CN104079520A - Impulse interference inhibition method of OFDM system - Google Patents

Abstract

The invention discloses an impulse interference inhibition method of an OFDM system. According to the method, solving the problem for calculating the estimation value of an unknown impulse noise vector is converted into solving the problem enabling the value of a l2-l1 norm type objective function to be the smallest, an optimization sub-problem is solved through the iteration mode to obtain the optimal solution enabling the value of the l2-l1 norm type objective function to be the smallest, and a receipt signal vector after the pulse noise interference is inhibited is obtained by subtracting the final estimation value of an impulse noise vector from the receipt signal vector with a cyclic prefix removed and the discrete Fourier transform implemented through the discrete Fourier transform. The method has the advantages that solving the original problem is converted into solving the problem enabling the value of the l2-l1 norm type objective function to be the smallest, and the NP-hard problem in the process of directly estimating the optimal sparse solution of the impulse noise can be avoided; the optimal solution enabling the value of the l2-l1 norm type objective function to be the smallest is obtained by solving the optimization sub-problem in the iteration mode, so that the time used for estimating the pulse noise is shortened, and the influence on the OFDM symbol error probability from the pulse noise is reduced.

Description

Pulse interference suppression method of OFDM system

Technical Field

The invention relates to a pulse interference suppression technology in the field of communication, in particular to a pulse interference suppression method of an OFDM system.

Background

Orthogonal Frequency Division Multiplexing (OFDM) technology has been adopted by IEEE802.11, IEEE802.16, IEEE802.20, etc., and is widely used in various digital broadband communication systems because of its good multipath interference resistance. However, in many practical communication systems, after an OFDM signal is transmitted through a channel, not only gaussian background noise but also many artificially generated impulse noises are contained in the received signal, and these impulse noises are completely different from the gaussian background noise in statistical characteristics, which results in that the performance of the conventional OFDM system designed based on the background noise is severely attenuated under the environment of impulse noise interference. Therefore, it is necessary to design an effective impulse noise interference suppression method to improve the performance of the OFDM system.

The problem of impulse noise suppression in OFDM systems has been widely studied at present. Himal a. suraweera et al filter impulse noise with large amplitude by adding a nonlinear filter with a preset decision threshold in front of a traditional OFDM receiver, and realize the suppression of impulse noise interference. Pablo Torio et al propose an OFDM system impulse noise suppression method based on cell interleaving. In addition, Takuya Kitamura et al have studied impulse noise interference suppression methods based on replica signals, and have implemented cancellation of impulse noise by iterative symbol decision and replica signal subtraction. However, the above studies assume that impulse noise is subject to a certain noise statistical distribution model, which results in that when processing signals with impulse noise interference, a data-aided training process is required to obtain specific impulse noise statistical distribution parameters, which not only increases the system complexity, but also severely degrades the performance of the method when the assumed noise statistical distribution model cannot reflect the actual impulse noise statistical characteristics. To solve the problem, Lin and Evans, and the like, provide an impulse noise elimination method based on a compressed sensing technology by using the Sparse characteristic of impulse noise in the time domain, and the method does not need to preset a statistical model of impulse noise, and can estimate a high-dimensional impulse noise vector from a known signal vector of lower dimension by using a Sparse Bayesian Learning (SBL) reconstruction algorithm, but because the SBL algorithm solves a hyperparameter by using a maximum likelihood method, all hyperparameters to be estimated are updated simultaneously in each iteration process by directly using condition expectation maximization, so that the convergence of the whole SBL algorithm is slow, the condition expectation maximization step is difficult to realize, and the time complexity of the whole method is high, and the practicability is not strong.

Disclosure of Invention

The technical problem to be solved by the present invention is to provide an impulse interference suppression method for an OFDM system, which can effectively reduce the time for impulse noise estimation and can effectively reduce the influence of impulse noise on the error probability of OFDM symbols.

The technical scheme adopted by the invention for solving the technical problems is as follows: an impulse interference suppression method for an OFDM system, comprising the steps of:

firstly, at a transmitting end, an OFDM signal vector to be transmitted is recorded as X, and if M known pilots exist in X, a vector formed by the M known pilots in X is recorded as X_T(ii) a Then, carrying out inverse discrete Fourier transform and adding cyclic prefix on the X in sequence to obtain a sending signal vector; wherein the dimension of X is Nx 1 dimension, N>2，1<M<N，X_TDimension of (a) is dimension M × 1, T denotes an index set composed of indexes of M known pilots in X, and length of T is M;

