CN116668249A - OFDM signal transmission method based on aliasing pilot frequency - Google Patents
OFDM signal transmission method based on aliasing pilot frequency Download PDFInfo
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Abstract
The invention discloses an OFDM signal transmission method based on an aliasing pilot frequency, which comprises the following steps: a: establishing a mathematical model of an aliased pilot OFDM iterative receiver; b: initializing an iterative algorithm variable; c: channel estimation is performed by using a unitary transformation approximate message passing method; d: performing aliasing pilot symbol detection by using a belief propagation algorithm to obtain an estimation of a transmitted information sequence; e: performing noise precision estimation; f: and (C) performing the steps (E) in an iteration mode, updating the established mathematical model of the aliased pilot OFDM iterative receiver, and finally completing signal transmission by using the updated mathematical model of the aliased pilot OFDM iterative receiver. The invention can take the aliasing pilot frequency as the priori distribution of the frequency domain symbol, completes the guidance of the iterative algorithm, does not need to change the existing receiver frame, and effectively improves the frequency spectrum utilization rate and the robustness of the OFDM system.
Description
Technical Field
The invention relates to the field of communication receiver design, in particular to an Orthogonal Frequency Division Multiplexing (OFDM) signal iterative transmission method applying an aliased pilot frequency.
Background
As a basic stone of a modern communication system, an Orthogonal Frequency Division Multiplexing (OFDM) technology is widely used in various fields such as wireless local area network, mobile communication, underwater acoustic communication, and visible light communication. In recent 30 years, intensive research on channel estimation and detection algorithms of an OFDM system has been carried out, and a great deal of research results are obtained. However, with the development of high-speed rail, unmanned aerial vehicle and low-orbit satellite, the rapid time-varying, sparse and Doppler effect of the channel in the high-speed moving scene brings new challenges to the existing OFDM receiver. Existing OFDM transmission systems typically select some subcarriers to transmit pilot signals for channel estimation and symbol detection. However, in high-speed communication, due to multipath effects, channel parameters are complex, and accurate channel estimation requires a large number of pilots, resulting in high spectrum and complexity overhead. In addition, the peak throughput of the 6 th generation mobile communication system reaches the order of the bit (Tbit), and the spectrum resource is expanded to the millimeter wave frequency band. Millimeter waves have larger bandwidth, can realize higher data rate, have more obvious multipath and sparse characteristics of channels, but put higher requirements on the complexity of channel estimation and detection algorithms.
OFDM systems typically add known information to information bits or channel coded bits as pilots, or select multiple subcarriers to transmit pilots. However, the insertion of pilots occupies valuable spectrum resources and creates more computational overhead, causing significant loss of spectrum efficiency and transmission rate.
The unitary transformation approximate message passing algorithm (UAMP) is a system modeling and parameter estimation method based on Bayesian theory, and the method comprises the steps of firstly factoring the joint probability distribution of all variables in a system; then according to the constraint relation among the variables, selecting an optimal message updating rule for calculation; and finally, designing a reasonable initialization and iteration mechanism to form an iteration algorithm.
Disclosure of Invention
The invention aims to provide an OFDM signal transmission method based on an aliased pilot frequency, which can take the aliased pilot frequency as the priori distribution of frequency domain symbols to finish the guidance of an iterative algorithm without changing the existing receiver frame, thereby effectively improving the spectrum utilization rate and the robustness of an OFDM system.
The invention adopts the following technical scheme:
an OFDM signal transmission method based on an aliasing pilot frequency comprises the following steps:
a: generating frequency domain data vector x d Frequency domain pilot vector x p The frequency domain transmission vector x, the OFDM channel h and the receiving vector y, and finally establishing an aliasing pilot OFDM iterative receiver mathematical model y=h.x+w; wherein,representing covariance matrix as lambda -1 I N Is the additive white Gaussian noise, lambda is the noise precision, I N Representing a unit array of dimension N;
b: initializing an iterative algorithm variable;
involving initializing the mean value of the frequency domain transmission vector x in the data symbol dependent variableVariance v x Initial value and noise precision->Is set to an initial value of (1); also includes initializing a mean value of a time domain channel tap vector alpha in the channel dependent variable>Variance v α An intermediate variable s and a super a priori variable y; and an observation matrix ψ, and a pseudo-frequency domain channel vector h';
c: channel estimation is performed by using a unitary transformation approximate message passing method;
d: performing aliasing pilot symbol detection by using belief propagation algorithm to obtain a transmission signalEstimation of the information sequence b
E: performing noise precision estimation;
f: and (C) performing the steps (E) in an iteration mode, updating the established mathematical model of the aliased pilot OFDM iterative receiver, and finally completing signal transmission by using the updated mathematical model of the aliased pilot OFDM iterative receiver.
