CN113179238B - Method for reducing peak-to-average power ratio of FBMC-OQAM system - Google Patents

Method for reducing peak-to-average power ratio of FBMC-OQAM system Download PDF

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CN113179238B
CN113179238B CN202110462128.XA CN202110462128A CN113179238B CN 113179238 B CN113179238 B CN 113179238B CN 202110462128 A CN202110462128 A CN 202110462128A CN 113179238 B CN113179238 B CN 113179238B
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papr
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CN113179238A (en
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曾诗莹
伍沛然
夏明华
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Sun Yat Sen University
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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
    • 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
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Abstract

The invention relates to the technical field of communication waveforms, in particular to a method for reducing the peak-to-average power ratio of an FBMC-OQAM system, which comprises the following steps: s1, generating a modulation signal by combining OQAM modulation and OFDM; then, the modulation signal passes through a prototype filter and is modulated on N subcarriers, and an output signal is obtained through superposition; s2, oversampling the output signal obtained in the step S1 to obtain a sampling signal; s3, processing the sampling signal by adopting a window-based segmentation method, and extracting a signal in a window to obtain a windowed signal; s4, processing the windowed signal through a partial transmission sequence PTS to obtain a PTS optimization objective function; s5, solving the PTS optimization objective function to obtain the optimal PAPR, thereby realizing the reduction of the PAPR. The invention adopts a windowing segmentation method to process the overlapped structure of FBMC-OQAM signals and eliminate the influence between adjacent data blocks; by introducing part of the transmission sequence PTS, the PAPR of the FBMC-OQAM system is effectively reduced.

Description

Method for reducing peak-to-average power ratio of FBMC-OQAM system
Technical Field
The invention relates to the technical field of communication waveforms, in particular to a method for reducing the peak-to-average power ratio of an FBMC-OQAM system.
Background
In recent years, a Filter-bank Multi-carrier (FBMC-OQAM) technique Of Offset quadrature Amplitude Modulation has been widely studied, and has a lower Out-Of-Band emission (OOB) characteristic compared to a conventional Orthogonal Frequency-Division Multiplexing (OFDM) technique. The FBMC-OQAM system can achieve higher spectrum utilization ratio than the OFDM system without using Cyclic Prefix (CP). In addition, the FBMC-OQAM system uses a single guard subcarrier to effectively remove Inter-Symbol Interference (ISI) and Inter-Carrier Interference (ICI). The advantages make the FBMC-OQAM technology the best candidate for the real-time application scene of frequently transmitting short frames in the future. However, as with the filter bank multicarrier OFDM system, the Peak-to-Average Power Ratio (PAPR) is still an inevitable problem for the FBMC-OQAM system.
Existing PAPR reduction schemes can be roughly divided into three categories: signal predistortion techniques, probability class techniques and coding techniques. Signal predistortion techniques mainly include clipping techniques and carrier Reservation (TR) techniques, which have low computational complexity but are prone to cause nonlinear interference and amplify noise power. The prior art introduces several improved schemes based on TR technology, such as Clipping Control TR (CC-TR) and Least square Approximation based TR (LSA-TR) schemes. In the coding technique, Selective Mapping (SLM) technique and partial transmission sequence PTS technique can reduce PAPR and bit error rate well, but have higher computational complexity.
However, the PAPR reduction scheme developed for the conventional filter bank multi-carrier OFDM system as described above cannot be directly applied to the FBMC-OQAM system due to the overlapping structure between FBMC-OQAM signal symbols. To solve this problem, the prior art adopts an Overlapping-SLM (O-SLM) scheme. In order to reduce the computational complexity, the prior art adopts an Iterative partial transmission sequence (PTS, I-PTS) scheme for searching an optimal weight factor sequence.
The Chinese patent publication No. CN108418774A (published as 2018, 08 and 17) discloses a PSO-GA joint optimization algorithm for reducing peak-to-average power ratio, belongs to the technical field of signal and information processing, and is applied to signal waveform design in radar communication integration research. The method of the invention integrates the ideas of individual extremum and global extremum in the PSO algorithm into the GA algorithm, and changes the method that the individual extremum approaches the global extremum through the updating of position and speed in the PSO into the method that the individual extremum approaches the global extremum through the intersection and the variation of the genetic algorithm, but has the defects of larger mutual influence between adjacent data blocks and overhigh peak-to-average power ratio (PAPR).
Disclosure of Invention
The invention aims to overcome the defects of large mutual influence between adjacent data blocks and overhigh peak-to-average power ratio (PAPR) in the prior art, and provides a method for reducing the PAPR of an FBMC-OQAM system, which can effectively eliminate the influence between the adjacent data blocks and effectively reduce the PAPR.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for reducing peak-to-average power ratio of FBMC-OQAM system comprises the following steps:
step S1, obtaining a modulation signal, and modulating and superposing the modulation signal to obtain an output signal;
step S2, sampling the output signal obtained in the step S1 to obtain a sampling signal;
step S3, processing the sampling signal by adopting a window-based segmentation method, and extracting the signal in a window to obtain a windowed signal;
step S4, processing the windowed signal through a partial transmission sequence PTS to obtain a PTS optimization objective function;
and step S5, solving the PTS optimization objective function to obtain the optimal PAPR, thereby realizing the reduction of the PAPR.
