A semi-blind OFDM receiver method combining channel estimation, phase noise compensation, and signal detection.

Abstract

This invention discloses a semi-blind OFDM receiving method that combines channel estimation, phase noise compensation, and signal detection. The method first constructs a constrained objective function for joint channel estimation, phase noise compensation, and signal detection based on phase noise modulo-1 constraints and the mapping constraint of the signal to be detected. Then, given the phase noise and the signal to be detected, the optimal channel estimate is obtained, and this estimate is brought back to the original optimization objective to obtain an updated objective function. Subsequently, by introducing a penalty term, a penalty factor, and auxiliary variables, an augmented Lagrangian function of the optimization objective is constructed, and the corresponding optimization problem is solved using the cross-direction multiplier method (ADMM) and the minimization-maximization (MM) algorithm. When the iteration termination condition is met, the joint estimate of the channel, phase noise, and transmitted signal is obtained. This invention ensures optimal performance from the optimization objective and can effectively save pilot overhead, thereby improving spectral efficiency.

Description

Technical Field

[0001] This invention relates to the field of wireless communication, and in particular to a joint channel estimation, phase noise compensation, and signal detection method for OFDM systems under the influence of phase noise. Background Technology

[0002] With the increasing diversification of service scenarios and the growing demand for differentiated performance in modern communications, high-frequency bands such as millimeter-wave and terahertz bands have attracted widespread attention. However, high carrier frequencies can have a detrimental impact on radio frequency hardware. Among these, phase noise introduced by the local oscillator can severely affect the performance of OFDM systems. Phase noise causes common phase error and inter-carrier interference, thereby disrupting the orthogonality between subcarriers in the OFDM system and posing new challenges to OFDM receiver design. Therefore, designing a reliable receiving scheme is crucial for improving system performance in OFDM systems affected by phase noise. Existing joint receiving schemes typically employ pilot-based estimation methods, such as using least squares or minimum mean square error to obtain channel and phase noise estimates before signal detection. R. Corvaja et al. proposed a joint channel and phase noise compensation for OFDM in fast-fading multipath applications based on comb pilots and decision feedback, but this scheme incurs high pilot overhead, resulting in a waste of spectrum resources. However, with the increase in communication speed and data volume, existing pilot-based schemes are no longer sufficient for the efficient transmission of large-scale data. On the other hand, existing algorithms do not consider the modulo-1 constraint of phase noise and the discrete characteristics of signal mapping in their receiving algorithm design, resulting in poor accuracy of phase noise compensation and poor signal detection performance. Summary of the Invention

[0003] Purpose of the Invention: To address the problems existing in the prior art, the present invention aims to provide a semi-blind OFDM joint reception method. It establishes a constrained objective function for joint channel estimation, phase noise compensation, and signal detection from a holistic perspective, ensuring optimal performance through the optimization objective. Furthermore, it comprehensively considers the constraints of phase noise and signal mapping, and solves the problems of joint channel estimation, phase noise compensation, and signal detection using ADMM and MM algorithms. This effectively utilizes pilot information and mitigates the ICI effect introduced by phase noise, significantly improving the system's BER performance.

[0004] Technical Solution: To achieve the above objectives, this invention provides a semi-blind OFDM reception method that combines channel estimation, phase noise compensation, and signal detection, comprising the following steps:

[0005] (1) Based on the phase noise modulo 1 constraint and the signal to be detected mapping constraint, construct the objective function of constrained joint channel estimation, phase noise compensation and signal detection;

[0006] (2) Fix the phase noise and the signal to be detected, obtain the best channel estimate according to the least squares criterion, and bring it back to the original optimization objective to obtain the updated objective function;

[0007] (3) By introducing penalty terms, penalty factors and auxiliary variables, an augmented Lagrangian function of the optimization objective was constructed, and the corresponding optimization problem was solved by using the cross-direction multiplier method ADMM and the maximization-minimization MM algorithm.

[0008] (4) When the iteration termination condition is met, the joint estimate of the channel, phase noise and transmitted signal is obtained.