secondly, assuming that the state information of a channel for transmitting signals is known, a transmitting end transmits a transmitting signal vector to a receiving end through the channel, and impulse noise vectors and background noise vectors generated in the channel in the transmission process of the transmitting signal vector are correspondingly marked as e and N, wherein the dimensions of the unknown impulse noise vectors e and the unknown background noise vectors N are N multiplied by 1 dimensions;

at a receiving end, successively removing cyclic prefix and discrete Fourier transform of a received signal vector to obtain a received signal vector to be processed, and marking the received signal vector as Y, wherein the Y is formed by superposing an impulse noise vector e and a background noise vector n by X; then extracting at X from Y_TA signal vector formed by superimposing the impulse noise vector e and the background noise vector n is denoted as Y_T(ii) a Then according to the state information of the channel, removing Y_TNeutralization of X_TObtaining a known vector Z only containing two components of an unknown impulse noise vector e and an unknown background noise vector n by corresponding known signal vectors; wherein the dimension of Y is Nx 1 dimension, Y_TDimension of (a) is Mx 1 dimension, and dimension of Z is Mx 1 dimension;

fourthly, the problem of solving the estimation value of the unknown impulse noise vector e is converted into the solution of the estimation value of e so that l₂-l₁Norm type objective functionWill then beIn (1)Expressed in functional form as f (e),wherein the symbol "| | | purple₂To find l₂Norm symbol, symbolTo find l₂Norm squared, symbol "| | | | non-conducting phosphor₁To find l₁Norm symbol, F_TRepresenting a known discrete Fourier transform matrix of dimension M x N, wherein tau represents a regularization parameter, and f () is a function expression mode;

solving the estimated value of e in an iterative mode to enable l₂-l₁Norm type objective functionThe specific process is as follows:

-1, setting the value of the regularization parameter tau to 0.1| (F)_T)^HZ||_∞Let the initial value of the estimated value of e be e₀，e₀＝((F_T)^HF_T)^-1(F_T)^HZ, and let k denote the number of iterations, the initial value of k is 1, wherein the symbol "| | | purple_∞"to solve infinite norm sign (F)_T)^HIs F_TConjugate transpose matrix of (1) ((F)_T)^HF_T)^-1Is (F)_T)^HF_TThe inverse matrix of (d);

-2, define a firstEvaluation factor alpha of k iterations_k， <math> <mrow> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>H</mi> </msup> <msub> <mi>r</mi> <mi>k</mi> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>H</mi> </msup> <msub> <mi>S</mi> <mi>k</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mi>k</mi> <mo>&NotEqual;</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> Reissue to orderWherein (S)_k)^HIs S_kConjugate transpose matrix of (1), S_k＝e_k-e_k-1，e_kRepresenting the estimated value of e, obtained after the kth iteration_k-1Representing the estimated value of e obtained after the k-1 iteration,means to find f (e) after the k iteration_k) The value of the first derivative of (a),means to find f (e) after the k-1 th iteration_k-1) The value of the first derivative of (a),

$f\left(e_{k-1}\right)=\frac{1}{2}{\left|\right|Z-F_T{e}_{k-1}\left|\right|}_2^2;$

fifthly to 3 according to alpha_kAnd u_kCalculating the estimated value of e obtained after the kth iteration and recording as e_k，Where max () is a function of taking the maximum value, the symbol "|" is a symbol of taking the absolute value,represents u_kI is more than or equal to 1 and less than or equal to N;

fifthly, judgingIf yes, executing the fifth step-5; otherwise, let k equal to k +1, then return to the step (c) -2 to continue execution, wherein the symbol "| | | | non-calculation₂To find l₂A norm symbol, wherein epsilon is a set minimum normal number, and k is an assignment symbol in k + 1;

fifthly, ending the iterative process to obtain the final estimated value of e, and marking asWherein,wherein, the symbol is an assignment symbol;

final estimate of Y minus eAnd then obtaining a frequency domain expression obtained by discrete Fourier transform, namely obtaining a received signal vector after inhibiting the interference of the impulse noise.

In the fifth step-4, taking epsilon as 10^-5。

Compared with the prior art, the invention has the advantages that:

1) the method of the invention converts the problem of solving the estimation value of unknown impulse noise vector into solving the problem of solving₂-l₁The problem of the minimum value of the norm-type objective function can effectively avoid the NP-hard problem when the optimal sparse solution of the impulse noise is directly estimated.

2) The method solves an optimization sub-problem in an iterative mode to obtain a lead₂-l₁The optimal solution with the minimum value of the norm type objective function not only obviously reduces the time for pulse noise estimation, but also effectively reduces the influence of the pulse noise on the error probability of OFDM symbolsThus, the practicability is improved.

