CN117221062A - Symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication - Google Patents
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Abstract
The invention discloses a symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication, and belongs to the field of signal processing. The invention obtains a two-dimensional symbol modulation domain by utilizing two-dimensional orthogonal transformation of a time-frequency domain, performs precoding on an information symbol to obtain a time-frequency domain symbol, obtains maximum time-frequency domain diversity, realizes maximum time-frequency diversity under a high mobility scene based on constant modulus characteristics of a basic function of orthogonal transformation in the time-frequency domain, obtains an equivalent channel matrix model by determining an input-output relationship of a system by utilizing a unitary approximate message transfer frame, constructs a unitary transformation matrix by decomposing a channel to obtain a linear model after unitary transformation, performs variable decomposition by utilizing a factor graph, obtains an estimated value of the information symbol based on a factor graph, a variational Bayes and an average field theory, and realizes iterative symbol detection. The invention can resist the double selectivity of the satellite-ground communication channel, improve the data transmission effectiveness and the detection performance and reduce the complexity.
Description
Technical Field
The invention relates to a symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication, and belongs to the field of signal processing.
Background
The ever-increasing data demands place higher demands on sixth generation mobile communication technologies (6G), including higher throughput, excellent reliability, global seamless coverage, low latency, and massive access, most of the existing terrestrial networks are deployed in densely populated places, and it is difficult to meet the demands of wide coverage areas, high frequent access handovers, and the like. The non-ground network is used as an extension of the ground network, can provide global communication service in all weather and all weather, has complementary and tight advantages with the ground network, and provides high-quality service for mass ground terminals in a more reliable, seamless, economical and effective manner. Recently, low Earth Orbit (LEO) satellites deployed 500km to 2000 km away from the earth are an important component of non-terrestrial networks due to their advantages in round trip delay, path loss, and production deployment costs. However, due to the high mobility of LEO satellites and the influence of scatterers near ground terminals, satellite-to-ground communication channels have time selectivity and frequency selectivity, signals are subjected to serious inter-carrier interference and inter-symbol interference, and the communication received signal quality is inevitably affected.
The traditional single carrier scheme utilizes one carrier to transmit all data symbols, is only suitable for a single-path transmission scene, and can generate a frequency selective fading effect for users in a building dense area due to multipath scattering of a wireless channel, so that intersymbol interference is caused, and the reliability of data transmission is affected; conventional Orthogonal Frequency Division Multiplexing (OFDM) modulation techniques multiplex information symbols in the time-frequency domain, exploiting one-dimensional frequency diversity against frequency selective fading: the OFDM modulation technique divides a carrier with a wider frequency into a plurality of narrowband orthogonal subcarriers, modulates symbols of different time slots onto a plurality of different subcarriers by using hessian burg transformation, and generally adopts a single tap frequency domain equalizer at a receiving end to perform symbol detection, wherein the single tap frequency domain equalizer assumes that multipath information slowly changes with time, that is, a channel remains unchanged in one OFDM symbol time, and each subcarrier remains orthogonal after being transmitted through the channel. The single tap equalizer provides very good performance in the medium-low speed-shifting communication scene, however, in the satellite communication system, the relative mobility of the satellite and the ground is strong, the satellite-ground communication link has high time variability and large Doppler spread, the orthogonality of OFDM subcarriers is destroyed, serious inter-carrier interference is generated, and the single tap equalizer suitable for OFDM waveforms is difficult to capture all information of time-varying multipath channels, and has poor symbol detection performance.
In a satellite communication system adopting OFDM, to improve the detection performance, reliability needs to be improved by sacrificing effectiveness, for example, to improve the signal-to-noise ratio, to use a more complex symbol detection method and to use a more precise transceiver, while space-borne resources are limited, space electromagnetic environment is complex, the temperature of the environment is high, and equipment is volatile, so that the difficulty in implementing the method is increased, and a modulation waveform and a low-complexity symbol detection method suitable for a high-mobility scene become bottleneck problems restricting the development of satellite-to-ground communication.
Disclosure of Invention
The invention aims to provide a symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication, which is based on time-frequency domain orthogonal transformation to resist the double selectivity of satellite-ground channels, and realizes low-complexity symbol detection by using orthogonal transformation corresponding to approximate message transmission and precoding matrixes, and has better bit error rate performance.
