Receiver digital baseband signal preprocessing method

Abstract

The invention discloses a preprocessing method for a digital baseband signal of a receiver, which comprises the following steps of: quantifying the sparse degree of the signal by selecting a proper sparsity measurement index, constructing an optimization problem based on the selected sparsity measurement index, and then minimizing the sparsity index of the signal in a transform domain, namely searching a group of compensation parameters. The sparsity of the compensated signal in the transform domain is restored to the level close to that of the original signal, and then the established optimization problem is solved by using a numerical optimization algorithm to find the optimal compensation parameter. According to the method, the sparsity of the signal can be effectively recovered, so that the nonlinear distortion at the front end of the receiver is compensated, and the signal quality and the system performance are improved.

Description

Technical Field

[0001] The invention relates to the technical field of satellite navigation, in particular to a preprocessing method for digital baseband signals of a receiver. Background Art

[0002] The Global Satellite Navigation System (GNSS) is an air-based radio navigation and positioning system that can provide users with all-weather three-dimensional coordinates, speed and time information at any location on the Earth's surface or in near-Earth space. It includes one or more satellite constellations and their augmentation systems required to support specific tasks. The four major satellite navigation system suppliers announced by the International Committee on Global Navigation Satellite Systems include the United States' Global Positioning System GPS, Russia's GLONASS, the European Union's Galileo Satellite Navigation System (GALILEO) and China's BeiDou Satellite Navigation System (BDS).

[0003] China's BeiDou-3 global satellite navigation system (hereinafter referred to as BeiDou-3 system) consists of 24 medium earth orbit satellites (MEO), 3 geostationary orbit satellites (GEO) and 3 inclined geosynchronous orbit satellites (IGSO), a total of 30 satellites. BeiDou-3 system broadcasts a new frequency signal B1C on MEO satellites and IGSO satellites. The B1C signal uses binary offset carrier (BOC, Binary Offset Carrier) modulation technology and is divided into a data transmission component and a pilot component. Because there is no modulation broadcast ephemeris on the pilot component, long-term coherent integration can be performed, thereby improving the sensitivity of the receiver. At the same time, the pilot component uses a layered code structure, so it has good cross-correlation characteristics. The above characteristics of the B1C signal have a significant impact on the improvement of the receiver's positioning performance and anti-interference performance.

[0004] A digital signal is a signal that represents information in the form of discrete numerical values. It encodes and transmits information through a series of discrete numerical values ​​or symbols, which are usually binary 0 and 1. Digital signals are different from analog signals, which change continuously. In modern communication and electronic systems, digital signals dominate. They have many advantages, including strong anti-interference ability, easy storage and processing, lossless reproduction, and the ability to use error detection and correction technology. Digital signals are widely used in computers, mobile communications, digital television, audio and video processing, etc. Digital signal processing techniques, such as sampling, quantization, encoding and compression, enable complex information to be transmitted and stored in an efficient and reliable manner. With the development of technology, digital signal processing has become the basis of modern electronic and communication systems, promoting the rapid development of the information age.

[0005] Compared with Beidou B1I signal, Beidou B1C signal consists of data transmission component and pilot component, which are modulated by different subcarrier forms. The data transmission component contains telegram and pseudo code, the pseudo code main code length is 10230, the main code period is 10ms, and the B1C pilot component contains not only the pseudo code main code, but also subcode, the subcode length is 1800, and the subcode period is 18000ms. The traditional fast capture algorithm is divided into Doppler frequency parallel algorithm and pseudo code phase parallel algorithm. Since the pseudo code main code length on B1C data transmission or pilot component is 10 times that of the pseudo code on B1I signal, if the traditional fast capture algorithm is used, the average capture time of B1C signal will be 10 times that of B1I signal. In the navigation and positioning of aircraft, UAV, guidance head and other high dynamic scenes, the longer capture time will reduce the capture probability of the signal because of the rapid change of navigation signal characteristics caused by dynamics, which is not conducive to the use of B1C signal in such scenes. Therefore, in order to ensure the reliable use of B1C signals in high-dynamic scenarios and give full play to their high positioning accuracy and strong anti-interference ability, it is necessary to first solve the problem of reliable capture of the signal. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a preprocessing method for a digital baseband signal of a receiver, which can effectively restore the sparsity of the signal, thereby compensating for the nonlinear distortion of the front end of the receiver and improving the signal quality and system performance.