[0009] Preferably, the objective function for constructing the joint channel estimation, phase noise compensation, and signal detection in step (1) is:

[0010]

[0011] Where Diag(·) represents constructing a diagonal matrix with the input vector as its diagonal elements, (·) H Let ||·|| denote the conjugate transpose, and ||·|| be the 2-norm of the vector; This is the time-domain received signal, where N represents the number of subcarriers. Represents the time-domain phase noise vector. It is the time-domain channel matrix, H = F H Diag(F h h)F, h=[h(0), h(1),…, h(L-1)] T It is a time-varying channel vector in the time domain, where L represents the channel path number. Represents the pilot vector, which is the data vector. All zero elements are removed to obtain the data subvector. N d Indicates the number of data subcarriers; This represents the projection matrix that maps data subvectors to data vectors. It is a Fourier matrix;

[0012] The constraints of the objective function are:

[0013] |e φ(n) |=1, n=1,2,…,N

[0014]

[0015] Where |·| represents the modulo operation, Indicates 4 q -QAM symbol mapping set, q = 1, 2, 3, ...; x represents the set The element in, x i x q Let x represent the real part and the imaginary part, respectively. Indicates will Extended to N d 3D space.

[0016] Preferably, in step (2), the phase noise and the signal to be detected are fixed, and the time-domain channel estimate h = (M) is obtained using the least squares method. H M) -1 M H FDiag(e jφ )y,M=(X p +X d )F h X p =Diag(x p ), (·) -1 This represents matrix inversion; substituting the estimated value back into the original objective function and setting θ = e -jφ The updated objective function is:

[0017]

[0018] The constraints are:

[0019] |θ(n)|=1, n=1, 2,…,N

[0020]

[0021] Where Y = Diag(y).

[0022] Preferably, in step (3), a penalty term is introduced to relax or tighten the constraints, and an auxiliary variable is introduced. and The following objective function is obtained:

[0023]

[0024] Constraints:

[0025] η = θ, |θ n |=1, n=1,2,…,N

[0026]

[0027] in, S = Diag(Js), Represents a set The elements in They represent The real and imaginary parts, Indicates will Extended to N d 2D space; β i >0 is what makes v i The penalty factor for elements close to -1 or 1;

[0028] The corresponding augmented Lagrangian function is obtained as follows:

[0029]

[0030] Where ρ1 is related to the constraints The penalty factor, ρ2, is the penalty factor with respect to the constraint η = θ. This indicates a constraint. Lagrange multipliers, This represents the Lagrange multiplier corresponding to the constraint η = θ. This indicates taking the real part of the variable.

[0031] As a preferred option, the solution to the optimization problem in step (3) is performed in the (k+1)th iteration according to the following formula:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] in:

[0039] Q = Y H F H (I N -P)FY

[0040]

[0041]

[0042]

[0043]

[0044] This means projecting each element of the input vector onto a space of magnitude 1. This means projecting each element of the input vector onto the interval [-1, 1]; A⊙B represents the Hadamard product of A and B, I N Represents an N×N identity matrix.

[0045] Preferably, the iteration termination condition in step (4) includes reaching a preset maximum number of iterations or the iteration result converging.

[0046] Based on the same inventive concept, this invention provides a semi-blind OFDM receiving system that combines channel estimation, phase noise compensation, and signal detection, comprising:

[0047] The objective construction module is used to construct a constrained joint objective function for channel estimation, phase noise compensation, and signal detection based on the phase noise modulo-1 constraint and the mapping constraint of the signal to be detected.

[0048] The optimization solution module is used to fix the phase noise and the signal to be detected, obtain the best channel estimate according to the least squares criterion, and substitute it back into the original optimization objective to obtain the updated objective function. In addition, by introducing a penalty term, a penalty factor and auxiliary variables, an augmented Lagrangian function of the optimization objective is constructed, and the corresponding optimization problem is solved using the cross-direction multiplier method (ADMM) and the maximization-minimization MM algorithm. When the iteration termination condition is met, the joint estimate of the channel, phase noise and transmitted signal is obtained.

[0049] Based on the same inventive concept, the present invention provides a computer system including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the steps of the semi-blind OFDM reception method for joint channel estimation, phase noise compensation, and signal detection.

[0050] Based on the same inventive concept, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the semi-blind OFDM reception method for joint channel estimation, phase noise compensation, and signal detection.

[0051] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0052] 1. This invention is based on a semi-blind joint reception algorithm. Taking a holistic approach, it establishes a constrained objective function for joint channel estimation, phase noise compensation, and signal detection, directly guaranteeing optimal performance from the optimization objective. Compared to traditional reception schemes, this invention directly estimates all channel, phase noise, and detected signal information at the receiver, effectively reducing pilot overhead and improving spectrum utilization.

[0053] 2. Compared with traditional phase noise compensation schemes, this invention fully considers the modulo-1 constraint of phase noise and adds this constraint to the objective function to achieve more accurate phase noise compensation performance.

[0054] 3. This invention utilizes the ADMM and MM algorithms to solve for an effective closed-form solution during the iterative process, achieving convergence with fewer iterations. This effectively mitigates inter-carrier interference caused by phase noise and significantly improves the performance of the OFDM system. Attached Figure Description

[0055] Figure 1 This is the algorithm flowchart of the present invention.