The step A comprises the following specific steps:
a1: generating frequency domain data vector x d ；
Let the transmitted information sequence b e 0,1] 2N×1 Obtaining frequency domain data vector through Q-order QAM modulationWherein the subscript d represents the data field and the symbol b e [0,1 ]] 2N×1 The element in the vector b is only 0 and 1, the length of the vector is 2N, N represents the number of subcarriers in the OFDM system, and the symbol is +.>Representing a complex value matrix, wherein the dimension is Nx1;
a2: randomly generated frequency domain pilot vector x p ；Frequency domain pilot vector x p Length of (2) and frequency domain data vector x d The same;
a3: weighting to generate a frequency domain transmission vector x;
vector x of frequency domain data d And frequency domain pilot vector x p Weighting to generate a frequency domain transmission vector x;
x＝∈x d +(1-∈)x p ；
wherein, the parameter E (0, 1) is a weighting coefficient;
a4: generating an OFDM channel;
representing the OFDM frequency domain equivalent channel as a time domain tap form, h=Φα; wherein,representing a time domain channel tap vector, L representing the channel tap length, the matrix Φ being the left L columns of an nxn discrete fourier transform matrix (DFT); the tap vector alpha has sparsity, namely, only K non-zero elements exist in alpha, wherein K represents the number of non-zero taps and depends on the scattering condition of a channel, and K is less than L;
a5: generating a received vector;
at the receiving end, the frequency domain is received with the vectorExpressed as:
y＝h·x+w；
wherein, the operation h.x represents multiplication of the vector h and the corresponding element of x,representing covariance matrix as lambda -1 I N Is the additive white Gaussian noise, lambda is the noise precision, I N Representing a unit array of dimension N;
finally, an aliasing pilot OFDM iterative receiver mathematical model y=h.x+w is obtained.
In the step A1, the modulation method of the information sequence b is as follows: first the information sequence b is divided into two vectors b 1 ,b 2 ∈[0,1] N×1 Elements ofRespectively represent the vectors b 1 and b2 An nth element of (a); then according to element->Will be->Modulated into corresponding complex value data s 1 ,s 2 ,s 3 Or s 4 The method comprises the steps of carrying out a first treatment on the surface of the S in QAM modulation 1 ,s 2 ,s 3 ,s 4 Called constellation point>Representing a frequency domain data vector x d An nth element of (a); the QAM modulation relationship is as follows, when +.>When (0, 0), (0, 1), (1, 0) and (1, 1) are taken respectively, they are modulated as s respectively 1 ,s 2 ,s 3 and s4 。
In the step A2, a frequency domain pilot vector x is randomly generated p The method of (1) is as follows: from constellation point s 1 S to s 4 Randomly selecting N times to generate a frequency domain pilot vector with the length of NThe subscript p denotes the frequency domain.
The step B comprises the following specific steps:
b1: initializing data-symbol-dependent variables including the mean of the frequency-domain transmission vectors xSum of variances v x Is to be added to the noise precision>Is set to an initial value of (1);
wherein, initializing the average value of the frequency domain transmission vector xSum of variances v x The initial values are +.> and vx ＝1 N I.e. assuming the original frequency domain transmission vector as pilot x p The noise precision initial value is +.> wherein 1N Representing a full 1 vector of length N;
b2: initializing channel-related variables including the mean of the time-domain channel tap vectors alphaSum of variances v α And intermediate variable s and super a priori variable γ;
wherein the mean value of the time domain channel tap vector alpha is initializedSum of variances v α The initial values are +.> and vα ＝I L The method comprises the steps of carrying out a first treatment on the surface of the Initializing an intermediate variable s=0 N And super a priori variable γ=1 L, wherein ,0N and 1L Representing all 0 of length N and L all 1 vectors of length, I L Representing the dimension as an L unit array;
b3: defining an observation matrix ψ;
singular Value Decomposition (SVD) of the matrix Φ, i.e., [ U, Λ, V ] =svd (Φ); according to a singular value decomposition theory, obtaining three matrixes obtained after decomposition, wherein U and V are unitary matrixes, and Λ is a diagonal matrix;
defining an observation matrix ψ as: ψ=u H Φ；
B4: defining a pseudo-frequency domain channel vector h 'as h' =u H h；
Where h' is defined as the pseudo-frequency domain channel vector, U H Representing the conjugate transpose of matrix U.