[0007] The technical solution of the present invention is:

[0008] A method for preprocessing a digital baseband signal of a receiver specifically comprises the following steps:

[0009] (1) Analyze the nonlinear distortion of the receiver front end, build a nonlinear distortion model of the concurrent dual-frequency receiver, bring the two-way input signal model of the concurrent dual-frequency receiver into the nonlinear distortion model, derive the distortion signal components at the corresponding frequencies, build the equivalent baseband expressions of the two-way input signals, and further derive the representation of the nonlinearly distorted signal in the baseband, thereby building a compensation model;

[0010] (2) Use discrete cosine transform to convert the time domain signal received by the receiver into the frequency domain, adopt L1 norm as the sparsity measurement index, use sequential quadratic programming to solve the optimization problem, and then obtain the optimal compensation parameters. The optimal compensation parameters are applied to the compensation model, and the actual received signal is processed to achieve compensation for the nonlinear distortion of the receiver front end.

[0011] The specific steps of analyzing the nonlinear distortion of the front end of the receiver and constructing the nonlinear distortion model of the concurrent dual-frequency receiver are as follows: defining the nonlinear distortion model of the front end of the receiver, as shown in the following formula (1):

[0012]

[0013] In formula (1), since the nonlinear distortion generated by even orders is far away from the signal frequency, it will be filtered out by the filter, so the even orders are ignored. represents the input signal, represents the output signal, ~ represents that the input signal is a radio frequency signal; a1, a3, a5 are the parameters of the nonlinear distortion model.

[0014] The two-way input signal model of the concurrent dual-frequency receiver is specifically shown in the following equations (2) and (3):

[0015]

[0016] In formula (2) and formula (3), They are the two input signals of the concurrent dual-frequency receiver, A L (t), A H (t) are the amplitudes of the two input signals, ω L ,ω H are the frequencies of the two input signals, φ L (t),φ H (t) are the initial phases of the two input signals respectively, and t represents the time t.

[0017] The specific steps of bringing the two-way input signal model of the concurrent dual-frequency receiver into the nonlinear distortion model to derive the distortion signal components at the corresponding frequencies are as follows:

[0018] Substituting equation (2) and equation (3) into equation (1), we can obtain the two input signals at ω L With ω H The distorted signal components at , see the following equations (4) and (5) for details:

[0019]

[0020]

[0021] In formula (4), and In formula (5) and represents the intermodulation component produced by the third-order nonlinear distortion; in formula (4) and In formula (5) and Both represent the intermodulation products produced by fifth-order nonlinear distortion.

[0022] The specific steps of constructing the equivalent baseband expressions of the two input signals, further deriving the representation of the nonlinearly distorted signals in the baseband, and thus constructing the compensation model are as follows:

[0023] The equivalent baseband expressions of the two input signals are shown in equations (6) and (7):

[0024] x L (t) = A L (t)exp(jφ L (t)) (6);

[0025] x H (t) = a H (t)exp(jφ H (t)) (7);

[0026] In formula (6) and formula (7), j is an imaginary unit;

[0027] in and x L (t), and x H The relationship between (t) is shown in the following equations (8) and (9):

[0028]

[0029] Substituting the above formula (8) into formula (4), and formula (9) into formula (5), we can obtain the following formulas (10) and (11):

[0030]

[0031] a in formula (10) and formula (11) ′ 1.a ′ 3.a ′ 5 is obtained by baseband conversion of a1, a3, and a5. ′ 1 represents the first-order nonlinear coefficient in the nonlinear distortion model, which reflects the amplification or attenuation of the signal itself; a ′ 3 represents the third-order nonlinear coefficient in the nonlinear distortion model, which reflects the degree of third-order intermodulation distortion; a ′ 5 represents the fifth-order nonlinear coefficient in the nonlinear distortion model, reflecting the degree of fifth-order intermodulation distortion;

[0032] Simplifying equation (10) and equation (11), we get equation (12) and equation (13):

[0033] y L (t) = F L (x L (t),x H (t)) (12);

[0034] y H (t) = F H (x L (t),x H (t)) (13);

[0035] The constructed compensation model is shown in the following formula (14):

[0036]

[0037] In formula (14), c q ′ ,r is the parameter to be solved of the compensation model, q represents the highest nonlinear order of the compensation model, Q represents the total number of nonlinear terms in the compensation model, and r represents the parameter vector to be solved in the compensation model.