[0056] Figure 2 This is a diagram showing the results of a simulation experiment. Detailed Implementation

[0057] The present invention will now be described in detail with reference to a preferred embodiment and the accompanying drawings.

[0058] A typical application scenario for this invention is OFDM systems affected by phase noise, where it effectively solves the joint channel estimation, phase noise compensation, and signal detection problems, such as... Figure 1 As shown in the figure, the present invention discloses a semi-blind OFDM reception method that combines channel estimation, phase noise compensation, and signal detection. The specific steps are as follows:

[0059] (1) Based on the phase noise modulo-1 constraint and the mapping constraint of the signal to be detected, a constrained joint objective function for channel estimation, phase noise compensation, and signal detection is constructed. In this embodiment, the objective function is expressed as:

[0060]

[0061] Where Diag(·) represents constructing a diagonal matrix with the input vector as its diagonal elements, (·) H Let ||·|| denote the conjugate transpose, and ||·|| be the 2-norm of the vector. This is the time-domain received signal, where N represents the number of subcarriers. Let φ(n) represent the time-domain phase noise vector, and its distribution satisfies in This represents a normal distribution with a mean of 0 and a variance of 4πβT, where T is the period of the OFDM symbol and β represents the 3dB linewidth of the phase noise. It is the time-domain channel matrix, which can be represented as H = F H Diag(F h h)F, where h=[h(0), h(1), …, h(L-1)] T It is a time-varying channel vector in the time domain, where L represents the channel path number. Let represent the pilot vector, where the value of its element at the data location is zero. Let This represents a data vector, where the value of each element at the pilot position is zero. Represents a data subvector, where the data vector x is... d Removing all zero elements from N yields a data subvector. d This represents the number of data subcarriers. Let i d =[i d (1), i d (1), …i d (N d ] represents the index of the data location. This represents the projection matrix that maps data subvectors to data vectors, where J(i) d (n), n)=1, n=1, 2,…N d The remaining elements in the matrix are 0. It is a Fourier matrix, and its (m, n)th element is represented as

[0062] The constraints of the objective function are expressed as follows:

[0063] |e φ(n) |=1, n=1,2,…,N

[0064]

[0065] Where |·| represents the modulo operation, Indicates 4 q -QAM symbol mapping set, q = 1, 2, 3, ...; x represents the set The element in, x i x q Let x represent the real part and the imaginary part, respectively. Indicates will Extended to N d 3D space.

[0066] (2) With the phase noise and the signal to be detected fixed, the optimal channel estimate is obtained according to the least squares criterion, and this estimate is then used back to the original optimization objective to obtain the updated objective function; specifically:

[0067] First, by rewriting the objective function, we obtain a function containing the time-domain channel vector h:

[0068]

[0069] Where X p =Diag(x p ),

[0070] With fixed phase noise and the signal to be detected, the time-domain channel estimate is obtained using the least squares method:

[0071] h=(M H M) -1 M H FDiag(e jφ )y

[0072] Where M = (X p +X d )F h ,(·) -1 This represents finding the inverse of a matrix.

[0073] Substitute this estimate back into the original objective function, and make θ = e -jφ Then the original objective function can be rewritten as:

[0074]

[0075] The constraints are:

[0076] |θ(n)|=1, n=1, 2,…,N

[0077]

[0078] Where Y = Diag(y).

[0079] (3) By introducing penalty terms, penalty factors and auxiliary variables, an augmented Lagrangian function of the optimization objective was constructed, and the corresponding optimization problem was solved by using the cross-direction multiplier method (ADMM) and the minimization-maximization (MM) algorithm.

[0080] 4 q The signal representation of a QAM set is a weighted sum of binary variables, i.e.

[0081]

[0082] in d represents a set The element in d i d q Let d represent the real and imaginary parts of d, respectively. Indicates will Extended to N d 3D space.

[0083] Introducing penalty terms to constraints Relaxation and tension are performed, and auxiliary variables are introduced. and The following objective function is obtained:

[0084]

[0085] Constraints:

[0086] η = θ, |θ n |=1, n=1,2,…,N

[0087]

[0088] in, S = Diag(Js), Represents a set The elements in They represent The real and imaginary parts, Indicates will Extended to N d 2D space; β i >0 is what makes v i The penalty factor for elements close to -1 or 1;

[0089] The corresponding augmented Lagrangian function is obtained as follows:

[0090]

[0091] Where ρ1 is related to the constraints The penalty factor, ρ2, is the penalty factor with respect to the constraint η = θ. This indicates a constraint. Lagrange multipliers, This represents the Lagrange multiplier corresponding to the constraint η = θ. This indicates taking the real part of the variable.

