CN112910810B - Synchronization method, apparatus and medium for mimo-ofdm system - Google Patents

Synchronization method, apparatus and medium for mimo-ofdm system Download PDF

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CN112910810B
CN112910810B CN202110137696.2A CN202110137696A CN112910810B CN 112910810 B CN112910810 B CN 112910810B CN 202110137696 A CN202110137696 A CN 202110137696A CN 112910810 B CN112910810 B CN 112910810B
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frequency
timing
frequency offset
pilot
synchronization
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CN112910810A (en
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马东堂
刘军
魏急波
熊俊
张晓瀛
梅楷
张校晨
曹阔
赵海涛
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National University of Defense Technology
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/0014Carrier regulation
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2647Arrangements specific to the receiver only
    • H04L27/2655Synchronisation arrangements
    • H04L27/2657Carrier synchronisation
    • H04L27/266Fine or fractional frequency offset determination and synchronisation
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2647Arrangements specific to the receiver only
    • H04L27/2655Synchronisation arrangements
    • H04L27/2668Details of algorithms
    • H04L27/2673Details of algorithms characterised by synchronisation parameters
    • H04L27/2675Pilot or known symbols
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/0014Carrier regulation
    • H04L2027/0024Carrier regulation at the receiver end
    • H04L2027/0026Correction of carrier offset

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Abstract

The application discloses a synchronization method, a synchronization device and a computer-readable storage medium of a multi-input multi-output orthogonal frequency division multiplexing system. The method comprises the steps of utilizing a training sample set to train in advance to obtain a timing error estimation model and a residual frequency offset estimation model; the training sample set includes a plurality of sets of training sample pairs of known timing offsets or known frequency offsets and pilots having corresponding known timing offsets or known frequency offsets. The pilot includes a first OFDM symbol for initial estimation of timing and fractional frequency offset and a second OFDM symbol for integer frequency offset estimation and channel estimation. And respectively inputting the frequency domain signals of the pilot frequency sequence subjected to initial synchronization processing into a timing error estimation model and a residual frequency deviation estimation model, and determining a timing synchronization position and frequency deviation estimation according to a timing synchronization error estimation value and a residual frequency deviation estimation value output by the models. The method and the device can effectively improve the synchronization precision of the multi-input multi-output orthogonal frequency division multiplexing system.

