vector snN is 1,2, …, N is first precoded by a precoder designed based on the mean square error minimization criterion to generate N precoding vectors wnN is 1,2, …, N; to wnThe signals are reordered according to the direction from the user to the transmitting antenna to obtain a frequency-domain transmission signal [ a ]1，…，aM]＝[w1，…，wN]TWherein a ism∈CN×1M denotes an OFDM frequency domain signal transmitted on the mth antenna.
Further: the S3 specifically includes: to am∈CN×1The corresponding time domain signal x can be obtained by carrying out Fourier inverse transformationm＝FHamM is 1,2, …, M; wherein FH∈CLN×NRepresenting the first N columns of the LN point Fourier transform matrix, wherein L is an oversampling factor; the time domain signal is added with a cyclic prefix, and the received frequency domain signal vector is represented as yn＝sn+bnN is epsilon Γ; wherein, ynIs the frequency domain signal vector received by the nth sub-carrier, HnChannel matrix representing the nth subcarrier of the MIMO-OFDM, bn∈CK×1Is independently and identically distributed complex Gaussian noise, the mean value of each component of the complex Gaussian noise is 0, and the variance is N0。
Further, the S4 specifically includes: time domain signal x obtained under L times oversamplingmThe PAPR table is:
Figure BDA0003307856250000031
further, the method for combining elimination of inter-user interference, PAPR reduction, and OFDM modulation into a convex optimization problem in S5 specifically includes:
a1: designing a convex optimization model, and jointly executing the steps of eliminating the interference among multiple users, OFDM modulation and reducing the PAPR:
the frequency domain signals transmitted by the subcarriers need to satisfy the following requirements:
sn＝Hnwn，n∈Γ (2)
the frequency domain signal transmitted by the free carrier wave is required to satisfy the following conditions:
0M×1＝wn，n∈Γc (3)
the constraints are combined as:
Figure BDA0003307856250000041
based on the nature of OFDM modulation, we can jointly express the precoding constraint and OFDM modulation as
Figure BDA0003307856250000042
Wherein,
Figure BDA0003307856250000043
is a combination of the above-mentioned conditions left signal,
Figure BDA0003307856250000044
is a collection of frequency-domain signals that,
Figure BDA0003307856250000045
in the form of a block-diagonal matrix,
Figure BDA0003307856250000046
diagonal block is Hn，
Figure BDA0003307856250000047
And IM，
Figure BDA0003307856250000048
Figure BDA0003307856250000049
Figure BDA00033078562500000410
Ψ is the corresponding permutation matrix,
Figure BDA00033078562500000411
a Kronecke product representing two matrices;
a2: in connection with (1) and (5), the downlink transmission scheme is described as an optimization problem as follows
Figure BDA00033078562500000412
A3: the square of infinite norm is used to replace formula (6) to obtain the convex objective function
Figure BDA00033078562500000413
Relaxing the equality constraint S ═ HX, i.e. mean square error
Figure BDA00033078562500000414
Instead of S ═ HX, the following convex optimization problem was obtained:
Figure BDA00033078562500000415
a4: converting the convex optimization problem into an ADMM algorithm form, specifically:
defining illustrative functions I of sets C, respectivelyC(x) And the near-end operator Prox of function f (x):
Figure BDA00033078562500000416
Figure BDA00033078562500000417
the convex optimization problem is expressed as an equivalent form of the ADMM algorithm:
Figure BDA00033078562500000418
the augmented Lagrange function of equation (8) is:
Figure BDA0003307856250000051
the following iterative formula is generated:
Figure BDA0003307856250000052
Figure BDA0003307856250000053
Figure BDA0003307856250000054
aj+1＝aj+Xj+1-Zj+1 (10d)
wj+1＝wj+Xj+1-Yj+1 (10e)
further, in S5, the process of solving the convex optimization problem by using a linear alternating direction multiplier method is as follows:
solving the sub-problem equation (10 a):
Figure BDA0003307856250000055
solving the sub-problem equation (10 b):
Figure BDA0003307856250000056
solving the sub-problem equation (10 c):
Figure BDA0003307856250000057
solving the convex optimization problem under the ADMM algorithm, wherein the process is as follows:
b1: initialization t 1, z1＝y1＝a1＝w1＝02WN×1Setting the maximum number of iterations tmax；
B2：whilet≤tmax；
B3: updating X using equation (11)j+1；
B4: updating Z using equation (12)j+1；
B5: updating Y using equation (13)j+1；
B6: updating the dual variable a using equation (10d)j+1；
B7: updating the dual variable w using equation (10e)j+1；
B8：endwhile；
B9: output Xj+1；
B10: and (4) carrying out simulation experiment of the algorithm, simulating by using software MATLAB, and verifying theoretical analysis.
