CN110336763B - ACE method and system for restraining peak-to-average power ratio of high-order modulation OFDM signal - Google Patents

ACE method and system for restraining peak-to-average power ratio of high-order modulation OFDM signal Download PDF

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CN110336763B
CN110336763B CN201910425640.XA CN201910425640A CN110336763B CN 110336763 B CN110336763 B CN 110336763B CN 201910425640 A CN201910425640 A CN 201910425640A CN 110336763 B CN110336763 B CN 110336763B
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王勇
刘玉卓
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Xidian University
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Abstract

The invention belongs to the technical field of electronic communication, and discloses an ACE method and a system for restraining a peak-to-average ratio of a high-order modulation OFDM signal, which redefine an expansion rule of a constellation in a frequency domain; the peak clipping threshold is dynamically adjusted according to the peak-to-average ratio of the current signal, so that effective peak-to-average ratio suppression gain is obtained, and meanwhile, the system error rate is not seriously deteriorated; after the effective peak-to-average ratio suppression gain is obtained, a proper expansion factor is obtained by modifying a least square approximation formula, the original time domain signal is amplified, and the signal peak-to-average ratio suppression effect is enhanced. Based on the optimization strategy, the peak-to-average ratio of the OFDM transmission signal is obviously reduced under the condition of only one iteration, the realization complexity of the system is greatly reduced, the error rate and the loss of the out-of-band power spectrum performance are ensured to be within an acceptable range, and the overall performance of the OFDM system is effectively improved.

Description

ACE method and system for restraining peak-to-average power ratio of high-order modulation OFDM signal
Technical Field
The invention belongs to the technical field of electronic communication, and particularly relates to an ACE method and system for restraining peak-to-average power ratio of a high-order modulation OFDM signal.
Background
Currently, the closest prior art:
the OFDM multi-carrier modulation technique has been widely applied to various wireless communication systems due to its advantages such as high spectrum utilization rate and high transmission reliability, and has become one of the key techniques of the fifth generation mobile communication system. The OFDM system adopts a data parallel transmission mode, utilizes mutually orthogonal subcarriers to transmit data, and generates larger instantaneous power when a plurality of signals with similar or identical phases are superposed after modulated signals are subjected to inverse discrete Fourier transform (IFFT), thereby causing the problem of higher peak-to-average power ratio (PAPR) of the signals.
The problem of high PAPR of OFDM signals has long been one of the problems that OFDM systems are urgently needed to solve. The high PAPR signal requires the rf power amplifier HPA to have an extremely wide dynamic range and the digital-to-analog converter DAC to have an extremely high accuracy, increasing the cost and implementation complexity of the system. If the parameters associated with the HPA and DAC do not meet the requirements of the OFDM signal, out-of-band spectral spreading and nonlinear distortion of the signal may result, thereby degrading the performance of the system. In order to solve the peak-to-average ratio problem of the OFDM system, researchers have proposed a number of solutions, such as Active Constellation Extension (ACE). The basic idea of the dynamic constellation expansion technology is as follows: under the condition of not changing the Euclidean distance between constellation points in the constellation diagram, the minimum Euclidean distance between the peripheral constellation diagrams is ensured to be unchanged, and the positions of the peripheral constellation points are properly expanded to reduce the value of the signal peak-to-average ratio. The essential idea is that extra frequency offset is superposed on the corresponding subcarrier to change the amplitude and phase of the transmission signal, reduce the probability that the phases are the same or similar after subcarrier modulation, and further reduce the peak-to-average ratio of the signal.
To date, scholars have proposed a variety of ACE approaches. For example, POCS (Projection on to the Convex set) ACE method proposed by d.l. jones has a very good absolute convergence property, but the convergence speed is slow, and it needs to go through many iterations to reduce the peak-to-average ratio of the signal to below the target value, thereby increasing the complexity of the system.
In view of the disadvantage of slow convergence rate of the POCS method, Krongold B S proposes an SGP (Smart Gradient Projection) ACE method, which increases the convergence rate by amplifying the original time domain signal, but requires additional complexity to calculate the Gradient step size. Under the circumstance, mount laradi proposes an LSA (Least square approximation) ACE method, which has a fast convergence speed and does not need extra complexity to calculate a step factor, but sacrifices a large amount of error rate performance.
In general, for a large-subcarrier, high-order modulated OFDM system, an excessive number of iterations means an increased amount of computational complexity, which makes its application cost in a practical communication system difficult to bear. Meanwhile, the conventional ACE method mainly aims at low-order modulation (QPSK-64-QAM) and OFDM systems with few subcarriers, and for high-order M-QAM modulation with 64-QAM and more than 64-QAM and broadband OFDM systems with a large number of subcarriers, the conventional ACE method consumes more system resources and cannot obtain considerable PAPR suppression gain.
In summary, the problems of the prior art are as follows:
for an Orthogonal Frequency Division Multiplexing (OFDM) system with large subcarriers and high-order modulation, in the prior art, multiple iterations are needed to reduce the peak-to-average ratio of signals to be below a target value, the implementation complexity of the system is increased, the error rate and the loss of the out-of-band power spectrum performance cannot be guaranteed to be within an acceptable range in real time, and the overall performance of the OFDM system is low.