The invention aims at realizing the following technical scheme:
a symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication firstly utilizes two-dimensional orthogonal transformation of time-frequency domain to obtain new two-dimensional symbol modulation domain (abbreviated as A-B transformation domain), then carries out precoding on information symbols of the two-dimensional symbol modulation domain to obtain time-frequency domain symbols, obtains maximum time-frequency domain diversity, and in one symbol frame, channel response of the two-dimensional symbol modulation domain is non-time-variant, so as to facilitate a receiver to carry out symbol detection, realizes maximum time-frequency diversity under high mobility scene based on constant mode characteristics of a basis function of orthogonal transformation in the time-frequency domain, then utilizes unitary approximate message transfer frame, obtains an equivalent channel matrix model through determining input-output relation of a system, constructs a unitary transformation matrix through decomposition of channels, obtains a linear model after unitary transformation, carries out variable decomposition by utilizing a factor graph, obtains an estimated value of the information symbols based on a Bayesian sub-graph, a variation and an average field theory, and realizes iterative symbol detection in the two-dimensional symbol modulation domain, and the method specifically comprises the following steps:
step one: performing a modulation processing process of the time-frequency domain two-dimensional orthogonal precoding signals, and determining the relation between the receiving and transmitting information symbols and the channels;
symbol the informationModulated on the A-B domain, using time-frequency orthogonal precoding to provide +.>Conversion to time-frequency domain symbol X FT ＝A F XA T ；
Wherein, the element of X is Q-QAM modulation symbol, and the alphabet is { a } 1 ，...a Q }，A F And A T All are orthogonal transformation;
under the condition that the receiving and transmitting waveforms are rectangular waves, the A-B domain signals are obtained by utilizing the Hassenberg transformation Obtaining a time domain transmit signal by serial-parallel conversion>Adding a cyclic prefix similar to an OFDM frame structure to each sub-block of s; after s passes through the channel, the receiver end obtains a received signal r=gs+n;
wherein,is a time domain equivalent channel matrix, n is Gaussian white noise;
the receiving end is the inverse process of the transmitting end, and performs serial-parallel conversion on r to obtain delay-time domain symbolsObtaining a time-frequency domain symbol Y by utilizing Wigner transformation FT ＝F M R, obtain the A-B domain received signal matrix Y = -by using combiner>The relationship between the information receiving and transmitting symbols and the channels in the A-B domain vectorization form obtained by vectorization operation is shown as the following formula (1):
y＝Hx+w (1)
wherein H is an A-B domain equivalent channel matrix,w is the noise vector, ">
Step two: constructing a unitary transformation matrix by utilizing the time-frequency two-dimensional orthogonal precoding modulation characteristics, and obtaining a new input-output relation model after unitary transformation;
singular value decomposition is carried out on the equivalent channel matrix H and is based on A T ，A F And F M The two-dimensional orthogonal precoding modulation system is a unitary matrix, singular value decomposition of H corresponds to singular value decomposition of G, and when rectangular transceiving waveforms are adopted under the cyclic prefix structure of OFDM, a time domain equivalent channel matrix G of the two-dimensional orthogonal precoding modulation system is a block diagonal, and the singular value decomposition form of G is shown as a formula (2):
wherein the left singular matrix of G is u=blkdiag (U 1 ，...，U N ) The right singular matrix is v=blkdiag (V 1 ，...，V N ) The singular value matrix is a=blkdiag (Λ 1 ，...，Λ N ) Vector d=diag (a), BLKdiag (·) is a block diagonal operation;
selecting unitary transformation matricesObtaining a linear model after unitary transformation, as shown in formula (3):
wherein r=t H y， Is zero-mean Gaussian noise, satisfies->σ -1 Is the noise variance;
using orthogonal transformation A T 、A F Fourier transform F M The computational complexity is simplified;
step three: based on the input-output relation model after unitary transformation, determining the joint condition distribution of unknown variables and obtaining a symbol detection estimation model;
