Peak-to-Average Power Ratio Reduction Method for OFDM Signals in Underwater Internet of Things

Abstract

The present invention discloses a method for suppressing the peak-to-average power ratio (PAPR) of OFDM signals in an underwater Internet of Things (IoT). It mainly solves the problem of high PAPR in underwater OFDM systems when high-order modulation and a large number of subcarriers are used to achieve high-speed transmission. The solution is as follows: Modulate the input data into an original frequency-domain signal and perform an inverse discrete Fourier transform on it to obtain the original time-domain signal; Calculate the clipping noise using this signal, and preliminarily expand the original frequency-domain signal by the clipping noise, and perform expansion correction according to the re-set expansion region; Generate a phase factor sequence using a chaotic sequence, and obtain a time-domain signal based on it and the signal after expansion correction; Arbitrarily combine two groups of time-domain signals to generate new time-domain alternative signals, calculate the PAPR of all time-domain signals, and select the smallest group as the transmitted signal. The present invention reduces the PAPR of OFDM signals, can ensure that the bit error loss is within an acceptable range, improves the overall performance of the OFDM system, and can be used for underwater IoT communication.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a method for suppressing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals, which can be used for underwater Internet of Things (IoT) communication. Background Art

[0002] In recent years, the exploration of the ocean has become increasingly important. However, traditional underwater wireless communication methods based on acoustic waves and radio frequency are difficult to meet the growing information transmission requirements. Underwater wireless optical communication systems based on blue / green light have become a current research hotspot due to their advantages of high speed and low latency. The underwater IoT creates intelligent wireless sensor areas and relies on the devices and transmission units it serves to transmit the collected data in real time and at high speed through the underwater wireless optical communication system. OFDM modulation, as an important means to improve the transmission rate, is widely used. High-capacity and high-speed transmission requires OFDM to adopt high-order modulation methods and a large number of subcarriers, which inevitably leads to too high PAPR of OFDM signals. Signals with a high PAPR will operate in the non-linear region of the high-power amplifier, resulting in clipping distortion and deteriorating the system performance.

[0003] Currently, the main methods for suppressing the PAPR include the clipping method of distortion type, the probability method, and the constellation expansion method. The clipping method suppresses the PAPR of the signal by distorting the signal with a high instantaneous peak power without changing the signal phase. Although this method is simple to implement, has a good PAPR suppression effect and low complexity, the clipped signal has serious in-band distortion and out-of-band spectrum expansion, deteriorating the bit error rate performance of the system, and is not suitable for relatively harsh underwater environments. The probability method processes the signal by introducing a phase weighting coefficient. Although this method does not cause the deterioration of the system bit error rate performance, it requires transmitting a large amount of sideband information and performing inverse processing operations at the receiving end, which not only increases the complexity but also reduces the system spectrum efficiency. Constellation expansion suppresses the PAPR by changing the mapping method, mapping some data to a specific region instead of a specific point. This method does not require processing at the receiving end, but when performing high-speed transmission underwater, high-order modulation and a large number of subcarriers are required, and its PAPR suppression performance is poor. Therefore, studying a method for suppressing the PAPR of OFDM signals suitable for underwater IoT is of great guiding significance for promoting the development of high-speed underwater wireless communication technology.

[0004] In their paper, "OFDM-based algorithm for peak average power ratio suppressing in underwater wireless optical communications," presented at the 2022 International Conference on Optical Communications and Networks (ICOCN), Liwei Yang et al. proposed an improved selective mapping (SLM) algorithm. This algorithm uses a chaotic sequence to generate a random phase sequence, thereby reducing data autocorrelation. Only the sequence number of the random phase is required, thereby reducing the amount of sideband information transmitted. The specific implementation steps are: Converting the mapped frequency-domain transmission signal string into multiple parallel data channels; then, using the chaotic sequence, generating multiple distinct random phase sequences of the same length as the parallel data. These random phase sequences are multiplied by the input data to produce multiple sets of point-product signals; finally, performing an inverse discrete Fourier transform on these multiple signals to the time domain, calculating the peak-to-average power ratio (PAPR) of the time-domain signals, selecting the signal with the lowest PAPR as the output signal, and recording the sequence number as the sideband information for transmission. While this method can reduce the transmission of sideband information, it requires multiple inverse discrete Fourier transform operations to generate multiple candidate signals, resulting in high computational complexity.

