CN113315732B - Low-complexity method suitable for reducing peak-to-average power ratio of MIMO-OFDM system - Google Patents
Low-complexity method suitable for reducing peak-to-average power ratio of MIMO-OFDM system Download PDFInfo
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Abstract
The invention discloses a low-complexity method suitable for reducing the peak-to-average power ratio of an MIMO-OFDM system, which comprises the following steps: setting base station configurationData, defining a set of subcarriers and a signal vector s for data transmission n (ii) a For signal vector s n Processing to obtain a frequency domain transmitting signal; acquiring a time domain transmitting signal through a frequency domain transmitting signal, adding a CP (content provider) to the time domain transmitting signal, and defining a baseband transmitting signal after OFDM (orthogonal frequency division multiplexing) modulation; measuring the fluctuation of a baseband transmitting signal by using a PAPR (peak-to-average power ratio), and measuring the PAPR by using a complementary cumulative distribution function; and combining the elimination of the interference among multiple users, OFDM modulation and reduction of PAPR into a convex optimization problem by using a designed acceleration near-end gradient algorithm, and solving the convex optimization problem. The invention can reduce the interference among multiple users and effectively reduce the PAPR value, and the PAPR of the transmitted signal can be reduced by using the APGM method with few iteration times, thereby improving the operation efficiency of the system, not influencing the SER performance of the system and being more in line with the application in engineering practice.
Description
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to a low-complexity method suitable for reducing the peak-to-average power ratio of a 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 technology and MIMO system can bring the advantages of both, and achieve faster communication rate and higher spectrum utilization rate, and this system has been identified as a reliable technology 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 massive 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 purpose of the invention is as follows: in order to overcome the defects in the prior art, the low-complexity method for reducing the peak-to-average power ratio of the MIMO-OFDM system is provided, the PAPR of a transmitted signal can be effectively inhibited in the downlink of the large-scale multi-user MIMO-OFDM system, meanwhile, the symbol error rate of the system is kept in a good state, and compared with other methods, the method can achieve a good effect only by a few iteration times.
The technical scheme is as follows: to achieve the above object, the present invention provides a low complexity method for reducing peak-to-average power ratio of a MIMO-OFDM system, comprising the steps of:
s1: setting base station configuration data, defining subcarrier sets and signal vectors s for data transmission n ；
S2: and (3) eliminating interference among multiple users by adopting MU precoding:
designing a signal vector s n For signal vector s n Processing to obtain a frequency domain transmitting signal;
s3: OFDM modulation:
acquiring a time domain transmitting signal through a frequency domain transmitting signal, adding a Cyclic Prefix (CP) to the time domain transmitting signal, and defining a baseband transmitting signal after OFDM modulation for the given frequency domain transmitting signal;
s4: and (3) reducing the PAPR:
measuring the fluctuation of a baseband transmitting signal by using a PAPR (peak-to-average power ratio), wherein the PAPR represents the ratio of a peak value to an average value of signal power, and measuring the PAPR by using a Complementary Cumulative Distribution Function (CCDF);
s5: and combining the elimination of the interference among multiple users, OFDM modulation and reduction of PAPR into a convex optimization problem by using a designed acceleration near-end gradient algorithm, and solving the convex optimization problem.
Further, the step 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 s n ∈Θ K Contains information transmitted to K users, N =1,2 n,k E 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 Γ c Used as band guard, i.e. when n ∈ Γ c When there is a signal vector s n ＝0 K×1 。
Further, the step S2 specifically includes: signal vector s n First, N precoding vectors are generated by a precoder designed based on a mean square error minimization criterion
To a is to n Normalization processing is carried out to obtain normalized precoding vector w n Reordering the users in the direction from the user to the transmitting antenna to obtain a frequency domain transmission signal [ x ] 1 ,…,x m ]＝P[w 1 ,…,w n ]Where P represents the corresponding ordering matrix, an N-dimensional vector x m That is, the frequency domain signal transmitted from the mth transmit antenna.
Further, the step S3 specifically includes: frequency domain transmission signal x m Performing inverse discrete Fourier transform to obtain a time domain transmission signal y m I.e. y m ＝IDFT(x m ) To the time domain transmission signal y m With the CP added, the frequency domain signal vector received by the receiver can be represented as: r is a radical of hydrogen n ＝H n w n +b n N = 1.., N, wherein r n Is the nth received signal vector, H n Channel matrix representing the nth subcarrier of the MIMO-OFDM, b n Is independently and identically distributed complex Gaussian noise, the mean value of each component of the complex Gaussian noise is 0, and the variance of each component is N 0 (ii) a For a given frequency domain signal
The OFDM modulated baseband transmit signal may be represented as:
wherein,
t is the OFDM symbol time, Δ f is the subcarrier frequency spacing, and N is the number of subcarriers.
