CN112953607B - Method, medium and equipment for eliminating quantization noise of MIMO-OFDM system - Google Patents
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Abstract
The invention discloses a method, a medium and equipment for eliminating quantization noise of an MIMO-OFDM system, wherein a mixed Gaussian model is used for fitting quantization noise e generated by a quantizer, and the quantized MIMO-OFDM system is used for receiving signals to obtain a probability density distribution function of the quantization noise e; combining Gaussian white noise existing in a channel with quantization noise e to serve as an error sum q, and constructing a total system error model; calculating parameters in the constructed system error model by using an expectation maximization method; and recovering the transmitted signal from the received signal by combining a generalized approximate message transfer method according to parameters in the system error model, so as to realize noise elimination. The invention performs non-Gaussian error distribution fitting on the error generated by the ADC, and provides an EM-GAMP data detection method based on the error model, thereby improving the accuracy of data detection.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a method, a medium and equipment for eliminating quantization noise of an MIMO-OFDM system.
Background
The MIMO-OFDM system is a communication system that combines MIMO technology and OFDM technology and divides more orthogonal subcarriers on a spectrum with a larger bandwidth. The OFDM can improve the anti-interference capability of the MIMO under a frequency selective channel and simplify the complexity of a receiver, the MIMO can utilize the spatial degree of freedom to improve the transmission rate of the OFDM, and the two technologies can form certain complementary advantages in wireless signal transmission by combining. The improvement of channel capacity brought by the MIMO-OFDM technology has great application potential in high-speed data transmission, and the inevitable trend is to use the MIMO-OFDM technology in a large scale to improve the communication quality in a wireless communication system. However, the hardware complexity and power consumption of signal processing increase with the number of antennas, and in order to reduce power and hardware cost, the MIMO system uses a high-speed but low-resolution ADC instead of a high-resolution ADC, which inevitably introduces quantization noise.
In many studies of MIMO-OFDM system architectures using ADCs, quantization noise is considered as additive white gaussian noise or uniformly distributed noise limited by the number of quantization bits, and the accuracy of this assumption still remains to be improved, especially when low-precision ADCs are used in the system. Many studies have shown that quantization noise caused by quantization is highly non-gaussian distributed, and considering quantization noise as white gaussian noise results in more severe data detection bias.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method, medium, and apparatus for removing quantization noise of MIMO-OFDM system, to solve the problem of data detection of MIMO-OFDM system using ADC, and to perform data detection by fitting non-gaussian quantization noise distribution.
The invention adopts the following technical scheme:
a quantization noise elimination method of a MIMO-OFDM system comprises the following steps:
s1, fitting quantization noise e generated by a quantizer by using a Gaussian mixture model, and receiving signals by using a quantized MIMO-OFDM system to obtain a probability density distribution function of the quantization noise e;
s2, combining Gaussian white noise existing in a channel with quantization noise e to serve as an error sum q, and constructing a total system error model;
s3, calculating parameters in the system error model constructed in the step S2 by using an expectation-maximization method;
and S4, recovering the transmitted signal from the received signal by combining a generalized approximate message transmission method according to the parameters in the system error model obtained in the step S3, and realizing noise elimination.
Specifically, in step S1, the quantization noise e is expressed by a gaussian mixture model as follows:
wherein J is the Gaussian mixture order, theta j 、ω j And phi j Coefficient, mean and covariance matrices for the jth gaussian component, respectively.
Specifically, in step S2, the error sum q is expressed by a gaussian mixture model as:
wherein K is the Gaussian mixture order, mu k 、λ k Sum-sigma k Coefficient, mean and covariance matrices of the kth gaussian component, respectively.
Specifically, step S3 specifically includes: selecting a Gaussian order for the error sum q in the system, wherein the number of Gaussian components is 2-4; setting an initial iteration value, diagonalizing the relative probability of the received signals belonging to the corresponding Gaussian classification to obtain a weighted least square matrix of the received signals, updating the parameters of the error sum q, and obtaining the Gaussian mixture parameters of a system error model through cyclic iteration calculation.