[0005] In their paper "Novel ACE Scheme for PAPR Reduction of High Broadband OFDM Systems" (2019 IEEE 19th International Conference on Communication Technology (ICCT)), Yuzhuo Liu et al. proposed a predistortion constellation expansion ACE algorithm. Its implementation steps are: performing an inverse discrete Fourier transform on the mapped frequency domain data to transform it into a time domain signal, limiting the time domain signal, calculating the limiting noise from the limited signal and the original time domain signal, and performing a Fourier transform on the limiting noise to obtain the frequency domain limiting noise; then expanding the original frequency domain signal; then correcting the extended signal based on the set constellation point expansion region, and performing an inverse discrete Fourier transform on the corrected frequency domain signal to transform it back to the time domain; calculating the peak-to-average ratio of the time domain signal, and selecting the group with the lowest peak-to-average ratio as the output signal. Although this method does not require the transmission of sideband information and expands the internal constellation points, its peak-to-average ratio suppression performance is poor when high-order modulation and a large number of subcarriers are used. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a method for suppressing the peak-to-average ratio of OFDM signals for underwater Internet of Things, so as to improve the peak-to-average ratio suppression performance of OFDM signals, reduce the complexity of the system, and meet the peak-to-average ratio suppression requirements of OFDM signals for underwater Internet of Things.

[0007] The key technical aspects of this invention are: redefining the constellation point expansion method, expanding both internal and external constellation points, and increasing the number of expanded constellation points; using a chaotic sequence to generate a random phase factor sequence, and multiplying the expanded frequency domain signal by the random phase factor sequence; and utilizing the linear properties of the inverse discrete Fourier transform to combine any two different sets of time domain candidate signals to generate a new candidate signal. Its implementation steps include the following:

[0008] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0009] (1) Modulate the binary bit stream at the system transmitter into the original frequency domain OFDM signal X;

[0010] (2) Upsampling the original frequency domain signal X to obtain the upsampled frequency domain signal X′, and performing an inverse discrete Fourier transform on X′ to obtain the upsampled time domain signal U;

[0011] (3) Perform a limiting operation on the time domain signal U and calculate the time domain limiting noise. Perform Fourier transform on the time domain limiting noise to obtain the frequency domain limiting noise C clip ;

[0012] (4) According to the frequency domain limiting noise C clip Perform preliminary expansion on the original OFDM signal X and modify the preliminary expanded signal according to the set expansion area:

[0013] (4a) By C clip Perform preliminary expansion on signal X to obtain preliminary expanded frequency domain signal ;

[0014] (4b) The constellation point expansion area is divided into two parts, the inner and outer parts. The outer area includes the two-dimensional square expansion area E square and the one-dimensional linear extension region E line , the internal expansion area is a two-dimensional circular expansion area E round ;

[0015] (4c) For each preliminary extended frequency domain signal The corresponding two-dimensional square expansion area E square The constellation point signal is corrected to obtain the corrected extended frequency domain signal Y i :

[0016]

[0017] in, represents the real part of the i-th preliminary extended frequency domain signal, represents the imaginary part of the i-th preliminary extended frequency domain signal, X i Represents the i-th original frequency domain signal, 0<i<N-1, O max =max(Real(X)) and Q max =max(Imag(X)) represents the maximum real and imaginary parts of the constellation points of the selected modulation mode respectively;

[0018] (4d) For each preliminary extended frequency domain signal The corresponding one-dimensional linear expansion area E line The constellation point signal is corrected to obtain the corrected extended frequency domain signal Y r :

[0019]

[0020]

[0021] Among them, X r Represents the rth original frequency domain signal, 0<r<N-1;

[0022] (4e) For each preliminary extended frequency domain signal The corresponding two-dimensional circular expansion area E round The constellation point signal is corrected to obtain the corrected extended frequency domain signal Y l :

[0023]

[0024] Among them, δ represents the maximum distortion, X l represents the lth original frequency domain signal, represents the phase of the lth frequency-domain limiting noise, Represents the imaginary unit, 0<l<N-1;

[0025] (4f) Each frequency domain signal Y after expansion correction i , Y r and Y l The frequency domain signal Y after all corrections is formed;

[0026] (5) Using chaotic sequences to generate M groups of random phase factor sequences P with a length of N;

[0027] (6) Multiply the corrected frequency domain signal Y with the random phase factor sequence P to obtain the frequency domain signal after dot product.

