Joint calculation method of baseband signals for reducing PAPR and out-of-band radiation in OFDM systems

Abstract

The present invention discloses a baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system. For a band-limited channel OFDM system in a multipath environment, the data combination that causes the maximum PAPR of the OFDM system is used as a restriction condition, and the PAPR of the OFDM signal in this case is reduced to a suitable value, thereby achieving the purpose of effectively reducing the PAPR of the system. In view of the problem of serious out-of-band leakage caused by rectangular signals, a pan-functional model that obeys the minimum out-of-band radiation criterion is introduced. On the basis of utilizing the characteristics of the model itself, boundary restriction conditions are added to further reduce the frequency domain out-of-band leakage of the baseband signal, and the OFDM signal formed by superposition has lower out-of-band radiation. In addition, while ensuring that the OFDM system PAPR of the rectangular signal does not increase significantly or remains basically the same, inter-symbol interference is artificially introduced to construct a baseband signal with faster attenuation, thereby further reducing the out-of-band radiation of the OFDM system.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and more particularly to a baseband signal joint calculation method for reducing PAPR and out-of-band radiation of an OFDM system. Background Art

[0002] At present, the traditional OFDM system is widely used in broadband wireless communication systems because of its strong resistance to multipath channels and frequency selective fading of wireless channels. However, OFDM itself also has some inherent challenges, among which the most prominent are the excessive out-of-band radiation and the excessive PAPR of the system. On the one hand, excessive out-of-band radiation will cause a waste of channel resources, and on the other hand, high spectrum leakage will seriously affect adjacent users, which is a great challenge in future wireless communication systems. Excessive out-of-band radiation is caused by the use of rectangular signals as baseband signals. Therefore, this problem can be solved by designing a suitable baseband signal.

[0003] The reason why PAPR is too large is that multiple subcarrier signals are superimposed on each other, which increases the probability of in-phase signals superimposing on each other, resulting in a large peak power, which in turn causes the problem of PAPR being too large. For the power amplifier at the transmitter end of the wireless system, a signal with too large PAPR will exceed its linear part, causing serious distortion. As for how to solve the problem of too large PAPR, many classic methods have emerged to effectively reduce the PAPR of the OFDM system, but these methods will more or less sacrifice some aspect of the system's performance.

[0004] Therefore, how to reduce the PAPR and out-of-band radiation of the OFDM system in a band-limited multipath channel is a problem that those skilled in the art need to solve urgently. Summary of the invention

[0005] In view of this, the present invention provides a baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of the OFDM system. In order to reduce the complexity and waste of system resources caused by reducing the out-of-band radiation and PAPR of the OFDM system, the present invention takes into account the two important parameters of out-of-band radiation (OOBE) and PAPR, and designs a joint baseband signal based on a pan-functional model. The main goal of the signal is to reduce the out-of-band radiation of the OFDM system to a certain extent, and to appropriately optimize the problem of excessive PAPR of the OFDM system. For the band-limited channel OFDM system in a multipath environment, according to the reason why the OFDM system PAPR is too large when the rectangular signal is used as the baseband signal, the data combination that causes the maximum PAPR of the OFDM system is used as a restriction condition, and the PAPR of the OFDM signal in this case is reduced to a suitable value, so as to achieve the purpose of effectively reducing the system PAPR. In view of the problem of serious out-of-band leakage caused by the rectangular signal, a pan-functional model that obeys the minimum out-of-band radiation criterion is introduced. On the basis of utilizing the characteristics of the model itself, a boundary restriction condition is added to further reduce the frequency domain out-of-band leakage of the baseband signal, and the OFDM signal formed by superposition will have lower out-of-band radiation. In addition, while ensuring that the PAPR of the OFDM system of rectangular signals does not increase significantly or remains basically the same, inter-symbol interference is artificially introduced to construct a baseband signal with faster decay, further reducing the OOBE of the OFDM system. Through simulation analysis, the baseband signal obtained using the numerical method is superior to the general OFDM system in reducing PAPR and OOBE.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system comprises the following steps:

[0008] Step 1: Through simulation analysis, obtain the data combination at the input end that causes the OFDM system PAPR to be the largest; according to the OFDM system structure, different data combinations at the input end will cause the OFDM system to generate different PAPRs, so through simulation analysis, analyze the reasons for the excessive PAPR of the signal, and summarize the data combination that causes the OFDM system PAPR to be the largest;