The step C comprises the following specific steps:
c1: by means of and vx Respectively calculating the estimated mean and the estimated variance of the frequency domain equivalent channel h as +.> and />The calculation is as follows:
wherein ,representation vector->Conjugation of->Representation vector->And the point multiplication of the frequency domain receiving vector y, namely the multiplication of corresponding elements;
c2: calculating the pre-estimated mean and the pre-estimated variance of the pseudo frequency domain channel h and />The method comprises the following steps of:
wherein ,|U|2 I, I represents a unit array,
and C3: sequentially calculating intermediate variables v p 、p、v s and s；
v p ＝|Ψ| 2 v α ；
wherein ψ is the observation matrix, v α Is the variance of the time domain tap vector;
wherein ,representing the mean value of the time domain channel tap vector alpha, s being an intermediate variable, and operatingThe symbol "·" represents the dot product of the vector;
wherein, the operation symbol "/" represents the dot division of the vector, namely the division of the corresponding elements of the two vectors;
and C4: sequentially calculating intermediate variables v q and q；
v q ＝1./(|Ψ H | 2 v s )，
wherein ,ΨH Representing the conjugate transpose of the matrix ψ;
c5: calculating the mean value of the time domain channel tap vector alpha by using the super prior variable gammaSum of variances v α ：
v α ＝v q ./(1+γ·v q )；
C6: updating and calculating a super prior variable gamma;
c7: respectively calculating the mean value v of the pseudo frequency domain channel h h′ Sum of variancesFinally, channel estimation is completed;
wherein , and vh′ Respectively are pseudoThe mean and variance of the frequency domain channel h',
wherein , and vh The mean and variance of the equivalent frequency domain channel h are respectively.
The step D comprises the following specific steps:
d1: using the obtained mean value of the frequency domain equivalent channel hSum of variances v h Calculating an estimated mean value of the frequency domain transmission vector xSum of variances v x Respectively is
wherein ,representation vector->Conjugation of (2);
d2: calculating a frequency domain data vector x d Is the estimated mean of (2)
D3: from the frequency domain data vector x d Is the estimated mean of (2)Judging the transmitted symbol to finally obtain the step A1Estimation of the transmission information sequence b>
In the step D3, four constellation points of the known QAM modulation are s 1 ～s 4 Sequentially judging the variablesFrom four constellation points s 1 ～s 4 Which of them is closer, will be->Judging to be the value of 0,1 corresponding to the constellation point, wherein the +_is>Representation vector->Is the nth element of (2); the specific method comprises the following steps:
first, calculateAnd s 1 ～s 4 Euclidean distance of (2), respectively +.>
Next, judgingIs the minimum value of (a); then, the transmitted information bits are obtained according to the minimum value judgmentIs recorded as +.>For example when->Middle->Minimum, then can decide
Finally, all ofArranged as vectors to obtain an estimate of the transmitted information sequence
In the step E, the average value of the equivalent frequency domain channel h obtained in the step B and the step C is usedSum of variances v h Mean value of frequency domain transmission symbol x>Sum of variances v x An estimated value of the noise precision lambda is calculated,
wherein I 2 Representing the 2-norm of the vector.