[0028] (7) The frequency-domain signal after dot multiplication Performs an inverse discrete Fourier transform operation to obtain a time-domain signal d, and uses the linear property of the inverse discrete Fourier transform to generate a new time-domain alternative signal s:

[0029] s z,k = cosθ·d g,k + j·sinθ·d h,k

[0030] Among them, s z,k represents the k-th data in the z-th group of new time-domain alternative signals, d g,k represents the k-th data in the g-th group of time-domain signals, d h,k represents the k-th data in the h-th group of time-domain signals, 1 ≤ z ≤ M·(M - 1) / 2, 1 ≤ g ≤ M, 1 ≤ h ≤ M, g ≠ h, 0 < θ < π / 2;

[0031] (8) Use the time-domain signal d and the new time-domain alternative signal s to form all time-domain signals f, calculate the peak-to-average power ratio of the time-domain signal f, and select the group with the smallest peak-to-average power ratio as the output signal.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] First, by adopting a method that combines the predistortion ACE algorithm and the SLM algorithm, the present invention redefines the constellation expansion method, expands both the internal and external points of the constellation, increases the number of constellation point expansions, and then combines with the SLM algorithm to further improve the peak-to-average ratio suppression performance. It can overcome the problem that the existing peak-to-average ratio suppression methods have poor suppression performance under high-order modulation and a large number of subcarriers while ensuring the unchanged bit error performance at the receiving end, thus improving the peak-to-average ratio suppression performance of the present invention.

[0034] Second, since the present invention adopts the method of generating a random phase factor sequence using a chaotic sequence, after determining the random phase factor sequence, only the specific serial number needs to be transmitted, thereby reducing the transmission of sideband information and overcoming the problem of low spectral efficiency caused by excessive transmission of sideband information in the prior art;

[0035] Third, by combining any two different groups of time-domain alternative signals to generate new alternative signals, the present invention can reduce the number of inverse discrete Fourier transform times when using the same alternative signals, thereby overcoming the problem of high complexity caused by multiple inverse discrete Fourier transform operations in the prior art, and enabling the present invention to reduce the system complexity while ensuring the peak-to-average ratio suppression performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is the implementation flowchart of the present invention;

[0037] Figure 2 It is a schematic diagram of the expandable area of constellation points in the first quadrant in the present invention;

[0038] Figure 3 It is a schematic diagram of the constellation point expansion method in the two-dimensional square area in the present invention;

[0039] Figure 4 It is a schematic diagram of the constellation point expansion method in the one-dimensional linear area in the present invention;

[0040] Figure 5 It is a schematic diagram of the constellation point expansion method in the two-dimensional circular area in the present invention;

[0041] Figure 6 It is a comparison chart of the peak-to-average power ratio suppression performance between the present invention and the prior art;

[0042] Figure 7 It is a comparison chart of the bit error rate performance between the present invention and the prior art. Specific embodiments

[0043] The following further describes the embodiments and effects of the present invention in conjunction with the accompanying drawings.

[0044] Refer to Figure 1 , the implementation steps of the present invention are as follows:

[0045] Step 1, modulate the binary bit stream at the system transmitter into the original frequency-domain OFDM signal X.

[0046] Perform quadrature amplitude modulation on the binary bit stream at the system transmitter to obtain the original frequency-domain signal X:

[0047] X = [X0, X1, ···, X k , ···, X N-1

[0048] Among them, X k represents the kth data in the original frequency-domain signal, k = 0, 1, ···, N - 1, N is the number of subcarriers included in the OFDM symbol, and the quadrature amplitude modulation adopted is 256QAM, N = 512.

[0049] Step 2, upsample the original frequency-domain signal X to obtain the upsampled time-domain signal U.

[0050] 2.1) Insert (J - 1) × N zeros in the middle of the original frequency-domain signal to obtain the upsampled frequency-domain signal X':

[0051]

[0052] Among them, X k represents the kth data in the original frequency-domain signal, X' n ​represents the nth data in the frequency domain signal after upsampling, J represents the upsampling factor, J=4, n=0,1,···,JN-1;

[0053] 2.2) X′ of the upsampled frequency domain signal n Perform inverse discrete Fourier transform to obtain the upsampled time domain signal U:

[0054] U=[U0,U1,···,U n ,···,U JN-1 ]

[0055] Among them, U n Represents the nth data in the upsampled time domain signal.

[0056] Step 3: Perform a limiting operation on the time domain signal U to obtain the frequency domain limiting noise C clip .

[0057] 3.1) Calculate the limit threshold A clip :

[0058]

[0059] Among them, C R Indicates the clipping rate, C R =4.68, represents the average power of the upsampled time domain signal U;

[0060] 3.2) According to the limit threshold A clip , perform a limiting operation on the upsampled time domain signal U to obtain the limited time domain signal

[0061]

[0062] in, It represents the nth data in the time domain signal after limiting. Its formula is as follows:

[0063]

[0064] In the formula, θ n is the upsampled time domain signal U n The phase, represents the imaginary unit, |·| is the modulus operation;

[0065] 3.3) According to the time domain signal after limiting Calculate the time domain limiting noise c from the upsampled time domain signal U clip :

[0066] c clip =[c clip,0 ,cclip,1 , ···, c clip,n , ···, c clip,JN-1

[0067] Among them, represents the nth data in the clipped noise signal;

[0068] 3.4) Perform discrete Fourier transform and downsampling on the time-domain clipped noise c clip to obtain the frequency-domain clipped noise C clip :

[0069] C clip = [C clip,0 , C clip,1 , ···, C clip,k , ···, C clip,N-1

[0070] Among them, C clip,k represents the kth data in the frequency-domain clipped noise signal.

