An OFDM signal transmission method based on aliasing pilot

Abstract

The application discloses an OFDM signal transmission method based on aliasing pilot, comprising the following steps: A: establishing an aliasing pilot OFDM iterative receiver mathematical model; B: performing iterative algorithm variable initialization; C: performing channel estimation by using a unitary transformation approximate message passing method; D: applying a belief propagation algorithm to perform aliasing pilot symbol detection to obtain estimation of a sending information sequence; E: performing noise precision estimation; F: iteratively performing steps C to E, updating the established aliasing pilot OFDM iterative receiver mathematical model, and finally completing signal transmission by using the updated aliasing pilot OFDM iterative receiver mathematical model. The application can take the aliasing pilot as a prior distribution of a frequency domain symbol, guide the iterative algorithm, does not need to change an existing receiver framework, and effectively improves the spectrum utilization and robustness of the OFDM system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication receiver design, and particularly relates to an iterative transmission method of an orthogonal frequency division multiplexing (OFDM) signal applying aliasing pilots. BACKGROUND

[0002] As the cornerstone of modern communication systems, orthogonal frequency division multiplexing (OFDM) technology has been widely used in many fields such as wireless local area networks, mobile communications, underwater acoustic communications and visible light communications. In the past 30 years, people have conducted in-depth research on channel estimation and detection algorithms of OFDM systems, and have made a lot of research results. However, with the development of high-speed rail, unmanned aerial vehicles and low-orbit satellites, the rapid time-varying, sparsity and Doppler effect of the channel in the high-speed mobile scenario bring new challenges to the existing OFDM receiver. The existing OFDM transmission system usually selects some subcarriers to transmit pilot signals for channel estimation and symbol detection. However, due to the effect of multipath effect in high-speed communication, the channel parameters are complex, and accurate channel estimation requires a large number of pilots, resulting in a large spectrum and complexity overhead. In addition, the peak throughput of the 6th generation mobile communication system will reach terabit (Tbit) level, and the spectrum resource will be expanded to the millimeter wave frequency band. Millimeter wave has a larger bandwidth and can achieve higher data rates, but the channel multipath and sparsity characteristics are more obvious, which puts higher requirements on the complexity of channel estimation and detection algorithms.

[0003] OFDM systems usually add known information to information bits or channel coded bits as pilots, or select multiple subcarriers to transmit pilots. However, the insertion of pilots will occupy valuable spectrum resources and will cause more computational overhead, thereby causing serious loss of spectrum efficiency and transmission rate.

[0004] The unitary transformation approximate message passing algorithm (UAMP) is a system modeling and parameter estimation method based on Bayesian theory. This kind of method first factorizes the joint probability distribution of all variables in the system; then according to the constraint relationship between the variables, the optimal message update rule is selected for calculation; finally, a reasonable initialization and iteration mechanism is designed to form an iterative algorithm. SUMMARY

[0005] The purpose of the present application is to provide an OFDM signal transmission method based on aliasing pilots, which can use aliasing pilots as the prior distribution of frequency domain symbols to guide the iterative algorithm, without changing the existing receiver framework, and effectively improve the spectrum utilization and robustness of the OFDM system.

[0006] The present application adopts the following technical solutions:

[0007] An OFDM signal transmission method based on aliasing pilots, comprising the following steps:

[0008] A: generating a frequency domain data vector x d , a frequency domain pilot vector x p , a frequency domain transmission vector x, an OFDM channel h and a receiving vector y, finally establishing a mathematical model of a mixed pilot OFDM iterative receiver y = h · x + w; wherein, represents a covariance matrix λ -1 I N represents an additive white Gaussian noise, λ is a noise precision, I N represents a unit matrix with a dimension of N;

[0009] B: performing variable initialization of an iterative algorithm;

[0010] including initializing an initial value of a mean variance v x of the frequency domain transmission vector x in the data symbol related variable, and an initial value of a noise precision ; also including initializing an initial value of a mean variance v α of the time domain channel tap vector α in the channel related variable, an intermediate variable s and a hyper-prior variable γ; and an observation matrix Ψ, and a pseudo frequency domain channel vector h';

[0011] C: performing channel estimation by using a unitary transformation approximate message passing method;

[0012] D: applying a belief propagation algorithm to perform mixed pilot symbol detection to obtain an estimate of the transmitted information sequence b

[0013] E: performing noise precision estimation;

[0014] F: iteratively performing steps C to E, updating the established mathematical model of the mixed pilot OFDM iterative receiver, and finally completing signal transmission by using the updated mathematical model of the mixed pilot OFDM iterative receiver.