The invention has the beneficial effects that:
in order to overcome the defects in the prior art and reduce the problem of high peak-to-average power ratio (PAPR) of a transmitted signal in a large-scale multi-user multi-input multi-output (MIMO) -Orthogonal Frequency Division Multiplexing (OFDM) system, the invention combines MU precoding, PAPR reduction and transmitted signal power constraint into a convex optimization problem by utilizing redundant degrees of freedom (DOF) provided by a large number of antennas in the MMU-MIMO-OFDM system, and designs a Linear Alternating Direction Multiplier Method (LADMM) to solve the convex optimization problem. Simulation results show that compared with the existing method, the designed LADMM method has lower peak-to-average ratio and better Symbol Error Rate (SER) performance, and meanwhile, the ADMM algorithm also has higher convergence speed and lower computational complexity and can meet the necessary condition of peak power constraint of a transmitted signal in engineering practice.
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The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and not to be construed as limiting the invention in any way, and in which:
FIG. 1 is a downlink diagram of a massive multi-user MIMO-OFDM system;
FIG. 2 is a time domain signal diagram of a different approach;
fig. 3 is a time domain signal comparison diagram of the ZF precoding method and the ADMM method;
FIG. 4 is a graph comparing PAPR reduction by different methods;
FIG. 5 is a comparison graph of different methods SER;
fig. 6 is a graph of PAPR convergence rate of ADMM method.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a low-complexity method suitable for reducing the peak-to-average power ratio of an MIMO-OFDM system, which comprises the following steps:
s1: referring to fig. 1, it is assumed that a base station is configured with M transmit antennas serving K single-antenna mobile users, and satisfies K < M, the number of OFDM subcarriers is N, and a signal vector sn∈ΘKContains information transmitted to K users, N is 1,2, N is the carrier index of OFDM, Θ is the complex constellation set, s is the complex constellation setn，kE theta represents a symbol sent to user k on carrier n; in order to shape the spectrum of the transmitted signal, the OFDM system prespecifies that certain subcarriers do not carry any information, defining the set of subcarriers used for data transmission as Γ, the complementary set of which ΓcUsed as band guard, i.e. when n ∈ ΓcWhen there is a signal vector sn＝0K×1。
S2: in order to eliminate the inter-user interference, MU precoding is adopted, which specifically comprises: designing a signal vector snSignal vector snN precoding vectors are generated after precoding by a precoder designed based on a mean square error minimization criterion. After pre-coding, the signals are reordered according to the direction from the user to the transmitting antenna to obtain a frequency domain transmitting signal [ a1，…，aM]＝[w1，…，wN]TWherein a ismRepresenting the OFDM frequency domain signal transmitted on the mth antenna.
S3: OFDM modulation: the method specifically comprises the following steps: to am∈CN×1M1, 2.. to M, an inverse fourier transform (IFFT) is performed to obtain a corresponding time-domain signal xm＝FHamAnd M is 1,2, …, M. Wherein FH∈CLN×NTo represent LN point FourierThe first N columns of the leaf transform matrix, L, are the oversampling factors. To avoid intersymbol interference (ISI), a Cyclic Prefix (CP) needs to be added to the time domain signal. Accordingly, the frequency domain signal vector received by the receiver may represent yn＝sn+bnN ∈ Γ. Wherein, ynIs the frequency domain signal vector received by the nth sub-carrier, HnChannel matrix representing the nth subcarrier of the MIMO-OFDM, bn∈CK×1Is independently and identically distributed complex Gaussian noise, the mean value of each component of the complex Gaussian noise is 0, and the variance is N0(ii) a If given an OFDM frequency domain signal bn∈CK×1The corresponding baseband signals are:
Figure BDA0003307856250000081
wherein,
Figure BDA0003307856250000082
t is the OFDM symbol time, Δ f is the subcarrier frequency spacing, and N is the number of subcarriers.