Further, in step S1, the FBMC-OQAM system combines offset quadrature amplitude modulation OQAM with orthogonal frequency division multiplexing OFDM, avoiding using a cyclic prefix CP; the modulated signal is expressed as the following equation:
Figure BDA0003042675700000021
wherein
Figure BDA0003042675700000031
N is more than or equal to 0 and less than or equal to N-1, M is more than or equal to 0 and less than or equal to M-1,
Figure BDA0003042675700000032
is that
Figure BDA0003042675700000033
An imaginary part of (d);
Figure BDA0003042675700000034
is that
Figure BDA0003042675700000035
An imaginary part of (d); in time domain, there is a delay of T/2 between the real part and the imaginary part of the FBMC-OQAM symbol, where T is the period of each data block;
the modulated signal is passed through a prototype filter and modulated on N subcarriers, given by the following equation:
Figure BDA0003042675700000036
where h (t) is the impulse response of the prototype filter, given by the equation:
Figure BDA0003042675700000037
finally, the M data blocks are superposed, and the obtained output signal is the following formula:
Figure BDA0003042675700000038
further, in step S2, the output signal is oversampled to obtain a sampled signal; the sampled signal is written as the following equation:
Figure BDA0003042675700000039
wherein, h [ k]H (kT/K), and
Figure BDA00030426757000000310
k is the delay length between each FBMC-OQAM symbol.
Further, in step S3, a window-based windowing segmentation method is adopted to improve the performance; firstly, extracting a signal in a window to obtain a windowed signal, wherein the expression is as follows:
Figure BDA00030426757000000311
the length of the window is set to be K, namely the delay length between each FBMC-OQAM symbol; the extracted signals are independently processed by partial transmission sequences PTS, and then the window is shiftedMoving K unit lengths; dividing signals of the M data blocks into M + A sections; a is xm＝1[k]And xm[k]The number of overlapping data blocks, the length of each segment is K.
Further, in step S4, the windowed signal is transmitted
Figure BDA00030426757000000312
Written in vector form, the following equation:
Figure BDA0003042675700000041
firstly, the following components are mixed
Figure BDA0003042675700000042
Is divided into V sub-blocks, provided
Figure BDA0003042675700000043
Represents the v sub-block, given by the following equation:
Figure BDA0003042675700000044
thus wm[k]Expressed in the following form:
Figure BDA0003042675700000045
wherein,
Figure BDA0003042675700000046
thus, the vth sub-block is represented as:
Figure BDA0003042675700000047
the subblocks after the blocking
Figure BDA0003042675700000048
By inverse fast Fourier transformThe transformation of the leaf into the time domain is followed by multiplication by a weighting factor
Figure BDA0003042675700000049
And accumulating to obtain an output symbol sequence sm[k]Given by the following equation:
Figure BDA00030426757000000410
wherein
Figure BDA00030426757000000411
W is the selectable phase, and the weighting factor is represented as a vector:
Figure BDA00030426757000000412
finally, a signal processed by the partial transmission sequence PTS is obtained, which is given by the following formula:
Figure BDA00030426757000000413
through the derivation, the partial transmission sequence PTS optimization objective function is obtained as follows:
Figure BDA00030426757000000414
Figure BDA00030426757000000415
wherein q represents the current number of windows,
Figure BDA00030426757000000416
is sq[k]I-0, 1, …, W-1, V-0, 2, …, V-1, q-0, 1, …, M + a-1.
Further, in step S5, the peak-to-average power ratio PAPR of the signal is defined as:
Figure BDA0003042675700000051
evaluating performance using a complementary cumulative distribution function; the complementary cumulative distribution function is defined as the PAPR value of the peak-to-average power ratio being larger than the PAPR threshold valueTHIs given by the following formula:
CCDF(PAPR{x[k]})＝Pr(PAPR{x[k]}＞PAPRTH)。
furthermore, in order to avoid the exhaustive search process of the traditional partial transmission sequence PTS and reduce the calculation complexity of the algorithm, on the basis of the partial transmission sequence PTS, a Particle Swarm Optimization (PSO) algorithm is introduced to improve the search efficiency of the weight factor;
in the particle swarm optimization PSO, the speed and position of each particle are continuously updated in an iterative process, and are expressed as the following formula:
Figure BDA0003042675700000052
pi(t+1)＝pi(t)+vi(t)
wherein i is 0,1, …, NpRepresenting the index of the particle, NpIs the total number of particles, t is the current number of iterations, pi(t) is the position of the particle, vi(t) is the velocity of the particles;
Figure BDA0003042675700000053
and g*(t) the optimal solution of the position of the ith particle and the position of the whole particle swarm in the iterative process respectively; ω is the inertial weight, c1And c2Are learning factors for particles and populations; r is1And r2Is [0,1 ]]Two random numbers in between; defining weight factors
Figure BDA0003042675700000054
And the position g of the whole particle groupv(t) a special translation relationship between them, defined as the following equation:
Figure BDA0003042675700000055
wherein G isin＝(Gmax-Gmin)/4，GmaxAnd GminIs the upper and lower limit of the particle population; the fitness function value for each particle is expressed as the following equation:
f(t)＝1/PAPR(βq)。
further, an improved particle swarm optimization algorithm IPSO is introduced, the searching speed of the particles in the PSO is dynamically adjusted, and the adjusting steps are as follows:
step A1, initializing particle swarm:
introducing the concept of particle entropy; the particle entropy, as a condition for whether a new particle is retained, is given by the following equation:
Figure BDA0003042675700000061
wherein P isni＝1-|pi-pn|/|Pmax-PminI, representing the position closeness of the particles i and n; first, an entropy threshold S is setTHWhich represents the maximum acceptable positional proximity between the particles; when S is more than or equal to STHIf so, retaining the new particle, otherwise, removing the new particle, and regenerating the particle;
step A2, calculating population diversity:
the position of the particle and the average center position of the population are defined as
Figure BDA0003042675700000066
And
Figure BDA0003042675700000065
the average distance of the particles to the mean center of the population is:
Figure BDA0003042675700000062
step A3, dynamically adjusting inertial weight:
dynamically adjusting inertia weight according to the current average center distance of the particle population by adopting a self-adaptive method; the update of the inertial weight is represented by the following equation:
Figure BDA0003042675700000063
wherein T ismaxIs the maximum number of iterations and μ is a constant to prevent stopping the search when the speed is 0.