given r and H, the joint probability function p (x, z, σ|r) for the unknown variable x, the auxiliary variable z, and σ is shown in equation (4):
wherein the auxiliary variable z=Φx, r n N element of r, z n An nth element of z;
step four: according to the factor graph of joint probability distribution p (x, z, sigma|r), building a forward message transmission model, and simplifying matrix multiplication by using orthogonal transformation;
according to the iterative relationship, the forward messaging model is as shown in equation (5):
p＝Φx (t) -v p ⊙s (t-1) (5)
wherein p is a vector, superscript (·) (t) Representing the result of the t-th iteration, v p As the variance of the vector p,lambda is a eigenvalue vector, lambda=djd * ；
Simplifying phix using orthogonal transformation (t) As shown in formula (6):
wherein the information symbol X of the t-th iteration (t) ＝unvec(x (t) )；
Determining variable node z n To function nodesVariance v of message z Mean->The compounds are respectively shown as formula (7) and formula (8):
wherein,an estimated value of the noise variance in the t-1 th iteration;
according to function nodeTo becomeMessage of quantity node sigma->Obtaining noise estimate variance->As shown in formula (9):
step five: establishing a backward message transmission process according to a joint probability distribution p (x, z, sigma|r) factor graph, and simplifying matrix multiplication by using orthogonal transformation;
determining function nodesTo variable node z n Mean value v of the messages of (2) s Variance s t As shown in the formulas (10) and (11):
s t ＝v s ⊙(r-p) (11)
determining function nodesTo variable node x n Mean value v of messages q And variance q are represented by the following expressions (12) and (13):
simplifying phi using orthogonal transformation H s (t) As shown in the formula (14):
wherein s is (t) ＝unvec(V(d * ⊙s (t) ))；
Obtaining a transmit information symbol estimate as shown in equation (15):
wherein,
under the condition that all element variances of x are the same, arithmetic average is carried out,
iterating the processes from the first step to the fifth step until convergence to obtain the detection value of the transmitted information symbol
The method further comprises the step six of: according to the iterative symbol detection method based on the approximate message transfer frame in the first to fifth steps, the robustness of the symbol detector to Doppler expansion and fractional Doppler expansion is improved under a high dynamic communication scene, and high-precision symbol detection is realized; the method is applied to the field of high-speed-shifting communication, such as satellite communication, high-speed-rail communication and high-altitude communication, and the computational complexity of a symbol detection method can be reduced through time-frequency domain orthogonal transformation.
The beneficial effects are that:
1. the symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication utilizes the principle of maximum time-frequency diversity realized by using a time-frequency orthogonal transformation basis function to resist the double selectivity of a satellite-to-ground communication channel and realize the high reliability of satellite-to-ground data transmission.
2. According to the symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication, the symbol detection performance is improved by using approximate message transmission and unitary transformation, a high-precision symbol detection effect is obtained, and the robustness of the method to noise is improved by using noise variance estimation.
3. According to the symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication, matrix multiplication calculation in the symbol detection process is simplified by orthogonal transformation, the symbol detection calculation complexity is reduced, and the calculation load is further reduced.
Drawings
FIG. 1 is a flow chart of a symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication according to the present invention;
fig. 2 is a frame structure of an OFDM cyclic prefix;
a factor graph of the joint probability distribution p (x, z, σ|r) in step three of the embodiment of fig. 3;
fig. 4 is a graph showing the variation of the achievable bit error rate with the snr according to the method of the present invention and the conventional detection method in an embodiment.
Detailed Description
For a better description of the objects and advantages of the present invention, the following description will be given with reference to the accompanying drawings and examples.