S4: calculating a time-domain signal xnPAPR of (a): the PAPR of the time domain signal x obtained by L times oversampling is:
Figure BDA0003307856250000083
s5: a1: designing a convex optimization model, and jointly executing the steps of eliminating the interference among multiple users, OFDM modulation and reducing the PAPR:
the frequency domain signals transmitted by the subcarriers need to satisfy the following requirements:
sn＝Hnwn，n∈Γ (2)
the frequency domain signal transmitted by the free carrier wave is required to satisfy the following conditions:
0M×1＝wn，n∈Γc (3)
the constraints are combined as:
Figure BDA0003307856250000084
wherein
Figure BDA0003307856250000091
Is a combination of the above-mentioned conditions left signal,
Figure BDA0003307856250000092
is a collection of frequency domain signals.
Figure BDA0003307856250000093
Is a block diagonal matrix with a main diagonal block of Hn，
Figure BDA0003307856250000094
And IM，
Figure BDA0003307856250000095
Based on the nature of OFDM modulation, we can jointly express the precoding constraint and OFDM modulation as
Figure BDA0003307856250000096
Wherein
Figure BDA0003307856250000097
Figure BDA0003307856250000098
Ψ is the corresponding permutation matrix,
Figure BDA0003307856250000099
representing the Kronecker product of the two matrices.
A2: in conjunction with (1) and (5), the downlink transmission scheme is described as an optimization problem as follows:
Figure BDA00033078562500000910
a3: in contrast to the convex optimization problem (5), due to the non-convexity of PAPR (X), first a convex objective function is obtained by replacing it with the square of the infinite norm
Figure BDA00033078562500000911
Not using the objective function | | X | | non-calculation of formula (5)∞Because of
Figure BDA00033078562500000912
The nearest neighbor operator of (1) can get an accurate solution, while the nearest neighbor operator of | | X | ∞ is only a truncated solution. Then the equality constraint S ═ HX is relaxed, i.e. the mean square error
Figure BDA00033078562500000913
Instead of S ═ HX. Combined ADMM method[9]And the proposed near-end algorithm of infinite norm square[10]Solving the following convex optimization problem
Figure BDA00033078562500000914
A4: in order to convert the optimization problem (7) into a form that can utilize the ADMM algorithm, first the sexual function I of the set C is defined separatelyC(x) And the near-end operator Prox of function f (x).
Figure BDA00033078562500000915
Figure BDA00033078562500000916
The optimization problem (7) can be expressed as an equivalent of the ADMM algorithm:
Figure BDA0003307856250000101
the augmented Lagrange function of problem (8) is
Figure BDA0003307856250000102
The iteration generated comprises the following steps:
Figure BDA0003307856250000103
Figure BDA0003307856250000104
Figure BDA0003307856250000105
aj+1＝aj+Xj+1-Zj+1 (10d)
wj+1＝wj+Xj+1-Yj+1 (10e)
solving the sub-problem (10a), we present the following calculation:
Figure BDA0003307856250000106
to a function
Figure BDA0003307856250000107
Its neighbor operator
Figure BDA0003307856250000108
Can be calculated by the following algorithm:
Algorithm 1
Figure BDA0003307856250000109
near-end operator solving step
1: input z
2: let b ═ z-
3：s＝sort(b，′descending') ofπ(i)Is the ith largest element in s
4: for i ═ 1,2, K, N, device
Figure BDA0003307856250000111
5: order to
Figure BDA0003307856250000112
6: for i ═ 1,2, K, N
If it is not
Figure BDA0003307856250000113
Algorithm 1 gives
Figure BDA0003307856250000114
The method of computing a neighbor operator. For the solution of the sub-problem (10b), the following calculation steps are given:
Figure BDA0003307856250000115
because of the inverse matrix (ρ I + 2H)HH)-1Is relatively large, therefore, we propose a linear admm (ladmm) method to reduce the complexity of calculating the inverse matrix. Specifically, we linearize the quadratic term in equation (12) as follows:
Figure BDA0003307856250000116
where η > 0 is a positive parameter.