[0092] The (k+1)th ADMM iteration process includes the following steps:

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] Solving each subproblem involves the following steps:

[0100] (3.1) Update the phase noise variable θ k+1 :

[0101]

[0102] in This means projecting each element of the input vector onto a space of magnitude 1.

[0103] (3.2) Update the auxiliary variable η k+1 :

[0104] The subproblem of optimizing η can be represented as:

[0105]

[0106] Where Q = Y H F H (I N -P)FY;

[0107] Solving the above equation yields a closed-form solution.

[0108] (3.3) Update the variable of the signal to be detected

[0109]

[0110] in This means projecting each element of the input vector onto the interval [-1, 1].

[0111] (3.4) Update auxiliary variable s k+1 :

[0112] The subproblem of optimizing s can be expressed by the following formula:

[0113]

[0114] in

[0115] Using the MM algorithm, a in the above formula H D -1 a is looking for an alternative function, i.e.

[0116]

[0117] in:

[0118]

[0119]

[0120] Where A⊙B represents the Hadamard product of A and B, I N Represents an N×N identity matrix.

[0121] Substituting the substitution function back into the optimization subproblem, the objective function is updated as follows:

[0122]

[0123] Solving the above equation, we get

[0124]

[0125] (3.5) Update the Lagrange multipliers

[0126]

[0127] (3.6) Update the Lagrange multipliers

[0128]

[0129] Based on the closed-form solutions for each variable calculated in the above steps, perform the (k+1)th iteration according to the following formula:

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136] (4) When the iteration termination condition is met, the joint estimate of the channel, phase noise and transmitted signal is obtained.

[0137] The iteration terminates under one of the following two conditions:

[0138] Case 1: The maximum number of iterations is preset to K. When the current number of iterations reaches K, the iteration termination condition is met, the iteration stops, and the result of the Kth iteration is output as the prediction value.

[0139] Case 2: After several iterations, the iteration results have converged, and the iteration termination condition is met. The result of the last iteration is then output as the predicted value.

[0140] To verify the effectiveness of the present invention, a simulation experiment was conducted. The parameters involved in the simulation experiment are shown in the table below:

[0141] Table 1 Simulation Experiment Parameters

[0142] parameter Value Number of subcarriers 64 Symbolic Number 14 carrier frequency 40GHz Subcarrier spacing 30kHz Channel Model Tapped Delay Line A Doppler Jakes model Phase noise model Wiener noise model 3-dB phase noise linewidth 1000Hz Pilot pattern comb pilot Pilot spacing 6

[0143] Figure 2 The simulation results show that the semi-blind OFDM receiving method proposed in this invention, which combines channel estimation, phase noise compensation, and signal detection, can save pilot overhead, improve spectrum utilization, and enhance system BER performance compared to existing solution algorithms.

[0144] Based on the same inventive concept, this invention discloses a semi-blind OFDM receiving system for joint channel estimation, phase noise compensation, and signal detection, comprising: a target construction module, used to construct a constrained objective function for joint channel estimation, phase noise compensation, and signal detection based on phase noise modulo-1 constraints and the mapping constraint of the signal to be detected; an optimization solution module, used to fix the phase noise and the signal to be detected, obtain the optimal channel estimate according to the least squares criterion, and substitute it back into the original optimization objective to obtain an updated objective function; and to construct an augmented Lagrangian function of the optimization objective by introducing a penalty term, a penalty factor, and auxiliary variables, and solve the corresponding optimization problem using the cross-direction multiplier method (ADMM) and the maximization-minimization MM algorithm; and to obtain the joint estimate of the channel, phase noise, and transmitted signal when the iteration termination condition is met. Specific implementation details are given in the above method embodiments and will not be repeated here.

[0145] Based on the same inventive concept, an embodiment of the present invention discloses a computer system including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the steps of the semi-blind OFDM reception method for joint channel estimation, phase noise compensation, and signal detection.

[0146] Based on the same inventive concept, embodiments of the present invention disclose a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the semi-blind OFDM reception method for joint channel estimation, phase noise compensation, and signal detection.