Further, an improved particle swarm optimization IPSO is introduced to obtain an IPSO-PTS;
in the IPSO-PTS, a specific procedure includes the steps of:
step B1: initializing the speed of particles of a particle population and the positions of the particles;
step B2: decoding the position information of the particle to obtain a weight factor, and dividing the weight factor and the windowed signal
Figure BDA0003042675700000064
Multiplying to calculate fitness function value f0；
Step B3: comparing the current fitness value of the particle with the optimal fitness value of the individual, and replacing the optimal fitness of the individual if the current fitness value is larger;
step B4: finding out the global optimal fitness value of the particle population, and comparing the optimal fitness of each particle with the optimal value of the population; if the fitness value of the individual is larger, replacing the global optimal fitness;
step B5: updating the speed and position of the particle;
step B6: judging whether the set maximum iteration times is reached, and if the current iteration times reaches the maximum value, taking the current optimal fitness value as a result; otherwise, adding 1 to the current iteration number, and repeating the steps B2 to B5;
step B7: and decoding the found population optimal fitness value to obtain an optimized weight factor.
Further, in step B1, a maximum number of iterations T is inputmaxThe window signal of the qth data block
Figure BDA0003042675700000071
Velocity v of the initiating particlei(t) position p of the particlei(t) total number of particles NpInertia weight ω;
in step B2, let the current iteration number t ← 0, obtain fitness function f0；
In step B3, according to f (t) 1/PAPR (β)q) Calculating a fitness function of the particles; the fitness value f of the present particlec(t) value of fitness to optimum particle
Figure BDA0003042675700000072
Comparing; if it is not
Figure BDA0003042675700000073
Then order
Figure BDA0003042675700000074
Let the index i ← i +1 of the particle; judging whether the index of the particles is less than the total number of the particles, i < NpIf yes, re-executing the step B4, otherwise, executing the step B5;
in step B4, the best fitness value f (g) of the population is foundv(t)), and then is solved with the global optimum
Figure BDA0003042675700000075
Comparing; if it is not
Figure BDA0003042675700000076
Then order
Figure BDA0003042675700000077
In step B5, according to
Figure BDA0003042675700000078
pi(t+1)＝pi(t)+vi(t)
Updating the velocity and position of each particle; further, according to
Figure BDA0003042675700000079
Updating the inertia weight omega; let the index of particle i ← 0;
in step B6, it is determined whether the current iteration count is less than the maximum iteration count, i.e., T < TmaxIf yes, making the current iteration number t ← t +1, and executing step B3, otherwise, executing step B7; in step B7, let
Figure BDA00030426757000000710
Output windowed signal
Figure BDA00030426757000000711
Weight factor of
Figure BDA00030426757000000712
Compared with the prior art, the invention has the beneficial effects that:
a method for reducing the peak-to-average power ratio of an FBMC-OQAM system adopts a windowing segmentation method to process an overlapped structure of FBMC-OQAM signals and eliminate the influence between adjacent data blocks; by introducing part of the transmission sequence PTS, the PAPR of the FBMC-OQAM system is effectively reduced.
Drawings
Fig. 1 is a flowchart of a method for reducing a peak-to-average power ratio of an FBMC-OQAM system according to an embodiment of the present invention.
Fig. 2 is a flowchart of an IPSO algorithm of a method for reducing a peak-to-average power ratio of an FBMC-OQAM system according to an embodiment of the present invention.
Fig. 3 is a structural diagram of an FBMC-OQAM transmission signal according to a method for reducing a peak-to-average power ratio of an FBMC-OQAM system in an embodiment of the present invention.
Fig. 4 is an overlapping structure diagram of FBMC-OQAM symbols in a method for reducing peak-to-average power ratio of an FBMC-OQAM system according to an embodiment of the present invention.
Fig. 5 is a diagram of a PTS-PSO scheme of a method for reducing a peak-to-average power ratio of an FBMC-OQAM system according to an embodiment of the present invention.
Fig. 6 is a graph comparing the performance of the direct introduction partial transmission sequence PTS and the introduction windowed partition partial transmission sequence W-PTS of a method for reducing the peak-to-average power ratio of the FBMC-OQAM system according to an embodiment of the present invention.
Fig. 7 is a graph comparing the performance of different PAPR reduction schemes of an FBMC-OQAM system according to an embodiment of the present invention.
Fig. 8 is a diagram illustrating the effect of different parameters V and Np on the system performance in a method for reducing the peak-to-average power ratio of the FBMC-OQAM system according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In the description of the present invention, it should be noted that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In addition, in the description of the present invention, "a plurality" means two or more unless otherwise specified.