Figure BDA0003307856250000117
To represent
Figure BDA0003307856250000118
When Z is equal to ZkThe gradient of points, equivalent to solving the following equation:
Figure BDA0003307856250000119
we can get the following closed-form solution:
Figure BDA00033078562500001110
regarding solving the sub-problem (10c), by IC(Y) definition, solving
Figure BDA0003307856250000121
Is equivalent to
Figure BDA0003307856250000122
Equation (14) can be viewed as point Xj+1+wjTo the center of origin at a radius of
Figure BDA0003307856250000123
A projection of the euclidean sphere of (a). Thus, Y can be obtainedj+1The update formula (15).
Figure BDA0003307856250000124
The LADMM algorithm proposed herein can be obtained from (11), (13), (15), and the LADMM algorithm for solving the problem (8) is shown in the following table:
LADMM Algorithm for solving problem (7) by Algorithm2
B1: initialization t 1, z1＝y1＝a1＝w1＝02WN×1Setting the maximum number of iterations tmax；
B2：while t≤tmax；
B3: updating X using equation (11)j+1；
B4: updating Z using equation (12)j+1；
B5: updating Y using equation (13)j+1；
B6: updating the dual variable a using equation (10d)j+1；
B7: updating the dual variable w using equation (10e)j+1；
B8：endwhile；
B9: output Xj+1；
B10: and (4) carrying out simulation experiment of the algorithm, simulating by using software MATLAB, and verifying theoretical analysis.
Based on the above scheme, in order to verify the effect of the method of the present invention, the present embodiment performs a simulation experiment of the algorithm, uses software MATLAB to perform simulation, and verifies theoretical analysis. The specific simulation results and analysis are as follows:
100 antennas are arranged at a base station, and 10 single-antenna users are simultaneously served. OFDM signals are used which are not coded and comprise 128 sub-carriers, wherein Q108 sub-carriers are used for data transmission and Qc20 sub-carriers are used for band protection. The modulation method is 16QAM modulation, and the sampling rate is L ═ 4.
Fig. 2 shows time domain signals obtained by the signals through the ZF precoding method, the clipping method, the PMP algorithm, and the ADMM algorithm, respectively, and it can be seen from the figure that the time domain signal obtained by the ZF precoding method has a very high peak value, the time domain signal obtained by the clipping method only eliminates the peak value signal, and the time domain signals obtained by the PMP algorithm and the ADMM algorithm always have a low peak value. In fig. 3, comparing the time domain signal obtained by the ZF precoding method with the time domain signal obtained by the ADMM method, it can be clearly seen that the amplitude of the time domain signal is significantly reduced by the proposed ADMM method.
In fig. 4, the PAPR suppression effect is compared with the ADMM algorithm, the ZF precoding method, the MF precoding method, the clipping method, the PMP algorithm, and the MU-PP-GDm algorithm. The number of OFDM signals selected in the experiment was 1000, and in CCDF ═ Pr (PAPR > C) ═ 10-3The PAPR of the ADMM algorithm can be reduced to 2.3dB through 40 iterations, the PAPR value obtained by the ZF precoding method and the MF precoding method is 13dB, the PAPR value is reduced to 5.2dB through 50 iterations by the MU-PP-GDm method, the PAPR value is reduced to 4.9dB through the clipping method, and the PAPR can be reduced to 2.9dB through 1800 iterations by the PMP method. Designed ADMM algorithm, PMP algorithm, clipping method, MU-PP-GDm algorithm and ZF precoding partyCompared with the MF pre-coding method, the PAPR value is lower by 0.6dB, 2.6dB, 2.9dB, 10.7dB and 10.7dB, and meanwhile, the method designed by the method has more conditions which must be met in the practical engineering realization of the peak power constraint of the transmission signal than other methods.