Drawings

FIG. 1 is a block diagram of a system for achieving impulse interference suppression using the method of the present invention;

FIG. 2 is a schematic diagram showing the comparison of the average running time of the CPU consumed in the impulse noise suppression of the OFDM system by the method of the present invention and the existing SBL-based impulse noise suppression method when the SNR is fixed;

fig. 3 is a schematic diagram illustrating the comparison of symbol error probability of the OFDM system when the method of the present invention and the conventional impulse noise suppression method based on the SBL vary with the signal-to-noise ratio.

Detailed Description

The invention is described in further detail below with reference to the accompanying examples.

Fig. 1 shows a system block diagram for implementing impulse interference suppression by using the method of the present invention, where the method of the present invention specifically includes the following steps:

firstly, at a transmitting end, an OFDM signal vector to be transmitted is recorded as X, and if M known pilots exist in X, a vector formed by the M known pilots in X is recorded as X_T(ii) a Then, carrying out inverse discrete Fourier transform and adding cyclic prefix on the X in sequence to obtain a sending signal vector; wherein the dimension of X is Nx 1 dimension, N>2，1<M<N，X_TDimension (e) is dimension (M × 1), T represents an index set composed of indexes of M known pilots in X, and length of T is M.

In specific implementation, N may generally be 16, 64, 128, 512, 1024, etc., and M is generally half of N, i.e., N is a value $M=\frac{N}{2}.$

And secondly, assuming that the state information of a channel for transmitting signals is known, the transmitting end transmits a transmitting signal vector to the receiving end through the channel, and the impulse noise vector and the background noise vector generated in the channel in the transmission process of the transmitting signal vector are correspondingly marked as e and N, wherein the dimensions of the unknown impulse noise vector e and the unknown background noise vector N are N multiplied by 1 dimensions.

At a receiving end, successively removing cyclic prefix and discrete Fourier transform of a received signal vector to obtain a received signal vector to be processed, and marking the received signal vector as Y, wherein the Y is formed by superposing an impulse noise vector e and a background noise vector n by X; then extracting at X from Y_TA signal vector formed by superimposing the impulse noise vector e and the background noise vector n is denoted as Y_T(ii) a Then according to the state information of the channel, removing Y_TNeutralization of X_TObtaining a known vector Z only containing two components of an unknown impulse noise vector e and an unknown background noise vector n by corresponding known signal vectors, wherein the vector Z can be called as a projection of the unknown impulse noise vector on a known pilot; wherein the dimension of Y is Nx 1 dimension, Y_TDimension of (a) is M × 1 dimension, and dimension of Z is M × 1 dimension.

Fourthly, the problem of solving the estimation value of the unknown impulse noise vector e is converted into the solution of the estimation value of e so that l₂-l₁Norm type objective functionWill then beIn (1)Expressed in functional form as f (e),wherein the symbol "| | | purple₂To find l₂Norm symbol, symbolTo find l₂Norm squared, symbol "| | | | non-conducting phosphor₁To find l₁Norm symbol, F_TRepresents a known discrete fourier transform matrix of dimension M × N, τ represents a regularization parameter, and the value of τ is a set positive constant, and f () is a functional expression.

Solving an optimization subproblem in an iterative mode to obtain an estimated value of e so that l₂-l₁Norm type objective functionThe specific process is as follows:

-1, setting the value of the regularization parameter tau to 0.1| (F)_T)^HZ||_∞Let the initial value of the estimated value of e be e₀，e₀＝((F_T)^HF_T)^-1(F_T)^HZ, and let k denote the number of iterations, the initial value of k is 1, wherein the symbol "| | | purple_∞"to solve infinite norm sign (F)_T)^HIs F_TConjugate transpose matrix of (1) ((F)_T)^HF_T)^-1Is (F)_T)^HF_TThe inverse matrix of (c).

Fifthly-2, defining an evaluation factor alpha of the kth iteration_k， <math> <mrow> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>H</mi> </msup> <msub> <mi>r</mi> <mi>k</mi> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>H</mi> </msup> <msub> <mi>S</mi> <mi>k</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mi>k</mi> <mo>&NotEqual;</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> Reissue to orderWherein (S)_k)^HIs S_kConjugate transpose matrix of (1), S_k＝e_k-e_k-1，e_kRepresenting the estimated value of e, obtained after the kth iteration_k-1Representing the estimated value of e obtained after the k-1 iteration,means to find f (e) after the k iteration_k) The value of the first derivative of (a),means to find f (e) after the k-1 th iteration_k-1) The value of the first derivative of (a),