[0071] Step 4: According to the frequency-domain clipped noise C clip preliminarily expand the original OFDM signal X, and correct the preliminarily expanded signal according to the set expansion region.

[0072] The original OFDM signal X corresponds to the standard constellation points of quadrature amplitude modulation. After clipping, the dispersion range of the constellation points is small. It is necessary to preliminarily expand it through the frequency-domain clipped noise C clip and the expansion factor to increase the nonlinear distortion caused by clipping, make the constellation points more dispersed, and obtain the preliminarily expanded frequency-domain signal, that is, the distorted and dispersed constellation points. And it is necessary to redefine the expansion region of the constellation points and correct the preliminarily expanded frequency-domain signals in both the inner and outer regions to increase the number of expanded constellation points and improve the peak-to-average ratio suppression performance. The specific implementation is as follows:

[0073] 4.1) Use the frequency-domain clipped noise C clip to preliminarily expand the signal X to obtain the preliminarily expanded frequency-domain signal

[0074]

[0075] Among them, represents the kth data in the preliminarily expanded frequency-domain signal, G represents the expansion factor, and the value in this example is 10 and 15;

[0076] 4.2) Divide the region:

[0077] Referring to Figure 2 , in this step, the expandable region of the constellation points is divided into two parts, the inner and the outer. The outer region includes the two-dimensional square expansion region E​​square and the one-dimensional linear extended region E line , the internal extended region is a two-dimensional circular extended region E round ;

[0078] 4.3) For each preliminary extended frequency-domain signal corresponding to the two-dimensional square extended region E square , perform extended correction on the constellation point signals:

[0079] Refer to Figure 3 , this step corrects the preliminary extended frequency-domain signal according to the following different situations:

[0080] When the preliminary extended frequency-domain signal is located within the two-dimensional square extended region E square , do not correct it, as shown in Figure 3 (a);

[0081] When the real part of the preliminary extended frequency-domain signal is greater than the real part of the original frequency-domain signal, but the imaginary part of the preliminary extended frequency-domain signal is less than the imaginary part of the original frequency-domain signal, correct the imaginary part of the preliminary extended frequency-domain signal to the imaginary part of the original frequency-domain signal X i , as shown in Figure 3 (b);

[0082] When both the real part and the imaginary part of the preliminary extended frequency-domain signal are less than the real part and the imaginary part of the original frequency-domain signal, correct the preliminary extended frequency-domain signal to the original frequency-domain signal X i , as shown in Figure 3 (c).

[0083] The frequency-domain signal Y after extended correction i is shown as follows:

[0084]

[0085] where represents the real part of the i-th preliminary extended frequency-domain signal, represents the imaginary part of the i-th preliminary extended frequency-domain signal, X i represents the i-th original frequency-domain signal, 0 < i < N - 1, O max = max(Real(X)) and Q max = max(Imag(X)) respectively represent the maximum real part and the maximum imaginary part of the constellation points of the selected modulation method;

[0086] 4.4) For each preliminary extended frequency-domain signal The corresponding one-dimensional linear expansion area E line Correct the constellation point signal:

[0087] Reference Figure 4 In this step, the initial extended frequency domain signal is processed according to the following different situations: To make corrections:

[0088] When the frequency domain signal is initially expanded Located in the one-dimensional linear extension region E line When it is updated, it is not corrected, such as Figure 4 (a)

[0089] When the frequency domain signal is initially expanded The real and imaginary parts are both greater than or equal to the original frequency domain signal X r When the real and imaginary parts of The real part of the original frequency domain signal X is corrected r The real part of Figure 4 (b)

[0090] When the frequency domain signal is initially expanded The real part is greater than or equal to the original frequency domain signal X r When the real part of the frequency domain signal is initially expanded The imaginary part is smaller than the original frequency domain signal X r When the imaginary part of Corrected to the original frequency domain signal X r ,like Figure 4 (c) shown.