Further, the method comprises the following specific steps:
s301, setting an initial iteration value, setting the mean value of Gaussian components in the Gaussian mixture model to be 0, and calculating a received signal during the t-th iteration
The relative probability that the nth row and the d column element in (b) belong to the kth gaussian component:
where t is the number of iterations, x md (t) is the mth row and the mth column element in the transmitted signal matrix at the tth iteration,
is the n-th row, d-th column element, h, of the received signal nm Is the element of the nth row and the mth column in the channel matrix, wherein N ranges from 1 to N, M ranges from 1 to M, K ranges from 1 to K, and lambda k (t) is the mean of the kth Gaussian component at the tth iteration, Σ k (t) is the covariance of the kth gaussian component at the tth iteration;
s302, receiving signals by means of t iteration
Of the nth row and the d column of the element in (b) belongs to the relative probability o of the kth gaussian component k (n, d, t), all of which are calculatedThe relative probability of an element belonging to the kth gaussian component constructs a diagonal matrix as follows:
O′ k (d,t)＝diag[o k (1,d,t),o k (2,d,t),...,o k (N,d,t)]
s303, by means of a diagonal matrix O' k (d, t), calculating the weighted least square matrix of the t-th received signal as follows:
s304, with the help of a weighted least square matrix, relative probability, a received signal, a channel matrix and a signal sending matrix in the t iteration, the parameters of a Gaussian mixture model of q are as follows:
wherein, x (t) is a signal matrix sent in the t iteration, and H is a channel matrix;
and S305, obtaining the final Gaussian mixture parameter through loop iterative calculation.
Specifically, in step S4, the data detection method using the error model parameters and the generalized approximate message passing algorithm is specifically:
s401, the product of Hx is expressed by z, and the quantized received signal is
Suppose the parameter z obeys
W is the mean of the complex Gaussian distribution, v w Is the covariance of the complex gaussian distribution;
s402, when solving the nonlinear calculation problem,obtaining z posterior probability distribution by combining prior probability distribution and conditional probability distribution
S403, according to the conditional probability distribution of the received signal
Multiplying the z prior probability distribution p (z) by the z variance to obtain the z variance and expectation in step S402;
s404, calculating an inverse variance matrix and expectation of the residual error component S according to the variance and expectation of z obtained in the step S403;
s405, calculating a related auxiliary parameter r of x by using an inverse variance matrix and expectation of the residual error component S;
s406, supposing that the transmitted signal is subjected to QAM modulation, randomly selecting x from constellation points md And obtaining the mean value and the variance of x and recovering the transmitted signal.
Further, the mean and variance of x are calculated as:
wherein,
x md is the mth row and the dint column element in the mean matrix of x,
is the mth row and the dint column element in the covariance matrix of x,
representing the nth row and mth column elements of the channel matrix covariance matrix.
Further advance toStep (S406), randomly selecting x md The method specifically comprises the following steps:
wherein,
c＝{1,2,3,...,C}。
another aspect of the invention is a computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods described.
Another aspect of the present invention is a computing device, including:
one or more processors, memory, and one or more programs stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a method for eliminating quantization noise of an MIMO-OFDM system, which is used for carrying out non-Gaussian error distribution fitting on the quantization output of the MIMO-OFDM system using an ADC; considering the white gaussian noise present in the channel in combination with the quantization noise as the total error; iteratively solving model parameters by using an expectation maximization algorithm; obtaining the mean value and the variance of the hidden variables by a Bayesian inference method according to the received signals and the estimated channel information, and estimating the transmitted signals; compared with the traditional research, the invention provides non-Gaussian error distribution fitting for the error generated by the ADC, and provides the EM-GAMP data detection algorithm based on the error model, thereby improving the accuracy of data detection.
Furthermore, a mixed Gaussian model is used for representing the quantization noise e, and the probability density function of the quantization noise is fitted.
Further, regarding the quantization noise and the white gaussian noise existing in the system as the total error, the step S2 is used to jointly fit the total error distribution.