As shown in fig. 1 to 8, a preferred embodiment of a method for reducing the peak-to-average power ratio of an FBMC-OQAM system according to the present invention:
a method for reducing peak-to-average power ratio of FBMC-OQAM system comprises the following steps:
step S1, adopting OQAM modulation and OFDM combination to generate modulation signal; then, the modulation signal passes through a prototype filter and is modulated on N subcarriers, and an output signal is obtained through superposition;
step S2, oversampling the output signal obtained in step S1 to obtain a sampling signal;
step S3, processing the sampling signal by adopting a window-based segmentation method, and extracting the signal in a window to obtain a windowed signal;
step S4, processing the windowed signal through a partial transmission sequence PTS to obtain a PTS optimization objective function;
and step S5, solving the PTS optimization objective function to obtain the optimal PAPR, thereby realizing the reduction of the PAPR.
In a specific embodiment, in step S1, the FBMC-OQAM system combines offset quadrature amplitude modulation OQAM with orthogonal frequency division multiplexing OFDM, avoiding the use of cyclic prefix CP and improving the spectrum utilization; fig. 4 describes a process of generating an FBMC-OQAM signal at a transmitting end. The modulated signal can be expressed as the following equation:
Figure BDA0003042675700000091
wherein
Figure BDA0003042675700000092
N is more than or equal to 0 and less than or equal to N-1, M is more than or equal to 0 and less than or equal to M-1,
Figure BDA0003042675700000093
is that
Figure BDA0003042675700000094
The imaginary part of (a) is,
Figure BDA0003042675700000095
is that
Figure BDA0003042675700000096
The imaginary part of (a) is shown in fig. 5; the FBMC-OQAM signal is composed of a plurality of FBMC-OQAM symbols; the FBMC-OQAM signals comprise signals processed and transmitted in an FBMC-OQAM system, such as modulation signals, output signals, windowing signals, signals processed by PTS (partial transmit sequence) and the like; in time domain, there is a delay of T/2 between the real part and the imaginary part of the FBMC-OQAM symbol, where T is the period of each data block;
the modulated signal is passed through a prototype filter and modulated on N subcarriers, given by the following equation:
Figure BDA0003042675700000097
where h (t) is the impulse response of the prototype filter, given by the equation:
Figure BDA0003042675700000098
finally, the M data blocks are superposed, and the obtained output signal is the following formula:
Figure BDA0003042675700000101
in a specific embodiment, in step S2, since most existing schemes for reducing PAPR are only applicable to discrete-time signals, the output signal needs to be oversampled to obtain a sampled signal; when the oversampling factor S is larger than or equal to 4, the PAPR of the original continuous signal can be similar to the PAPR of the sampled signal; thus, without loss of generality, S is set to 4; the sampled signal can be written as the following equation:
Figure BDA0003042675700000102
wherein, h [ k]H (kT/K), and
Figure BDA0003042675700000103
k is the delay length between each FBMC-OQAM symbol; and after the subsequent optimization processing is completed, converting the FBMC-OQAM signal to a radio frequency RF frequency band for transmission.
In a specific embodiment, in step S3, the actual signal is affected by the adjacent data blocks due to the overlapping structure of the FBMC-OQAM signals; therefore, it is not obvious to apply the conventional partial transmission sequence PTS scheme directly to the FBMC-OQAM system; to solve this problem, we use a window-based windowing segmentation method to improve performance; firstly, extracting a signal in a window to obtain a windowed signal, wherein the expression is as follows:
Figure BDA0003042675700000104
the length of the window is set to be K, namely the delay length between each FBMC-OQAM symbol; the extracted signals are independently processed through a partial transmission sequence PTS scheme, and then a window is moved by K unit lengths; thus, as the window moves until the maximum number of iterations is reached, the signals of the M data blocks can be divided into M + a segments; a is xm＝1[k]And xm[k]The number of overlapping data blocks, the length of each segment is K.
In a specific embodimentIn step S4, the window signal is added
Figure BDA0003042675700000105
Can be written in vector form, as follows:
Figure BDA0003042675700000106
firstly, the following components are mixed
Figure BDA0003042675700000111
Is divided into V sub-blocks, provided
Figure BDA0003042675700000112
Represents the v sub-block, given by the following equation:
Figure BDA0003042675700000113
thus wm[k]Can be expressed in the following form:
Figure BDA0003042675700000114
wherein,
Figure BDA0003042675700000115
thus, the vth sub-block can be expressed as:
Figure BDA0003042675700000116
subblocks after blocking
Figure BDA0003042675700000117
Converted to the time domain by an Inverse Fast Fourier Transform (IFFT), then multiplied by a weighting factor
Figure BDA0003042675700000118
And accumulating to obtain an output symbol sequence sm[k]Given by the following equation:
Figure BDA0003042675700000119
wherein
Figure BDA00030426757000001110
W is the selectable phase, and the weighting factor is represented as a vector:
Figure BDA00030426757000001111
finally, a signal processed by the partial transmission sequence PTS is obtained, which is given by the following formula:
Figure BDA00030426757000001112
through the derivation, the partial transmission sequence PTS optimization objective function is obtained as follows:
Figure BDA00030426757000001113
Figure BDA00030426757000001114
wherein q represents the current number of windows,
Figure BDA00030426757000001115
is sq[k]I-0, 1, …, W-1, V-0, 2, …, V-1, q-0, 1, …, M + a-1.