[0091] Frequency domain signal Y after expansion and correction r As shown below:

[0092]

[0093]

[0094] Among them, Real(Y r ) represents the real part of the frequency domain signal after the rth extended correction, Imag(Y r ) represents the imaginary part of the rth extended and corrected frequency domain signal, represents the real part of the rth preliminary extended frequency domain signal, represents the imaginary part of the rth preliminary extended frequency domain signal, X r Represents the rth original frequency domain signal, 0<r<N-1;

[0095] 4.5) For each preliminary extended frequency domain signal The corresponding two-dimensional circular expansion area E roundCorrect the constellation point signals:

[0096] Refer to Figure 5 , in this step, the preliminary extended frequency-domain signal is corrected according to the following different situations:

[0097] When the preliminary extended frequency-domain signal is located inside the two-dimensional circular extended area E round , it is not corrected, as shown in Figure 5 (a);

[0098] When the preliminary extended frequency-domain signal is located outside the two-dimensional circular extended area E round , the preliminary extended frequency-domain signal is corrected to inside the two-dimensional circular extended area E round , as shown in Figure 5 (b).

[0099] The extended and corrected frequency-domain signal Y l is shown as the following formula:

[0100]

[0101] where, δ represents the maximum distortion amount, and its value is 0.01, represents the l-th preliminary extended frequency-domain signal, X l represents the l-th original frequency-domain signal, represents the phase of the l-th frequency-domain limiting noise, 0 < l < N - 1;

[0102] 4.6) Use the extended and corrected frequency-domain signal Y i in the two-dimensional square extended area, the extended and corrected frequency-domain signal Y r in the one-dimensional linear extended area, and the extended and corrected frequency-domain signal Y l in the two-dimensional circular extended area to form the fully extended and corrected frequency-domain signal Y.

[0103] Step 5, use the chaotic sequence to generate M groups of random phase factor sequences P with length N.

[0104] The traditional phase factor sequence P is generated by randomly generating a group of numbers, and all the phase factor information needs to be transmitted, resulting in a low spectral efficiency of the system. In this example, the chaotic sequence is used to generate the random phase factor sequence. After determining the random phase factor sequence, only the specific serial number needs to be sent, reducing the transmission of sideband information to improve the spectral efficiency of the system. The specific implementation is as follows:

[0105] 5.1) Use the chaotic sequence to generate a random number x:

[0106] x = [x1, x2, ···, x a , x a+1 ···, x N

[0107] where x a+1 = μ · x a · (1 - x a ) represents the value of the (a + 1)-th chaotic sequence, μ represents the fractal parameter, a = 0, 1, ···, N - 1. In this example, μ = 4. When a = 0, the initial value of the chaotic sequence x0 = 0.0019;

[0108] 5.2) After binary quantization of the random number x, the selection signal B is obtained:

[0109] B = [B0, B1, ···, B b , ···, B N-1

[0110] where represents the result after the b-th binary quantization, b = 0, 1, ···, N - 1;

[0111] 5.3) Select phase factors by the selection signal B to generate the first group of random phase factor sequences T:

[0112] T = [T0, T1, ···, T k , ···, T N-1

[0113] where represents the k-th value of the first group of random phase factor sequences,

[0114] 5.4) Circularly shift the first group of random phase factor sequences T by λ bits to generate the remaining M - 1 groups of random phase factor sequences W:

[0115] W = [W1, W2, ···, W λ , ···, W M-1

[0116] where W λ = [T λ , ···, T N-1 , T0, T1, ···, T λ-1 represents the λ-th group of random phase factor sequences, λ = 1, 2, ···, M - 1, M represents the number of groups of all random phase factor sequences P, and the value of M is 2 or 4;

[0117] 5.5) Use the first group of random phase factor sequences T and the remaining M - 1 groups of random phase factor sequences W to form all phase factor sequences P. ​​​​

[0118] Step 6: Using the linear property of the inverse discrete Fourier transform, generate a new time-domain alternative signal s.

[0119] In this example, according to the linear property of the inverse discrete Fourier transform, any two different groups of time-domain alternative signals are combined to generate a new alternative signal s, so as to reduce the number of inverse discrete Fourier transforms when using the same alternative signal, enabling the present invention to reduce the system complexity while ensuring the peak-to-average power ratio suppression performance. The implementation steps are as follows:

[0120] 6.1) Multiply the extended and corrected frequency-domain signal Y by the random phase factor sequence P to obtain the frequency-domain signal after dot product

[0121]

[0122] where represents the k-th data of the m-th group of signals after dot product, X k represents the k-th data in the original frequency-domain signal, P m,k represents the k-th data of the m-th group of random phase factor sequences, 1 ≤ m ≤ M;

[0123] 6.2) Perform an inverse discrete Fourier transform operation on the frequency-domain signal after dot product to obtain the time-domain signal d, and use the linear property of the inverse discrete Fourier transform to generate a new time-domain alternative signal s:

[0124] s z,k = cosθ · d g,k + j · sinθ · d h,k

[0125] where s z,k represents the k-th data in the z-th group of new time-domain alternative signals, d g,k represents the k-th data in the g-th group of time-domain signals, d h,k represents the k-th data in the h-th group of time-domain signals, 1 ≤ z ≤ M · (M - 1) / 2, 1 ≤ g ≤ M, 1 ≤ h ≤ M, g ≠ h, θ = π / 4;

[0126] Step 7: Calculate the peak-to-average power ratio F of the time-domain signal according to the time-domain signal d and the new time-domain alternative signal s.