[0038] The specific steps of using discrete cosine transform to convert the time domain signal received by the receiver into the frequency domain, using L1 norm as a sparsity measurement indicator, using sequential quadratic programming to solve the optimization problem, and then obtaining the optimal compensation parameters are as follows:

[0039] S21. Construct the compensation model in the form of a matrix, as shown in the following formula (15):

[0040] S L =Y T C(15):

[0041] in,

[0042]

[0043] N represents the Nth item, C is the parameter vector to be solved for the compensation model; C T =[c 1,0 ,c 3,0 ,v 3,2 ,v 5,0 ,c 5,2 ,c 5,4 ,…,c Q,Q-3 ,c Q,Q-1 ], Q represents the total number of nonlinear terms in the compensation model;

[0044] S32. Use discrete cosine transform to transform the signal from the time domain to the frequency domain, as shown in the following formula (16):

[0045] ΦS L =ΦY T C (16);

[0046] In formula (16), Φ is the discrete cosine transform matrix;

[0047] S33, using L1 norm as a sparsity measurement index, using sequential quadratic programming to solve the optimization problem, the function of the optimization problem is specifically as follows (17):

[0048]

[0049] In formula (17), is the L1 norm, and the equality constraint st is to prevent the occurrence of c i =0;

[0050] S34, define the original signal as s, then the global mapping is shown in the following formula (18):

[0051] y i =βs+γh(s) (18);

[0052] In equation (18), βs is the linear term of the compensation signal, and γh(s) is the nonlinear term. The nonlinear distortion of the receiver front end is defined as The nonlinear model of digital post-compensation is: The right side obtains the following formula (19):

[0053]

[0054] The frequency domain parameters of the compensated output signal y are as follows (20):

[0055] y c =Φy (20);

[0056] In formula (20), Φ is the discrete cosine transform matrix;

[0057] Substituting formula (20) into formula (18), we get the following formula (21):

[0058] y c =Φ(βs+γh(s))=βs c +γΦh(s) (21);

[0059] In formula (21), s c =Φs, which represents the frequency domain representation of the original signal;

[0060] S35. Measure the sparsity according to the L1 norm, which specifically satisfies the following formula (22):

[0061] ||x+y||0≤||x||0+||y||0 (22);

[0062] Derived from formula (22) The following formula (23) is derived from the following formula (23): The following formula (24) is obtained:

[0063]

[0064] ||xy||0≥|||x||0-||y||0| (24);

[0065] Definition: ||βs||0=||s||0;

[0066] According to formula (24), it can be deduced from formula (21) The following formula (25) is obtained:

[0067] ||y c ||0=||βs c +γΦh(s)||0=||βs c -(-γΦh(s))||0

[0068] ≥|||βs c ||0-||-γΦh(s)||0|

[0069] =|||s c ||0-||γΦh(s)||0|

[0070] Definition||s c ||0=K、||γΦh(s)||0=L; then we get ||y c ||0≥|KL|;

[0071] When γ=0, we get: ||y c ||0=||s c ||0;

[0072] When γ≠0, we get ||γΦh(s)||0=||Φh(s)||0=L;

[0073] From this, we can see that the definition of nonlinear distortion causes the input signal to be more than twice as sparse in frequency as the original signal; when the digital post-compensation algorithm achieves perfect compensation, the sparsity after compensation is equal to the sparsity of the original signal; when it is not perfect compensation, the sparsity after compensation is greater than the sparsity of the original signal.