In a specific embodiment, in step S5, the peak-to-average power ratio PAPR of the signal is defined as:
Figure BDA0003042675700000121
in order to facilitate comparison of the influence of different schemes on reduction of the PAPR, a Complementary Cumulative Distribution Function (CCDF) is used to evaluate the performance; the complementary cumulative distribution function is defined as the PAPR value of the peak-to-average power ratio being larger than the PAPR threshold valueTHProbability of (Pr), given by the following equation:
CCDF(PAPR{x[k]})＝Pr(PAPR{x[k]}＞PAPRTH)。
in fig. 6 to 8 are abbreviated:
CCDF(Pr[PAPR＞PAPR0])。
in a specific embodiment, to avoid the exhaustive search process of the conventional partial transmit sequence PTS and reduce the computational complexity of the algorithm, the step S3 is implemented as: since each iteration is necessary to calculate and compare the PAPR value, the computational complexity of the PTS method for partial transmission sequences increases exponentially as the number of sub-blocks V increases; therefore, the embodiment proposes that on the basis of the conventional partial transmission sequence PTS scheme, a particle swarm optimization PSO is introduced to improve the search efficiency of the weight factor; FIG. 6 shows a procedure for performing PAPR reduction using the PTS-PSO scheme; the PSO is originally proposed by Kenndy and Eberhart and is a calculation model established on the basis of researching foraging behavior of bird colonies; in the searching process, the particles continuously approach to the optimal position of the particles per se, and the particles continuously approach to the optimal position of the population; through continuous learning, the whole population gradually reaches an optimal solution;
in the particle swarm optimization PSO, the velocity and position of each particle are continuously updated in the iterative process, which can be expressed as the following formula:
Figure BDA0003042675700000122
pi(t+1)＝pi(t)+vi(t)
wherein i is 0,1, …, NpIndex of the particle, NpIs the total number of particles, t is the current number of iterations, pi(t) is the position of the particle, vi(t) is the velocity of the particles;
Figure BDA0003042675700000123
and g*(t) the position of the ith particle and the optimal solution of the whole particle swarm in the iterative process are respectively; ω is the inertial weight, c1And c2Are learning factors for particles and populations; r is1And r2Is [0,1 ]]Two random numbers in between; defining weight factors
Figure BDA0003042675700000124
And the position g of the whole particle groupv(t) a special translation relationship between them, defined as the following equation:
Figure BDA0003042675700000131
wherein G isin＝(Gmax-Gmin)/4，GmaxAnd GminIs the upper and lower limit of the particle population; the fitness function value for each particle is expressed as the following equation:
f(t)＝1/PAPR(βq)。
in a specific embodiment, an improved particle swarm optimization algorithm IPSO is introduced, and the specific implementation of step S4 is as follows: at the initial stage of the algorithm, the convergence rate is very low because the diversity of the particle population is low and the search rate is low; however, the later convergence speed of the algorithm is high, so that the population easily crosses the global optimal solution and falls into the local optimal solution; therefore, the particle search speed in the particle swarm optimization PSO needs to be dynamically adjusted, and the adjusting steps are as follows:
step A1, initializing particle swarm:
when a population of particles is randomly generated, the particles may be distributed in the same area, the diversity of the population is poor, which results in a long iteration time; therefore, we introduce the concept of particle entropy; the particle entropy, as a condition for whether a new particle is retained, is given by the following equation:
Figure BDA0003042675700000132
wherein P isni＝1-|pi-pn|/|Pmax-PminI, representing the position closeness of the particles i and n; first, an entropy threshold S is setTHWhich represents the maximum acceptable positional proximity between the particles; when S is more than or equal to STHIf so, retaining the new particle, otherwise, removing the new particle, and regenerating the particle;
step A2, calculating population diversity:
the position of the particle and the average center position of the population are defined as
Figure BDA0003042675700000133
And
Figure BDA0003042675700000134
the average distance of the particles to the mean center of the population is:
Figure BDA0003042675700000135
step A3, dynamically adjusting inertial weight:
dynamically adjusting inertia weight according to the current average center distance of the particle population by adopting a self-adaptive method; the update of the inertial weights can be expressed as the following equation:
Figure BDA0003042675700000141
wherein T ismaxIs the maximum number of iterations and μ is a relatively small constant (typically set to 0.01) to prevent stopping the search when the speed is 0.
In a specific embodiment, an improved Particle Swarm Optimization (PSO) algorithm is introduced to obtain an IPSO-PTS;
according to the analysis, in the IPSO-PTS scheme, the sampling improved particle swarm optimization IPSO algorithm comprises the following steps:
step B1: initializing the speed of particles of a particle population and the positions of the particles;
step B2: decoding the position information of the particle to obtain a weight factor, and dividing the weight factor and the windowed signal
Figure BDA0003042675700000146
Multiplying to calculate fitness function value f0；
Step B3: comparing the current fitness value of the particle with the optimal fitness value of the individual, and replacing the optimal fitness of the individual if the current fitness value is larger;
step B4: finding out the global optimal fitness value of the particle population, and comparing the optimal fitness of each particle with the optimal value of the population; if the fitness value of the individual is larger, replacing the global optimal fitness;
step B5: updating the speed and position of the particle;
step B6: judging whether the set maximum iteration times is reached, and if the current iteration times reaches the maximum value, taking the current optimal fitness value as a result; otherwise, adding 1 to the current iteration number, and repeating the steps B2 to B5;
step B7: and decoding the found population optimal fitness value to obtain an optimized weight factor.