[0015] The step A includes the following specific steps:

[0016] A1: generating a frequency domain data vector x d ;

[0017] Suppose that the transmitted information sequence b ∈ [0, 1] 2N×1 is obtained by Q-order QAM modulation to obtain a frequency domain data vector wherein the subscript d represents a data domain, the symbol b ∈ [0, 1] 2N×1 indicates that the elements in the vector b only have two values of 0 and 1, the vector length is 2N, N represents the number of subcarriers in the OFDM system, and the symbol represents a complex value matrix with a dimension of N × 1;

[0018] A2: Randomly generating a frequency domain pilot vector x p ; A2: Randomly generating a frequency domain pilot vector x p ; d A2: Randomly generating a frequency domain pilot vector x d ;

[0019] A3: Weighted generating a frequency domain transmission vector x

[0020] A3: Weighted generating a frequency domain transmission vector x p ;

[0021] x = ∈x d + (1 - ∈) x p ;

[0022] wherein, the parameter ∈ ∈ (0, 1) is a weighting coefficient;

[0023] A4: Generating an OFDM channel;

[0024] The OFDM frequency domain equivalent channel is expressed in the form of a time domain tap, h = Φα; wherein, represents a time domain channel tap vector, L represents a channel tap length, and the matrix Φ is a left side L column of an N × N discrete Fourier transform matrix (DFT); the tap vector α has sparsity, that is, only K non-zero elements in α, wherein K represents a non-zero tap number, which depends on a channel scattering condition, and K << L;

[0025] A5: Generating a receiving vector;

[0026] At the receiving end, the frequency domain receiving vector is expressed as:

[0027] y = h · x + w;

[0028] wherein, the operation h · x represents multiplication of corresponding elements of the vectors h and x, represents a covariance matrix λ -1 I N is additive white Gaussian noise, λ is noise precision, and I N represents a unit matrix with a dimension of N;

[0029] Finally, the mathematical model of the aliasing pilot OFDM iterative receiver y = h · x + w is obtained.

[0030] In the step A1, the modulation method of the information sequence b is: first, the information sequence b is divided into two vectors b1, b2 ∈ [0, 1] N×1 , and the elements represent the nth elements in the vectors b1 and b2 respectively; then according to the value of the element , the The modulation is represented by the corresponding complex-valued data s1, s2, s3, or s4; in QAM modulation, s1, s2, s3, and s4 are called constellation points. Represents the frequency domain data vector x d The nth element in; the QAM modulation relationship is as follows, when When the values ​​are (0,0), (0,1), (1,0), and (1,1), they are modulated into s1, s2, s3, and s4, respectively.

[0031] In step A2, a frequency domain pilot vector x is randomly generated. p The method is as follows: randomly select N times from constellation points s1 to s4 to generate a frequency domain pilot vector of length N. The subscript p indicates the pilot domain.

[0032] Step B includes the following specific steps:

[0033] B1: Initialize data symbol-related variables, including the mean of the frequency domain transfer vector x. Sum of variance v x The initial value, and the noise accuracy. The initial value;

[0034] Wherein, the mean of the initial frequency domain transmission vector x Sum of variance v x The initial values ​​are respectively and v x =1 N That is, assuming the initial frequency domain transmission vector is the pilot x p The initial value of noise accuracy is Among them 1 N This represents a vector of length N consisting entirely of 1s.