[0009] Step 2: Use the pan-function model to solve the baseband signal of the OFDM system; to solve the problem of serious out-of-band leakage caused by rectangular signals, introduce the pan-function model that obeys the minimum out-of-band radiation criterion;

[0010] Step 3: Add boundary constraints to the pan-function model, and add the data combination that causes the maximum PAPR of the OFDM system as a power limitation condition to the pan-function model; on the basis of utilizing the characteristics of the model itself, add boundary constraints to further reduce the frequency domain out-of-band leakage of the baseband signal, so that the OFDM signal formed by superposition will have lower out-of-band radiation; according to the reason why the OFDM system PAPR is too large when the rectangular signal is used as the baseband signal, add the data combination that causes the maximum PAPR of the OFDM system as a limitation condition to the pan-function model, and reduce the PAPR of the OFDM signal in this case to a suitable value, so as to achieve the purpose of effectively reducing the system PAPR;

[0011] Step 4: Express the baseband signal in the general function model using Fourier series, and according to the boundary constraints and the power constraints, construct the general function model as a Lagrange equation for solution to obtain the optimal baseband signal. Through general function modeling and expressing the baseband signal to be solved using Fourier series, the entire problem is summarized in the form of Lagrange equations; through numerical simulation, the Fourier series expression of the signal to be solved x(t) is obtained, and it is applied to the OFDM system to analyze the complementary cumulative distribution function (CCDF) of the system PAPR and the distribution of the energy spectrum density.

[0012] Preferably, in the OFDM system, each subcarrier is modulated as BPSK, and the input data stream rate is R b After serial-to-parallel conversion, the serial binary data stream is converted into N parallel sub-data streams, and the rate of each sub-data stream becomes R b / N; the frequency of each subcarrier is f i =iΔf, i=1,2,…,N; subcarrier spacing Δf=R b / N;

[0013] The transmitter signal s(t) is expressed as:

[0014]

[0015] Among them, d k,i is the BPSK data symbol on the i-th subcarrier of the k-th OFDM signal; x(t) is the baseband signal;

[0016] The PAPR of the OFDM system is:

[0017]

[0018] where |s(t)| 2 is the square of the modulus of the signal at the transmitting end of the OFDM system, and E{.} is the mean operator;

[0019] The functional model is expressed as:

[0020]

[0021] in, I(ω) represents the Fourier transform of the baseband signal x(t); h(ω) = ω 2n ,n is a positive integer, n=1,2,…; |I(ω)| 2 is the energy spectral density of x(t);

[0022] The spectral density function of the baseband signal x(t) is expressed as:

[0023]

[0024]

[0025] Where [-T,T] is the range of x(t) under the signal; T is the set constant;

[0026] Substituting formula (5) into formula (3), we get:

[0027]

[0028] The function h(ω) is expressed as:

[0029]

[0030] Substituting formula (7) into formula (6), we get:

[0031]

[0032] Preferably, in step 4, the Taylor series expansion is applied to the following form:

[0033]

[0034] The inverse Fourier transform gives the following form:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] Wherein, (2n) represents the 2n-order derivative of the baseband signal x(t); from equation (4), we can take the baseband signal x(t) as a variable and solve for the minimum G; j represents a complex number, n = 1, 2, ...;

[0043] If the baseband signal x(t) is set as an even function, there are only even-order harmonic components in the Fourier series, and the baseband signal x(t) is expressed as follows:

[0044]

[0045] in, is the coefficient in the Fourier series, and m takes values ​​up to 6.

[0046] Preferably, in step 3, the baseband signal x(t) replaces the position of the rectangular signal in the OFDM system, and the baseband signal x(t) is set to unit energy

[0047] Set the boundary constraints as: x(t)| t＝±T =x'(t)| t＝±T =…=x (n-1 )(t)| t＝±T =0.

[0048] Preferably, all constraints and functional models are expressed as Lagrange equations:

[0049]

[0050] where γ is the Lagrange coefficient.