[0074] Advantages of the present invention:

[0075] The core principle of the present invention is that most actual signals are sparsely distributed in the transform domain (such as the frequency domain), that is, most of the transform coefficients are close to zero, and only a few coefficients carry the main information. When the signal passes through the nonlinear components of the receiver front end, the nonlinear distortion will generate new frequency components, and these newly generated components destroy the original sparsity of the signal. Therefore, the nonlinear distortion can be compensated by restoring the sparsity of the signal, thereby restoring the original signal.

[0076] The present invention quantifies the sparsity of the signal by selecting a suitable sparsity measurement indicator, and then constructs an optimization problem based on the selected sparsity measurement indicator, and then minimizes the sparsity indicator of the signal in the transform domain, that is, finds a set of compensation parameters so that the sparsity of the compensated signal in the transform domain is restored to a level close to that of the original signal, and then uses a numerical optimization algorithm to solve the optimization problem established above to find the optimal compensation parameters.

[0077] The present invention can realize compensation of nonlinear distortion without relying on the original signal information at the transmitting end, has strong applicability and flexibility, and has high algorithm calculation efficiency. Compared with the traditional method based on out-of-band distortion components, the method based on sparsity is more efficient in calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 This is an architectural diagram of a concurrent dual-frequency receiver.

[0079] Figure 2 It is a block diagram of the compensation model of the present invention. DETAILED DESCRIPTION

[0080] 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.

[0081] See Figure 1 , the architecture diagram of the concurrent dual-frequency receiver, in which the center frequencies of the two input signals are ω1 and ω2 respectively. After arriving at the front end of the receiver at the same time, they pass through the same LNA (low noise amplifier), and then go through their respective processing links (bandpass filter BPF, low-pass filter LPF, analog-to-digital converter ADC) to obtain the digital baseband signal, but the digital baseband signal at this time contains nonlinear distortion.

[0082] A method for preprocessing a digital baseband signal of a receiver specifically comprises the following steps:

[0083] (1) Analyze the nonlinear distortion of the receiver front end, build a nonlinear distortion model of the concurrent dual-frequency receiver, bring the two-way input signal model of the concurrent dual-frequency receiver into the nonlinear distortion model, derive the distortion signal components at the corresponding frequencies, build an equivalent baseband expression of the two-way input signal, further derive the representation of the signal after nonlinear distortion in the baseband, and thus build a compensation model. The specific steps include:

[0084] S11. Define the nonlinear distortion model of the receiver front end, as shown in the following formula (1):

[0085]

[0086] In formula (1), since the nonlinear distortion generated by even orders is far away from the signal frequency, it will be filtered out by the filter, so the even orders are ignored. represents the input signal, represents the output signal, ~ represents that the input signal is a radio frequency signal; a1, a3, a5 are the parameters of the nonlinear distortion model;

[0087] S12. Define the two-way input signal model of the concurrent dual-frequency receiver, as shown in the following equations (2) and (3):

[0088]

[0089] In formula (2) and formula (3), They are the two input signals of the concurrent dual-frequency receiver, A L (t), a H (t) are the amplitudes of the two input signals, ω L ,ω H are the frequencies of the two input signals, φ L (t),φ H (t) are the initial phases of the two input signals, and t represents time t;

[0090] S13, Substitute equation (2) and equation (3) into equation (1), and we get the two input signals in ω L With ω H The distorted signal components at , see the following equations (4) and (5) for details:

[0091]

[0092] In formula (4), and In formula (5) and represents the intermodulation component produced by the third-order nonlinear distortion; in formula (4) and In formula (5) and All represent intermodulation products produced by fifth-order nonlinear distortion;

[0093] S14, the equivalent baseband expressions of the two input signals are shown in the following equations (6) and (7):

[0094] x L (t) = A L (t)exp(jφ L (t)) (6);

[0095] x H (t) = A H (t)exp(jφ H (t)) (7);

[0096] In formula (6) and formula (7), j is an imaginary unit;

[0097] in and x L (t), and x H The relationship between (t) is shown in the following equations (8) and (9):

[0098]

[0099] Substituting the above formula (8) into formula (4), and formula (9) into formula (5), we can obtain the following formulas (10) and (11):

[0100]