$f\left(e_{k-1}\right)=\frac{1}{2}{\left|\right|Z-F_T{e}_{k-1}\left|\right|}_2^2.$

fifthly to 3 according to alpha_kAnd u_kCalculating the estimated value of e obtained after the kth iteration and recording as e_k， <math> <mrow> <msub> <mi>e</mi> <mi>k</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>u</mi> <mi>k</mi> <mi>i</mi> </msubsup> <mo>|</mo> <mo>-</mo> <mfrac> <mi>&tau;</mi> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> </mfrac> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>u</mi> <mi>k</mi> <mi>i</mi> </msubsup> <mo>|</mo> <mo>-</mo> <mfrac> <mi>&tau;</mi> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> </mfrac> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>&tau;</mi> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> </mfrac> </mrow> </mfrac> <msubsup> <mi>u</mi> <mi>k</mi> <mi>i</mi> </msubsup> <mo>,</mo> </mrow> </math> Wherein, here will be <math> <mrow> <mfrac> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>u</mi> <mi>k</mi> <mi>i</mi> </msubsup> <mo>|</mo> <mo>-</mo> <mfrac> <mi>&tau;</mi> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> </mfrac> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>u</mi> <mi>k</mi> <mi>i</mi> </msubsup> <mo>|</mo> <mo>-</mo> <mfrac> <mi>&tau;</mi> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> </mfrac> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>&tau;</mi> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> </mfrac> </mrow> </mfrac> <msubsup> <mi>u</mi> <mi>k</mi> <mi>i</mi> </msubsup> </mrow> </math> Called the optimization sub-problem, max () is takenThe maximum function, the symbol "|" is the absolute value symbol,represents u_kI is more than or equal to 1 and less than or equal to N.

Fifthly, judgingIf yes, executing the fifth step-5; otherwise, let k equal to k +1, then return to the step (c) -2 to continue execution, wherein the symbol "| | | | non-calculation₂To find l₂Norm symbol, epsilon is a set extremely small normal number, and epsilon is 10 in the present embodiment^-5And k is given as "k + 1" as an assignment symbol.

Fifthly, ending the iterative process to obtain the final estimated value of e, and marking asWherein,wherein, the symbol is assigned.

Final estimate of Y minus eAnd then obtaining a frequency domain expression obtained by discrete Fourier transform, namely obtaining a received signal vector after inhibiting the interference of the impulse noise.

The feasibility and effectiveness of the impulse interference suppression method of the OFDM system of the present invention is further illustrated by the following simulations.

Selecting simulation system as baseband OFDM system using QPSK modulation, and orderingThe simulation environment is MATLAB2011b, and the adopted computer is provided with an Intel Pentium dual-core processor and has a memory of 2.96GBThe main frequency is 2.16GHz, the operating system is Windows XP SP3, and the unit of signal-to-noise ratio (dB) is expressed by dB. The impulse noise used in the simulation was generated according to the midelton Class a model (0.2 for the overlap exponent and 0.01 for the power ratio factor).

Fig. 2 shows the comparison of the average running time of the CPU consumed in performing impulse noise suppression of the OFDM system by the method of the present invention and the existing SBL-based impulse noise suppression method when N is 16, 64, 128, 256, 512, and 1024, respectively, and the snr is-5 dB. As can be seen from fig. 2, the average running time of the CPU consumed by the method of the present invention is significantly less than the average running time of the CPU consumed by the conventional SBL-based impulse noise suppression method, i.e., the method of the present invention significantly reduces the time for suppressing impulse noise interference, and has higher practicability.

Fig. 3 shows the symbol error probability variation of the OFDM system after the present invention method and the existing SBL-based impulse noise suppression method are adopted under different snr conditions when N is 256. The total number of transmitted OFDM symbols is set to 5000, and the variation range of the signal-to-noise ratio is-10 dB to 30 dB. As can be seen from fig. 3, compared with the existing SBL-based impulse noise suppression method, when the signal-to-noise ratio is less than 10dB, the performance of the method of the present invention is slightly lower than that of the existing SBL-based impulse noise suppression method, and when the signal-to-noise ratio is greater than 10dB, the performance of the method of the present invention is significantly better than that of the existing SBL-based impulse noise suppression method, and the OFDM system using the method of the present invention has a performance gain of more than 5dB compared with the OFDM system without impulse noise suppression.