[0035] B2: Initialize channel-related variables, including the mean of the time-domain channel tap vector α. Sum of variance v α The initial values ​​of , as well as the intermediate variable s and the super-prior variable γ;

[0036] Wherein, the mean of the initial time-domain channel tap vector α Sum of variance v α The initial values ​​are respectively and v α =I L Initialize intermediate variable s = 0 N and the prior variable γ=1 L , of which 0 N and 1 L Let I represent vectors of length N consisting entirely of zeros and vectors of length L consisting entirely of one units, respectively. L This represents an identity matrix of dimension L;

[0037] B3: define the observation matrix Ψ;

[0038] Singular Value Decomposition (SVD) is performed on the matrix Φ, i.e., [U, Λ, V] = SVD(Φ); according to the singular value decomposition theory, among the three matrices obtained after decomposition, U and V are unitary matrices, and Λ is a diagonal matrix;

[0039] Thus, the observation matrix Ψ is defined as: Ψ = U H Φ;

[0040] B4: define the pseudo-frequency domain channel vector h' as h' = U H h;

[0041] wherein h' is defined as a pseudo-frequency domain channel vector, U H represents the conjugate transpose of the matrix U.

[0042] The C includes the following specific steps:

[0043] C1: calculate the estimated mean and the estimated variance of the frequency domain equivalent channel h respectively using and v x and respectively, which are calculated as follows:

[0044]

[0045] wherein represents the conjugate of the vector , and represents the dot product of the vector and the frequency domain receiving vector y, i.e., the multiplication of the corresponding elements.

[0046] C2: calculate the estimated mean and the estimated variance of the pseudo-frequency domain channel h' respectively and which are calculated as follows:

[0047]

[0048] wherein |U| 2 = I, I represents the unit matrix,

[0049] C3: calculate the intermediate variables v p , p, v s and s in sequence.

[0050] v p = |Ψ| 2 v α ;

[0051] wherein Ψ is the observation matrix, v α ​variance of the time-domain tap vector;

[0052]

[0053] wherein, denotes the mean of the time-domain channel tap vector α, s is an intermediate variable, and the operator "·" denotes the dot product of vectors;

[0054]

[0055] wherein the operator ". / " denotes the dot division of vectors, i.e. the division of corresponding elements of two vectors;

[0056] C4: sequentially calculating the intermediate variable v q and q;

[0057] v q = 1. / ( | Ψ H | 2 v s ),

[0058] wherein Ψ H denotes the conjugate transpose of the matrix Ψ;

[0059] C5: calculating the mean and the variance v α of the time-domain channel tap vector α using the hyper-prior variable γ:

[0060] v α = v q . / ( 1 + γ · v q ) ;

[0061] C6: updating the calculation of the hyper-prior variable γ;

[0062]

[0063] C7: calculating the mean v h′ and the variance of the pseudo-frequency-domain channel h' respectively, and finally completing the channel estimation;

[0064]

[0065] wherein, and v h′ are the mean and the variance of the pseudo-frequency-domain channel h' respectively,

[0066]

[0067] wherein, and v h are the mean and the variance of the equivalent frequency-domain channel h respectively.

[0068] Step D includes the following specific steps:

[0069] D1: Using the mean of the obtained frequency domain equivalent channel h Sum of variance v h Calculate the estimated mean of the frequency domain transmission vector x. Sum of variance v x , respectively

[0070]

[0071] in, Representing vectors The conjugate;

[0072] D2: Calculate the frequency domain data vector x d The estimated mean

[0073]

[0074] D3: Based on the frequency domain data vector x d The estimated mean The transmitted symbols are judged to obtain the estimate of the transmitted information sequence b in step A1.

[0075] In step D3, given that the four constellation points of the QAM modulation are s1 to s4, the variables are judged sequentially. Which of the four constellation points s1 to s4 is closer? The decision is based on the 0 or 1 value corresponding to that constellation point, where... Representing vectors The nth element; the specific method is as follows:

[0076] First, calculate The Euclidean distances from s1 to s4 are denoted as follows:

[0077] Secondly, judgment The minimum value in the range is used to determine the transmitted information bits; then, the minimum value is used to determine the transmitted information bits. The estimated value is denoted as For example when middle If the minimum value is reached, then a decision can be made.

[0078] Finally, all of them Arranged into a vector, an estimate of the transmitted information sequence is obtained.

[0079] In step E, the mean value of the equivalent frequency domain channel h obtained from steps B and C is used. Sum of variance v h The mean value of the frequency domain transmission symbol x Sum of variance v x Calculate the estimated value of the noise accuracy λ.