Further, the expression of PAPR in step S4 is as follows:
the PAPR of the time-domain signal y at L times oversampling is expressed as:
further, the complementary cumulative distribution function in step S4 is represented as:
CCDF(α)＝Pr{PAPR＞α}＝1-(1-e -α ) N (4)
wherein, α represents a threshold value of the designated PAPR, and N is the number of OFDM signal subcarriers.
Further, the specific method for combining elimination of inter-user interference, OFDM modulation, and PAPR reduction into a convex optimization problem by using the designed accelerated near-end gradient algorithm in step S5 is:
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:
s n ＝H n w n ,n∈Γ (5)
the frequency domain signal transmitted by the free carrier wave is required to satisfy the following conditions:
0 M×1 ＝w n ,n∈Γ c (6)
the constraints are combined as:
based on the nature of OFDM modulation, we can jointly express the precoding constraint and OFDM modulation as
Wherein,
is a combination of the left signals of the formula (5) and the formula (6),
is formed by a channel matrix
n ∈ Γ and unit matrix I M ,n∈Γ c Composed of P being a rearranged matrix, its internal matrix block
Except that (m, n) is 1, all the values of the other elements are 0;
is a matrix block F lN Formed block diagonal matrix, diagonal elements
Representing the first N columns of the lN point discrete Fourier transform matrix;
a2: in connection with (3) and (8), the downlink transmission scheme is described as the following optimization problem:
a3: the square of infinite norm is used to replace formula (9) to obtain the convex objective function
Relaxing equality constraints
Mean square error of instant use
Instead of the former
The following convex optimization problem was obtained:
further, the solving process of the convex optimization problem (10) in the step A3 is as follows:
where λ is a regularization parameter, equations (10) and (11) are equivalent by selecting the appropriate parameters λ and δ, and determining the step size γ by a linear search method j Function of
The near-end operator of (a) can be written in the form:
calculating out
The optimization problem (11) is solved.
Further, the solution process of the optimization problem (11) is as follows:
b1: computing
The near-end operator of (2), comprising the steps of:
b2: calculation step for solving optimization problem (11):
b3: and (4) carrying out a simulation experiment of the algorithm, carrying out simulation by using software MATLAB, and verifying theoretical analysis.
Has the advantages that: compared with the prior art, the invention provides a low-complexity APGM method for the problem of higher PAPR value in a large-scale multi-user MIMO-OFDM system, the core is that MU pre-coding, OFDM modulation and PAPR suppression are combined into a convex optimization problem by utilizing the extra degree of freedom of a transmitting antenna, and the solution is carried out, so that the interference among multiple users can be reduced, the PAPR value can be effectively reduced, the PAPR of a transmitted signal can be reduced by using the APGM method with few iterations, the system operation efficiency is improved, the SER performance of the system is not influenced, and the APGM method is more suitable for the application in engineering practice.
Drawings
FIG. 1 is a downlink diagram of a massive multi-user MIMO-OFDM system;
FIG. 2 is a graph of the effect of different methods on reducing the PAPR of a transmitted signal;
FIG. 3 is a SER comparison graph of different methods;
fig. 4 is a comparison graph of PAPR reduction of a transmitted signal under different iteration numbers of different methods.
Detailed Description
The present invention is further illustrated by the following detailed description in conjunction with the accompanying drawings, it is to be understood that such embodiments are merely illustrative of and not restrictive on the broad invention, and that various equivalent modifications of the invention may occur to those skilled in the art upon reading the appended claims.
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 s n ∈Θ K Contains information transmitted to K users, N =1,2 n,k E theta represents a symbol sent to user k on carrier n; in order to shape the spectrum of the transmitted signal, an 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 Γ c Used as band-guard, i.e. when n ∈ Γ c When there is a signal vector s n ＝0 K×1 。
S2: in order to eliminate the inter-user interference, MU precoding is adopted, which specifically comprises: designing a signal vector s n Signal vector s n First, N precoding vectors are generated by a precoder designed based on a mean square error minimization criterion
The pre-coding will result in a n Power sum signal vector s n And channel dependence, for a to guarantee unit transmit power n Normalization processing is carried out to obtain normalized precoding vector w n Reordering the signals according to the direction from the user to the transmitting antenna to obtain frequency domain signalsRadio signal [ x ] 1 ,…,x m ]＝P[w 1 ,…,w n ]Where P denotes the corresponding sorting matrix, an N-dimensional vector x m That is, the frequency domain signal transmitted from the mth transmit antenna.