The invention can complete the guidance of the iterative algorithm by taking the aliasing pilot frequency as the priori distribution of the frequency domain symbols without changing the existing receiver frame, and is very suitable for being applied to the construction scene of the OFDM receiver. Firstly, UAMP is introduced as a processing scheme of time/frequency domain channel conversion, and a Sparse Bayesian Learning (SBL) model is embedded as a priori model of a time domain channel; secondly, the confidence propagation rule is applied to carry out modulation and demodulation processing in detection, and the aliased pilot frequency can be embedded into the existing message transmission detection algorithm only by changing the prior distribution of a modulation system, so that the invention can greatly improve the spectrum utilization rate and the robustness of an OFDM system with the same complexity.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a graph showing the error rate performance of different algorithms according to the signal to noise ratio;
fig. 3 is a graph comparing BER performance of different algorithms with signal to noise ratio under LDPC coding conditions.
Detailed Description
The invention is described in detail below with reference to the attached drawings and examples:
as shown in fig. 1, the OFDM signal transmission method based on the aliasing pilot according to the present invention includes the following steps:
a: generating frequency domain data vector x d Frequency domain pilot vector x p Establishing an aliasing pilot OFDM iterative receiver mathematical model by using the frequency domain transmission vector x, the OFDM channel h and the receiving vector y;
the step A comprises the following specific steps:
a1: generating frequency domain data vector x d ；
Let the transmitted information sequence b e 0,1] 2N×1 Obtaining frequency domain data vector through Q-order QAM modulation (quadrature amplitude modulation)Wherein the subscript d represents the data field and the symbol b e [0,1 ]] 2N×1 The element in the vector b is only 0 and 1, the length of the vector is 2N, N represents the number of subcarriers in the OFDM system, and the symbol is +.>Representing a complex value matrix, wherein the dimension is Nx1;
the modulation method of the information sequence b is that firstly, the information sequence b is divided into two vectors b 1 ,b 2 ∈[0,1] N×1 Elements ofRespectively represent the vectors b 1 and b2 An nth element of (a); then according to element->Will be->Modulated into corresponding complex value data s 1 ,s 2 ,s 3 Or s 4 The method comprises the steps of carrying out a first treatment on the surface of the S in QAM modulation 1 ,s 2 ,s 3 ,s 4 Called constellation point>Representing a frequency domain data vector x d An nth element of (a); the QAM modulation relationship is as follows, when +.>When (0, 0), (0, 1), (1, 0) and (1, 1) are taken respectively, they are modulated as s respectively 1 ,s 2 ,s 3 and s4 ；
A2: randomly generated frequency domain pilot vector x p ；
Randomly generated frequency domain pilot vectorsFrequency domain pilot vector x p Length of (2) and frequency domain data vector x d The same is generated by the following constellation point s 1 ～s 4 Randomly selected N times to generate a frequency domain pilot vector with length N>The subscript p represents the pilot frequency domain;
a3: weighting to generate a frequency domain transmission vector x;
vector x of frequency domain data d And frequency domain pilot vector x p Weighting to generate frequency domain transmission vectors
x＝∈x d +(1-∈)x p ； (1)
The parameter E (0, 1) is a weighting coefficient;
a4: generating an OFDM channel;
representing the OFDM frequency domain equivalent channel as a time domain tap form, h=Φα; wherein,representing the time domain channel tap vector, L representing the channel tap length, the matrix Φ being the left side of the NxN discrete Fourier transform matrix (DFT)L columns;
in a high-speed OFDM communication system, a tap vector alpha has sparsity, namely, only K non-zero elements exist in alpha, wherein K represents the number of non-zero taps and depends on the scattering condition of a channel, and K is less than L;
a5: generating a received vector;
at the receiving end, the frequency domain is received with the vectorExpressed as:
y＝h·x+w
wherein, the operation h.x represents multiplication of the vector h and the corresponding element of x,representing covariance matrix as lambda -1 I N Is the additive white Gaussian noise, lambda is the noise precision, I N Representing a unit array of dimension N;
finally, obtaining an aliasing pilot OFDM iterative receiver mathematical model y=h.x+w;
b: initializing an iterative algorithm variable;
the step B comprises the following specific steps:
b1: initializing data-symbol-dependent variables including the mean of the frequency-domain transmission vectors xSum of variances v x Is to be added to the noise precision>Is set to an initial value of (1);
in the invention, the mean value of the frequency domain transmission vector x is initializedSum of variances v x The initial values are +.> and vx ＝1 N I.e. assuming the original frequency domain transmission vector as pilot x p The noise precision initial value is +.> wherein 1N Representing an all 1 vector of length N.