[0080]

[0081] Where |||2 represents the 2-norm of the vector.

[0082] This invention only requires using the aliasing pilot as a priori distribution of frequency domain symbols to guide the iterative algorithm, without changing the existing receiver framework, making it highly suitable for OFDM receiver construction scenarios. First, this invention introduces UAMP as a processing scheme for time / frequency domain channel conversion and embeds a sparse Bayesian learning (SBL) model as a priori model for the time domain channel. Second, it applies confidence propagation rules for modulation and demodulation during detection. By simply changing the priori distribution of the modulation system, the aliasing pilot can be embedded into existing message-passing detection algorithms. This invention significantly improves the spectral efficiency and robustness of OFDM systems with the same complexity. Attached Figure Description

[0083] Figure 1 This is a schematic diagram of the process of the present invention;

[0084] Figure 2 A comparison of bit error rate performance versus signal-to-noise ratio under different algorithms;

[0085] Figure 3 This is a comparison of the BER performance of different algorithms as a function of signal-to-noise ratio under LDPC coding conditions. Detailed Implementation

[0086] The present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0087] like Figure 1 As shown, the OFDM signal transmission method based on aliasing pilots of the present invention includes the following steps:

[0088] A: Generate frequency domain data vector x d Frequency domain pilot vector x p Using the frequency domain transmission vector x, OFDM channel h, and receiver vector y, a mathematical model for an aliased pilot OFDM iterative receiver is established.

[0089] Step A includes the following specific steps:

[0090] A1: Generate frequency domain data vector x d ;

[0091] Let the transmitted information sequence b∈[0,1] 2N×1 After Q-order QAM modulation (Quadrature Amplitude Modulation), a frequency domain data vector x is obtained, where subscript d represents the data domain, and symbol b∈[0,1] 2N×1 represents that the elements in vector b only have two values of 0 and 1, the vector length is 2N, N represents the number of subcarriers in the OFDM system, and symbol represents a complex value matrix with a dimension of N×1.

[0092] The modulation method of the information sequence b is as follows: first, the information sequence b is divided into two vectors b1 and b2∈[0,1] N×1 , and elements represent the nth elements in vectors b1 and b2 respectively; then, according to the values of the elements , the elements are modulated into corresponding complex value data s1, s2, s3 or s4; in the QAM modulation, s1, s2, s3 and s4 are called constellation points, represents the nth element in the frequency domain data vector x d ; the QAM modulation relationship is as follows: when , (0, 0), (0, 1), (1, 0) and (1, 1) are respectively modulated into s1, s2, s3 and s4.

[0093] A2: Randomly generate a frequency domain pilot vector x p ;

[0094] Randomly generate a frequency domain pilot vector The length of the frequency domain pilot vector x p is the same as that of the frequency domain data vector x d , and the generation method is as follows: randomly select N times from the constellation points s1 to s4 to generate a frequency domain pilot vector with a length of N. Subscript p represents the pilot domain.

[0095] A3: Weighted generation of a frequency domain transmission vector x;

[0096] The frequency domain data vector x d is weighted with the frequency domain pilot vector x p to generate a frequency domain transmission vector

[0097] x=∈x d +(1-∈)x p ; (1)

[0098] The parameter ∈∈(0, 1) is a weighting coefficient.

[0099] A4: Generation of an OFDM channel;

[0100] The OFDM frequency domain equivalent channel is expressed as a time domain tap form, h = Φα; wherein, The time domain channel tap vector is represented, L represents the channel tap length, and the matrix Φ is the left L columns of an N x N discrete Fourier transform matrix (DFT);

[0101] In a high-speed OFDM communication system, the tap vector α has sparsity, that is, only K non-zero elements in α, wherein K represents the number of non-zero taps, depends on the channel scattering condition, and K << L;

[0102] A5: generating a received vector;

[0103] At the receiving end, the frequency domain received vector is expressed as:

[0104] y = h · x + w

[0105] wherein the operation h · x represents multiplication of corresponding elements of the vectors h and x, the covariance matrix is λ -1 I N , the additive white Gaussian noise is λ, λ is the noise precision, and I N represents a unit matrix with a dimension of N;

[0106] Finally, the mathematical model of the aliasing pilot OFDM iterative receiver y = h · x + w is obtained.