S3: OFDM modulation:
frequency domain transmission signal x m Performing inverse discrete Fourier transform to obtain a time domain transmission signal y m I.e. y m ＝IDFT(x m ) To avoid ISI (intersymbol interference), it is necessary to transmit the signal y in the time domain m With the CP added, the frequency domain signal vector received by the receiver can be represented as: r is n ＝H n w n +b n N = 1.., N, wherein r n Is the nth received signal vector, H n Channel matrix representing the nth subcarrier of the MIMO-OFDM, b n Is independently and identically distributed complex Gaussian noise, the mean value of each component of the complex Gaussian noise is 0, and the variance is N 0 (ii) a For a given frequency domain signal
The OFDM modulated baseband transmit signal may be represented as:
wherein,
t is the OFDM symbol time, Δ f is the subcarrier frequency spacing, and N is the number of subcarriers.
S4: and (3) reducing the PAPR:
because the phases of the sub-carriers are independent of each other, the superimposed OFDM signals have a very large dynamic range. The fluctuation of the transmitted signal is measured by the PAPR, which represents the peak-to-average ratio of the signal power, i.e.
In practical systems, usually only a few discrete-time samples of the transmitted signal y (t), the PAPR of a continuous-time signal can be better approximated by L-times oversampling, where the PAPR of the time-domain signal y can be expressed as
The Complementary Cumulative Distribution Function (CCDF) is used to measure the peak-to-average ratio of a signal, which means the probability that the peak-to-average ratio of the transmitted signal exceeds a threshold, and is specifically expressed as:
CCDF(α)＝Pr{PAPR＞α}＝1-(1-e -α ) N (4)
wherein alpha represents the threshold value of the designated PAPR, and N is the number of the OFDM signal sub-carriers.
S5: and combining the elimination of the interference among multiple users, OFDM modulation and reduction of PAPR into a convex optimization problem by using a designed acceleration near-end gradient algorithm, and solving the convex optimization problem.
The near-end gradient algorithm is used to solve the problem of the form
minimize f(y)+g(y)
Wherein, f is R n → R is a convex function, g: R n → R { + ∞ } is a convex function and differentiable.
The basic iterative process of the accelerated near-end gradient algorithm is as follows:
x k+1 :＝y k +ω k (y k -y k-1 )
wherein, ω is k E [0, 1) is an extrapolation parameter, usually chosen to be ω k K/(k + 3), using a fixed step size λ ∈ (0,1/L)]The algorithm is represented by o (1/k) 2 ) Converges to a target value.
In the step S5, a specific method for combining MU precoding to eliminate interference among multiple users, OFDM modulation and reduce PAPR (peak-to-average power ratio) into a convex optimization problem by using a designed acceleration near-end gradient algorithm is as follows:
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:
s n ＝H n w n ,n∈Γ (5)
the frequency domain signal transmitted by the free carrier wave needs to satisfy the following conditions:
0 M×1 ＝w n ,n∈Γ c (6)
the constraints are combined as:
based on the nature of OFDM modulation, we can jointly express the precoding constraint and OFDM modulation as
Wherein,
is a combination of the left signals of the formula (5) and the formula (6),
is formed by a channel matrix
n ∈ Γ and unit matrix I M ,n∈Γ c Composed of P being a rearranged matrix, its internal matrix block
Except that (m, n) is 1, the values of the other elements are all 0;
is a matrix block F lN Component block diagonal matrix, diagonal elements
Representing the first N columns of the lN point discrete Fourier transform matrix;
a2: in conjunction with (3) and (8), the downlink transmission scheme is described as an optimization problem as follows:
a3: substituting equation (9) with the square of infinite norm to obtain a convex objective function
Relaxing the equality constraint
Mean square error of instant use
Substitute for
The following convex optimization problem was obtained:
the solving process of the convex optimization problem (10) comprises the following steps:
where λ is a regularization parameter, equations (10) and (11) are equivalent by selecting the appropriate parameters λ and δ, and determining the step size γ by a linear search method j Function of
The near-end operator of (a) can be written in the form:
computing
The optimization problem (11) is solved.
The solving process of the optimization problem (11) is as follows:
b1: computing
The near-end operator of (2), comprising the steps of:
b2: calculation step for solving optimization problem (11):
the embodiment also provides a system for reducing the peak-to-average power ratio of the MIMO-OFDM system, which includes a network interface, a memory and a processor; the network interface is used for receiving and sending signals in the process of receiving and sending information with other external network elements; a memory for storing computer program instructions executable on the processor; a processor for performing the steps of the consensus method described above when executing computer program instructions.