[0051] Preferably, under the condition of a band-limited channel, the restriction conditions for the data combination that causes the maximum PAPR in the full response OFDM system include:

[0052] When the BPSK symbol mappings are all the same:

[0053]

[0054] When BPSK symbol mapping +1 and -1 alternately:

[0055]

[0056] Where Z1 and Z2 are constants; Δf is the subcarrier spacing;

[0057] In the universal function model, the boundary condition is set to 0. When the BPSK symbol mapping is +1 and -1 alternating, the peak value becomes 0, and the restriction condition (20) is omitted. When the BPSK symbol mapping is all the same, the maximum PAPR actually occurs at time t = 0, so (19) is simplified to:

[0058] x(0)=X1(21)

[0059] Where X1 is the value of the signal x(t) at time 0, and the complementary cumulative distribution function of the PAPR under the same BPSK symbol mapping is affected by adjusting X1;

[0060] The whole problem can be summarized as:

[0061]

[0062] Therefore, according to formula (18), the Lagrange equation is obtained:

[0063]

[0064] Where γ and ρ are Lagrange coefficients respectively;

[0065] The solution is obtained according to the Lagrange solution rule, which is:

[0066]

[0067] Preferably, under the condition of a band-limited channel, the length of the baseband signal in the partial response OFDM system is twice the length of the baseband signal in the full response OFDM system, wherein the kth OFDM signal is expressed as:

[0068]

[0069] Due to the introduction of inter-symbol interference, the kth OFDM signal contains the second half of the (k-1)th signal and the first half of the (k+1)th signal:

[0070]

[0071]

[0072] Among them, d k-1,n is the data symbol on the nth subcarrier of the kth OFDM signal; u(t) is a unit step function;

[0073] The baseband signal x(t) is expressed as follows:

[0074]

[0075] The constraints on data combinations that maximize PAPR in a partial response OFDM system include:

[0076] When the BPSK symbol mappings are all the same:

[0077]

[0078] When BPSK symbol mapping +1 and -1 alternately:

[0079]

[0080] Where Z1 and Z2 are constants;

[0081] In the universal function model, the boundary condition is set to 0. When the BPSK symbol mapping is +1 and -1 alternating, the peak value becomes 0, and the restriction condition (20) is omitted. When the BPSK symbol mapping is all the same, the maximum PAPR actually occurs at time t = 0, so (19) is simplified to: x(0) = X2, where X2 is the value of the signal x(t) at time 0, and X2 is a constant.

[0082] The whole problem can be summarized as:

[0083]

[0084] According to (18), we get the Lagrange equation:

[0085]

[0086] where γ and ρ are Lagrangian systems;

[0087] The length of the baseband signal x(t) is twice the length of the baseband signal of the full response OFDM system. The Lagrange solution rule is used to obtain the Fourier series coefficients a0 and a k , the Lagrange solution rule is:

[0088]

[0089] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of the OFDM system. The present invention is aimed at the full response OFDM system, and jointly designs an optimized baseband signal that effectively reduces the system PAPR and out-of-band radiation. At the same time, for the partial response BPSK-OFDM system, a 2-fold longer optimized baseband signal is designed and applied to the OFDM system. The optimized baseband signal can not only reduce the PAPR of the system, but also more effectively reduce the out-of-band radiation of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0091] Figure 1 The accompanying drawing is a schematic diagram of a design optimization baseband signal rectification process provided by the present invention;

[0092] Figure 2 The accompanying drawing is a schematic diagram of an OFDM system transmitter provided by the present invention;

[0093] Figure 3 The accompanying drawing is a schematic diagram of an OFDM system receiving end provided by the present invention;

[0094] Figure 4 The accompanying drawings are schematic diagrams of time domain diagrams of four optimized signals and two commonly used signals of a full-response OFDM system provided by the present invention;

[0095] Figure 5 The accompanying drawings are CCDF schematic diagrams of 6 signals and a rectangular signal applied to the PAPR of a full-response OFDM system provided by the present invention;

[0096] Figure 6 The accompanying drawing is a schematic diagram of energy spectrum density of six signals and a rectangular signal as baseband signals in a full-response OFDM system provided by the present invention;

[0097] Figure 7 The accompanying drawing is a schematic diagram of energy spectrum density of six signals and a rectangular signal provided by the present invention applied to a full-response OFDM system;

[0098] Figure 8 The accompanying drawings are schematic diagrams of the time domain structures of four optimized signals and two commonly used signals of the partial response OFDM system provided by the present invention;

[0099] Fig. 9 The accompanying drawing is a CCDF schematic diagram of six signals and a rectangular signal provided by the present invention applied to a partial response OFDM system PAPR;

[0100] Fig.10 The accompanying drawing is a schematic diagram of energy spectrum density of six signals and a rectangular signal as baseband signals in a partial response OFDM system provided by the present invention;

[0101] Fig.11 The accompanying drawing is a schematic diagram of energy spectrum density of six signals and a rectangular signal provided by the present invention applied to a partial response OFDM system. DETAILED DESCRIPTION

[0102] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0103] The embodiment of the invention discloses a baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system.