Fig. 5 compares the SER performance of different algorithms on an Additive White Gaussian Noise (AWGN) channel, at SER ═ 10-2In the process, compared with the ZF precoding method, the algorithm is only about 1.7dB more, compared with the PMP algorithm, the algorithm is 0.5dB less, compared with the MF precoding method, the algorithm is 3.4dB less, compared with the clipping method, the algorithm is 3.5dB less, and compared with the MU-PP-GDm algorithm, the algorithm is 7dB less.
Fig. 6 shows the speed of reducing PAPR by ADMM algorithm, where CCDF is Pr (PAPR > C) is 10-3In the process, the PAPR value of the ADMM algorithm can be reduced to 6.5dB only by 3 times of iteration, the PAPR value of 25 times of iteration is reduced to 2.9dB, the PAPR value of 40 times of iteration can be reduced to 2.3dB, and the PAPR value is more than 10dB lower than that of the ZF precoding method. The PAPR value of the PMP method is 3.5dB after 1000 iterations, and the PAPR value of 1800 iterations is reduced to 2.9 dB; the MU-PP-GDm method can reduce the PAPR to 5.2dB through 50 iterations. From these simulation results, it can be seen that the ADMM algorithm has lower complexity and faster convergence speed, and compared with other methods, the ADMM method has lower SER and better PAPR suppression effect.
Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope defined by the appended claims.

Claims (7)

1. A low complexity reduction method for peak-to-average power ratio of MIMO-OFDM system is characterized by comprising the following steps:
s1: setting base station configuration data, defining subcarrier set for data transmission and subcarrier set for band guard, generating signal vector sn；
S2: for signal vector snPrecoding to obtain a precoded signal wn(ii) a To wnReordering in a computer systemTo obtain a frequency domain transmission signal an；
S3: OFDM: by transmitting the signal a in the frequency domainnIFFT is carried out to obtain a time domain transmitting signal xn；
S4: calculating a time-domain signal xnThe PAPR of (1);
s5: the method is characterized in that interference among multiple users is eliminated, PAPR is reduced, OFDM modulation is combined into a convex optimization problem, the convex optimization problem is solved by adopting a linear alternating direction multiplier method, and complexity reduction is achieved.
2. The method for low complexity reduction of peak-to-average power ratio of MIMO-OFDM system of claim 1, wherein said S1 is specifically: setting a base station to be configured with M transmitting antennas to serve K single-antenna mobile users and satisfy K<<M, the number of OFDM subcarriers is N, and a signal vector sn∈ΘKContains information transmitted to K users, N is 1,2, N is the carrier index of OFDM, Θ is the complex constellation set, s is the complex constellation setn,kE theta represents a symbol sent to user k on carrier n; the set of subcarriers used for data transmission is defined as Γ, the complementary set of which ΓcUsed as band guard, i.e. when n ∈ ΓcWhen there is a signal vector sn＝0K×1。
3. The method for low complexity reduction of peak-to-average power ratio of MIMO-OFDM system of claim 1, wherein said S2 is specifically: signal vector snN is 1,2, …, N is first precoded by a precoder designed based on the mean square error minimization criterion to generate N precoding vectors wnN is 1,2, …, N; to wnThe signals are reordered according to the direction from the user to the transmitting antenna to obtain a frequency-domain transmission signal [ a ]1,…,aM]＝[w1,…,wN]TWherein a ism∈CN×1M denotes an OFDM frequency domain signal transmitted on the mth antenna.