[0127] 7.1) Use the time-domain signal d and the new time-domain alternative signal s to form the time-domain signal f:

[0128] f = [d1, d2, ···, d m , ···, d M , s1, s2, ···, s z , ···, s M·(M-1) / 2 ​

[0129] Among them, d m represents the m-th group of time-domain signals, and s z represents the z-th group of new time-domain alternative signals;

[0130] 7.2) Calculate the average power value α of all time-domain signals f:

[0131] Calculate the average power value α of the v-th group of time-domain signals f v : v :

[0132]

[0133] Among them, f v,k represents the k-th data of the v-th group of time-domain signals, 1 ≤ v ≤ M + M·(M - 1) / 2,

[0134] Use this formula to complete the calculation of the average power value for each group, and obtain the average power values α of all groups:

[0135] α = [α0, α1, ···, α v , ···, α M+M·(M-1) / 2 ;

[0136] 7.3) Calculate the maximum power value β of all time-domain signals f:

[0137] β = [β0, β1, ···, β v , ···, β M+M·(M-1) / 2

[0138] Among them, β v = max(|f v | 2 ) represents the maximum power value of the v-th group of time-domain signals f v ;

[0139] 7.4) Calculate the peak-to-average power ratio F of all time-domain signals f according to the average power value α and the maximum power value β of the time-domain signals f:

[0140]

[0141] Among them, represents the peak-to-average power ratio of the v-th group of time-domain signals;

[0142] 7.5) Select the time-domain signal corresponding to the minimum value in the peak-to-average power ratio F as the transmitted signal.

[0143] Combined with the following simulation experiments, the technical effects of the present invention are further described.

[0144] 1. Simulation experiment conditions: ​

[0145] The simulation used an AMD Ryzen R7-4800H CPU with a main frequency of 2.90 GHz, 16.0 GB of memory, a 64-bit operating system, Microsoft Windows 10 Professional, and MATLAB 2020b simulation software. The modulation scheme was 256QAM quadrature amplitude modulation, with the number of subcarriers N set to 512, the upsampling factor J to 4, the clipping rate CR to 4.68 dB, the spreading factor G to 15, and the number of packets M to 2 and 4.

[0146] 2. Simulation content and result analysis:

[0147] Simulation 1: Under the above simulation conditions, the present invention sets the expansion factor to 15 and the number of groups to 4. The existing predistortion constellation expansion method sets the expansion factor to 15 and the existing selective mapping method sets the number of groups to 4. The three methods are used to suppress the peak-to-average ratio of the original OFDM signal respectively. The peak-to-average ratio suppression gain is as follows: Figure 6 shown.

[0148] Depend on Figure 6 The simulation results show that when the complementary cumulative distribution function value is 10 -4 When the existing pre-distortion constellation expansion method can only obtain a 2dB peak-to-average ratio suppression gain, and the existing selective mapping method can only obtain a 2.5dB peak-to-average ratio suppression gain, while the present invention can obtain a 3dB peak-to-average ratio suppression gain. Compared with the existing selective mapping method and the existing pre-distortion constellation diagram expansion method, the present invention significantly reduces the peak-to-average ratio of the ODFM signal.

[0149] Simulation 2: Under the above simulation conditions, the present invention sets the expansion factor to 15 and the number of groups to 2 and 4; the existing predistortion constellation expansion method sets the expansion factor to 15, and uses these two methods to suppress the peak-to-average ratio of the original OFDM signal. The bit error rate performance obtained is as follows: Figure 7 shown.

[0150] Depend on Figure 7 The results show that the expansion factor of the present invention and the existing predistortion constellation expansion are both 15, and the bit error rate is the same, that is, both are 10 -3 , the signal-to-noise ratio loss of the two methods is the same. It can also be seen that when the expansion factor is 15, the present invention does not affect the system bit error rate when the number of groups is 2 or 4. Therefore, compared with existing predistortion constellation expansion methods, the present invention does not cause the system bit error rate to deteriorate.