[0104] like Figure 2-3 This is a schematic diagram of an OFDM system. In an OFDM system, each subcarrier is modulated as BPSK, and the input data stream rate is R b After serial-to-parallel conversion, the serial binary data stream is converted into N parallel sub-data streams, and the rate of each sub-data stream becomes R b / N; the frequency of each subcarrier is f i =iΔf, i=1,2,…,N; subcarrier spacing Δf=R b / N.

[0105] The transmitter signal s(t) can be expressed as:

[0106]

[0107] where d k,i is the BPSK data symbol on the i-th subcarrier of the k-th OFDM signal; x(t) is the baseband signal waveform (target signal), and the traditional x(t) is a rectangular signal;

[0108] The PAPR of a BPSK-OFDM system is defined as:

[0109]

[0110] In an OFDM system with N subcarriers, the signal has maximum power when all N subcarriers are added with the same phase. Therefore, there are two cases where the BPSK data combination with maximum power should be: one is when all data symbols are the same, and the other is when the BPSK data symbols appear in the form of alternating +1 and -1; when the baseband signal is added with -T s / 2≤t≤T s / 2 (where T s is the time domain length of the OFDM signal). When all data symbols are identical, the maximum power occurs at t = 0; when they alternate between +1 and -1, the maximum power occurs at t = ±T s / 2. The commonly used baseband signal (such as cosine signal) is at t = ±T sThe value at the moment of / 2 is usually 0. Therefore, when designing the baseband signal, the main problem is the design of the baseband signal at the moment t=0 when all data symbols are the same. In addition, when N increases, the possibility of the signal appearing at the maximum power decreases. Therefore, the baseband signal design under the condition of less subcarriers in the band-limited channel is designed, and the CCDF of PAPR and system OOBE are suppressed only for the two forms of data symbols being all the same and data symbols appearing alternately as +1 and -1.

[0111] Optimizing baseband signal design under the pan-functional model:

[0112]

[0113] in I(ω) represents the Fourier transform of the target signal x(t); h(ω) = ω 2n ,n=1,2,…, h(ω) is chosen to be in this form in order to make |I(ω)| 2 It has a controllable decay rate, because when G converges in the above formula, |I(ω)| 2 The decay rate must be faster than the rise rate of h(ω), and |I(ω)| 2 is the energy spectrum density of x(t). The obtained x(t) will have an energy spectrum density that is both controllable and rapidly decaying, which is beneficial for the system to effectively reduce OOBE.

[0114] Derivation process:

[0115] The spectral density function of the target signal x(t) is expressed as:

[0116]

[0117]

[0118] Substituting formula (5) into formula (3), we get:

[0119]

[0120] The function h(ω) is expressed as follows:

[0121]

[0122] Substituting formula (7) into formula (6), we get:

[0123]

[0124] Apply the Taylor series expansion to the following form:

[0125]

[0126] The inverse Fourier transform gives the following form:

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] Where (2n) represents the 2n-order derivative of x(t). From formula (4), it can be found that the entire solution is simplified to solving the minimum G with the target signal x(t) as the variable.

[0135] One of the main purposes of using this functional model is to express the target signal x(t) to be solved in the form of Fourier series, and set x(t) to be an even function, that is, there are only even harmonic components in the Fourier series. Therefore, x(t) is expressed as follows:

[0136]

[0137] in It is the coefficient in the Fourier series. Usually, m is set to 6 to ensure a high approximation of the target signal x(t).