Furthermore, a Gaussian order is selected for the error sum q in the system, and 2-4 Gaussian components are selected, so that the purpose of better and accurately fitting the distribution of noise is achieved; setting an initial iteration value, diagonalizing the relative probability of the received signal belonging to a certain Gaussian classification to obtain a weighted least square matrix of the received signal, and realizing the iterative update of the parameters of the error sum q.
Further, the probability density function parameter of the error sum q is obtained by step S3.
Furthermore, the sending signal is recovered by means of error model parameters and a data detection method of a generalized approximate message transfer algorithm.
Further, the mean and the variance of x are used to realize the recovery of the transmitted signal.
Further, assuming that the transmitted signal is QAM modulated, x is randomly selected from the constellation points md By using QAM modulation in step S406, QAM modulation is widely applied to high-speed data transmission systems, and can make full use of bandwidth and has strong noise immunity.
In conclusion, the invention performs non-Gaussian error distribution fitting on the error generated by the ADC, and provides the EM-GAMP data detection method based on the error model, thereby improving the accuracy of data detection.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a graph comparing BER performance of the conventional algorithm and the EM-GAMP algorithm under different quantization bits.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
Various structural schematics according to the disclosed embodiments of the invention are shown in the drawings. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The invention provides a method for eliminating quantization noise of an MIMO-OFDM system, which considers that the number of subcarriers is N c The MIMO-OFDM system with L channel multipath number has N at the transmitting end and the receiving end respectively t And N r The received signal on the r-th receiving antenna can be expressed as:
wherein n is r Represents channel Additive White Gaussian Noise (AWGN),e r which is indicative of the quantization noise, is,
is a circulant matrix whose first column can be represented as
While
Is the channel matrix representation between the t-th transmitting antenna and the r-th receiving antenna, the elements in the matrix are in accordance with complex Gaussian
Independent and equally distributed random variables.
Representing a discrete FFT matrix.
With the cyclic prefix and Multiple Measurement Vector (MMV) framework, the received signal can be written in matrix form:
wherein,
is a quantized received signal matrix, x is a transmitted signal matrix, H is a channel matrix, n is a channel additive white gaussian noise matrix, and e is a quantized noise matrix.
The invention selects the proper model type to carry out quantization noise distribution fitting, automatically and accurately estimates the model parameters, and realizes the purpose of accurate data detection.
Referring to fig. 1, a method for removing quantization noise in a MIMO-OFDM system according to the present invention includes the following steps:
s1, collecting the quantized received signals of the MIMO-OFDM system, and representing the quantization noise e introduced by the quantizer by using a Gaussian Mixture Model (GMM), namely:
wherein J is the Gaussian mixture order, theta j 、ω j And phi j Coefficient, mean and covariance matrices for the jth gaussian component, respectively.
And S2, combining the Gaussian white noise and the quantization noise in the channel due to the inevitable noise in the channel to obtain an error sum q, wherein the error sum q is expressed by a Gaussian mixture model as follows:
wherein K is the Gaussian mixture order, mu k 、λ k Sum-sigma k Coefficient, mean and covariance matrices of the kth gaussian component, respectively.
Expressed by the conversion as a continuous multiplication form:
wherein, a k Indicating whether the k-th gaussian component is selected.
S3, obtaining parameters of the error sum q by using an expectation maximization algorithm;
firstly, selecting a Gaussian order for the error sum q in the system, wherein generally 2-4 Gaussian components can be used for better fitting signals, and the proper order is extremely important in order to maximally reduce the calculation complexity on the premise of ensuring the fitting effect; setting an initial iteration value, diagonalizing the relative probability of the received signal belonging to a certain Gaussian classification, and obtaining a weighted least square matrix of the received signal, thereby updating the parameter of the error sum q.
S301, setting an initial iteration value, setting the mean value of Gaussian components in the Gaussian mixture model to be 0, and calculating a received signal during the t-th iteration
The relative probability that the nth row and the d column element in (b) belong to the kth gaussian component:
where t is the number of iterations, x md (t) is the mth row and the mth column element in the transmitted signal matrix at the tth iteration,
is the n-th row, d-th column element, h, of the received signal nm Is the element of the nth row and the mth column in the channel matrix, wherein N ranges from 1 to N, M ranges from 1 to M, K ranges from 1 to K, and lambda k (t) is the mean of the kth Gaussian component at the tth iteration, Σ k (t) is the covariance of the kth Gaussian component at the tth iteration.