[0107] B: performing variable initialization of an iterative algorithm;

[0108] The step B includes the following specific steps:

[0109] B1: initializing data symbol related variables, including initial values of the mean and the variance v x of the frequency domain transmission vector x, and an initial value of the noise precision ;

[0110] In the present application, the initial values of the mean and the variance v x of the frequency domain transmission vector x are and v x = 1 N , that is, the initial frequency domain transmission vector is assumed to be the pilot x p , and the initial value of the noise precision is wherein 1 N represents a full one vector with a length of N.

[0111] B2: initializing channel related variables, including the mean and the variance v α of the time domain channel tap vector α.The initial values ​​of , as well as the intermediate variable s and the super-prior variable γ;

[0112] In this invention, the mean of the initial time-domain channel tap vector α is... Sum of variance v α The initial values ​​are respectively and v α =I L Initialize intermediate variable s = 0 N and the prior variable γ=1 L , of which 0 N and 1 L Let I represent vectors of length N consisting entirely of zeros and vectors of length L consisting entirely of one units, respectively. L This represents an identity matrix of dimension L;

[0113] B3: Define the observation matrix Ψ;

[0114] Perform singular value decomposition (SVD) on matrix Φ, i.e.

[0115] [U,Λ,V]=SVD(Φ);

[0116] According to the singular value decomposition theory, among the three matrices obtained after decomposition, U and V are unitary matrices, and Λ is a diagonal matrix;

[0117] Therefore, the observation matrix Ψ can be defined as:

[0118] Ψ=U H Φ;

[0119] B4: Define the pseudo-frequency domain channel vector h′ as

[0120] h′=U H h;

[0121] Where h′ is defined as the pseudo-frequency domain channel vector, U H Represents the conjugate transpose of matrix U;

[0122] The initialization steps of the iterative receiver design are finally completed.

[0123] C: Channel estimation using the unitary transform approximate message passing method;

[0124] Step C includes the following specific steps:

[0125] C1: Utilize and v x The estimated mean and estimated variance of the frequency domain equivalent channel h are calculated respectively. and Calculated separately as follows:

[0126]

[0127] where denotes the conjugate of the vector , denotes the dot product of the vector and the frequency domain received vector y, i.e. the multiplication of the corresponding elements;

[0128] C2: compute the estimated mean and the estimated variance of the pseudo frequency domain channel h' from and respectively:

[0129]

[0130] Since U is a unitary matrix, it is known that |U| 2 = I, where I denotes the identity matrix, and it follows that

[0131] C3: compute the intermediate variables v p , p, v s and s in sequence;

[0132] v p = |Ψ| 2 v α , where Ψ is the observation matrix and v α is the variance of the time domain tap vector;

[0133] where denotes the mean of the time domain channel tap vector a, s is an intermediate variable and the operator "•" denotes the dot product of vectors;

[0134]

[0135] where the operator ". / " denotes the dot division of vectors, i.e. the division of the corresponding elements of two vectors;

[0136] C4: compute the intermediate variables v q and q in sequence;

[0137] v q = 1. / (|Ψ H | 2 v s ),

[0138] where Ψ H denotes the conjugate transpose of the matrix Ψ;

[0139] C5: compute the mean and the variance v α of the time domain channel tap vector a from the hyper-prior variable γ:

[0140] vα =v q . / (1+γ·v q );

[0141] C6: Update the calculation of the prior variable γ.

[0142]

[0143] C7: Calculate the mean value v of the pseudo-frequency domain channel h′ respectively. h′ and variance

[0144]

[0145] in, and v h′ The mean and variance of the pseudo-frequency domain channel h′ need to be converted to the mean of the equivalent frequency domain channel h. Sum of variance v h ,Right now

[0146] v h =v h′ ;

[0147] Finally, the channel estimation is completed;

[0148] In this invention, the vector used in the first iteration is... v x α, v α γ and s are the initial values ​​corresponding to step B, and the values ​​used in subsequent iterations are updated by subsequent iterations.