[0138] The target signal x(t) needs to replace the rectangular signal in the OFDM system. Therefore, it needs to be energy-limited. Here, it is set to unit energy, that is: In addition, in order to make the target signal x(t) have a faster frequency domain roll-off speed, the boundary constraint condition is set: x(t)| t＝±T =x'(t)| t＝±T =…=x (n-1 )(t)| t＝±T =0;

[0139] All the above constraints and functional models are then expressed as Lagrange equations:

[0140]

[0141] Fully responsive OFDM system optimized waveform design:

[0142] According to the analysis of the PAPR of the OFDM system, a very important factor causing the PAPR to be too large is that when the in-phase signals are superimposed, a large peak power will appear. From formula (2), it can be seen that the size of the peak will seriously affect the CCDF of the PAPR; therefore, according to the simulation results, the purpose of the bit data arrangement that causes the OFDM system to have a large peak is found, and the peaks in these cases are constrained to a relatively suitable value in the form of restriction conditions to achieve the purpose of affecting the overall CCDF of the system. Because when the number of subcarriers increases, the arrangement and combination of bit data will also become very complicated. Therefore, only under the condition of a band-limited channel (i.e., a narrow channel and fewer subcarriers), the OFDM full response system is optimized for waveform design. Specifically, when there are 8 subcarriers, the baseband signal joint design is used to reduce the PAPR and out-of-band radiation of the OFDM system.

[0143] In a rectangular signal OFDM system with N subcarriers, the signal has maximum power when all N subcarriers are added with the same phase. Maximum power will occur when the BPSK symbol mapping is all the same or alternates between +1 and -1. For an 8-subcarrier system, the probability of maximum power is 2 2 / 2 8 Generally speaking, as the number of subcarriers increases, the peak limiting capability gradually weakens.

[0144] From formula (2), we can see that when the average energy remains basically unchanged, the peak value will be the decisive factor affecting the CCDF of the system PAPR. Taking the PAPR of several combinations as the limiting condition, it is sorted as follows:

[0145] When the BPSK symbol mappings are all the same:

[0146]

[0147] When BPSK symbol mapping +1 and -1 alternately:

[0148]

[0149] Where Z1 and Z2 are constants and Δf is the subcarrier spacing.

[0150] Because the boundary conditions in the referenced functional model are set to 0, it can be inferred that when the BPSK symbol mapping is alternating between +1 and -1, the peak value will become 0, so the constraint (20) can be omitted. In addition, through simulation analysis, when the BPSK symbol mapping is all the same, the maximum power actually occurs at t = 0, so (19) can be simplified to:

[0151] x(0)=X1(21)

[0152] Wherein, X1 is the value of the signal x(t) at time 0, so the CCDF of the PAPR under the same BPSK symbol mapping can be affected by adjusting X1.

[0153] The whole problem can be summarized as:

[0154]

[0155] Therefore, according to the functional model (18), the Lagrange equation is obtained:

[0156]

[0157] And then according to Lagrange's solution rule, we can solve it:

[0158]

[0159] Optimized waveform design for partial response OFDM system:

[0160] In the communication system, in order to improve the utilization of the frequency band and reduce the out-of-band radiation of the system, the partial response method is used to utilize the corresponding nature relationship between the time domain and the frequency domain in the Fourier transform, that is, the time domain signal is extended and the corresponding frequency domain signal is compressed. Therefore, the time domain signal can be appropriately extended to compress the frequency domain signal. In partial response, a major problem is that it is considered to introduce inter-code interference. The usual solution to this problem is usually "with coding-related coding-modulo 2 decision".

[0161] The main purpose of using a partial response OFDM system is to further accelerate the frequency domain attenuation of the baseband signal and reduce the out-of-band radiation of the system while ensuring that the CCDF of the PAPR remains basically unchanged or slightly better than that of the rectangular OFDM system. Here, only a baseband signal with a length twice that of the baseband signal of the full response OFDM system is designed.

[0162] Assume that the kth OFDM signal is expressed as:

[0163]

[0164] Due to the artificial introduction of inter-symbol interference, the kth OFDM signal should contain the second half of the (k-1)th signal and the first half of the (k+1)th signal.

[0165]

[0166] Among them, d k-1,n represents the kth OFDM signal, the data symbol on the nth subcarrier; u(t) represents the unit step function.

[0167] Therefore, the kth OFDM signal at this time will have a significant impact on its own energy distribution due to the superposition of the previous and next signals. The CCDF of the PAPR will also be different from that of the full-response OFDM system. It is still assumed that at t = 0, the baseband signal has a maximum value, and the BPSK symbol mapping combination with the maximum peak power of the [-T, T] length signal is still used as a constraint to design the baseband signal of [-2T, 2T] length.