[0151] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for suppressing the peak-to-average power ratio of OFDM signals in an underwater Internet of Things, characterized in that, It includes the following steps: (1) Modulate the binary bit stream at the system transmitter end into the original frequency-domain OFDM signal X; (2) Upsample the original frequency-domain signal X to obtain the upsampled frequency-domain signal X′, and perform the inverse discrete Fourier transform on X′ to obtain the upsampled time-domain signal U; (3) Perform a clipping operation on the time-domain signal U and calculate the time-domain clipping noise. Perform a Fourier transform on the time-domain clipping noise to obtain the frequency-domain clipping noise C clip ; (4) According to the frequency-domain limited noise C clip Perform preliminary expansion on the original OFDM signal X, and correct the preliminarily expanded signal according to the set expansion region: (4a) Preliminary expansion of signal X by C clip to obtain a preliminarily expanded frequency-domain signal (4b) Divide the constellation point expandable region into an inner part and an outer part. The outer region includes a two-dimensional square expansion region E square and a one-dimensional linear expansion region E line , and the inner expansion region is a two-dimensional circular expansion region E round ; (4c) For each preliminary extended frequency-domain signal corresponding to the two-dimensional square extended region E square perform correction on the constellation point signals to obtain the extended and corrected frequency-domain signal Y i : Among them, represents the real part of the i-th preliminary extended frequency-domain signal, represents the imaginary part of the i-th preliminary extended frequency-domain signal, X i represents the i-th original frequency-domain signal, 0 < i < N - 1, O max = max(Real(X)) and Q max = max(Imag(X)) respectively represent the maximum real part and the maximum imaginary part of the constellation points of the selected modulation method; (4d) For each preliminary extended frequency-domain signal corresponding to the one-dimensional linear extended region E line perform correction on the constellation point signals to obtain the extended and corrected frequency-domain signal Y r : where X r represents the r-th original frequency-domain signal, where 0 < r < N - 1; (4e) For each preliminary extended frequency-domain signal corresponding to the two-dimensional circular extended region E round correct the constellation point signals to obtain the extended and corrected frequency-domain signal Y l : where δ represents the maximum distortion variable, X l represents the l-th original frequency-domain signal, represents the phase of the l-th frequency-domain clipped noise, represents the imaginary unit, 0 < l < N - 1; (4f) Each frequency-domain signal Y after extended correction i , Y r and Y l constitute all the corrected frequency-domain signals Y; (5) Generate M groups of random phase factor sequences P with a length of N using a chaotic sequence; (6) Multiply the corrected frequency-domain signal Y by the random phase factor sequence P to obtain the frequency-domain signal after dot multiplication. (7) The frequency-domain signal after dot multiplication Perform an inverse discrete Fourier transform operation to obtain the time-domain signal d, and use the linear property of the inverse discrete Fourier transform to generate a new time-domain alternative signal s: s z,k = cosθ·d g,k + j·sinθ·d h,k Among them, s z,k represents the k-th data in the z-th group of new time-domain alternative signals, and d g,k represents the k-th data in the g-th group of time-domain signals, and d h,k represents the k-th data in the h-th group of time-domain signals, where 1 ≤ z ≤ M·(M - 1) / 2, 1 ≤ g ≤ M, 1 ≤ h ≤ M, g ≠ h, and 0 < θ < π / 2; (8) Combine the time-domain signal d and the new time-domain alternative signal s to form the entire time-domain signal f, calculate the peak-to-average power ratio of the time-domain signal f, and select the group with the smallest peak-to-average power ratio as the output signal.

2. The method according to claim 1, wherein The original frequency-domain OFDM signal X generated in step (1) is expressed as follows: X = [X0, X1, ···, X k , ···, X N-1 ​ where X k represents the k-th data in the original frequency-domain signal, where k = 0, 1, ···, N - 1, and N is the number of subcarriers included in the OFDM symbol.

3. The method according to claim 1, wherein The upsampled time-domain signal U obtained in step (2) is realized as follows: (2a) Insert (J - 1)×N zeros in the middle of the original frequency-domain signal to obtain the upsampled frequency-domain signal X′: where X k represents the k-th data in the original frequency-domain signal, k = 0, 1, ···, N - 1, and X' n represents the n-th data in the frequency-domain signal after upsampling, J represents the upsampling factor, J ≥ 4, n = 0, 1, ···, JN - 1, and N is the number of subcarriers included in the OFDM symbol; (2b) Inverse discrete Fourier transform is performed on X′ n to obtain the upsampled time-domain signal U: U = [U0, U1, ···, U n , ···, U JN-1 ​ Among them, U n represents the nth data in the time-domain signal after upsampling.