[0149] D: Apply the belief propagation algorithm for aliasing pilot symbol detection;

[0150] Step D includes the following specific steps:

[0151] D1: The mean of the frequency-domain equivalent channel h obtained using step C7. Sum of variance v h Calculate the estimated mean of the frequency domain transmission vector x. Sum of variance v x , respectively

[0152]

[0153] in, Representing vectors The conjugate;

[0154] D2: Calculate the frequency domain data vector x d The estimated mean

[0155] According to equation (1), the frequency domain data vector x can be obtained. d The estimated mean for

[0156]

[0157] D3: Based on the frequency domain data vector x d The estimated mean Make a decision on the transmitted symbol;

[0158] In step A1, given that the four constellation points of the QAM modulation are s1 to s4, the variables can be determined sequentially. Which of the four constellation points s1 to s4 is closer? The decision is based on the 0 or 1 value corresponding to that constellation point, where... Representing vectors The nth element; the specific method is as follows:

[0159] First, calculate The Euclidean distances from s1 to s4 are denoted as follows:

[0160] Secondly, judgment The minimum value in the range is used to determine the transmitted information bits; then, the minimum value is used to determine the transmitted information bits. The estimated value is denoted as For example when middle If the minimum value is reached, then a decision can be made.

[0161] Finally, all of them Arranged into a vector, an estimate of the transmitted information sequence is obtained.

[0162] Finally, the estimated value of the information sequence b sent in step A1 is obtained.

[0163] E: Perform noise accuracy estimation;

[0164] The mean value of the equivalent frequency domain channel h obtained from steps B and C Sum of variance v h The mean value of the frequency domain transmission symbol x Sum of variance v x Calculate the estimated value of the noise accuracy λ, i.e.

[0165]

[0166] Where |||2 represents the 2-norm of the vector.

[0167] F: Iterate through steps C to E to update the established aliasing pilot OFDM iterative receiver mathematical model, and finally use the updated aliasing pilot OFDM iterative receiver mathematical model to complete signal transmission.

[0168] The method proposed in this invention is an iterative algorithm. Steps A and B establish a mathematical model of the aliased pilot OFDM iterative receiver, and the intermediate variables and matrices required for the iteration are initialized. Steps C, D, and E perform 10 iterative calculations to update the mathematical model of the aliased pilot OFDM iterative receiver. Finally, the updated mathematical model is used to complete signal transmission. Using the aliased pilot OFDM signal transmission method described in this invention, an estimate of the initial transmitted information sequence b is obtained from the initial transmitted information sequence b. Complete the entire signal output process.

[0169] like Figure 2 As shown, this invention compares the bit error rate (BER) performance of different algorithms with signal-to-noise ratio when the number of non-zero taps K=10, the (5,7)8 convolutional code is used, and the weighting coefficients ∈=0.8. Figure 2 The paper compares four methods: known channel (no pilot), known channel (aliased pilot), unknown channel (independent pilot), and unknown channel (independent pilot). The known channel method assumes an ideal situation where the entire channel is known, and can be used as an upper bound for the algorithm's performance. Figure 2 It can be seen that the independent pilot method has a performance advantage of about 1dB over the aliased pilot method, highlighting the effectiveness of the aliased pilot method.

[0170] like Figure 3 As shown, this invention compares the BER performance of various algorithms under LDPC coding conditions as a function of signal-to-noise ratio. Figure 3 The number of non-zero taps is set to 10, and the weighting coefficients are 0.7 and 0.8 respectively. It can be seen that introducing LDPC channel coding can significantly improve the receiver's bit error rate performance. From... Figure 3 It can also be derived from the above. Figure 2 The same conclusion can be drawn: aliased pilot OFDM receivers can achieve high spectral efficiency.

[0171] The OFDM signal transmission method based on aliasing pilots described in this invention has a wide range of applications, such as home WiFi, vehicle-to-everything (V2X) communication, and underwater acoustic communication.