[0168] For the target signal x(t) of length [-2T, 2T], it is expressed as follows:

[0169]

[0170] When BPSK symbol mapping is used, the probability of a large peak power is higher when all symbols are the same or +1 and -1 alternate. Therefore, the boundary value of the target signal x(t) and the value at t=0 are still restricted. x(t)| t＝±2T =x'(t)| t＝±2T =…=x (n-1) (t)| t＝±2T =0 is the boundary constraint; the other constraint is still x(0)=X2, where X2 is a constant.

[0171] The whole problem can be summarized as:

[0172]

[0173] In this way, (18) can be transformed into the following Lagrange equation:

[0174]

[0175] It should be noted that the length of the target signal x(t) here is twice the length of the full response. Similarly, all the Fourier series coefficients a0 and a1 can be obtained according to equation (24): k .

[0176] Example

[0177] 1) Full response OFDM system PAPR and OOBE simulation analysis:

[0178] Set n to 3 and 5 respectively, m=6, and set a suitable value of x(0) to obtain the expression of the Fourier series of the baseband signal x(t).

[0179] The expressions when n is 3, m is 6, and x(0) is 0.6 and 0.4 respectively:

[0180]

[0181]

[0182] The expressions when n is 5, m is 6, and x(0) is 0.6 and 0.4 respectively:

[0183]

[0184]

[0185] In addition, several commonly used time domain signals are introduced, such as cosine signal, Hanning signal, etc., and their expressions are as follows:

[0186]

[0187]

[0188] Only the OFDM system with 8 subcarriers under the band-limited channel is simulated, where the subcarrier spacing is set to 1 KHz. Figure 4 It is the time domain diagram of the four optimized signals expressed by equations (30)-(33) and the two common signals (34) and (35); Figure 5 The CCDF of the above six signals and rectangular signal applied to the PAPR of OFDM system; Figure 6 is the energy spectrum density of the above six signals and the rectangular signal as baseband signals.

[0189] In addition, in order to obtain the OOBE of the OFDM system, the energy spectrum expression of the OFDM signal is derived. According to (1) and Fourier transform, we can get:

[0190]

[0191] where X(f) is the Fourier transform of the time domain signal.

[0192] Figure 7 This is the energy spectrum density of the above six signals and rectangular signals applied to the OFDM system.

[0193] 2) Partial response OFDM system PAPR and OOBE simulation analysis:

[0194] Set n to 3 and 5 respectively, m = 6, and set a suitable value of x(0) to obtain the expression of the Fourier series of the signal x(t).

[0195] The expression when n is 3, m is 6, and x(0) is 0.95 and 0.9 respectively:

[0196]

[0197]

[0198] The expression when n is 5, m is 6, and x(0) is 0.9 and 1 respectively:

[0199]

[0200]

[0201] Only the OFDM system with 8 subcarriers under the band-limited channel is simulated, where the subcarrier spacing is set to 0.5KHz. Figure 8 It is the time domain diagram of the four optimized signals (37)-(40) and the two commonly used signals (34) and (35); Fig. 9 The CCDF of the above six signals and rectangular signal applied to the PAPR of OFDM system; Fig.10 is the energy spectrum density of the above six signals and the rectangular signal as baseband signals. Fig.11 This is the energy spectrum density of the above six signals and rectangular signals applied to the OFDM system.

[0202] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0203] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system, characterized in that: The following steps are involved: Step 1: Through simulation analysis, obtain the data combination at the input end that causes the maximum PAPR of the OFDM system; Step 2: Use the universal function model to solve the baseband signal of the OFDM system; Step 3: adding boundary constraints to the pan-functional model, and adding the data combination that causes the maximum PAPR of the OFDM system as a power constraint to the pan-functional model; Step 4: Expressing the baseband signal in the universal function model using Fourier series, and constructing the universal function model as a Lagrange equation to solve it according to the boundary constraint condition and the power constraint condition to obtain an optimal baseband signal; In the OFDM system, each subcarrier is modulated as BPSK, and the input data stream rate is R b After serial-to-parallel conversion, the serial binary data stream is converted into N parallel sub-data streams, and the rate of each sub-data stream becomes R b / N; the frequency of each subcarrier is f i =iΔf, i=1,2,…,N; subcarrier spacing Δf=R b / N; The transmitter signal s(t) is expressed as: Among them, d k,i is the BPSK data symbol on the i-th subcarrier of the k-th OFDM signal; x(t) is the baseband signal; The PAPR of the OFDM system is: where |s(t)| 2 is the square of the modulus of the signal at the transmitting end of the OFDM system, and E{.} is the mean operator; The functional model is: in, I(ω) represents the Fourier transform of the baseband signal x(t); h(ω) = ω 2n ,n=1,2,…;|I(ω)| 2 is the energy spectral density of x(t); The spectral density function of the baseband signal x(t) is expressed as: Where [-T,T] is the range of the signal x(t); Substituting formula (5) into formula (3), we get: The function h(ω) is expressed as: Substituting formula (7) into formula (6), we get:

2. The baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system according to claim 1, characterized in that: In step 4, the Taylor series expansion is applied to the following form: The inverse Fourier transform gives the following form: Where (2n) represents the 2n-order derivative of the baseband signal x(t); taking the baseband signal x(t) as a variable, solving for the minimum G; If the baseband signal x(t) is set as an even function, there are only even-order harmonic components in the Fourier series, and the baseband signal x(t) is expressed as follows: in, is the coefficient in the Fourier series, and m takes values ​​up to 6.

3. The baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system according to claim 2, characterized in that: In step 3, the baseband signal x(t) replaces the position of the rectangular signal in the OFDM system, and the baseband signal x(t) is set to unit energy in the pan-functional model Set the boundary constraints as: x(t)| t＝±T =x'(t)| t＝±T =…=x (n-1) (t)| t＝±T =0.

4. The baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system according to claim 3, characterized in that: All constraints and functional models are expressed as Lagrange equations: Where γ is the Lagrange coefficient; G represents the functional model; is the coefficient in the Fourier series; E represents the unit energy of the baseband signal x(t), [-T,T] is the range of the signal x(t); m takes values ​​up to 6.

5. The baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system according to claim 3, characterized in that: Under band-limited channel conditions, the constraints on data combinations that result in maximum PAPR in a full-response OFDM system include: When the BPSK symbol mappings are all the same: When BPSK symbol mapping +1 and -1 alternately: Where Z1 and Z2 are constants; Δf is the subcarrier spacing; In the universal function model, the boundary condition is set to 0. When the BPSK symbol mapping is +1 and -1 alternating, the peak value becomes 0, and the restriction condition (20) is omitted. When the BPSK symbol mapping is all the same, the maximum PAPR actually occurs at time t = 0, so (19) is simplified to: x(0)=X1(21) Where X1 is the value of the signal x(t) at time 0, and the complementary cumulative distribution function of the PAPR under the same BPSK symbol mapping is affected by adjusting X1; The whole problem solving can be summarized as: Therefore, according to formula (18), the Lagrange equation is obtained: Where γ and ρ are Lagrange coefficients respectively; The solution is obtained according to the Lagrange solution rule, which is:

6. The baseband signal joint calculation method for reducing the PAPR and out-of-band radiation of an OFDM system according to claim 3, characterized in that: Under the condition of band-limited channel, the baseband signal length of the partial response OFDM system is twice that of the full response OFDM system, where the kth OFDM signal is expressed as: Due to the introduction of inter-symbol interference, the kth OFDM signal contains the second half of the (k-1)th signal and the first half of the (k+1)th signal: Among them, d k-1,n is the data symbol on the nth subcarrier of the kth OFDM signal; u(t) is a unit step function; The baseband signal x(t) is expressed as follows: The constraints on data combinations that maximize PAPR in a partial response OFDM system include: When the BPSK symbol mappings are all the same: When BPSK symbol mapping +1 and -1 alternately: Where Z1 and Z2 are constants; In the universal function model, the boundary condition is set to 0. When the BPSK symbol mapping is +1 and -1 alternating, the peak value becomes 0, and the restriction condition (20) is omitted. When the BPSK symbol mapping is all the same, the maximum PAPR actually occurs at time t = 0, so (19) is simplified to: x(0) = X2, where X2 is the value of the signal x(t) at time 0, and X2 is a constant. The whole problem solving can be summarized as: According to (18), we get the Lagrange equation: where γ and ρ are Lagrangian systems; The length of the baseband signal x(t) is twice the length of the baseband signal of the full response OFDM system. The Lagrange solution rule is used to obtain the Fourier series coefficients a0 and a k , the Lagrange solution rule is:

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