S302, constructing a diagonal matrix by using the calculated relative probability of all elements belonging to the kth Gaussian component as follows:
O′ k (d,t)＝diag[o k (1,d,t),o k (2,d,t),...,o k (N,d,t)]
s303, calculating to obtain a weighted least square matrix of the t-th received signal as follows:
s304, calculating parameters of a Gaussian mixture model of q as follows:
where x (t) is the transmit signal matrix at the t-th iteration, and H is the channel matrix.
And S305, obtaining the final Gaussian mixture parameter through loop iterative calculation.
S4, estimating the transmitted signal by using a generalized approximate message transfer method, establishing an approximate likelihood function through the approximate posterior probability of x, and realizing the estimation of the transmitted signal by combining with the Gaussian mixture model parameter obtained by the expectation-maximization algorithm; through loop iteration, the mean value of x in the generalized approximate message transmission method is the obtained sending signal;
the data detection method combining the generalized approximate message transfer algorithm by means of the error model parameters specifically comprises the following steps:
s401, the product of Hx is expressed by z, the received signal is determined, and the parameter z is assumed to obey
The received signal is represented as:
wherein w is the mean of the complex Gaussian distribution, v w Is the covariance of the complex gaussian distribution; the variance of w and the expectation are calculated as follows:
wherein,
representing the time of the t-th iteration v w Row n, column d element, w nd (t) denotes the w, n, th row, d, column elements at the t iteration.
S402, when solving the nonlinear calculation problem, combining the prior probability distribution and the conditional probability distribution to obtain the posterior probability distribution of z;
according to the Bayesian criterion, the posterior probability distribution of the parameter z is expressed as:
wherein,
for the probability distribution of the received signal, the conditional probability distribution of the received signal
The prior probability distribution p (z) product with z is expressed as:
s403, obtaining the variance and expectation of z as follows according to the posterior estimator:
wherein,
represents the nth row and the d column of the covariance matrix of z at the t iteration, z nd (t) denotes the nth row and the d column elements of the mean value of z at the t iteration.
S404, the inverse variance matrix and the expectation of the residual component S are expressed as:
wherein,
representing the nth row and the d column element of the inverse variance matrix of s at the t iteration nd (t) denotes the mean nth row and column elements of s at the tth iteration.
The associated auxiliary parameter r of S405, x is calculated as:
wherein,
represents the mth row and the mth column of the covariance matrix at the tth iteration, r md (t) denotes the mean mth row and the d column element of r at the tth iteration.
S406, supposing that the transmitted signal is QAM-modulated, x md Randomly chosen from the following constellation points:
wherein,
c＝{1,2,3,...,C}。
thus, the mean and variance of x are calculated as:
wherein,
x md is the mth row and the dint column element in the mean matrix of x,
is the mth row and the dint column element in the covariance matrix of x,
representing the nth row and mth column elements of the channel matrix covariance matrix.
In yet another embodiment of the present invention, a terminal device is provided that includes a processor and a memory for storing a computer program comprising program instructions, the processor being configured to execute the program instructions stored by the computer storage medium. The Processor may be a Central Processing Unit (CPU), or may be other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable gate array (FPGA) or other Programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, etc., which is a computing core and a control core of the terminal, and is adapted to implement one or more instructions, and is specifically adapted to load and execute one or more instructions to implement a corresponding method flow or a corresponding function; the processor of the embodiment of the invention can be used for the operation of eliminating the quantization noise of the MIMO-OFDM system, and comprises the following steps:
fitting quantization noise e generated by a quantizer by using a Gaussian mixture model, and receiving signals by using a quantized MIMO-OFDM system to obtain a probability density distribution function of the quantization noise e; combining Gaussian white noise existing in a channel with quantization noise e to serve as an error sum q, and constructing a total system error model; calculating parameters in the constructed system error model by using an expectation maximization method; and recovering the transmitted signal from the received signal by combining a generalized approximate message transfer method according to parameters in the system error model, so as to realize noise elimination.