B2: initializing channel-related variables including the mean of the time-domain channel tap vectors alphaSum of variances v α And intermediate variable s and super a priori variable γ;
in the invention, the mean value of the time domain channel tap vector alpha is initializedSum of variances v α The initial values are +.> and vα ＝I L The method comprises the steps of carrying out a first treatment on the surface of the Initializing an intermediate variable s=0 N And super a priori variable γ=1 L, wherein ,0N and 1L Representing all 0 of length N and L all 1 vectors of length, I L Representing the dimension as an L unit array;
b3: defining an observation matrix ψ;
singular Value Decomposition (SVD) of matrix Φ, i.e.
[U,Λ,V]＝SVD(Φ)；
According to the singular value decomposition theory, in three matrixes obtained after decomposition, U and V are unitary matrixes, and Λ is a diagonal matrix;
the observation matrix ψ can thus be defined as:
Ψ＝U H Φ；
b4: defining a pseudo-frequency domain channel vector h' as
h′＝U H h；
Where h' is defined as the pseudo-frequency domain channel vector, U H Representing the conjugate transpose of matrix U;
finally, the initialization step of the iterative receiver design is completed.
C: channel estimation is performed by using a unitary transformation approximate message passing method;
the step C comprises the following specific steps:
c1: by means of and vx Respectively calculating the estimated mean and the estimated variance of the frequency domain equivalent channel h as +.> and />The calculation is as follows:
wherein Representation vector->Conjugation of->Representation vector->And the point multiplication of the frequency domain receiving vector y, namely the multiplication of corresponding elements;
c2: calculating the pre-estimated mean and the pre-estimated variance of the pseudo frequency domain channel h and />The method comprises the following steps of:
since U is a unitary matrix, it can be known that U 2 I, where I represents a unit array, can be obtained
And C3: sequentially calculating intermediate variables v p 、p、v s and s；
v p ＝|Ψ| 2 v α wherein ψ is the observation matrix, v α Is the variance of the time domain tap vector;
wherein ,/>Representing the mean value of the time domain channel tap vector alpha, s being an intermediate variable, the operator "·" representing the dot product of the vector;
wherein, the operation symbol "/" represents the dot division of the vector, namely the division of the corresponding elements of the two vectors;
and C4: sequentially calculating intermediate variables v q and q；
v q ＝1./(|Ψ H | 2 v s )，
wherein ,ΨH Representing the conjugate transpose of the matrix ψ;
c5: calculating the mean value of the time domain channel tap vector alpha by using the super prior variable gammaSum of variances v α ：
v α ＝v q ./(1+γ·v q )；
C6: the super a priori variable gamma is updated and calculated,
c7: respectively calculating the mean value v of the pseudo frequency domain channel h h′ Sum of variances
wherein , and vh′ Is the mean and variance of the pseudo frequency domain channel h', which needs to be converted into the mean +.>Sum of variances v h I.e.
v h ＝v h′ ；
Finally, channel estimation is completed;
in the present invention, the vectors used in the first iterationv x 、α、v α And (3) gamma and s are the corresponding initialization values in the step B, and the values used in the subsequent iteration are updated by the subsequent iteration.