4. The method for low complexity reduction of peak-to-average power ratio of MIMO-OFDM system of claim 1, wherein S3 is embodiedComprises the following steps: to am∈CN×1The corresponding time domain signal x can be obtained by carrying out Fourier inverse transformationm＝FHamM is 1,2, …, M; wherein FH∈CLN×NRepresenting the first N columns of the LN point Fourier transform matrix, wherein L is an oversampling factor; the time domain signal is added with a cyclic prefix, and the received frequency domain signal vector is represented as yn＝sn+bnN is epsilon Γ; wherein, ynIs the frequency domain signal vector received by the nth sub-carrier, HnChannel matrix representing the nth subcarrier of the MIMO-OFDM, bn∈CK×1Is independently and identically distributed complex Gaussian noise, the mean value of each component of the complex Gaussian noise is 0, and the variance is N0。
5. The method for low complexity reduction of peak-to-average power ratio of MIMO-OFDM system of claim 1, wherein said S4 is specifically: time domain signal x obtained under L times oversamplingmThe PAPR table is:
Figure FDA0003307856240000021
6. the method for reducing the peak-to-average power ratio of the MIMO-OFDM system according to claim 1, wherein the method for combining the elimination of the inter-user interference, the reduction of the PAPR, and the OFDM modulation into the convex optimization problem in S5 specifically comprises:
a1: designing a convex optimization model, and jointly executing the steps of eliminating the interference among multiple users, OFDM modulation and reducing the PAPR:
the frequency domain signals transmitted by the subcarriers need to satisfy the following requirements:
sn＝Hnwn,n∈Г (2)
the frequency domain signal transmitted by the free carrier wave is required to satisfy the following conditions:
0M×1＝wn,n∈Гc (3)
the constraints are combined as:
Figure FDA0003307856240000031
based on the nature of OFDM modulation, we can jointly express the precoding constraint and OFDM modulation as
Figure FDA0003307856240000032
Wherein,
Figure FDA0003307856240000033
is a combination of the above-mentioned conditions left signal,
Figure FDA0003307856240000034
is a collection of frequency-domain signals that,
Figure FDA0003307856240000035
in the form of a block-diagonal matrix,
Figure FDA0003307856240000036
diagonal block is
Figure FDA0003307856240000037
And
Figure FDA0003307856240000038
Figure FDA0003307856240000039
Ψ is the corresponding permutation matrix,
Figure FDA00033078562400000310
a Kronecke product representing two matrices;
a2 description of the downlink transmission scheme as an optimization problem in connection with (1) and (5)
Figure FDA00033078562400000311
A3: the square of infinite norm is used to replace formula (6) to obtain the convex objective function
Figure FDA00033078562400000312
Relaxing the equality constraint S ═ HX, i.e. mean square error
Figure FDA00033078562400000313
Instead of S ═ HX, the following convex optimization problem was obtained:
Figure FDA00033078562400000314
a4: converting the convex optimization problem into an ADMM algorithm form, specifically:
defining illustrative functions I of sets C, respectivelyC(x) And the near-end operator Prox of function f (x):
Figure FDA00033078562400000315
Figure FDA00033078562400000316
the convex optimization problem is expressed as an equivalent form of the ADMM algorithm:
Figure FDA00033078562400000317
the augmented Lagrange function of equation (8) is:
Figure FDA0003307856240000041
the following iterative formula is generated:
Figure FDA0003307856240000042
Figure FDA0003307856240000043
Figure FDA0003307856240000044
aj+1＝aj+Xj+1-Zj+1 (10d)
wj+1＝wj+Xj+1-Yj+1 (10e)
7. the method for reducing the complexity of the peak-to-average power ratio of the MIMO-OFDM system as claimed in claim 6, wherein the solving the convex optimization problem by the linear alternating direction multiplier method in S5 is performed as follows:
solving the sub-problem equation (10 a):
Figure FDA0003307856240000045
solving the sub-problem equation (10 b):
Figure FDA0003307856240000046
solving the sub-problem equation (10 c):
Figure FDA0003307856240000047
solving the convex optimization problem under the ADMM algorithm, wherein the process is as follows:
b1: initialization t 1, z1＝y1＝a1＝w1＝02WN×1Setting the maximum number of iterations tmax；
B2：while t≤tmax；
B3 updating X using equation (11)j+1；
B4: updating Z using equation (12)j+1；
B5: updating Y using equation (13)j+1；
B6: updating the dual variable a using equation (10d)j+1；
B7: updating the dual variable w using equation (10e)j+1；
B8：end while；
B9: output Xj+1；
B10: and (4) carrying out simulation experiment of the algorithm, simulating by using software MATLAB, and verifying theoretical analysis.
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