The difficulty of solving the technical problems is as follows:
(1) due to the increase of the number of subcarriers of the Orthogonal Frequency Division Multiplexing (OFDM) system, the calculation complexity of discrete Fourier transform is increased, and the conventional ACE technology for reducing the peak-to-average power ratio of the OFDM system through multiple iterations is not suitable for engineering application. How to design an iteration flow so that a significant peak-to-average ratio gain can be obtained under the condition of one iteration is a first difficulty to be solved urgently.
(2) As the modulation order used by an orthogonal frequency division multiplexing, OFDM, system increases, the constellation becomes more complex and the scalable constellation point ratio decreases. How to design an extension rule for a high-order constellation point so as to ensure that the error rate of a system is not seriously deteriorated while reducing the peak-to-average ratio of a signal is a second difficulty which needs to be solved urgently.
The significance of solving the technical problems is as follows: if the considerable peak-to-average ratio gain can be obtained by one iteration while the error rate and the out-of-band power spectrum performance of the system are not seriously deteriorated, the realization complexity of the orthogonal frequency division multiplexing OFDM system can be greatly reduced, and the application cost of the communication system is reduced.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an ACE method and system for restraining the peak-to-average power ratio of a high-order modulation OFDM signal. The invention particularly relates to an ACE (Active Constellation Extension) scheme for restraining a peak-to-average ratio of a high-order modulation OFDM (Orthogonal frequency division Multiplexing) signal in the technical field of wireless communication. The method is suitable for a high-order modulation OFDM system in wireless communication, and achieves PAPR (Peak-to-Average Power) suppression of signals by expanding signal constellation points of a frequency domain of a transmitting end so as to avoid out-of-band spectrum expansion and nonlinear distortion caused by the fact that high Peak-to-Average ratio signals work in a nonlinear area of an HPA (high Power amplifier), and system performance is deteriorated.
The invention is realized in such a way that an ACE method for restraining peak-to-average power ratio of a high-order modulation OFDM signal comprises the following steps:
redefining an expansion mode for a high-order constellation; the peak clipping threshold is dynamically changed by utilizing a self-adaptive peak clipping strategy to adapt to OFDM signals with different peak-to-average ratios, so that the error rate performance is not seriously deteriorated while the peak-to-average ratio is reduced; and generating a proper expansion coefficient by correcting a least square approximation formula to amplify the original time domain signal, thereby accelerating the convergence speed of the scheme.
The method comprises the following specific steps:
step one, carrying out orthogonal amplitude modulation on binary bit stream of a sending end of an Orthogonal Frequency Division Multiplexing (OFDM) system to obtain an original frequency domain signal X ═ X0,X1,...,Xk]TAnd then, after performing J-time interpolation on the original frequency domain signal, performing inverse discrete fourier transform on the original frequency domain signal to obtain an oversampled time domain original OFDM signal x ═ x ·, N-10,x1,...,xn]TWherein N is 0,1, J represents an upsampling factor and J is more than or equal to 4, and N is the number of subcarriers contained in the OFDM system; the signal x is subjected to the peak-to-average ratio suppression processing described below;
step two, calculating the peak-to-average ratio of the current signal and recording as xi, and according to the peak-to-average ratio xi required by the systemtarAnd setting initial amplitude limiting rate CR for system bit error rate BERinitInitial compensation factor gammainitAnd η;
step three, according to the peak-to-average ratio xi of the current signal, adjusting the peak clipping threshold A, and performing peak clipping on the original over-sampled signal to obtain the signal after peak clipping
Figure BDA0002067397630000041
And peak clipping noise cclip＝[cclip,0,cclip,1,…,cclip,n]TWherein n is 0,1,. cndot, JN-1;
step four, setting p as peak clipping noise cclip,nThe set of the serial numbers of the sampling points with middle amplitude not equal to zero, i.e. p ═ n | | cclip,nIf | ≠ 0}, then the peak clipping signal cclip,nThe set of amplitudes of the sample points whose middle sequence number n belongs to p is denoted ceI.e. ce＝{|cclip,nI n belongs to p, and c is calculatedeThe mean value of all the elements is marked as tau;
fifthly, signals are transformed by JN point discrete Fourier transform FFT
Figure BDA0002067397630000042
And cclipTransforming to frequency domain to obtain frequency domain peak clipping signal
Figure BDA0002067397630000043
Sum frequency domain peak clipping noise Cclip＝[Cclip,0,Cclip,1,...,Cclip,k]TWherein k is 0,1,.., JN-1;
step six, peak clipping signals are compared in the frequency domain
Figure BDA0002067397630000044
The constellation diagram is expanded to obtain the expanded frequency domain peak clipping noise
Figure BDA0002067397630000045
Step seven, frequency domain peak clipping noise is carried out by utilizing inverse discrete Fourier transform (IFFT) of JN point
Figure BDA0002067397630000046
Conversion to time-domain peak clipping noise
Figure BDA0002067397630000047
Wherein n is 0,1,., JN-1;
step eight, the expanded peak clipping noise
Figure BDA0002067397630000048
The set of amplitudes of the sample points whose middle sequence number n belongs to p is recorded as
Figure BDA0002067397630000049
Namely, it is
Figure BDA00020673976300000410
Computing
Figure BDA00020673976300000411
The mean value of all elements in
Figure BDA00020673976300000412
Step nine, inputting a correction factor k, and utilizing c in the flowe、τ、
Figure BDA00020673976300000413
And
Figure BDA00020673976300000414
calculating an expansion coefficient mu, and amplifying an original time domain signal x to obtain a peak-to-average ratio inhibition signal
Figure BDA00020673976300000415
Step ten, suppressing the signal after the peak-to-average ratio
Figure BDA00020673976300000416
After inserting the guard interval, the signal is sent to a radio frequency amplifier HPA to be transmitted into a channel.