Example 1:
in LEO satellite communication systems involving Ka-band, i.e. carrier frequency f c =20 GHz, the subcarrier spacing is set to Δf=120 kHz. Selecting a non-terrestrial network rice channel model defined by a third generation partnership project (3 GPP) Release 16 standard, wherein the non-terrestrial network rice channel model comprises a line-of-sight path and a plurality of non-line-of-sight paths, and the rice parameter is 12dB;
based on the knowledge of satellite motion rules and a timing advance technology of 3GPP, the delay and Doppler of satellite-to-ground information transmission are compensated, delay residual error is compensated to be [0,0.8 mu s ], doppler caused by satellite motion is compensated, doppler frequency shift of a satellite communication system is mainly caused by the speed of ground equipment, and user speed is generalized to 500km/h;
under the condition that the channel state information is completely known at the receiver, the signal to noise ratio range is 0-24dB, and the experiment is repeated 10000 times to realize Monte Carlo simulation;
for the frame structure of the communication process, the Walsh-Hadamard transform is selected as the time domain transform, and the corresponding precoding matrix is a Walsh matrixThe frequency domain is transformed into inverse Fourier transform, and the corresponding precoding matrix is Fourier matrix +.> The obtained two-dimensional symbol modulation domain is a delay-sequence domain, the size of a symbol frame of the delay-sequence domain (namely the A-B domain) is (32, 32), and the information symbols are modulated by adopting 4-QAM;
under the above satellite communication system and corresponding conditions, the symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication of the present invention is implemented as shown in fig. 1, and the specific steps are as follows:
step one: performing a modulation processing process of the time-frequency domain two-dimensional orthogonal precoding signals, and determining the relation between the receiving and transmitting information symbols and the channels;
symbol the informationModulating in delay-sequence domain using time-frequency orthogonal precoding>Conversion to time-frequency domain symbol X FT ＝F M XW N ；
Wherein, the element of X is Q-QAM modulation symbol, and the alphabet is { a } 1 ，...a Q }，A F And A T All are orthogonal transformation;
under the condition that the receiving and transmitting waveforms are rectangular waves, the Hassenberg transformation is utilized to obtain a delay-sequence domain signal Obtaining a time domain transmit signal by serial-parallel conversion>
In the embodiment, according to the OFDM-based delay-sequence domain symbol transmission method, a cyclic prefix similar to an OFDM frame structure is added to each sub-block of a time domain transmission signal s, as shown in fig. 2, after the time domain transmission signal s passes through a channel, a receiver obtains a reception signal r=gs+n;
wherein,is a time domain equivalent channel matrix, n is Gaussian white noise;
the receiving end is the inverse process of the transmitting end, and performs serial-parallel conversion on r to obtain delay-time domain symbolsObtaining a time-frequency domain symbol Y by utilizing Wigner transformation FT ＝F M R, delay-sequence domain received signal matrix is obtained by using combiner>The relationship between the received and transmitted information symbols and the channel in the form of delay-sequence domain vectorization is obtained as shown in the formula (1):
y＝Hx+w (1)
wherein H is a delay-sequence domain equivalent channel matrix, noise vector->
Step two: constructing a unitary transformation matrix by utilizing the time-frequency two-dimensional orthogonal precoding modulation characteristics, and obtaining a new input-output relation model after unitary transformation;
singular value decomposition is carried out on the equivalent channel matrix H and is based on A T ，A F And F M The two-dimensional orthogonal precoding modulation system is a unitary matrix, singular value decomposition of H corresponds to singular value decomposition of G, and when rectangular transceiving waveforms are adopted under the cyclic prefix structure of OFDM, a time domain equivalent channel matrix G of the two-dimensional orthogonal precoding modulation system is a block diagonal, and the singular value decomposition form of G is shown as a formula (2):
wherein the left singular matrix of G is u=blkdiag (U 1 ，...，U N ) The right singular matrix is v=blkdiag (V 1 ，...，V N ) The singular value matrix is Λ=blkdiag (Λ 1 ，...，Λ N ) Vector d=diag (Λ), BLKdiag (·) is a block diagonal operation;
selecting unitary transformation matricesObtaining a linear model after unitary transformation, as shown in formula (3):
wherein r=t H y， Is zero-mean Gaussian noise, satisfies->σ -1 Is the noise variance;
using orthogonal transformation W N Fourier transform F M The computational complexity is simplified;