In a specific embodiment, in step B1, the maximum iteration number T is inputmaxThe window signal of the qth data block
Figure BDA0003042675700000142
Velocity v of the initiating particlei(t) position p of the particlei(t) total number of particles NpInertia weight ω;
in step B2, let the current iteration count t ← 0, obtain fitness function f0；
In step B3, according to f (t) 1/PAPR (β)q) MeterCalculating a fitness function of the particles; the fitness value f of the present particlec(t) value of fitness to optimum particle
Figure BDA0003042675700000143
Comparing; if it is used
Figure BDA0003042675700000144
Then order
Figure BDA0003042675700000145
Let the index i ← i +1 of the particle; judging whether the index of the particles is less than the total number of the particles, i < NpIf not, re-executing the step B4, otherwise, executing the step B5;
in step B4, the best fitness value f (g) of the population is foundv(t)), and then is solved with the global optimum
Figure BDA0003042675700000151
Comparing; if it is not
Figure BDA0003042675700000152
Then order
Figure BDA0003042675700000153
In step B5, according to
Figure BDA0003042675700000154
pi(t+1)＝pi(t)+vi(t)
Updating the velocity and position of each particle; in addition, according to
Figure BDA0003042675700000155
Updating the inertia weight omega; let the index of particle i ← 0;
in step B6, it is determined whether the current iteration count is less than the maximum iteration count, i.e., T < TmaxWhether or not it is establishedIf yes, making the current iteration number t ← t +1, and executing step B3, otherwise, executing step B7; in step B7, let
Figure BDA0003042675700000156
Outputting windowed signals
Figure BDA0003042675700000157
Weight factor of
Figure BDA0003042675700000158
In summary, the system is optimized, comprising the steps of:
step C1: processing the FBMC-OQAM symbols by adopting a windowing division method to eliminate the influence between adjacent data blocks;
step C2: introducing a partial transmission sequence PTS on the basis of a windowing segmentation method to obtain a windowed partial transmission sequence W-PTS, so that the PAPR (peak-to-average power ratio) of the FBMC-OQAM system is reduced;
step C3: introducing a PSO (particle swarm optimization) algorithm into the W-PTS of the windowed partial transmission sequence to obtain the PSO-PTS, so that the exhaustive search process of the PTS of the traditional partial transmission sequence is avoided, and the calculation complexity of the algorithm is reduced;
step C4: an improved particle swarm optimization algorithm IPSO is introduced into the PSO-PTS to obtain the IPSO-PTS, and the problems that the PSO-PTS is low in convergence speed and is prone to falling into a local optimal solution are solved.
By introducing a Particle Swarm Optimization (PSO), an exhaustive search process of a partial transmission sequence PTS scheme is avoided, and the calculation complexity is reduced; by introducing the improved particle swarm optimization IPSO, the problems that the PSO of the traditional particle swarm optimization algorithm is low in convergence speed and easy to fall into a local optimal solution are solved.
In order to verify the method for reducing the peak-to-average power ratio of the FBMC-OQAM system in this embodiment, a simulation experiment is performed on this embodiment, specifically as follows:
respectively introducing traditional partial transmission sequence PTS and windowing division partial transmission sequence W-PTS (Windows PTS) schemes into an FBMC-OQAM system; as can be seen from fig. 6, sinceThe overlapping phenomenon exists between adjacent symbols, the reduction effect of the PAPR is very limited when a traditional partial transmission sequence PTS algorithm is introduced, and the PAPR can be more effectively reduced by introducing a windowing division partial transmission sequence W-PTS scheme; when the value of CCDF is 10-3When the window division partial transmission sequence W-PTS scheme is introduced, the PAPR of the FBMC-OQAM system is reduced by about 2.0dB, and when the partial transmission sequence PTS is directly introduced, the value is only 0.8 dB.
Next, we compare the performance of PSO-PTS and IPSO-PTS, where V is set to 2 or 4; as can be seen from FIG. 7, the CCDF is 10-3When V is 4, compared with the original FBMC-OQAM, the PAPR of the PSO-PTS is reduced by 2.2dB, and the PAPR of the IPSO-PTS is reduced by 2.8 dB; it is clear that better performance than PSO-PTS can be achieved via IPSO-PTS.
Finally, we studied the parameters V and N using the IPSO-PTS in the FBMC-OQAM systempThe influence on the performance of reducing the PAPR; selecting a number V of blocks from {2, 4, 8, 16} and N from {10, 20}, simultaneouslyp(ii) a As can be seen from fig. 8, the PAPR can be significantly reduced by increasing the V value, while a larger N is usedpThe effect has certain limitation when the value is up; this indicates that in practice the population numbers are small (e.g.N)p10) are sufficient to achieve satisfactory performance results, the value of V should be carefully considered in order to make a better trade-off between performance and complexity; in fig. 8, we also compare the CCDF curves for peak-to-average power ratio PAPR when using a suboptimal scheme (i.e. MBJO-partial transmission sequence PTS-Suc scheme), where V is 4; we can observe that the proposed IPSO-PTS in this patent can achieve better performance and has lower complexity than it.
In summary, the proposed PTS combined particle swarm optimization PSO and IPSO algorithm can effectively reduce the PAPR of the FBMC-OQAM system and keep a relatively low computational complexity.
The working process of the invention is as follows:
step S1, obtaining a modulation signal, and modulating and superposing the modulation signal to obtain an output signal;
step S2, sampling the output signal obtained in the step S1 to obtain a sampling signal;
step S3, processing the sampling signal by adopting a window-based segmentation method, and extracting the signal in a window to obtain a windowed signal;
step S4, processing the windowed signal through a partial transmission sequence PTS to obtain a PTS optimization objective function;
and step S5, solving the PTS optimization objective function to obtain the optimal PAPR, thereby realizing the reduction of the PAPR.