Furthermore, the invention only needs one iteration, and the iteration method specifically comprises the following steps:
modulating the binary bit stream into an original oversampled OFDM signal;
setting corresponding optimization parameters;
carrying out self-adaptive peak clipping processing;
calculating the mean value of the amplitude vectors;
fourier transform FFT;
constellation expansion;
inverse Fourier transform (IFFT);
calculating the mean value of the amplitude vector after constellation expansion;
calculating an expansion coefficient and amplifying an original OFDM signal;
and transmitting the signal after the peak-to-average ratio is suppressed.
Further, the quadrature amplitude modulation in step one comprises 16-QAM, 64-QAM, 256-QAM and 1024-QAM; the J-times interpolation operation is that the modulated frequency domain data X is [ X ═ X%0,X1,...,Xk]TN-1, where (J-1) × N zeros are inserted, so that after IFFT, a J-times oversampled original time domain signal x ═ x may be obtained0,x1,...,xn]TN ═ 0, 1., JN-1, which can be expressed by the following formula:
Figure BDA0002067397630000051
wherein XkIs frequency domain data before interpolation, Xk' is the frequency domain data after interpolation.
Further, the peak-to-average ratio ξ of the current signal in the step two is calculated by the following formula:
Figure BDA0002067397630000052
wherein n is 0, 1., JN-1, max { | xn|2Denotes the maximum power of the signal x, E { | xn|2Denotes the average power of the signal x.
Further, the adaptive peak clipping strategy in step three is to adjust an initial amplitude limiting rate according to a peak-to-average ratio PAPR value of a current signal, and further adjust a peak clipping threshold to avoid cutting off excessive non-peak points. The relation between the clipping threshold a and the clipping rate CR is shown as follows:
Figure BDA0002067397630000061
where σ is the average power of the signal x:
Figure BDA0002067397630000062
the amplitude limiting ratio CR is adjusted by the following formula:
CR＝CRinit+(γ-1)·α·(ξ-ξtar)
wherein the content of the first and second substances,
Figure BDA0002067397630000063
gamma and eta are compensation factors, the values of which are selected according to the peak-to-average ratio xi of the current signal and the initial limiting rate CRinit。
The specific steps of the clipping operation include:
first, for | xnPerforming peak clipping operation on all sampling points with the peak value greater than A to obtain a signal subjected to peak clipping
Figure BDA0002067397630000064
Figure BDA0002067397630000065
Wherein n is 0,1, JN-1,
Figure BDA0002067397630000066
representing the unit of an imaginary number, exp (-) representing an exponential operation based on a natural constant e, θnIs an original time domain signal xnThe phase, | · | is a modulo value operation;
second, using the peak-clipped signal
Figure BDA0002067397630000067
Subtracting the original time domain signal x to obtain the peak clipping noise:
Figure BDA0002067397630000068
further, in the sixth step, the peak clipping signal is compared in the frequency domain
Figure BDA0002067397630000069
The constellation diagram expansion comprises the following steps:
step one, reserving an internal constellation point without expansion;
secondly, the vertex angle constellation points are expanded to a region far away from the center of the constellation diagram;
and thirdly, expanding the boundary constellation points to a region far away from the center of the constellation diagram along the coordinate axis direction.
Further, the correction factor k is inputted in the ninth step, and c in the above process is utilizede、τ、
Figure BDA00020673976300000610
And
Figure BDA00020673976300000611
calculating a spreading factor mu and amplifying the original time-domain signal x comprises:
firstly, selecting a proper correction factor k from [ -1,2 ];
secondly, a least squares approximation formula is modified, and the optimization target can be expressed as:
Figure BDA0002067397630000071
wherein min {. is } represents the minimum operator,
Figure BDA0002067397630000072
denotes the vector two norm operator, l denotes the length sum vector ceThe same, but the elements are all row vectors of 1, mu is the optimal expansion coefficient to be solved;
thirdly, solving the optimal expansion coefficient mu which accords with the optimization target in the second step:
order to
Figure BDA0002067397630000077
Let the gradient of f (μ) be zero:
Figure BDA0002067397630000073
wherein {. } represents gradient calculation, and the optimal expansion coefficient μ is:
Figure BDA0002067397630000074
fourthly, amplifying the original time domain signal x by using the optimal expansion coefficient to accelerate the convergence speed and obtain the time domain signal after the peak-to-average ratio is restrained
Figure BDA0002067397630000075
Figure BDA0002067397630000076
Another object of the present invention is to provide a system for suppressing the ACE of the peak-to-average ratio of a high order modulated OFDM signal, which implements the method for suppressing the ACE of the peak-to-average ratio of a high order modulated OFDM signal as claimed.