Claims

1. A method for OFDM signal transmission based on aliasing pilots, characterized in that, Includes the following steps: A: Generate frequency domain data vector x d Frequency domain pilot vector x p The frequency domain transmission vector x, OFDM channel h, and receive vector y are used to establish the mathematical model of the aliased pilot OFDM iterative receiver: y = h·x + w; where, Let the covariance matrix be λ -1 I N Additive white Gaussian noise, where λ is the noise precision, I N Represents an identity matrix of dimension N; B: Initialize the variables for the iterative algorithm; Including the mean of the frequency domain transfer vector x in the initialization data symbol related variables. variance v x initial value and noise accuracy The initial values; also including the mean of the time-domain channel tap vector α in the initialization of channel-related variables. variance v α The initial value, intermediate variable s, and prior variable γ; as well as the observation matrix ψ and the pseudo-frequency domain channel vector h'; C: Channel estimation using the unitary transform approximate message passing method; D: Apply the belief propagation algorithm to detect aliasing pilot symbols and obtain an estimate of the transmitted information sequence b. E: Perform noise accuracy estimation; F: Iterate through steps C to E to update the established mathematical model of the aliasing pilot OFDM iterative receiver, and finally use the updated mathematical model of the aliasing pilot OFDM iterative receiver to complete the signal transmission. Specifically, C includes the following steps: C1: Utilize and v x The estimated mean and estimated variance of the frequency domain equivalent channel h are calculated respectively. and Calculated separately as follows: in, Representing vectors conjugate, Representing vectors The dot product of the frequency domain received vector y, i.e., the element-wise multiplication; C2: Calculate the predicted mean and predicted variance of the pseudo-frequency domain channel h'. and They are respectively: Among them, |U| 2 =I, where I represents the identity matrix. C3: Calculate the intermediate variable v sequentially. p p, v s and s; v p =|Ψ| 2 v α ; Where Ψ is the observation matrix, v α Let V be the variance of the time-domain tap vector; in, represents the mean of the time-domain channel tap vector α, s is an intermediate variable, and the operator "·" represents the dot product of vectors; The operator ". / " represents dot division of vectors, that is, dividing corresponding elements of two vectors. C4: Calculate the intermediate variable v sequentially. q and q; Among them, Ψ H Represents the conjugate transpose of matrix Ψ; C5: Calculate the mean of the time-domain channel tap vector α using the prior variable γ. Sum of variance v α : C6: Update the calculation of the prior variable γ; C7: Calculate the mean value v of the pseudo-frequency domain channel h' respectively. h' and variance Finally, the channel estimation is completed; in, and v h' Let h' be the mean and variance of the pseudo-frequency domain channel, respectively. in, and v h denoted as mean and variance, respectively, of the equivalent frequency domain channel h.

2. The OFDM signal transmission method based on aliasing pilots according to claim 1, characterized in that: Step A includes the following specific steps: A1: Generate frequency domain data vector x d ; Let the transmitted information sequence be b∈[0,1] 2N×1 Frequency domain data vector is obtained after Q-order QAM modulation. Here, the subscript d represents the data field, and the symbol b ∈ [0,1]. 2N×1 This indicates that the elements in vector b can only take the values ​​0 and 1, and the vector length is 2N, where N represents the number of subcarriers in the OFDM system. This represents a complex-valued matrix with dimension N×1; A2: Randomly generate frequency domain pilot vector x p ; Frequency domain pilot vector x p Length and frequency domain data vector x d same; A3: Weighted generation of frequency domain transfer vector x; frequency domain data vector x d With frequency domain pilot vector x p Weighted generation of frequency domain transmission vector x; ； Among them, parameters ∈(0,1) are weighting coefficients; A4: Generate OFDM channel; The OFDM frequency-domain equivalent channel is represented in time-domain tapped form, where h = Φα; where... Let α represent the time-domain channel tap vector, L represent the channel tap length, and matrix Φ be the left L column of the N×N discrete Fourier transform matrix (DFT). The tap vector α is sparsity, that is, α has only K non-zero elements, where K represents the number of non-zero taps, which depends on the channel scattering, and K << L. A5: Generate the receive vector; At the receiving end, the frequency domain receive vector Represented as: y = h·x + w; The operation h·x represents the element-wise multiplication of vectors h and x. Let the covariance matrix be λ -1 I N Additive white Gaussian noise, where λ is the noise precision, I N Represents an identity matrix of dimension N; Finally, the mathematical model for the aliased pilot OFDM iterative receiver is obtained as y = h·x + w.