In still another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a Memory device in a terminal device and is used for storing programs and data. It is understood that the computer readable storage medium herein may include a built-in storage medium in the terminal device, and may also include an extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space storing an operating system of the terminal. Also, one or more instructions, which may be one or more computer programs (including program code), are stored in the memory space and are adapted to be loaded and executed by the processor. It should be noted that the computer-readable storage medium may be a high-speed RAM memory, or may be a non-volatile memory (non-volatile memory), such as at least one disk memory.
One or more instructions stored in the computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of the quantization noise elimination method for the MIMO-OFDM system in the above embodiments; one or more instructions in the computer-readable storage medium are loaded by the processor and perform the steps of:
fitting quantization noise e generated by a quantizer by using a Gaussian mixture model, and receiving signals by using a quantized MIMO-OFDM system to obtain a probability density distribution function of the quantization noise e; combining Gaussian white noise existing in a channel with quantization noise e to serve as an error sum q, and constructing a total system error model; calculating parameters in the constructed system error model by using an expectation maximization method; and recovering the transmitted signal from the received signal by combining a generalized approximate message transfer method according to parameters in the system error model, so as to realize noise elimination.
Referring to fig. 2, the present invention provides simulation results of different data detection methods using GMM to represent ADC quantization noise. The method comprises the following steps: a minimum mean square error parallel interference cancellation algorithm (MMSE-PIC), a minimum mean square error parallel interference cancellation algorithm when passing through a 5-bit quantizer (MMSE-PIC-5bit), a minimum mean square error parallel interference cancellation algorithm when passing through a 4-bit quantizer (MMSE-PIC-4bit), a linear minimum mean square error algorithm based on Bussgan (BLMMSE-5bit) when passing through a 5-bit quantizer, a linear minimum mean square error algorithm based on Bussgan (BLMMSE-4bit) when passing through a 4-bit quantizer, a generalized approximate message transfer method (GAMP), a generalized approximate message transfer method when passing through a 5-bit quantizer (GAMP-5bit), a generalized approximate message transfer method when passing through a 4-bit quantizer (GAMP-4bit), a joint generalized approximate message transfer (EM-GAMP) algorithm is desired to be maximized, the method comprises the steps of expecting a maximum joint generalized approximate message passing (EM-GAMP-5bit) algorithm in a 5-bit quantizer and expecting a maximum joint generalized approximate message passing (EM-GAMP-4bit) algorithm in a 4-bit quantizer.
The simulation sets the number of the antennas at the transmitting end and the number of the antennas at the receiving end to be 128. At a bit error rate of 10 -2 And under the condition that the received signal is not quantized, the EM-GAMP algorithm can obtain 6.11dB gain compared with the BLMMSE algorithm. When the received signal passes through the 5-bit quantizer, the gain increases to 6.59 dB. At a bit error rate of 10 -4 Under the condition that the EM-gam ratio GAMP can obtain a gain of 0.76dB when the received signal is not quantized, but the gain is increased to 0.90dB when the received signal passes through the 5-bit quantizer.