In summary, the advantages and positive effects of the invention are:
the invention provides an ACE method and system for restraining peak-to-average ratio of a high-order modulation OFDM signal, which mainly solve the problem of signal peak-to-average ratio in an orthogonal frequency division multiplexing OFDM system with large subcarriers and high-order modulation. The invention defines the expansion mode of the high-order constellation, and dynamically adjusts the peak clipping threshold according to the peak-to-average ratio of the current signal, thereby ensuring that the system error rate is not seriously deteriorated while obtaining the effective peak-to-average ratio restraining gain. In addition, the invention obtains a proper expansion factor by modifying the least square approximation formula and amplifies the original time domain signal, thereby accelerating the convergence speed of the algorithm and enhancing the signal peak-to-average ratio inhibition effect of the algorithm. Based on the optimization strategy, the peak-to-average ratio of OFDM transmission signals is obviously reduced under the condition of only one iteration, the realization complexity of a system is greatly reduced, and meanwhile, the error rate and the loss of the out-of-band power spectrum performance are ensured to be within an acceptable range.
Because the invention redefines the constellation expansion rule in the frequency domain and properly amplifies the original signal in the time domain, the invention can obtain considerable PAPR gain in one iteration and overcomes the defect of insufficient suppression gain of the OFDM system signal peak-to-average ratio in a high-order quadrature amplitude modulation mode in the prior art. Meanwhile, the invention greatly reduces the iteration times and the operation complexity required for obtaining the needed PAPR gain, so that the invention can be better applied to an Orthogonal Frequency Division Multiplexing (OFDM) system with high-order modulation and large subcarriers.
Because the invention uses the self-adaptive peak clipping strategy, the peak clipping threshold can be dynamically adjusted according to the peak-to-average ratio (PAPR) value of the current signal, so that excessive non-peak points are prevented from being clipped, the BER performance and the PAPR suppression performance can be improved at the same time, and the overall performance of the OFDM system can be further improved.
Drawings
Fig. 1 is a flowchart of an ACE method for suppressing a peak-to-average ratio of a high-order modulated OFDM signal according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a constellation scalable region and a constellation scalable method provided by an embodiment of the present invention.
Fig. 3 is a comparison graph of the peak-to-average ratio suppression performance of the present invention and three existing ACE methods in a high-order modulation and large subcarrier OFDM system according to an embodiment of the present invention.
Fig. 4 is a graph comparing the error rate performance of the present invention and three existing ACE methods in a high order modulation and large subcarrier OFDM system under an additive white gaussian noise channel according to an embodiment of the present invention.
Fig. 5 is a graph comparing power spectral density performance in a high order modulation and large subcarrier OFDM system for the present invention and three prior ACE methods according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In the prior art, a signal peak-to-average power ratio suppression effect in an Orthogonal Frequency Division Multiplexing (OFDM) system with large subcarriers and high-order modulation is poor, the implementation complexity of the system cannot be reduced, and the error rate and the loss of the out-of-band power spectrum performance cannot be guaranteed within an acceptable range in real time, so that the overall performance of the OFDM system is very low. In the prior art, the application cost in the communication system is high.
To solve the above problems, the present invention will be described in detail with reference to specific embodiments.
Aiming at the problems of low convergence rate, high iteration times and calculation complexity and serious error rate deterioration existing in the conventional dynamic extended ACE scheme, the method can obtain considerable peak-to-average ratio inhibition gain only by one iteration, greatly reduces the calculation complexity, simultaneously gives consideration to the peak-to-average ratio inhibition performance and the error rate performance, and utilizes a special optimization strategy to ensure that the error rate cannot be seriously deteriorated while the signal peak-to-average ratio is reduced.
As shown in fig. 1, an ACE method for suppressing a peak-to-average ratio of a high-order modulation OFDM signal provided by an embodiment of the present invention includes the following steps:
s101: modulating the binary bit stream into an original oversampled OFDM signal;
s102: setting corresponding optimization parameters;
s103: carrying out self-adaptive peak clipping processing;
s104: calculating the mean value of the amplitude vectors;
s105: fourier transform FFT;
s106: constellation expansion;
s107: inverse Fourier transform (IFFT);
s108: calculating the mean value of the amplitude vector after constellation expansion;
s109: calculating an expansion coefficient and amplifying an original OFDM signal;
s110: and transmitting the signal after the peak-to-average ratio is suppressed.