D: performing aliasing pilot symbol detection by applying a belief propagation algorithm;
the step D comprises the following specific steps:
d1: using the average value of the frequency domain equivalent channel h obtained in the step C7Sum of variances v h Calculating an estimated mean value of the frequency domain transmission vector x>Sum of variances v x Respectively is
wherein ,representation vector->Conjugation of (2);
d2: calculating a frequency domain data vector x d Is the estimated mean of (2)
From the equation (1), a frequency domain data vector x can be obtained d Is the estimated mean of (2)Is that
D3: from the frequency domain data vector x d Is the estimated mean of (2)Judging the transmitted symbols;
the four constellation points of the known QAM modulation in step A1 are s 1 ～s 4 The variables can be judged sequentiallyFrom four constellation points s 1 ～s 4 Which of them is closer, will be->Judging to be the value of 0,1 corresponding to the constellation point, wherein the +_is>Representing vectors/>Is the nth element of (2); the specific method comprises the following steps:
first, calculateAnd s 1 ～s 4 Euclidean distance of (2), respectively +.>
Next, judgingIs the minimum value of (a); then, the transmitted information bits are obtained according to the minimum value judgmentIs recorded as +.>For example when->Middle->Minimum, then can decide
Finally, all ofArranged as vectors to obtain an estimate of the transmitted information sequence
Finally, the estimation of the transmitted information sequence b in the step A1 is obtained
E: performing noise precision estimation;
according to the mean value of the equivalent frequency domain channel h obtained in the step B and the step CSum of variances v h Mean value of frequency domain transmission symbol xSum of variances v x Calculating an estimate of noise accuracy lambda, i.e
Wherein I 2 Representing the 2-norm of the vector.
F: c to E are executed iteratively, the established mathematical model of the aliased pilot OFDM iterative receiver is updated, and finally, signal transmission is completed by using the updated mathematical model of the aliased pilot OFDM iterative receiver;
the method provided by the invention is an iterative algorithm, a mathematical model of the aliased pilot OFDM iterative receiver is established through the steps A and B, and the intermediate variables and matrixes required in iteration are defined in an initializing way; and (3) carrying out iterative computation for 10 times through steps C, D and E, updating the mathematical model of the aliased pilot OFDM iterative receiver, and finally completing signal transmission by using the updated mathematical model of the aliased pilot OFDM iterative receiver. The initial transmission information sequence b is utilized to finally obtain the estimation of the transmission information sequence b by utilizing the aliasing pilot OFDM signal transmission methodThe whole signal output process is completed.
As shown in FIG. 2, the present invention compares the number of non-zero taps K=10, with (5, 7) 8 The error rate (BER) performance of different algorithms varies with the signal-to-noise ratio for convolutional codes, weighting coefficients e=0.8. The four methods of known channels (no pilots), known channels (aliased pilots), unknown channels (independent pilots), and unknown channels (independent pilots) are compared in fig. 2. Wherein the known channel is an ideal case assuming that the channel is known in its entirety, and can be used as an algorithmIs a performance upper bound of (2). As can be seen from fig. 2, the independent pilot method has about 1dB of performance advantage over the aliased pilot method, and the effectiveness of the aliased pilot method is highlighted.
As shown in FIG. 3, the present invention compares the BER performance of various algorithms with the signal-to-noise ratio under LDPC coding conditions, and the number of non-zero taps is set to 10 in FIG. 3, and the weighting coefficients E are respectively 0.7 and 0.8. It can be seen that the introduction of LDPC channel coding can greatly improve the bit error rate performance of the receiver. From fig. 3 it can also be concluded that the same conclusion as in fig. 2 is that an aliased pilot OFDM receiver can achieve a higher spectral efficiency.
The OFDM signal transmission method based on the aliasing pilot frequency has wide application scenes, for example, the method can be adopted in the scenes of home WiFi, vehicle networking communication, underwater acoustic communication and the like.
Claims (9)
1. An OFDM signal transmission method based on an aliased pilot frequency, comprising the steps of:
a: generating frequency domain data vector x d Frequency domain pilot vector x p The frequency domain transmission vector x, the OFDM channel h and the receiving vector y, and finally establishing an aliasing pilot OFDM iterative receiver mathematical model y=h.x+w; wherein,representing covariance matrix as lambda -1 I N Is the additive white Gaussian noise, lambda is the noise precision, I N Representing a unit array of dimension N;
b: initializing an iterative algorithm variable;
involving initializing the mean value of the frequency domain transmission vector x in the data symbol dependent variableVariance v x Initial value and noise precision->Is set to an initial value of (1); also include initializing a channelMean value of time domain channel tap vector alpha in correlation variable +.>Variance v α An intermediate variable s and a super a priori variable y; and an observation matrix ψ, and a pseudo-frequency domain channel vector h';
c: channel estimation is performed by using a unitary transformation approximate message passing method;
d: performing aliased pilot symbol detection by using belief propagation algorithm to obtain estimation of the transmitted information sequence b
E: performing noise precision estimation;
f: and (C) performing the steps (E) in an iteration mode, updating the established mathematical model of the aliased pilot OFDM iterative receiver, and finally completing signal transmission by using the updated mathematical model of the aliased pilot OFDM iterative receiver.