[0147] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A semi-blind OFDM receiving method that combines channel estimation, phase noise compensation, and signal detection, characterized in that, Includes the following steps: (1) Based on the phase noise modulo 1 constraint and the signal to be detected mapping constraint, construct the objective function of constrained joint channel estimation, phase noise compensation and signal detection; (2) Fix the phase noise and the signal to be detected, obtain the best channel estimate according to the least squares criterion, and bring it back to the original optimization objective to obtain the updated objective function; (3) By introducing penalty terms, penalty factors and auxiliary variables, an augmented Lagrangian function of the optimization objective was constructed, and the corresponding optimization problem was solved by using the cross-direction multiplier method ADMM and the maximization-minimization MM algorithm. (4) When the iteration termination condition is met, the joint estimate of the channel, phase noise and transmitted signal is obtained; The objective function for constructing the joint channel estimation, phase noise compensation, and signal detection in step (1) is as follows: Where Diag(·) represents constructing a diagonal matrix with the input vector as its diagonal elements, (·) H Let ||·|| denote the conjugate transpose, and ||·|| be the 2-norm of the vector; This is the time-domain received signal, where N represents the number of subcarriers. Represents the time-domain phase noise vector. It is the time-domain channel matrix, H = F H Diag(F h h)F, h=[h(0), h(1),…, h(L-1)] T It is a time-varying channel vector in the time domain, where L represents the channel path number. Represents the pilot vector, which is the data vector. All zero elements are removed to obtain the data subvector. N d Indicates the number of data subcarriers; This represents the projection matrix that maps data subvectors to data vectors. It is a Fourier matrix; The constraints of the objective function are: |e φ(n) |=1,n=1,2,…,N Where |·| represents the modulo operation, and χ represents 4. q -QAM symbol mapping set, q = 1, 2, 3, ...; x represents an element in set χ, x i x q Let x represent the real part and the imaginary part, respectively. This means extending χ to N. d 3D space; In step (2), the phase noise and the signal to be detected are fixed, and the time-domain channel estimate h = (M) is obtained using the least squares method. H M) -1 M H FDiag(e jφ )y,M=(X p +X d )F h X p =Diag(x p ), (·) -1 This represents matrix inversion; substituting the estimated value back into the original objective function and making θ = e^(-π / 2) jφ The updated objective function is: The constraints are: θ(n)|=1,n=1,2,…,N Where, Y = Diag(y); In step (3), a penalty term is introduced to relax or tighten the constraints, and an auxiliary variable is also introduced. and The following objective function is obtained: Constraints: η=θ,|θ n |=1,n=1,2,…,N in, S = Diag(Js), Represents a set The elements in They represent The real and imaginary parts, Indicates will Extended to N d 2D space; β i >0 is what makes v i The penalty factor for elements close to -1 or 1; The corresponding augmented Lagrangian function is obtained as follows: Where ρ1 is related to the constraints The penalty factor, ρ2, is the penalty factor with respect to the constraint η = θ. This indicates a constraint. Lagrange multipliers, This represents the Lagrange multiplier corresponding to the constraint η = θ. This indicates taking the real part of the variable; The optimization problem in step (3) is solved using the following formula for the (k+1)th iteration: in: Q=Y H F H (I N -P)FY This means projecting each element of the input vector onto a space of magnitude 1. This means projecting each element of the input vector onto the interval [-1, 1]; A⊙B represents the Hadamard product of A and B, I N Represents an N×N identity matrix.

2. The semi-blind OFDM receiving method based on joint channel estimation, phase noise compensation, and signal detection according to claim 1, characterized in that, The iteration termination conditions in step (4) include reaching the preset maximum number of iterations or the iteration results converging.

3. A semi-blind OFDM receiving system combining channel estimation, phase noise compensation, and signal detection, used to implement the semi-blind OFDM receiving method combining channel estimation, phase noise compensation, and signal detection as described in claim 1, characterized in that, include: The objective construction module is used to construct a constrained joint objective function for channel estimation, phase noise compensation, and signal detection based on the phase noise modulo-1 constraint and the mapping constraint of the signal to be detected. The optimization solution module is used to fix the phase noise and the signal to be detected, obtain the best channel estimate based on the least squares criterion, and bring it back to the original optimization objective to obtain the updated objective function. Furthermore, by introducing penalty terms, penalty factors, and auxiliary variables, an augmented Lagrangian function for the optimization objective was constructed, and the corresponding optimization problem was solved using the cross-direction multiplier method (ADMM) and the maximization-minimization MM algorithm. When the iteration termination condition is met, the joint estimates of the channel, phase noise, and transmitted signal are obtained.

4. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the steps of a semi-blind OFDM reception method for joint channel estimation, phase noise compensation, and signal detection as described in claim 1 or 2.

5. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of a semi-blind OFDM reception method for joint channel estimation, phase noise compensation, and signal detection as described in claim 1 or 2.

Images