In step S101, the binary bit stream at the transmitting end of the OFDM system is quadrature amplitude modulated to obtain an original frequency domain signal X ═ X0,X1,...,Xk]TAnd then, after performing J-time interpolation on the original frequency domain signal, performing inverse discrete fourier transform on the original frequency domain signal to obtain an oversampled time domain original OFDM signal x ═ x ·, N-10,x1,...,xn]TWherein N is 0,1, J represents an upsampling factor, J is more than or equal to 4, N is the number of subcarriers contained in the OFDM system, and the modulation modes to be adopted comprise 16-QAM, 64-QAM, 256-QAM and 1024-QAM; the signal x is subjected to the peak-to-average ratio suppression processing described below;
the J-fold interpolation operation is performed according to the following formula:
Figure BDA0002067397630000101
wherein N represents the number of sub-carriers of OFDM system, J represents the up-sampling factor selected according to requirement, and XkAnd Xk' denotes the frequency domain signals on the k-th sub-carrier before and after up-sampling, respectively, k is more than or equal to 0 and less than or equal to JN-1.
In step S102, the peak-to-average ratio of the current signal is calculated and recorded as xi, and the peak-to-average ratio xi is required by the systemtarAnd setting initial amplitude limiting rate CR for system bit error rate BERinitInitial compensation factor gammainitAnd η;
the calculation formula of the peak-to-average ratio xi is as follows:
Figure BDA0002067397630000102
wherein n is 0, 1., JN-1, max { | xn|2Denotes the maximum power of the original time-domain signal x, E { | xn|2Denotes the average power of the original time-domain signal x.
In step S103, a peak clipping threshold A is adjusted according to a peak-to-average ratio xi of the current signal, and the original over-sampled signal is subjected to peak clipping to obtain a peak-clipped signal
Figure BDA0002067397630000103
And peak clipping noiseSound cclip＝[cclip,0,cclip,1,...,cclip,n]TWherein n ═ 0, 1., JN-1, specifically includes:
3a) according to the peak-to-average ratio xi of the current signal, adjusting the amplitude limiting rate according to the following formula:
CR＝CRinit+(γ-1)·α·(ξ-ξtar)
wherein gamma and eta are compensation factors, and the values are selected according to the peak-to-average ratio xi and the initial limiting rate CR of the current signalinit；
3b) Calculating the peak clipping threshold A at the moment:
Figure BDA0002067397630000111
where σ is the average power of the original time-domain signal x, which is calculated as follows:
Figure BDA0002067397630000112
3c) carrying out peak clipping operation on the original time domain signal x to obtain a peak-clipped signal
Figure BDA0002067397630000113
Figure BDA0002067397630000114
Wherein n is 0,1, JN-1,
Figure BDA0002067397630000115
representing the unit of an imaginary number, exp (-) representing an exponential operation based on a natural constant e, θnIs an original time domain signal xnThe phase, | · | is a modulo value operation;
3d) signal after peak clipping
Figure BDA00020673976300001115
Subtracting the original time domainObtaining time domain peak clipping noise c from signal xclip：
Figure BDA0002067397630000116
In step S104, let p be the peak clipping noise cclip,nThe set of the serial numbers of the sampling points with middle amplitude not equal to zero, i.e. p ═ n | | cclip,nIf | ≠ 0}, then the peak clipping signal cclip,nThe set of amplitudes of the sample points whose middle sequence number n belongs to p is denoted ceI.e. ce＝{|cclip,nI n belongs to p, and c is calculatedeThe mean value of all the elements is marked as tau;
in step S105, the signal is processed by JN point discrete Fourier transform FFT
Figure BDA0002067397630000117
And cclipTransforming to frequency domain to obtain frequency domain peak clipping signal
Figure BDA0002067397630000118
Sum frequency domain peak clipping noise Cclip＝[Cclip,0,Cclip,1,...,Cclip,k]TWherein k is 0,1,.., JN-1;
said signal
Figure BDA0002067397630000119
The discrete fourier transform FFT of (a) is performed as follows:
Figure BDA00020673976300001110
the peak clipping noise cclipThe discrete fourier transform FFT of (a) is performed as follows:
Figure BDA00020673976300001111
in step S101, the peak clipping signal is processed in the frequency domain
Figure BDA00020673976300001112
The constellation diagram is expanded to obtain the expanded frequency domain peak clipping noise
Figure BDA00020673976300001113
The constellation diagram expandable region provided by the invention is shown in figure 2, if the signal is subjected to peak clipping processing
Figure BDA00020673976300001114
If the frequency domain constellation point falls in the expandable region, the constellation point is reserved, otherwise, the constellation point is expanded according to the following rule: the vertex constellation point is far away from the regional extension of complex plane coordinate distant point to the shadow part, and the boundary constellation point is far away from the direction extension of complex plane coordinate origin to the direction that the arrow point pointed to, and inside constellation point need not expand, specifically includes:
6a) the constellation points are divided into two parts according to the position distribution of the constellation points in the constellation diagram: inner constellation points and boundary constellation points;
6b) for the inner constellation point, as shown in fig. 2C, it is modified in the following way:
Figure BDA0002067397630000121
Figure BDA0002067397630000122
6c) for the boundary constellation point, as shown at A, B, D in fig. 2, it is modified in the following manner:
Figure BDA0002067397630000123
Figure BDA0002067397630000124
where Real (-) denotes Real arithmetic, and Imag (-) denotes imaginary arithmeticX denotes the original frequency domain signal, XkRepresenting the original frequency domain signal corresponding to the kth sampling point,
Figure BDA0002067397630000125
representing the extended frequency domain signal after clipping and peak clipping,
Figure BDA0002067397630000126
representing the modified extended frequency domain signal;
6d) expanded signal
Figure BDA0002067397630000127
Subtracting the original frequency domain signal X to obtain the extended frequency domain peak clipping noise
Figure BDA0002067397630000128
In step S107, the expanded frequency domain peak clipping noise is performed by using the inverse discrete Fourier transform (IFFT) of JN point
Figure BDA0002067397630000129
Conversion to time-domain peak clipping noise
Figure BDA00020673976300001210
Wherein n is 0,1,., JN-1;
the frequency domain peak clipping noise
Figure BDA00020673976300001211
The inverse discrete fourier transform IFFT of (a) is performed by:
Figure BDA00020673976300001212
wherein the content of the first and second substances,
Figure BDA00020673976300001213
represents a square-on operation; Σ denotes a summation operation; denotes the multiplication operation; exp represents an exponential operation with a natural constant e as the base;
Figure BDA00020673976300001214
is an imaginary unit; and pi represents the circumferential ratio.