2. The method for transmitting an OFDM signal based on an aliased pilot according to claim 1, wherein: the step A comprises the following specific steps:
a1: generating frequency domain data vector x d ；
Let the transmitted information sequence b e 0,1] 2N×1 Obtaining frequency domain data vector through Q-order QAM modulationWherein the subscript d represents the data field and the symbol b e [0,1 ]] 2N×1 The element in the vector b is only 0 and 1, the length of the vector is 2N, N represents the number of subcarriers in the OFDM system, and the symbol is +.>Representing a complex value matrix, wherein the dimension is Nx1;
a2: randomly generated frequency domain pilot vector x p ；Frequency domain pilot vector x p Length of (2) and frequency domain data vector x d The same;
a3: weighting to generate a frequency domain transmission vector x;
vector x of frequency domain data d And frequency domain pilot vector x p Weighting to generate a frequency domain transmission vector x;
x＝∈x d +(1-∈)x p ；
wherein, the parameter E (0, 1) is a weighting coefficient;
a4: generating an OFDM channel;
representing the OFDM frequency domain equivalent channel as a time domain tap form, h=Φα; wherein,representing a time domain channel tap vector, L representing the channel tap length, the matrix Φ being the left L columns of an nxn discrete fourier transform matrix (DFT); the tap vector alpha has sparsity, namely, only K non-zero elements exist in alpha, wherein K represents the number of non-zero taps and depends on the scattering condition of a channel, and K is less than L;
a5: generating a received vector;
at the receiving end, the frequency domain is received with the vectorExpressed as:
y＝h·x+w；
wherein, the operation h.x represents multiplication of the vector h and the corresponding element of x,representing covariance matrix as lambda -1 I N Is the additive white Gaussian noise, lambda is the noise precision, I N Representing a unit array of dimension N;
finally, an aliasing pilot OFDM iterative receiver mathematical model y=h.x+w is obtained.
3. According toThe method for transmitting OFDM signals based on aliased pilots as claimed in claim 1, wherein in the step A1, the modulation method of the information sequence b is as follows: first the information sequence b is divided into two vectors b 1 ,b 2 ∈[0,1] N×1 Elements ofRespectively represent the vectors b 1 and b2 An nth element of (a); then according to element->Will be->Modulated into corresponding complex value data s 1 ,s 2 ,s 3 Or s 4 The method comprises the steps of carrying out a first treatment on the surface of the S in QAM modulation 1 ,s 2 ,s 3 ,s 4 Called constellation point>Representing a frequency domain data vector x d An nth element of (a); the QAM modulation relationship is as follows, when +.>When (0, 0), (0, 1), (1, 0) and (1, 1) are taken respectively, they are modulated as s respectively 1 ,s 2 ,s 3 and s4 。
4. The method for transmitting OFDM signals based on aliased pilots as claimed in claim 1, wherein in the step A2, the frequency domain pilot vector x is randomly generated p The method of (1) is as follows: from constellation point s 1 S to s 4 Randomly selecting N times to generate a frequency domain pilot vector with the length of NThe subscript p denotes the frequency domain.
5. The method for transmitting an OFDM signal based on an aliased pilot according to claim 1, wherein: the step B comprises the following specific steps:
b1: initializing data-symbol-dependent variables including the mean of the frequency-domain transmission vectors xSum of variances v x Is to be added to the noise precision>Is set to an initial value of (1);
wherein, initializing the average value of the frequency domain transmission vector xSum of variances v x The initial values are +.> and vx ＝1 N I.e. assuming the original frequency domain transmission vector as pilot x p The noise precision initial value is +.> wherein 1N Representing a full 1 vector of length N;
b2: initializing channel-related variables including the mean of the time-domain channel tap vectors alphaSum of variances v α And intermediate variable s and super a priori variable γ;
wherein the mean value of the time domain channel tap vector alpha is initializedSum of variances v α The initial values are +.> and vα＝IL The method comprises the steps of carrying out a first treatment on the surface of the Initializing an intermediate variable s=0 N And super a priori variable γ=1 L, wherein ,0N and 1L Representing all 0 of length N and L all 1 vectors of length, I L Representing the dimension as an L unit array;
b3: defining an observation matrix ψ;
singular Value Decomposition (SVD) of the matrix Φ, i.e., [ U, Λ, V ] =svd (Φ); according to a singular value decomposition theory, obtaining three matrixes obtained after decomposition, wherein U and V are unitary matrixes, and Λ is a diagonal matrix;
defining an observation matrix ψ as: ψ=u H Φ；
B4: defining a pseudo-frequency domain channel vector h 'as h' =u H h；
Where h' is defined as the pseudo-frequency domain channel vector, U H Representing the conjugate transpose of matrix U.