step three: based on the input-output relation model after unitary transformation, determining the joint condition distribution of unknown variables and obtaining a symbol detection estimation model;
given r and H, the joint probability function p (x, z, σ|r) for the unknown variable x, the auxiliary variable z, and σ is shown in equation (4):
wherein the auxiliary variable z=Φx, r n N element of r, z n An nth element of z;
in an embodiment, the factor graph established according to formula (4) is shown in fig. 3;
step four: according to the factor graph of joint probability distribution p (x, z, sigma|r), building a forward message transmission model, and simplifying matrix multiplication by using orthogonal transformation;
according to the iterative relationship, the forward messaging model is as shown in equation (5):
p＝Φx (t) -v p ⊙s (t-1) (5)
wherein p is a vector, superscript (·) (t) Representing the result of the t-th iteration, v p As the variance of the vector p,lambda is a eigenvalue vector, lambda=djd * ；
Simplifying phix using orthogonal transformation (t) As shown in formula (6):
wherein the information symbol X of the t-th iteration (t) ＝unvec(x (t) )；
Determining variable node z n To function nodesVariance v of message z Mean->The compounds are respectively shown as formula (7) and formula (8):
wherein,an estimated value of the noise variance in the t-1 th iteration;
according to function nodeMessage to variable node sigma->Obtaining noise estimate variance->As shown in formula (9):
step five: establishing a backward message transmission process according to a joint probability distribution p (x, z, sigma|r) factor graph, and simplifying matrix multiplication by using orthogonal transformation;
determining function nodesTo variable node z n Mean value v of the messages of (2) s Variance s t As shown in the formulas (10) and (11):
s t ＝v s ⊙(r-p) (11)
determining function nodesTo variable node x n Mean value v of messages q And variance q are represented by the following expressions (12) and (13):
simplifying phi using orthogonal transformation H s (t) As shown in the formula (14):
wherein S is (t) ＝unvec(V(d * ⊙s (t) ))；
Obtaining a transmit information symbol estimate as shown in equation (15):
wherein,
under the condition that all element variances of x are the same, arithmetic average is carried out,
iterating the first to fifth steps until convergence to obtain the detection value of the transmitted information symbol
The experiment is repeated 10000 times, the SNR range of 0dB to 24dB is considered, the stepping is 2dB, and compared with the traditional OFDM-based single-tap frequency domain equalization symbol detection method, the obtained Bit Error Rate (BER) curve is shown in figure 4, when the SNR is more than 5dB, the BER performance of the method is far more than that of the traditional method, in the SNR range of 0-24dB, the performance of the traditional method is slowed down along with the increase of the SNR, and the rate of the BER performance of the method is increased along with the increase of the SNR;
the method further comprises the step six of: according to the iterative symbol detection method based on the approximate message transfer frame in the first to fifth steps, the robustness of the symbol detector to Doppler expansion and fractional Doppler expansion is improved under a high dynamic communication scene, and high-precision symbol detection is realized; the method is applied to the field of high-speed-shifting communication, such as satellite communication, high-speed-rail communication and high-altitude communication, and the computational complexity of a symbol detection method can be reduced through time-frequency domain orthogonal transformation.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (3)
1. A symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication is characterized by comprising the following steps: a new two-dimensional symbol modulation domain is obtained by utilizing two-dimensional orthogonal transformation of a time-frequency domain, information symbols of the two-dimensional symbol modulation domain are precoded, a time-frequency domain symbol is obtained, maximum time-frequency domain diversity is obtained, and in one symbol frame, the channel response of the two-dimensional symbol modulation domain is non-time-varying, so that a receiver can conveniently detect symbols, and the maximum time-frequency diversity is realized in a high mobility scene based on the constant modulus characteristic of a basis function of orthogonal transformation in a time-frequency domain; the method comprises the steps of utilizing a unitary approximate message transmission frame, obtaining an equivalent channel matrix model by determining an input-output relation of a system, constructing a unitary transformation matrix by decomposing channels, obtaining a linear model after unitary transformation, utilizing a factor graph to conduct variable decomposition, obtaining an estimated value of an information symbol based on a factor graph, a variant Bayesian and an average field theory, and realizing iterative symbol detection in a two-dimensional symbol modulation domain.