In step S108, the extended peak clipping noise
Figure BDA00020673976300001215
The set of amplitudes of the sample points whose middle sequence number n belongs to p is recorded as
Figure BDA0002067397630000131
Namely, it is
Figure BDA0002067397630000132
Computing
Figure BDA0002067397630000133
The mean value of all elements in
Figure BDA0002067397630000134
In step S109, the correction factor k is input, and c in the above-mentioned flow is usede、τ、
Figure BDA0002067397630000135
And
Figure BDA0002067397630000136
calculating an expansion coefficient mu, and amplifying an original time domain signal x to obtain a peak-to-average ratio inhibition signal
Figure BDA0002067397630000137
The method specifically comprises the following steps:
9a) selecting a proper correction factor k in [ -1,2] according to the convergence rate and the error rate required by the system, wherein the higher the k value is, the higher the convergence rate is;
9b) the modified least squares approximation formula, the optimization goal of which can be expressed as:
Figure BDA0002067397630000138
wherein min {. is } represents the minimum operator,
Figure BDA0002067397630000139
denotes the vector two norm operator, l denotes the length sum vector ceThe same row vector but with all elements of 1, mu is the optimal expansion coefficient to be solved;
9c) solving the optimal expansion coefficient mu meeting the optimization target to ensure that
Figure BDA00020673976300001310
Let the gradient of f (μ) be 0:
Figure BDA00020673976300001311
wherein {. } represents gradient calculation, and the optimal expansion coefficient μ is:
Figure BDA00020673976300001312
9d) using the optimum expansion coefficient mu and the peak clipping noise after expansion
Figure BDA00020673976300001313
Amplifying the original time domain signal x to accelerate the convergence speed to obtain the time domain signal after the peak-to-average ratio is restrained
Figure BDA00020673976300001314
Figure BDA00020673976300001315
In step S110, the signal with suppressed peak-to-average ratio
Figure BDA00020673976300001316
Insertion guard interval postambleTo the radio frequency amplifier HPA into the channel.
The effect of the present invention is further explained by simulation experiments.
1) Simulation conditions are as follows:
matlab R2017b simulation software is used in the simulation experiment, the modulation mode is 256-QAM quadrature amplitude modulation, the number N of subcarriers is set to 8192, the upsampling multiple J is set to 4, and the initial amplitude limiting rate CR is set to be 4initSet to 4.68dB, compensation factor gammainit1.3 and 1.3, and the adjustment factor k 2.
2) Simulation content and result analysis:
simulation 1, the peak-to-average ratio suppression is respectively carried out on the original OFDM signal by using the method of the invention and the conventional convex set mapping dynamic constellation expansion method POCS-ACE, intelligent gradient projection dynamic constellation expansion method SGP-ACE and least square approximation dynamic constellation expansion method LSA-ACE, and the peak-to-average ratio PAPR suppression gain obtained by the method is shown in figure 3.
Simulation 2, under an additive white gaussian noise channel, the peak-to-average ratio suppression is respectively carried out on the original OFDM signal by using the method of the present invention and the existing convex set mapping dynamic constellation extension method POCS-ACE, intelligent gradient projection dynamic constellation extension method SGP-ACE, and least square approximation dynamic constellation extension method LSA-ACE, and the obtained error rate performance is shown in fig. 4.
Simulation 3, the peak-to-average ratio suppression is respectively carried out on the original OFDM signal by using the method of the invention and the existing convex set mapping dynamic constellation expansion method POCS-ACE, intelligent gradient projection dynamic constellation expansion method SGP-ACE and least square approximation dynamic constellation expansion method LSA-ACE, and the obtained out-of-band spectrum performance is shown in FIG. 5.