To sum up, the method for reducing the peak-to-average power ratio of the FBMC-OQAM system according to the embodiment of the present invention processes the overlapping structure of the FBMC-OQAM signals by using a windowing segmentation method, and eliminates the influence between adjacent data blocks; by introducing part of the transmission sequence PTS, the PAPR of the FBMC-OQAM system is effectively reduced.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and substitutions can be made without departing from the technical principle of the present invention, and these modifications and substitutions should also be regarded as the protection scope of the present invention.

Claims (9)

1. A method for reducing peak-to-average power ratio of an FBMC-OQAM system is characterized in that: the method comprises the following steps:
step S1, obtaining a modulation signal, and modulating and superposing the modulation signal to obtain an output signal;
step S2, sampling the output signal obtained in the step S1 to obtain a sampling signal;
step S3, processing the sampling signal by adopting a window-based segmentation method, and extracting the signal in a window to obtain a windowed signal;
step S4, processing the original windowing signal through a partial transmission sequence PTS to obtain a windowing signal PTS optimization objective function;
step S5, solving the PTS optimization objective function to obtain the optimal PAPR, thereby realizing the reduction of the PAPR;
in step S1, the FBMC-OQAM system combines offset quadrature amplitude modulation OQAM with orthogonal frequency division multiplexing OFDM, avoiding the use of cyclic prefix CP; the modulated signal is expressed as the following equation:
Figure FDA0003560574970000011
wherein
Figure FDA0003560574970000012
N is more than or equal to 0 and less than or equal to N-1, M is more than or equal to 0 and less than or equal to M-1,
Figure FDA0003560574970000013
is that
Figure FDA0003560574970000014
An imaginary part of (d);
Figure FDA0003560574970000015
is that
Figure FDA0003560574970000016
An imaginary part of (d); in time domain, there is a delay of T/2 between the real part and the imaginary part of the FBMC-OQAM symbol, where T is the period of each data block;
the modulated signal is passed through a prototype filter and modulated on N subcarriers, given by the following equation:
Figure FDA0003560574970000017
where h (t') is the impulse response of the prototype filter, given by the following equation:
Figure FDA0003560574970000018
finally, the M data blocks are superposed, and the obtained output signal is the following formula:
Figure FDA0003560574970000019
2. the method of reducing peak-to-average power ratio of an FBMC-OQAM system according to claim 1, wherein:
in step S2, oversampling the output signal to obtain a sampled signal; the sampled signal is written as the following equation:
Figure FDA0003560574970000021
wherein, h [ k]H (kT/K), and
Figure FDA0003560574970000022
k is the delay length between each FBMC-OQAM symbol.
3. The method of reducing peak-to-average power ratio of an FBMC-OQAM system according to claim 2, wherein: in step S3, a window-based windowing segmentation method is employed to improve performance; firstly, extracting a signal in a window to obtain a windowed signal, wherein the expression is as follows:
Figure FDA0003560574970000023
the length of the window is set to be K, namely the delay length between each FBMC-OQAM symbol; the extracted signal is independently processed through a partial transmission sequence PTS, and then a window is moved by K unit lengths; dividing signals of the M data blocks into M + A sections; a is xm＝1[k]And xm[k]Number of overlapping data blocks perThe length of each segment is K.
4. A method for reducing peak-to-average power ratio of an FBMC-OQAM system according to claim 3, characterized in that:
in step S4, the original windowed signal is processed
Figure FDA0003560574970000024
Written in vector form, the following equation:
Figure FDA0003560574970000025
firstly, the following components are mixed
Figure FDA0003560574970000026
Is divided into V sub-blocks, provided
Figure FDA0003560574970000027
Represents the v-th sub-block, given by the following equation:
Figure FDA0003560574970000028
thus wm[k]Expressed in the following form:
Figure FDA0003560574970000029
wherein,
Figure FDA00035605749700000210
thus, the vth sub-block is represented as:
Figure FDA0003560574970000031
subblocks after blocking
Figure FDA0003560574970000032
By conversion to the time domain by an inverse fast Fourier transform, followed by multiplication by a weighting factor
Figure FDA0003560574970000033
And accumulating to obtain an output symbol sequence sm[k]Given by the following equation:
Figure FDA0003560574970000034
wherein
Figure FDA0003560574970000035
W is the selectable phase, and the weighting factor is represented as a vector:
Figure FDA0003560574970000036
finally, a signal processed by the partial transmission sequence PTS is obtained, which is given by the following formula:
Figure FDA0003560574970000037
through the above derivation, the optimized objective function of the PTS of the windowed signal portion transmission sequence is obtained as follows:
Figure FDA0003560574970000038
Figure FDA0003560574970000039
wherein q represents the current number of windows,
Figure FDA00035605749700000310
for windowed signal representation, s is representedq[k]The v sub-block of (1); wherein i is 0,1, …, W-1, V is 0,2, …, V-1, q is 0,1, …, M + a-1.