4. The method according to claim 1, wherein Generate the frequency-domain limited noise C in step (3) clip , which is implemented as follows: (3a) Calculate the clipping threshold A clip : Among them, C R represents the clipping ratio, represents the average power of the time-domain signal U after upsampling, U n represents the nth data in the time-domain signal after upsampling, where n = 0, 1, ···, JN - 1, J represents the upsampling factor, J ≥ 4, and N is the number of subcarriers included in the OFDM symbol; (3b) According to the clipping threshold A clip , perform a clipping operation on the upsampled time-domain signal U to obtain the clipped time-domain signal Among them, represents the nth data in the time-domain signal after amplitude limiting, and θ n is the phase of the time-domain signal U n after upsampling, and |·| represents the modulus operation; (3c) Calculate the time-domain clipping noise c based on the time-domain signal after clipping and the time-domain U of the time-domain signal after upsampling clip : c clip = [c clip,0 , c clip,1 , ···, c clip,n , ···, c clip,JN-1 ​ Among them, represents the nth data in the clipped noise signal; (3d) Discrete Fourier transform and downsampling are performed on the time-domain limited noise c clip to obtain the frequency-domain limited noise C clip : C clip = [C clip,0 , C clip,1 , ···, C clip,k , ···, C clip,N-1 ​ Among them, C clip,k represents the k-th data in the frequency-domain limited noise signal.

5. The method according to claim 1, wherein The preliminary extended frequency-domain signal generated in step (4a) is expressed as follows: Among them, represents the k-th data in the preliminary extended frequency-domain signal, G represents the spreading factor, k = 0, 1, ···, N - 1, N is the number of subcarriers included in the OFDM symbol, and C clip,k represents the k-th data in the frequency-domain clipping noise.

6. The method according to claim 1, characterized in that The generation of the random phase factor sequence P in step (5) is realized as follows: (5a) Generate a random number x using a chaotic sequence; x = [x1, x2, ···, x a , x a+1 ···, x N ​ where x a+1 = μ·x a ·(1 - x a ) represents the value of the (a + 1)-th chaotic sequence, μ represents the fractal parameter, 3.566 ≤ μ ≤ 4, a = 0, 1, ···, N - 1, and N is the number of subcarriers included in the OFDM symbol; (5b) Perform binary quantization on the random number x to obtain the selection signal B; B = [B0, B1, ···, B b , ···, B N-1 ​ Among them, represents the result after the b-th binary quantization, where b = 0, 1, ···, N - 1; (5c) Select phase factors by the selection signal B to generate the first group of random phase factor sequences T; T = [T0, T1, ···, T k , ···, T N-1 ​ Among them, represents the k-th value of the first group of random phase factor sequences, and conforms to a uniform distribution within [0, 2π], where k = 0, 1, ···, N - 1; (5d) Circularly shift the first group of random phase factor sequences T by λ bits to generate the remaining M - 1 groups of random phase factor sequences W; W = [W1, W2, ···, W λ , ···, W M-1 ​ Among them, W λ = [T λ , ···, T N-1 , T0, T1, ···, T λ-1 represents the λ-th group of random phase factor sequences, where λ = 1, 2, ···, M - 1, and M represents the number of groups of all random phase factor sequences P; (5f) Combine the first group of random phase factor sequences T and the remaining M - 1 groups of random phase factor sequences W to form the entire phase factor sequence P.

7. The method according to claim 1, wherein The signal after dot product obtained in step (6) is expressed as follows: Among them, represents the k-th data of the signal after the m-th dot product, X k represents the k-th data in the original frequency-domain signal, P m,k represents the k-th data of the m-th group of random phase factor sequences, 1 ≤ m ≤ M, k = 0, 1, ···, N - 1, M represents the number of groups of all random phase factor sequences P, and N is the number of subcarriers included in the OFDM symbol.

8. The method according to claim 1, wherein The calculation of the peak-to-average power ratio of the entire time-domain signal f in step (8) is realized as follows: (8a) Calculate the average power value α of the entire time-domain signal f; α＝[α0,α1,···,α v ,···,α M+M·(M-1) / 2 ] Among them, represents the average power value of the v-th group of time-domain signals f v , where f v,k represents the k-th data of the v-th group of time-domain signals, N is the number of subcarriers included in the OFDM symbol, 1 ≤ v ≤ M + M·(M - 1) / 2, k = 0, 1, ···, N - 1, and M represents the number of groups of all random phase factor sequences P; (8b) Calculate the maximum power value β of the entire time-domain signal f; β＝[β0,β1,···,β v ,···,β M+M·(M-1) / 2 ] where β v = max(|f v | 2 ) represents the maximum power value of the v-th group of time-domain signals f v ; (8c) Calculate the peak-to-average power ratio F of the entire time-domain signal f according to the average power value α and the maximum power value β of the time-domain signal f;

Images