From the simulation results of FIG. 3, it can be seen that the present invention has a given complementary cumulative distribution function value of 10-4In the method, the POCS-ACE method can obtain the peak-to-average ratio gain of 1.80dB after being iterated sixty times, the SGP-ACE method can obtain the peak-to-average ratio gain of 3.10dB once, the LSA-ACE method can obtain the peak-to-average ratio gain of 3.10dB once, and the LSA-ACE method can obtain the peak-to-average ratio gain of 3.05dB twice. This is seen. The inventionCompared with the traditional constellation diagram extension method, the peak-to-average ratio of the ODFM transmission signal can be remarkably reduced.
From the simulation results shown in fig. 4, it is found that the bit error rate is 10-4The loss of the signal-to-noise ratio of the invention is less than the loss of the signal-to-noise ratio brought by the LSA-ACE method under one iteration, and the loss of the signal-to-noise ratio brought by the SGP-ACE method under one iteration is the same as the loss of the signal-to-noise ratio brought by the SGP-ACE method under one iteration. Considering the peak-to-average ratio suppression gain brought by the invention, the signal-to-noise ratio loss is within an acceptable range.
From the simulation results of fig. 5, it can be seen that the invention can obtain almost the same power spectral density as the LSA-ACE and SGP-ACE methods in one iteration.
As can be seen from fig. 3, 4 and 5, the peak-to-average power ratio suppression method can obtain better peak-to-average power ratio suppression performance than that of the POCS-ACE, SGP-ACE and LSA-ACE methods under multiple iterations, greatly reduces the computational complexity of the system, and simultaneously can ensure that the error rate performance and the power spectrum performance are not seriously deteriorated. In summary, compared with the prior art, the scheme of the invention has better overall performance for the orthogonal frequency division multiplexing OFDM system with large carrier and high-order modulation.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (2)

1. A method for inhibiting ACE of peak-to-average ratio of high order modulation OFDM signals is characterized by comprising the following steps:
redefining the constellation expansion rule in the frequency domain;
the peak clipping threshold is dynamically adjusted according to the peak-to-average ratio of the current signal, so that effective peak-to-average ratio suppression gain is obtained, and meanwhile, the system error rate is not seriously deteriorated;
after the effective peak-to-average ratio suppression gain is obtained, a proper expansion factor is obtained by modifying a least square approximation formula, the original time domain signal is amplified, and the signal peak-to-average ratio suppression effect is enhanced;
the method for suppressing the ACE of the peak-to-average ratio of the high-order modulation OFDM signal further comprises the following steps:
step one, modulating a binary bit stream into an original over-sampling OFDM signal;
step two, setting corresponding optimization parameters;
step three, self-adaptive peak clipping processing;
step four, calculating the mean value of the amplitude vector;
fifthly, Fourier transform FFT;
step six, constellation expansion;
step seven, inverse Fourier transform IFFT;
step eight, calculating the mean value of the amplitude vector after constellation expansion;
calculating an expansion coefficient and amplifying an original OFDM signal;
step ten, sending the signal after the peak-to-average ratio inhibition;
the first step further comprises the following steps: carrying out orthogonal amplitude modulation on binary bit stream of a transmitting end of an Orthogonal Frequency Division Multiplexing (OFDM) system to obtain an original frequency domain signal X ═ X0,X1,...,Xk]TAnd then, after performing J-time interpolation on the original frequency domain signal, performing inverse discrete fourier transform on the original frequency domain signal to obtain an oversampled time domain original OFDM signal x ═ x ·, N-10,x1,...,xn]TWherein N is 0,1, J represents an upsampling factor and J is more than or equal to 4, and N is the number of subcarriers contained in the OFDM system; the signal x is subjected to the peak-to-average ratio suppression processing described below;
the quadrature amplitude modulation comprises 16-QAM, 64-QAM, 256-QAM and 1024-QAM, and the J-times interpolation operation is performed on modulated frequency domain data X ═ X0,X1,...,Xk]TN-1, where (J-1) × N zeros are inserted, so that after IFFT, a J-times oversampled original time domain signal x ═ x may be obtained0,x1,...,xn]TN ═ 0, 1., JN-1, which can be expressed by the following formula:
Figure FDA0003098036370000021
wherein XkIs frequency domain data before interpolation, Xk' is the frequency domain data after interpolation;
the second step further comprises: calculating the peak-to-average ratio of the current signal and recording as xi, and according to the peak-to-average ratio xi required by the systemtarAnd setting initial amplitude limiting rate CR for system bit error rate BERinitInitial compensation factor gammainitAnd η;
step three further comprises adjusting the peak clipping threshold A according to the peak-to-average ratio xi of the current signal, and clipping the peak of the original over-sampled signal to obtain the signal after clipping the peak
Figure FDA0003098036370000022
And peak clipping noise cclip＝[cclip,0,cclip,1,...,cclip,n]TWherein n is 0,1,. cndot, JN-1;