5. The method of reducing peak-to-average power ratio of an FBMC-OQAM system of claim 4, wherein:
in step S5, the peak-to-average power ratio PAPR of the signal is defined as:
Figure FDA00035605749700000311
evaluating performance using a complementary cumulative distribution function; the complementary cumulative distribution function is defined as the PAPR value of the peak-to-average power ratio being larger than the PAPR threshold valueTHIs given by the following formula:
CCDF(PAPR{x[k]})＝Pr(PAPR{x[k]}＞PAPRTH)。
6. a method for reducing the peak-to-average power ratio of an FBMC-OQAM system as claimed in any one of claims 1 to 5, wherein:
in order to avoid the exhaustive search process of the traditional partial transmission sequence PTS and reduce the calculation complexity of the algorithm, on the basis of the partial transmission sequence PTS, a Particle Swarm Optimization (PSO) algorithm is introduced to improve the search efficiency of the weight factor;
in the particle swarm optimization PSO, the speed and position of each particle are continuously updated in an iterative process, and are expressed as the following formula:
Figure FDA0003560574970000041
pi(t+1)＝pi(t)+vi(t)
wherein i is 0,1, …, NpRepresenting the index of the particle, NpIs the total number of particles, t is the current number of iterations, pi(t) is the position of the particle, vi(t) isThe velocity of the particles;
Figure FDA0003560574970000042
and g*(t) the optimal solution of the position of the ith particle and the position of the whole particle swarm in the iterative process respectively; ω is the inertial weight, c1And c2Are learning factors for particles and populations; r is1And r2Is [0,1 ]]Two random numbers in between; defining weight factors
Figure FDA0003560574970000043
And the position g of the whole particle groupv(t) a special translation relationship between them, defined as the following equation:
Figure FDA0003560574970000044
wherein G isin＝(Gmax-Gmin)/4，GmaxAnd GminIs the upper and lower limit of the particle population; the fitness function value for each particle is expressed as the following equation:
f(t)＝1/PAPR(βq)。
7. the method of reducing peak-to-average power ratio of an FBMC-OQAM system according to claim 6, wherein: introducing an improved particle swarm optimization IPSO, dynamically adjusting the searching speed of particles in the PSO, wherein the adjusting steps are as follows:
step A1, initializing particle swarm:
introducing the concept of particle entropy; the particle entropy, as a condition for whether a new particle is retained, is given by the following equation:
Figure FDA0003560574970000045
wherein P isni＝1-|pi-pn|/Pmax-PminI, representing particlesThe position closeness of i and n; first, an entropy threshold S is setTHWhich represents the maximum acceptable positional proximity between the particles; when S is more than or equal to STHIf so, retaining the new particle, otherwise, removing the new particle, and regenerating the particle;
step A2, calculating population diversity:
the position of the particle and the average center position of the population are defined as
Figure FDA0003560574970000055
And
Figure FDA0003560574970000056
the average distance of the particles to the mean center of the population is:
Figure FDA0003560574970000051
step A3, dynamically adjusting inertial weight:
dynamically adjusting inertia weight according to the current average center distance of the particle population by adopting a self-adaptive method;
the update of the inertial weight is represented by the following equation:
Figure FDA0003560574970000052
wherein T ismaxIs the maximum number of iterations and μ is a constant to prevent stopping the search when the speed is 0.
8. The method of reducing peak-to-average power ratio of an FBMC-OQAM system according to claim 7, wherein: obtaining IPSO-PTS by introducing an improved particle swarm optimization algorithm IPSO;
in the IPSO-PTS, a specific procedure includes the steps of:
step B1: initializing the speed of particles of a particle population and the positions of the particles;
step B2: from granuleDecoding the position information of the sub-frame to obtain a weight factor, and dividing the weight factor and the representation form of the windowed signal after windowing
Figure FDA0003560574970000053
Multiplying to calculate fitness function value f0；
Step B3: comparing the current fitness value of the particle with the optimal fitness value of the individual, and replacing the optimal fitness of the individual if the current fitness value is larger;
step B4: finding out the global optimal fitness value of the particle population, and comparing the optimal fitness of each particle with the optimal value of the population; if the fitness value of the individual is larger, replacing the global optimal fitness;
step B5: updating the speed and position of the particle;
step B6: judging whether the set maximum iteration times is reached, and if the current iteration times reaches the maximum value, taking the current optimal fitness value as a result; otherwise, adding 1 to the current iteration number, and repeating the steps B2 to B5;
step B7: and decoding the found population optimal fitness value to obtain an optimized weight factor.
9. The method of reducing peak-to-average power ratio of an FBMC-OQAM system according to claim 8, wherein:
in step B1, the maximum number of iterations T is inputmaxRepresentation of the windowed signal of the qth data block
Figure FDA0003560574970000054
Velocity v of the initiating particlei(t) position p of the particlei(t) total number of particles NpInertia weight ω;
in step B2, let the current iteration count t ← 0, obtain fitness function f0；
In step B3, according to f (t) 1/PAPR (β)q) Calculating a fitness function of the particles; the fitness value f of the present particlec(t) value of fitness to optimum particle
Figure FDA0003560574970000061
Comparing; if it is not
Figure FDA0003560574970000062
Then order
Figure FDA0003560574970000063
Let the index i ← i +1 of the particle; judging whether the index of the particles is less than the total number of the particles, i < NpIf not, re-executing the step B4, otherwise, executing the step B5;
in step B4, the best fitness value f (g) of the population is foundv(t)), and then is solved with the global optimum
Figure FDA0003560574970000064
Comparing; if it is not
Figure FDA0003560574970000065
Then order
Figure FDA0003560574970000066
In step B5, according to
Figure FDA0003560574970000067
pi(t+1)＝pi(t)+vi(t)
Updating the velocity and position of each particle; in addition, according to
Figure FDA0003560574970000068
Updating the inertia weight omega; let the index of particle i ← 0;
in step B6, it is determined whether the current iteration count is less than the maximum iteration count, i.e., t＜TmaxIf yes, making the current iteration number t ← t +1, and executing step B3, otherwise, executing step B7;
in step B7, let
Figure FDA0003560574970000069
Outputting windowed signals
Figure FDA00035605749700000610
Weight factor of
Figure FDA00035605749700000611
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