In summary, the method, medium, and apparatus for eliminating quantization noise of a MIMO-OFDM system according to the present invention describe quantization noise caused by an ADC in the system using a hybrid gaussian model, and implement fitting of a sum of errors by combining errors of the MIMO-OFDM system. And acquiring key parameters of total error distribution by using an EM (effective magnetic field) algorithm, and providing a GAMP (gamma-ray fluorescence) data detection method based on non-Gaussian error fitting.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (5)
1. A quantization noise elimination method of a MIMO-OFDM system is characterized by comprising the following steps:
s1, fitting quantization noise e generated by a quantizer by using a Gaussian mixture model, and receiving signals by using a quantized MIMO-OFDM system to obtain a probability density distribution function of the quantization noise e;
s2, combining Gaussian white noise existing in a channel with quantization noise e to serve as an error sum q, and constructing a total system error model;
s3, calculating parameters in the system error model constructed in the step S2 by using an expectation maximization method, and selecting a Gaussian order for the error sum q in the system, wherein the number of Gaussian components is 2-4; setting an initial iteration value, diagonalizing the relative probability of the received signal belonging to the corresponding Gaussian classification to obtain a weighted least square matrix of the received signal, updating the parameter of the error sum q, and obtaining the Gaussian mixture parameter of a system error model through loop iteration calculation, wherein the method comprises the following specific steps:
s301, setting an initial iteration value, setting the mean value of Gaussian components in the Gaussian mixture model to be 0, and calculating a received signal during the t-th iteration
The relative probability that the nth row and the mth column element in (b) belong to the kth gaussian component:
where t is the number of iterations, x md (t) is the mth row and the mth column element in the transmitted signal matrix at the tth iteration,
is the n-th row, d-th column element, h, of the received signal nm Is the element of the nth row and the mth column in the channel matrix, wherein N ranges from 1 to N, M ranges from 1 to M, K ranges from 1 to K, and lambda k (t) isMean of the kth Gaussian component at the t-th iteration, Sigma k (t) is the covariance of the kth gaussian component at the tth iteration;
s302, receiving signals by means of t iteration
Of the nth row and the d column of the element in (b) belongs to the relative probability o of the kth gaussian component k (n, d, t), constructing a diagonal matrix by using the calculated relative probability of all the elements belonging to the kth Gaussian component as follows:
O′ k (d,t)＝diag[o k (1,d,t),o k (2,d,t),...,o k (N,d,t)]
s303, by means of a diagonal matrix O' k (d, t), calculating the weighted least square matrix of the t-th received signal as follows:
s304, with the help of a weighted least square matrix, relative probability, a received signal, a channel matrix and a signal sending matrix in the t iteration, the parameters of a Gaussian mixture model of q are as follows:
wherein, x (t) is a signal matrix sent in the t iteration, and H is a channel matrix;
s305, obtaining a final Gaussian mixture parameter through loop iterative calculation;
s4, recovering the transmitted signal from the received signal by combining the generalized approximate message transmission method according to the parameters in the system error model obtained in the step S3, so as to realize noise elimination, wherein the data detection method combining the generalized approximate message transmission algorithm by means of the error model parameters specifically comprises the following steps:
s401, the product of Hx is expressed by z, and the quantized received signal is
Suppose the parameter z obeys
W is the mean of the complex Gaussian distribution, v w Is the covariance of the complex gaussian distribution;
s402, when solving the nonlinear calculation problem, obtaining the posterior probability distribution of z by combining the prior probability distribution and the conditional probability distribution
S403, according to the conditional probability distribution of the received signal
Multiplying the z prior probability distribution p (z) by the z variance to obtain the z variance and expectation in step S402;
s404, calculating an inverse variance matrix and expectation of the residual error component S according to the variance and expectation of z obtained in the step S403;
s405, calculating a related auxiliary parameter r of x by using an inverse variance matrix and expectation of the residual error component S;
s406, supposing that the transmitted signal is subjected to QAM modulation, randomly selecting x from constellation points md And obtaining the mean and variance of x, and recovering the transmitted signal, wherein the mean and variance of x are calculated as:
wherein,
x md is the mth row and the dint column element in the mean matrix of x,
is the mth row and the dint column element in the covariance matrix of x,
representing the nth row and the mth column of the channel matrix covariance matrix;
randomly choosing x md The method specifically comprises the following steps:
wherein,
c＝{1,2,3,...,C}。
2. the method according to claim 1, wherein in step S1, the quantization noise e is expressed by a gaussian mixture model as follows:
wherein J is the Gaussian mixture order, theta j 、ω j And phi j Respectively coefficient, mean and covariance matrix of the jth gaussian component.
3. The method according to claim 1, wherein in step S2, the error sum q is expressed by a gaussian mixture model as:
wherein K is the Gaussian mixture order, mu k 、λ k Sum-sigma k Coefficient, mean and covariance matrices of the kth gaussian component, respectively.
4. A computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods of claims 1 or 2 or 3.
5. A computing device, comprising:
one or more processors, memory, and one or more programs stored in the memory and configured for execution by the one or more processors, the one or more programs including instructions for performing any of the methods of claims 1, 2, or 3.
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