6. The method for transmitting OFDM signals based on aliased pilots as claimed in claim 1, wherein C comprises the specific steps of:
c1: by means of and vx Respectively calculating the estimated mean and the estimated variance of the frequency domain equivalent channel h as +.> and />The calculation is as follows:
wherein ,representation vector->Conjugation of->Representation vector->And the point multiplication of the frequency domain receiving vector y, namely the multiplication of corresponding elements;
c2: calculating the pre-estimated mean and the pre-estimated variance of the pseudo frequency domain channel h and />The method comprises the following steps of:
wherein ,|U|2 I, I represents a unit array,
and C3: sequentially calculating intermediate variables v p 、p、v s and s；
v p ＝|Ψ| 2 v α ；
wherein ψ is the observation matrix, v α Is the variance of the time domain tap vector;
wherein ,representing the mean value of the time domain channel tap vector alpha, s being an intermediate variable, the operator "·" representing the dot product of the vector;
wherein, the operation symbol "/" represents the dot division of the vector, namely the division of the corresponding elements of the two vectors;
and C4: sequentially calculating intermediate variables v q and q；
wherein ,ΨH Representing the conjugate transpose of the matrix ψ;
c5: calculating the mean value of the time domain channel tap vector alpha by using the super prior variable gammaSum of variances v α ：
C6: updating and calculating a super prior variable gamma;
c7: respectively calculating the mean value v of the pseudo frequency domain channel h h' Sum of variancesFinally, channel estimation is completed;
wherein , and vh' The mean and variance of the pseudo-frequency domain channel h' respectively,
wherein , and vh The mean and variance of the equivalent frequency domain channel h are respectively.
7. The method for transmitting an OFDM signal based on an aliased pilot according to claim 6, wherein: the step D comprises the following specific steps:
d1: using the obtained mean value of the frequency domain equivalent channel hSum of variances v h Calculating an estimated mean value of the frequency domain transmission vector x>Sum of variances v x Respectively is
wherein ,representation vector->Conjugation of (2);
d2: calculating a frequency domain data vector x d Is the estimated mean of (2)
D3: from the frequency domain data vector x d Is the estimated mean of (2)Judging the transmitted symbol to finally obtain the estimated +.f of the transmitted information sequence b in the step A1>
8. The method for transmitting an OFDM signal based on an aliased pilot according to claim 7, wherein: in the step D3, four constellation points of the known QAM modulation are s 1 ～s 4 Sequentially judging the variablesFrom four constellation points s 1 ～s 4 Which of them is closer, will be->Judging to be the value of 0,1 corresponding to the constellation point, wherein the +_is>Representation vector->Is the nth element of (2); the specific method comprises the following steps:
first, calculateAnd s 1 ～s 4 Euclidean distance of (2), respectively +.>
Next, judgingIs the minimum value of (a); then, the transmission information bit +_ is obtained based on the minimum value decision>Is recorded as +.>For example when->Middle->Minimum, then decision +.>
Finally, all ofArranged as vectors, resulting in an estimate of the transmitted information sequence>
9. The method for transmitting an OFDM signal based on an aliased pilot according to claim 1, wherein:in the step E, the average value of the equivalent frequency domain channel h obtained in the step B and the step C is usedSum of variances v h Mean value of frequency domain transmission symbol x>Sum of variances v x An estimated value of the noise precision lambda is calculated,
wherein I 2 Representing the 2-norm of the vector.
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