The present embodiment also provides a computer storage medium storing a computer program that when executed by a processor can implement the method described above. The computer-readable medium may be considered tangible and non-transitory. Non-limiting examples of a non-transitory tangible computer-readable medium include non-volatile memory circuits (e.g., flash memory circuits, erasable programmable read-only memory circuits, or masked read-only memory circuits), volatile memory circuits (e.g., static random access memory circuits or dynamic random access memory circuits), magnetic storage media (e.g., analog or digital tapes or hard drives), and optical storage media (e.g., CD, DVD, or blu-ray disc), among others. The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also comprise or rely on stored data. The computer programs may include a basic input/output system (BIOS) that interacts with the hardware of the special purpose computer, a device driver that interacts with specific devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, and the like.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
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, performs simulation by using software MATLAB, and verifies theoretical analysis. The specific simulation results and analysis are as follows:
fig. 2 is a graph showing the effect of reducing the PAPR of the transmitted signal by different methods, comparing the performance of the APGM algorithm with the performance of the ZF algorithm, the MF algorithm, the PMP algorithm, the PRO-ADMM algorithm, and the MU-PP-GDm algorithm in PAPR suppression. At CCDF = Pr (PAPR > C) =10 -3 The PAPR of the APGM algorithm can be reduced to 2.3dB only by 50 iterations, the PAPR is reduced by more than 10dB compared with that of a ZF method, the PAPR is reduced by 1.1dB compared with that of a FITRA algorithm, the PAPR is reduced by 2.5dB compared with that of an MU-PP-GDm algorithm, and the PAPR is reduced by 3.6dB compared with that of a PRO-ADMM algorithm; the FITRA algorithm may reduce the PAPR to 3.4dB, the MU-PP-GDm algorithm may reduce the PAPR of the transmitted signal to 4.8dB, and the PRO-ADMM algorithm reduces the PAPR of the signal to 5.9dB. The APGM method can achieve the effect only by 50 iterations, while the FITRA method can reduce the PAPR value to 2.3dB only by about 2000 iterations. As can be seen from the figure, the present inventionThe PAPR reduction performance of the APGM algorithm provided by the invention is superior to algorithms such as FITRA, PRO-ADMM, MU-PP-GDm and the like.
As shown in fig. 3, which is a graph of SER effect for different methods, it can be seen that compared to ZF scheme (at SER = 10) -2 In the process), the symbol error rate of the APGM algorithm is only about 2dB more than an ideal value, compared with the FITRA algorithm, the algorithm provided by the invention is 0.2dB less, 2dB less than the PRO-ADMM algorithm, compared with the MF method, the algorithm provided by the invention is 3.4dB less, and meanwhile, the algorithm is 7dB less than the MU-PP-GDm algorithm.
Fig. 4 is a graph comparing the PAPR of the transmitted signal reduced by different iterations of the method, where CCDF = Pr (PAPR > α) =10 -3 During the process, the PAPR of the designed APGM algorithm can be reduced to 5.9dB through 10 iterations, the PAPR can be reduced to 3.3dB through 30 iterations, and the PAPR value can be reduced to 2.3dB through 50 iterations, which is reduced by more than 10dB compared with the PAPR value of a zero forcing pre-coding method; the PRO-ADMM method carries out external iteration for 200 times and internal iteration for 2 times, and the PAPR value can be reduced to 5.9dB by 400 times of iteration in total; the MU-PP-GDm method can reduce the PAPR value to 4.8dB through 50 iterations; the FITRA algorithm only reduces to 10dB after 100 iterations, reaches 5.2dB after 500 iterations, reduces the PAPR value to 3dB after 1500 iterations, and requires about 2000 iterations when the FITRA algorithm reduces the PAPR to 2.3dB.
From the simulation experiments, the APGM algorithm has lower complexity and faster convergence speed, and can obtain lower SER and better PAPR inhibition effect only by a small amount of iteration, so that the APGM method is more efficient than other existing methods, and is more beneficial to application in engineering practice.