step four, setting p as peak clipping noise cclip,nThe set of the serial numbers of the sampling points with middle amplitude not equal to zero, i.e. p ═ n | | cclip,nIf | ≠ 0}, then the peak clipping signal cclip,nThe set of amplitudes of the sample points whose middle sequence number n belongs to p is denoted ceI.e. ce＝{|cclip,nI n belongs to p, and c is calculatedeThe mean value of all the elements is marked as tau;
the fifth step further comprises: signal using JN point discrete Fourier transform FFT
Figure FDA0003098036370000028
And cclipTransforming to frequency domain to obtain frequency domain peak clipping signal
Figure FDA0003098036370000023
Sum frequency domain peak clipping noise Cclip＝[Cclip,0,Cclip,1,...,Cclip,k]TWherein k is 0,1,.., JN-1;
step six further comprises: cutting in the frequency domainPeak signal
Figure FDA0003098036370000024
The constellation diagram is expanded to obtain the expanded frequency domain peak clipping noise
Figure FDA0003098036370000025
The peak clipping signal is subjected to frequency domain
Figure FDA0003098036370000026
The constellation diagram expansion comprises the following steps:
step one, reserving an internal constellation point without expansion;
secondly, the vertex angle constellation points are expanded to a region far away from the center of the constellation diagram;
thirdly, the boundary constellation points are expanded to a region far away from the center of the constellation diagram along the coordinate axis direction;
the seventh step further comprises: frequency domain peak clipping noise by inverse discrete Fourier transform (IFFT) of JN point
Figure FDA0003098036370000027
Conversion to time-domain peak clipping noise
Figure FDA0003098036370000031
Wherein n is 0,1,., JN-1;
step eight further comprises: extended peak clipping noise
Figure FDA0003098036370000032
The set of amplitudes of the sample points whose middle sequence number n belongs to p is recorded as
Figure FDA0003098036370000033
Namely, it is
Figure FDA0003098036370000034
Computing
Figure FDA0003098036370000035
The mean value of all elements in
Figure FDA0003098036370000036
The ninth step further comprises: inputting correction factor k, using c in the above processe、τ、
Figure FDA0003098036370000037
And
Figure FDA0003098036370000038
calculating an expansion coefficient mu, and amplifying an original time domain signal x to obtain a peak-to-average ratio inhibition signal
Figure FDA0003098036370000039
The step decimal includes the following steps: signal with suppressed peak-to-average ratio
Figure FDA00030980363700000310
Inserting a guard interval and then sending the signal to a radio frequency amplifier (HPA) to be transmitted into a channel;
in the third step, the adaptive peak clipping strategy adjusts an initial amplitude limiting rate according to a peak-to-average ratio (PAPR) value of a current signal, so as to adjust a peak clipping threshold and avoid cutting off excessive non-peak points, wherein a relationship between the peak clipping threshold A and the amplitude limiting rate CR is as follows:
Figure FDA00030980363700000311
where σ is the average power of the signal x:
Figure FDA00030980363700000312
the amplitude limiting ratio CR is adjusted by the following formula:
CR＝CRinit+(γ-1)·α·(ξ-ξtar)；
wherein the content of the first and second substances,
Figure FDA00030980363700000313
gamma and eta are compensation factors, the values of which are selected according to the peak-to-average ratio xi of the current signal and the initial limiting rate CRinit；
The specific steps of the clipping operation include:
first, for | xnPerforming peak clipping operation on all sampling points with the peak value greater than A to obtain a signal subjected to peak clipping
Figure FDA00030980363700000316
Figure FDA00030980363700000314
Wherein n is 0,1, JN-1,
Figure FDA00030980363700000315
representing the unit of an imaginary number, exp (-) representing an exponential operation based on a natural constant e, θnIs an original time domain signal xnThe phase, | · | is a modulo value operation;
second, using the peak-clipped signal
Figure FDA0003098036370000041
Subtracting the original time domain signal x to obtain the peak clipping noise:
Figure FDA0003098036370000042
inputting the correction factor k in the ninth step, using c in the above processe、τ、
Figure FDA0003098036370000043
And
Figure FDA0003098036370000044
calculating a spreading factor mu and amplifying the original time-domain signal x comprises:
1) selecting a suitable correction factor k from [ -1,2 ];
2) and correcting a least squares approximation formula, wherein an optimization target is expressed as:
Figure FDA0003098036370000045
wherein min {. is } represents the minimum operator,
Figure FDA0003098036370000046
denotes the vector two norm operator, l denotes the length sum vector ceThe same, but the elements are all row vectors of 1, mu is the optimal expansion coefficient to be solved;
3) solving the optimal expansion coefficient mu which meets the optimization target in the step 2):
order to
Figure FDA0003098036370000047
Let the gradient of f (μ) be zero:
Figure FDA0003098036370000048
wherein {. } represents gradient calculation, and the optimal expansion coefficient μ is:
Figure FDA0003098036370000049
4) amplifying the original time-domain signal x with an optimal expansion coefficient to addFast convergence rate, and obtaining the time domain signal after peak-to-average ratio suppression
Figure FDA00030980363700000411
Figure FDA00030980363700000410
2. A system for suppressing the ACE of peak-to-average ratio of a high order modulated OFDM signal implementing the method of suppressing the ACE of peak-to-average ratio of a high order modulated OFDM signal of claim 1.
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