Claims (2)

1. An impulse interference suppression method for an OFDM system, comprising the steps of:

firstly, at a transmitting end, an OFDM signal vector to be transmitted is recorded as X, and if M known pilots exist in X, a vector formed by the M known pilots in X is recorded as X_T(ii) a Then, carrying out inverse discrete Fourier transform and adding cyclic prefix on the X in sequence to obtain a sending signal vector; wherein the dimension of X is Nx 1 dimension, N>2，1<M<N，X_TIs of dimension M X1, T represents an index set consisting of indexes of M known pilots in X, and T has a length ofM；

Secondly, assuming that the state information of a channel for transmitting signals is known, a transmitting end transmits a transmitting signal vector to a receiving end through the channel, and impulse noise vectors and background noise vectors generated in the channel in the transmission process of the transmitting signal vector are correspondingly marked as e and N, wherein the dimensions of the unknown impulse noise vectors e and the unknown background noise vectors N are N multiplied by 1 dimensions;

at a receiving end, successively removing cyclic prefix and discrete Fourier transform of a received signal vector to obtain a received signal vector to be processed, and marking the received signal vector as Y, wherein the Y is formed by superposing an impulse noise vector e and a background noise vector n by X; then extracting at X from Y_TA signal vector formed by superimposing the impulse noise vector e and the background noise vector n is denoted as Y_T(ii) a Then according to the state information of the channel, removing Y_TNeutralization of X_TObtaining a known vector Z only containing two components of an unknown impulse noise vector e and an unknown background noise vector n by corresponding known signal vectors; wherein the dimension of Y is Nx 1 dimension, Y_TDimension of (a) is Mx 1 dimension, and dimension of Z is Mx 1 dimension;

fourthly, the problem of solving the estimation value of the unknown impulse noise vector e is converted into the solution of the estimation value of e so that l₂-l₁Norm type objective functionWill then beIn (1)Expressed in functional form as f (e),wherein the symbol "| | | purple₂To find l₂Norm symbol, symbolTo find l₂Norm squared, symbol "| | | | non-conducting phosphor₁To find l₁Norm symbol, F_TRepresenting a known discrete Fourier transform matrix of dimension M x N, wherein tau represents a regularization parameter, and f () is a function expression mode;

solving the estimated value of e in an iterative mode to enable l₂-l₁Norm type objective functionThe specific process is as follows:

-1, setting the value of the regularization parameter tau to 0.1| (F)_T)^HZ||_∞Let the initial value of the estimated value of e be e₀，e₀＝((F_T)^HF_T)^-1(F_T)^HZ, and let k denote the number of iterations, the initial value of k is 1, wherein the symbol "| | | purple_∞"to solve infinite norm sign (F)_T)^HIs F_TConjugate transpose matrix of (1) ((F)_T)^HF_T)^-1Is (F)_T)^HF_TThe inverse matrix of (d);

fifthly-2, defining an evaluation factor alpha of the kth iteration_k， <math> <mrow> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>H</mi> </msup> <msub> <mi>r</mi> <mi>k</mi> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>H</mi> </msup> <msub> <mi>S</mi> <mi>k</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mi>k</mi> <mo>&NotEqual;</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> Reissue to orderWherein (S)_k)^HIs S_kConjugate transpose matrix of (1), S_k＝e_k-e_k-1，e_kRepresenting the estimated value of e, obtained after the kth iteration_k-1Representing the estimated value of e obtained after the k-1 iteration,means to find f (e) after the k iteration_k) The value of the first derivative of (a),means to find f (e) after the k-1 th iteration_k-1) The value of the first derivative of (a),

$f\left(e_{k-1}\right)=\frac{1}{2}{\left|\right|Z-F_T{e}_{k-1}\left|\right|}_2^2;$

fifthly to 3 according to alpha_kAnd u_kCalculating the estimated value of e obtained after the kth iteration and recording as e_k，Where max () is a function of taking the maximum value, the symbol "|" is a symbol of taking the absolute value,represents u_kI is more than or equal to 1 and less than or equal to N;

fifthly, judgingIf yes, executing the fifth step-5; otherwise, let k equal to k +1, then return to the step (c) -2 to continue execution, wherein the symbol "| | | | non-calculation₂To find l₂A norm symbol, wherein epsilon is a set minimum normal number, and k is an assignment symbol in k + 1;

fifthly, ending the iterative process to obtain the final estimated value of e, and marking asWherein,wherein, the symbol is an assignment symbol;

final estimate of Y minus eAnd then obtaining a frequency domain expression obtained by discrete Fourier transform, namely obtaining a received signal vector after inhibiting the interference of the impulse noise.

2. The method as claimed in claim 1, wherein ∈ 10 is selected from the step of (6-4) to suppress the impulse interference in the OFDM system^-5。