[0101] a in formula (10) and formula (11) ′ 1.a ′ 3.a ′ 5 is obtained by baseband conversion of a1, a3, and a5. ′ 1 represents the first-order nonlinear coefficient in the nonlinear distortion model, which reflects the amplification or attenuation of the signal itself; a ′ 3 represents the third-order nonlinear coefficient in the nonlinear distortion model, which reflects the degree of third-order intermodulation distortion; a ′ 5 represents the fifth-order nonlinear coefficient in the nonlinear distortion model, reflecting the degree of fifth-order intermodulation distortion;

[0102] Simplifying equation (10) and equation (11), we get equation (12) and equation (13):

[0103] y L (t) = F L (x L (t),x H (t)) (12);

[0104] y H (t) = F H (x L (t),x H (t)) (13);

[0105] The constructed compensation model is shown in the following formula (14):

[0106]

[0107] In formula (14), c q ′ ,r is the parameter to be solved in the compensation model, q represents the highest nonlinear order of the compensation model, Q represents the total number of nonlinear terms in the compensation model, and r represents the parameter vector to be solved in the compensation model;

[0108] (2) Use discrete cosine transform to convert the time domain signal received by the receiver into the frequency domain, use L1 norm as the sparsity measurement index, use sequential quadratic programming to solve the optimization problem, and then obtain the optimal compensation parameters. Apply the optimal compensation parameters to the compensation model, process the actual received signal, and realize compensation for the nonlinear distortion of the receiver front end;

[0109] Among them, the discrete cosine transform is used to convert the time domain signal received by the receiver into the frequency domain, the L1 norm is used as the sparsity measurement index, and the sequential quadratic programming is used to solve the optimization problem. Then, the specific steps of obtaining the optimal compensation parameters are as follows:

[0110] S21, the compensation model (see Figure 2 ) is constructed in the form of a matrix, as shown in the following formula (15):

[0111] S L =Y T C(15):

[0112] in,

[0113]

[0114] N represents the Nth item, C is the parameter vector to be solved for the compensation model; C T =[c 1,0 ,c 3,0 ,c 3,2 ,c 5,0 ,c 5,2 ,c 5,4 ,…,c Q,Q-3 ,c Q,Q-1 ], Q represents the total number of nonlinear terms in the compensation model;

[0115] S32. Use discrete cosine transform to transform the signal from the time domain to the frequency domain, as shown in the following formula (16):

[0116] ΦS L =ΦY T C (16);

[0117] In formula (16), Φ is the discrete cosine transform matrix;

[0118] S33, using L1 norm as a sparsity measurement index, using sequential quadratic programming to solve the optimization problem, the function of the optimization problem is specifically as follows (17):

[0119]

[0120] In formula (17), is the L1 norm, and the equality constraint st is to prevent the occurrence of c i =0;

[0121] S34, define the original signal as s, then the global mapping is shown in the following formula (18):

[0122] y i =βs+γh(s) (18);

[0123] In equation (18), βs is the linear term of the compensation signal, and γh(s) is the nonlinear term. The nonlinear distortion of the receiver front end is defined as The nonlinear model of digital post-compensation is: The right side obtains the following formula (19):

[0124]

[0125] The frequency domain parameters of the compensated output signal y are as follows (20):

[0126] y c =Φy (20);

[0127] In formula (20), Φ is the discrete cosine transform matrix;

[0128] Substituting formula (20) into formula (18), we get the following formula (21):

[0129] y c =Φ(βs+γh(s))=βs c +γΦh(s) (21);

[0130] In formula (21), s c =Φs, which represents the frequency domain representation of the original signal;

[0131] S35. Measure the sparsity according to the L1 norm, which specifically satisfies the following formula (22):

[0132] ||x+y||0≤||x||0+||y||0 (22);

[0133] Derived from formula (22) The following formula (23) is derived from the following formula (23): The following formula (24) is obtained:

[0134]

[0135] ||xy||0≥|||x||0-||y||0| (24);

[0136] Definition: ||βs||0=||s||0;

[0137] According to formula (24), it can be deduced from formula (21) The following formula (25) is obtained:

[0138] ||y c ||0=||βs c +γΦh(s)||0=||βs c -(-γΦh(s))||0

[0139] ≥|||βs c ||0-||-γΦh(s)||0|

[0140] =|||s c ||0-||γΦh(s)||0|

[0141] Definition||s c ||0=K、||γΦh(s)||0=L; then we get ||y c ||0≥|KL|;

[0142] When γ=0, we get: ||y c ||0=||s c ||0;

[0143] When γ≠0, we get ||γΦh(s)||0=||Φh(s)||0=L;

[0144] From this, we can see that the definition of nonlinear distortion causes the input signal to be more than twice as sparse in frequency as the original signal; when the digital post-compensation algorithm achieves perfect compensation, the sparsity after compensation is equal to the sparsity of the original signal; when it is not perfect compensation, the sparsity after compensation is greater than the sparsity of the original signal.

[0145] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for preprocessing a digital baseband signal of a receiver, characterized in that: The specific steps include: (1) Analyze the nonlinear distortion of the receiver front end, build a nonlinear distortion model of the concurrent dual-frequency receiver, bring the two-way input signal model of the concurrent dual-frequency receiver into the nonlinear distortion model, derive the distortion signal components at the corresponding frequencies, build the equivalent baseband expressions of the two-way input signals, and further derive the representation of the nonlinearly distorted signal in the baseband, thereby building a compensation model; (2) Use discrete cosine transform to convert the time domain signal received by the receiver into the frequency domain, adopt L1 norm as the sparsity measurement index, use sequential quadratic programming to solve the optimization problem, and then obtain the optimal compensation parameters. The optimal compensation parameters are applied to the compensation model, and the actual received signal is processed to achieve compensation for the nonlinear distortion of the receiver front end.

2. The method for preprocessing a digital baseband signal of a receiver according to claim 1, characterized in that: The specific steps of analyzing the nonlinear distortion of the front end of the receiver and constructing the nonlinear distortion model of the concurrent dual-frequency receiver are as follows: defining the nonlinear distortion model of the front end of the receiver, as shown in the following formula (1): In formula (1), since the nonlinear distortion generated by even orders is far away from the signal frequency, it will be filtered out by the filter, so the even orders are ignored. represents the input signal, represents the output signal, ~ represents that the input signal is a radio frequency signal; a1, a3, a5 are the parameters of the nonlinear distortion model.

3. The method for preprocessing a digital baseband signal of a receiver according to claim 2, characterized in that: The two-way input signal model of the concurrent dual-frequency receiver is specifically shown in the following equations (2) and (3): In formula (2) and formula (3), They are the two input signals of the concurrent dual-frequency receiver, A L (t), A H (t) are the amplitudes of the two input signals, ω L ,ω H are the frequencies of the two input signals, φ L (t),φ H (t) are the initial phases of the two input signals respectively, and t represents the time t.

4. The method for preprocessing a digital baseband signal of a receiver according to claim 3, characterized in that: The specific steps of bringing the two-way input signal model of the concurrent dual-frequency receiver into the nonlinear distortion model to derive the distortion signal components at the corresponding frequencies are as follows: Substituting equation (2) and equation (3) into equation (1), we can obtain the two input signals at ω L With ω H The distorted signal components at , see the following equations (4) and (5) for details: In formula (4), and In formula (5) and represents the intermodulation component produced by the third-order nonlinear distortion; in formula (4) and In formula (5) and Both represent the intermodulation products produced by fifth-order nonlinear distortion.