Claims (3)
1. A low complexity method for reducing a peak-to-average power ratio of a MIMO-OFDM system, comprising the steps of:
s1: setting base station configuration data, defining subcarrier sets and signal vectors s for data transmission n ；
S2: and (3) eliminating interference among multiple users by adopting MU precoding:
designing a signal vector s n For signal vector s n Processing to obtain frequency domain transmission signal；
S3: OFDM modulation:
acquiring a time domain transmitting signal through a frequency domain transmitting signal, adding a cyclic prefix to the time domain transmitting signal, and defining a baseband transmitting signal after OFDM modulation for the given frequency domain transmitting signal;
s4: and (3) reducing the PAPR:
measuring the fluctuation of a baseband transmitting signal by using a PAPR (peak-to-average power ratio), wherein the PAPR represents the ratio of a peak value to an average value of signal power, and measuring the PAPR by using a complementary cumulative distribution function;
s5: combining the elimination of the interference among multiple users, OFDM modulation and reduction of PAPR into a convex optimization problem by using a designed acceleration near-end gradient algorithm, and solving the convex optimization problem;
the step S1 specifically comprises the following steps: setting a base station to be provided with M transmitting antennas serving K single-antenna mobile users, and satisfying K & lt M, the number of OFDM sub-carriers is N, and a signal vector s n ∈Θ K Contains information transmitted to K users, N =1,2 n,k E 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 Γ c Used as band guard, i.e. when n ∈ Γ c When there is a signal vector s n ＝0 K×1 ；
The step S2 specifically includes: signal vector s n First, N precoding vectors are generated by a precoder designed based on a mean square error minimization criterion
To a n Normalization processing is carried out to obtain normalized precoding vector w n Reordering the users in the direction from the user to the transmitting antenna to obtain a frequency domain transmission signal [ x ] 1 ,…,x m ]＝P[w 1 ,…,w n ]Where P represents the corresponding ordering matrix, an N-dimensional vector x m Namely, the frequency domain signal transmitted from the mth transmitting antenna;
the step S3 specifically comprises the following steps: frequency domain transmission signal x m Performing inverse discrete Fourier transformObtaining a time-domain transmit signal y m I.e. y m ＝IDFT(x m ) For time domain transmission signal y m With the CP added, the frequency domain signal vector received by the receiver can be represented as: r is n ＝H n w n +b n N = 1.., N, wherein r n Is the nth received signal vector, H n Channel matrix representing the nth subcarrier of the MIMO-OFDM, b n Is independently and identically distributed complex Gaussian noise, the mean value of each component of the complex Gaussian noise is 0, and the variance is N 0 (ii) a For a given frequency domain signal
The OFDM modulated baseband transmit signal may be represented as:
wherein,
t is OFDM symbol time, delta f is subcarrier frequency interval, and N is subcarrier number;
the expression of PAPR in step S4 is as follows:
the PAPR of the time-domain signal y at L times over-sampling is expressed as:
the complementary cumulative distribution function in step S4 is represented as:
CCDF(α)＝Pr{PAPR＞α}＝1-(1-e -α ) N (4)
wherein, alpha represents the threshold value of the designated PAPR, and N is the number of the OFDM signal sub-carriers;
the specific method for combining elimination of interference among multiple users, OFDM modulation and reduction of PAPR into the convex optimization problem by using the designed near-end gradient acceleration algorithm in the step S5 is as follows:
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:
s n ＝H n w n ,n∈Γ (5)
the frequency domain signal transmitted by the free carrier wave is required to satisfy the following conditions:
0 M×1 ＝w n ,n∈Γ c (6)
the constraints are combined as:
depending on the nature of the OFDM modulation, the precoding constraint and the OFDM modulation can be jointly expressed as
Wherein,
is a combination of the left signals of the formula (5) and the formula (6),
is formed by a channel matrix
And unit array I M ,M∈Γ c Composed of P being a rearranged matrix, its internal matrix block
Except that (m, n) is 1, all the values of the other elements are 0;
is a matrix block F lN Formed block diagonal matrix, diagonal elements
Representing the first N columns of the lN point discrete Fourier transform matrix;
a2: in conjunction with (3) and (8), the downlink transmission scheme is described as an optimization problem as follows:
a3: substituting equation (9) with the square of infinite norm to obtain a convex objective function
Relaxing the equality constraint
I.e. mean square error
Instead of the former
The following convex optimization problem is obtained:
2. the low complexity method for peak-to-average power ratio reduction in MIMO-OFDM systems according to claim 1, wherein the solving of the convex optimization problem (10) in step A3 is:
where λ is a regularization parameter, by choosing the parameters λ and δ, equations (10) and (11) are equivalent, and the step size γ is determined by a linear search method j Function of
The near-end operator of (a) can be written in the form:
computing
The near-end operator of (2), solving the optimization problem (11).
3. A low complexity method for reducing the peak-to-average ratio of a MIMO-OFDM system as claimed in claim 2, wherein the optimization problem (11) is solved by:
b1: calculating out
The near-end operator of (2), comprising the steps of:
b2: calculation step for solving optimization problem (11):
b3: and (4) carrying out simulation experiment of the algorithm, simulating by using software MATLAB, and verifying theoretical analysis.
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