3. The OFDM signal transmission method based on aliasing pilots according to claim 2, characterized in that, In step A1, the modulation method for the information sequence b is as follows: First, the information sequence b is divided into two vectors b1, b2 ∈ [0, 1]. N×1 ,element Let b1 and b2 represent the nth elements respectively; then, based on the elements... The value of will The modulation is represented by the corresponding complex-valued data s1, s2, s3, or s4; in QAM modulation, s1, s2, s3, and s4 are called constellation points. Represents the frequency domain data vector x d The nth element in; The QAM modulation relationship is as follows: when When the values ​​are (0,0), (0,1), (1,0), and (1,1), they are modulated into s1, s2, s3, and s4, respectively.

4. The OFDM signal transmission method based on aliasing pilots according to claim 2, characterized in that, In step A2, a frequency domain pilot vector x is randomly generated. p The method is as follows: randomly select N times from constellation points s1 to s4 to generate a frequency domain pilot vector of length N. The subscript p indicates the pilot domain.

5. The OFDM signal transmission method based on aliasing pilots according to claim 1, characterized in that: Step B includes the following specific steps: B1: Initialize data symbol-related variables, including the mean of the frequency domain transfer vector x. Sum of variance v x The initial value, and the noise accuracy. The initial value; Wherein, the mean of the initial frequency domain transmission vector x Sum of variance v x The initial values ​​are respectively and v x =1 N That is, assuming the initial frequency domain transmission vector is the pilot x p The initial value of noise accuracy is Among them 1 N This represents a vector of length N consisting entirely of 1s. B2: Initialize channel-related variables, including the mean of the time-domain channel tap vector α. Sum of variance v α The initial values ​​of , as well as the intermediate variable s and the super-prior variable γ; Wherein, the mean of the initial time-domain channel tap vector α Sum of variance v α The initial values ​​are respectively and v α =I L Initialize intermediate variable s = 0 N and the prior variable γ=1 L , of which 0 N and 1 L Let I represent vectors of length N consisting entirely of zeros and vectors of length L consisting entirely of one units, respectively. L This represents an identity matrix of dimension L; B3: Define the observation matrix Ψ; Perform singular value decomposition (SVD) on matrix Φ, i.e., [U,Λ,V]=SVD(Φ); according to the singular value decomposition theory, among the three matrices obtained after decomposition, U and V are unitary matrices, and Λ is a diagonal matrix; Therefore, the observation matrix Ψ is defined as: Ψ = U H Φ; B4: Define the pseudo-frequency domain channel vector h' as ​​h' = U H h; Where h' is defined as the pseudo-frequency domain channel vector, U H This represents the conjugate transpose of matrix U.

6. The OFDM signal transmission method based on aliasing pilots according to claim 1, characterized in that: Step D includes the following specific steps: D1: Using the mean of the obtained frequency domain equivalent channel h Sum of variance v h Calculate the estimated mean of the frequency domain transmission vector x. Sum of variance v x , respectively in, Representing vectors Conjugate; D2: Calculate the frequency domain data vector x d The estimated mean D3: Based on the frequency domain data vector x d The estimated mean The transmitted symbols are judged to obtain the estimate of the transmitted information sequence b in step A1.

7. The OFDM signal transmission method based on aliasing pilots according to claim 6, characterized in that: In step D3, given that the four constellation points of the QAM modulation are s1 to s4, the variables are judged sequentially. Which of the four constellation points s1 to s4 is closer? The decision is based on the 0 or 1 value corresponding to that constellation point, where... Representing vectors The nth element; the specific method is as follows: First, calculate The Euclidean distances from s1 to s4 are denoted as follows: Secondly, judgment The minimum value in the range is used to determine the transmitted information bits; then, the minimum value is used to determine the transmitted information bits. The estimated value is denoted as when d n4 If the minimum value is reached, then a decision can be made. Finally, all of them Arranged into a vector, an estimate of the transmitted information sequence is obtained.

8. The OFDM signal transmission method based on aliasing pilots according to claim 1, characterized in that: In step E, the mean value of the equivalent frequency domain channel h obtained from steps B and C is used. Sum of variance v h The mean value of the frequency domain transmission symbol x Sum of variance v x Calculate the estimated value of the noise accuracy λ. Where |||2 represents the 2-norm of the vector.

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