2. The symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication according to claim 1, wherein: the method specifically comprises the following steps:
step one: performing a modulation processing process of the time-frequency domain two-dimensional orthogonal precoding signals, and determining the relation between the receiving and transmitting information symbols and the channels;
symbol the informationModulated on the A-B domain, using time-frequency orthogonal precoding to provide +.>Conversion to time-frequency domain symbol X FT ＝A F XA T ；
Wherein, the element of X is Q-QAM modulation symbol, and the alphabet is { a } 1 ,…a Q }，A F And A T All are orthogonal transformation;
under the condition that the receiving and transmitting waveforms are rectangular waves, the A-B domain signals are obtained by utilizing the Hassenberg transformation Obtaining a time domain transmit signal by serial-parallel conversion>Adding a cyclic prefix similar to an OFDM frame structure to each sub-block of s; after s passes through the channel, the receiver end obtains a received signal r=gs+n;
wherein,is a time domain equivalent channel matrix, n is Gaussian white noise;
the receiving end is the inverse process of the transmitting end, and performs serial-parallel conversion on r to obtain delay-time domain symbolsObtaining a time-frequency domain symbol Y by utilizing Wigner transformation FT ＝F M R, A-B domain receiving signal matrix is obtained by utilizing combiner>The relationship between the information receiving and transmitting symbols and the channels in the A-B domain vectorization form obtained by vectorization operation is shown as the following formula (1):
y＝Hx+w (1)
wherein H is an A-B domain equivalent channel matrix,w is noise->
Step two: constructing a unitary transformation matrix by utilizing the time-frequency two-dimensional orthogonal precoding modulation characteristics, and obtaining a new input-output relation model after unitary transformation;
singular value decomposition is carried out on the equivalent channel matrix H and is based on A T ，A F And F M The two-dimensional orthogonal precoding modulation system is a unitary matrix, singular value decomposition of H corresponds to singular value decomposition of G, and when rectangular transceiving waveforms are adopted under the cyclic prefix structure of OFDM, a time domain equivalent channel matrix G of the two-dimensional orthogonal precoding modulation system is a block diagonal, and the singular value decomposition form of G is shown as a formula (2):
wherein the left singular matrix of G is u=blkdiag (U 1 ,…,U N ) The right singular matrix is v=blkdiag (V 1 ,…,V N ) The singular value matrix is Λ=blkdiag (Λ 1 ,…,Λ N ) Vector d=diag (Λ), BLKdiag (·) is a block diagonal operation;
selecting unitary transformation matricesObtaining a linear model after unitary transformation, as shown in formula (3):
wherein r=t H y,Is zero-mean Gaussian noise, satisfies->Sigma is noiseVariance;
using orthogonal transformation A T 、A F Fourier transform F M The computational complexity is simplified;
step three: based on the input-output relation model after unitary transformation, determining the joint condition distribution of unknown variables and obtaining a symbol detection estimation model;
given r and H, the joint probability function p (x, z, σ|r) for the unknown variable x, the auxiliary variable z, and σ is shown in equation (4):
wherein the auxiliary variable z=Φx, r n N element of r, z n An nth element of z;
step four: according to the factor graph of joint probability distribution p (x, z, sigma|r), building a forward message transmission model, and simplifying matrix multiplication by using orthogonal transformation;
according to the iterative relationship, the forward messaging model is as shown in equation (5):
p＝Φx (t) -v p ⊙s (t-1) (5)
wherein p is a vector, superscript (·) (t) Representing the result of the t-th iteration, v p As the variance of the vector p,lambda is a eigenvalue vector, lambda=djd * ；
Simplifying phix using orthogonal transformation (t) As shown in formula (6):
wherein the information symbol X of the t-th iteration (t) ＝unvec(x (t) )；
Determining variable node z n To function nodesVariance v of message z Mean->The compounds are respectively shown as formula (7) and formula (8):
wherein,an estimated value of the noise variance in the t-1 th iteration;
according to function nodeMessage to variable node sigma->Obtaining the variance of the noise estimateAs shown in formula (9):
step five: establishing a backward message transmission process according to a joint probability distribution p (x, z, sigma|r) factor graph, and simplifying matrix multiplication by using orthogonal transformation;
determining function nodesTo variable node z n Mean value v of the messages of (2) s Variance s t As shown in the formulas (10) and (11):
s t ＝v s ⊙(r-p) (11)
determining function nodesTo variable node x n Mean value v of messages q And variance q are represented by the following expressions (12) and (13):
simplifying phi using orthogonal transformation H s (t) As shown in the formula (14):
wherein S is (t) ＝unvec(V(d * ⊙s (t) ))；
Obtaining a transmit information symbol estimate as shown in equation (15):
wherein,
at xUnder the condition that the variances of all elements are the same, arithmetic average is carried out,
iterating the processes from the first step to the fifth step until convergence to obtain the detection value of the transmitted information symbol
3. A symbol detection method based on time-frequency two-dimensional orthogonal precoding in satellite communication according to claim 1 or 2, wherein: the method further comprises the step six of: according to the iterative symbol detection method based on the approximate message transfer frame in the first to fifth steps, the robustness of the symbol detector to Doppler expansion and fractional Doppler expansion is improved under a high dynamic communication scene, and high-precision symbol detection is realized; the computational complexity of the symbol detection method can be reduced through time-frequency domain orthogonal transformation.
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