5. The method for preprocessing a digital baseband signal of a receiver according to claim 4, characterized in that: The specific steps of constructing the equivalent baseband expressions of the two input signals, further deriving the representation of the nonlinearly distorted signals in the baseband, and thus constructing the compensation model are as follows: The equivalent baseband expressions of the two input signals are shown in equations (6) and (7): x L (t)=A L (t)exp(jφ L (t)) (6); x H (t)=A H (t)exp(jφ H (t)) (7); In formula (6) and formula (7), j is an imaginary unit; in and x L (t), and x H The relationship between (t) is shown in the following equations (8) and (9): Substituting the above formula (8) into formula (4), and formula (9) into formula (5), we can obtain the following formulas (10) and (11): a in formula (10) and formula (11) ′ 1.a ′ 3.a ′ 5 is obtained by baseband conversion of a1, a3, and a5. ′ 1 represents the first-order nonlinear coefficient in the nonlinear distortion model, which reflects the amplification or attenuation of the signal itself; a ′ 3 represents the third-order nonlinear coefficient in the nonlinear distortion model, which reflects the degree of third-order intermodulation distortion; a ′ 5 represents the fifth-order nonlinear coefficient in the nonlinear distortion model, reflecting the degree of fifth-order intermodulation distortion; Simplifying equation (10) and equation (11), we get equation (12) and equation (13): y L (t)=F L (x L (t),x H (t)) (12); y H (t)=F H (x L (t),x H (t)) (13); The constructed compensation model is shown in the following formula (14): In formula (14), c q ′ ,r is the parameter to be solved of the compensation model, q represents the highest nonlinear order of the compensation model, Q represents the total number of nonlinear terms in the compensation model, and r represents the parameter vector to be solved in the compensation model.

6. A method for preprocessing a digital baseband signal of a receiver according to claim 5, characterized in that: The specific steps of using discrete cosine transform to convert the time domain signal received by the receiver into the frequency domain, using L1 norm as a sparsity measurement indicator, using sequential quadratic programming to solve the optimization problem, and then obtaining the optimal compensation parameters are as follows: S21. Construct the compensation model in the form of a matrix, as shown in the following formula (15): S L =Y T C(15): in, N represents the Nth item, C is the parameter vector to be solved for the compensation model; C T =[c 1，0 , c 3，0 , c 3，2 , c 5，0 , c 5，2 , c 5，4 , ..., c Q,Q-3 , C Q,Q-1 ], Q represents the total number of nonlinear terms in the compensation model; S32. Use discrete cosine transform to transform the signal from the time domain to the frequency domain, as shown in the following formula (16): ΦS L =ΦY T C (16); In formula (16), Φ is the discrete cosine transform matrix; S33, using L1 norm as a sparsity measurement index, using sequential quadratic programming to solve the optimization problem, the function of the optimization problem is specifically as follows (17): In formula (17), is the L1 norm, and the equality constraint st is to prevent the occurrence of c i =0; S34, define the original signal as s, then the global mapping is shown in the following formula (18): y i =βs+γh(s) (18); In equation (18), βs is the linear term of the compensation signal, and γh(s) is the nonlinear term. The nonlinear distortion of the receiver front end is defined as The nonlinear model of digital post-compensation is: The right side obtains the following formula (19): The frequency domain parameters of the compensated output signal y are as follows (20): y c =Φy (20); In formula (20), Φ is the discrete cosine transform matrix; Substituting formula (20) into formula (18), we get the following formula (21): y c =Φ(βs+γh(s))=βs c +γΦh(s) (21); In formula (21), s c =Φs, which represents the frequency domain representation of the original signal; S35. Measure the sparsity according to the L1 norm, which specifically satisfies the following formula (22): ||x+y||0≤||x||0+||y||0 (22); Derived from formula (22) The following formula (23) is derived from the following formula (23): The following formula (24) is obtained: ||xy||0≥|||x||0-||y||0| (24); Definition: ||βs||0=||s||0; According to formula (24), it can be deduced from formula (21) The following formula (25) is obtained: ||y c ||0=||βs c +γΦh(s)||0=||βs c -(-γΦh(s))||0 ≥|||βs c ||0-||-γΦh(s)||0| =|||s c ||0-||γΦh(s)||0| Definition||s c ||0=K、||γΦh(s)||0=L; then we get ||y c ||0≥|KL|; When γ=0, we get: ||y c ||0=||s c ||0; When γ≠0, we get ||γΦh(s)||0=||Φh(s)||0=L; From this, we can see that the definition of nonlinear distortion causes the input signal to be more than twice as sparse in frequency as the original signal; when the digital post-compensation algorithm achieves perfect compensation, the sparsity after compensation is equal to the sparsity of the original signal; when it is not perfect compensation, the sparsity after compensation is greater than the sparsity of the original signal.

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