Description

Synchronization method, apparatus and medium for MIMO OFDM system
Technical Field
The present application relates to the field of physical layer technologies for wireless communications, and in particular, to a synchronization method and apparatus for a mimo ofdm system, and a computer-readable storage medium.
Background
A multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) technology is an efficient physical layer solution, a MIMO-OFDM-based system can be called an MIMO-OFDM system (multiple-input multiple-output orthogonal frequency division multiplexing system), the spectral efficiency of the MIMO-OFDM-based system is superior to that of a conventional single carrier system, and the MIMO-OFDM-based system is widely applied to the technical field of wireless communication. The MIMO-OFDM system effectively counters inter-symbol interference caused by multipath effect by converting a frequency selective fading channel into a plurality of parallel flat fading sub-channels, and its multi-antenna configuration can fully utilize space to implement diversity or multiplexing.
Because the carrier frequency offset can destroy the orthogonality among the sub-carriers of the OFDM symbol, and the timing synchronization error can introduce intersymbol interference to the OFDM symbol, the performance of the MIMO-OFDM system is not only sensitive to the carrier frequency offset, but also has high requirements on the timing synchronization precision. In order to solve the technical problem, in the existing method, a transmitter transmits a pilot frequency sequence with a specific structure, and a receiver performs autocorrelation and other operations on the received pilot frequency to estimate and obtain a timing synchronization position and carrier frequency offset. However, the timing synchronization precision of the method is sensitive to a multipath channel, and the performance of frequency offset estimation still has a room for improvement.
Disclosure of Invention
The application provides a synchronization method, a synchronization device and a computer readable storage medium for a multi-input multi-output orthogonal frequency division multiplexing system, which improve the precision of a timing synchronization position and carrier frequency offset and effectively improve the synchronization precision of the multi-input multi-output orthogonal frequency division multiplexing system.
In order to solve the above technical problems, embodiments of the present invention provide the following technical solutions:
an embodiment of the present invention provides a synchronization method for a mimo-ofdm system, including:
training a timing error estimation model and a residual frequency offset estimation model by using a delay sample set in advance;
respectively inputting the frequency domain signals of the pilot frequency sequence subjected to initial synchronization processing into the timing error estimation model and the residual frequency offset estimation model to obtain a timing synchronization error estimation value and a residual frequency offset estimation value of the pilot frequency sequence;
determining a timing synchronization position and frequency offset estimation according to the timing synchronization error estimation value and the residual frequency offset estimation value;
wherein the delayed sample set comprises a plurality of groups of training sample pairs consisting of known timing offsets and pilots containing the known timing offsets; the frequency offset sample set comprises a plurality of groups of training sample pairs consisting of known frequency offsets and pilots containing the known frequency offsets; the pilot includes a first OFDM symbol for initial estimation of timing and fractional frequency offset and a second OFDM symbol for integer frequency offset estimation and channel estimation.
Optionally, the inputting, to the timing error estimation model and the residual frequency offset estimation model, the frequency domain signal of the pilot sequence processed through the initial synchronization respectively includes:
for each pilot frequency in the pilot frequency sequence, determining an initial timing position, estimating frequency offset and compensating frequency offset according to a first OFDM symbol and a second OFDM symbol of each pilot frequency;
carrying out frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence;
and respectively inputting the pilot frequency sequences after frequency domain equalization to the timing error estimation model and the residual frequency offset estimation model.
Optionally, the determining the initial timing position, estimating the frequency offset, and compensating the frequency offset according to the first OFDM symbol and the second OFDM symbol of each pilot frequency includes:
for each pilot frequency in the pilot frequency sequence, calculating a timing measurement function according to a first OFDM symbol of the current pilot frequency to obtain an initial timing position;
after the initial timing position is obtained, fractional and integer frequency offset estimation is carried out by utilizing a first OFDM symbol and a second OFDM symbol of the current pilot frequency;
and performing frequency offset compensation on the current pilot frequency after initial timing by using the frequency offset estimation value.
Optionally, the performing frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence includes:
performing fast Fourier transform operation on the compensated current pilot frequency to obtain a frequency domain signal of the current pilot frequency;
estimating a channel by using a second OFDM symbol of the current pilot frequency to obtain channel response information;
and performing frequency domain equalization on the current pilot frequency by using the channel response information.
Optionally, the training of the timing error estimation model and the training of the residual frequency offset estimation model in advance by using the delayed sample set includes:
training an extreme learning machine frame by using the delay sample set to obtain the timing error estimation model so as to establish a mapping relation between pilot frequency containing timing deviation and corresponding timing deviation;
and training an extreme learning machine frame by using the frequency offset sample set to obtain the residual frequency offset estimation model so as to establish a mapping relation between the pilot frequency containing the residual frequency offset and the corresponding residual frequency offset.
Optionally, the set of delayed samples includes a plurality of sets of training sample pairs that do not contain channel fading and noise and are composed of a known timing offset and a pilot with a known timing offset; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset.
Another aspect of the embodiments of the present invention provides a synchronization apparatus for a mimo-ofdm system, including:
the model pre-training module is used for pre-training a timing error estimation model and a residual frequency offset estimation model by utilizing a delay sample set; the delay sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known timing deviation and pilot frequency containing known timing deviation; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset; the pilot frequency comprises a first OFDM symbol used for initial estimation of timing and fractional frequency offset and a second OFDM symbol used for integral frequency offset estimation and channel estimation;
the initial synchronization processing module is used for carrying out initial synchronization processing on the received pilot frequency sequence;
the secondary synchronization processing module is used for respectively inputting the frequency domain signals of the pilot frequency sequence subjected to the initial synchronization processing into the timing error estimation model and the residual frequency offset estimation model to obtain a timing synchronization error estimation value and a residual frequency offset estimation value of the pilot frequency sequence; and determining a timing synchronization position and frequency offset estimation according to the timing synchronization error estimation value and the residual frequency offset estimation value.
Optionally, the initial synchronization processing module includes:
the coarse synchronization sub-module is used for carrying out initial timing position determination, frequency offset estimation and frequency offset compensation on each pilot frequency in the pilot frequency sequence according to a first OFDM symbol and a second OFDM symbol of each pilot frequency;
and the equalization processing submodule is used for carrying out frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence.
An embodiment of the present invention further provides a synchronization apparatus for a mimo-ofdm system, including a processor, where the processor is configured to implement the steps of the synchronization method for the mimo-ofdm system when executing a computer program stored in a memory.
Finally, an embodiment of the present invention provides a computer-readable storage medium, where a synchronization program of a mimo-ofdm system is stored, and when the synchronization program of the mimo-ofdm system is executed by a processor, the step of implementing the synchronization method of the mimo-ofdm system as in any of the foregoing is implemented.
The technical scheme provided by the application has the advantages that the timing error estimation model and the residual frequency offset estimation model are trained to establish the mapping relation between the pilot frequency containing the timing error and the corresponding timing error and the mapping relation between the pilot frequency containing the residual frequency offset and the corresponding residual frequency offset. Firstly, carrying out initial synchronization processing on a pilot frequency signal, then estimating a timing deviation contained in the pilot frequency according to the input pilot frequency signal, and carrying out fine timing synchronization on the pilot frequency by utilizing the estimated timing deviation; estimating residual frequency offset contained in the pilot frequency according to the input pilot frequency signal, and realizing fine frequency synchronization of the signal by utilizing the estimated residual frequency offset; and performing secondary synchronous estimation on the pilot frequency output by the transmitter to estimate a timing synchronous position and carrier frequency offset with higher precision, thereby effectively improving the synchronous precision of the MIMO OFDM system.
In addition, the embodiment of the invention also provides a corresponding implementation device and a computer readable storage medium for the synchronization method of the MIMO OFDM system, so that the method has higher practicability, and the device and the computer readable storage medium have corresponding advantages.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the related arts, the drawings used in the description of the embodiments or the related arts will be briefly described below, it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart illustrating a synchronization method of a mimo-ofdm system according to an embodiment of the present invention;
FIG. 2 is a block diagram of an exemplary application scenario provided by an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a transmitting antenna 1 in a pilot sequence according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a transmitting antenna 2 in a pilot sequence according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of an extreme learning machine-based timing deviation estimator according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a residual frequency offset estimator based on an extreme learning machine according to an embodiment of the present invention;
FIG. 7 is a timing deviation diagram for an AWGN channel and an exponentially fading multipath channel in accordance with an embodiment of the present invention;
FIG. 8 is a diagram illustrating timing estimation MSE in AWGN channel and exponential fading multipath channel in accordance with an embodiment of the present invention;
FIG. 9 is a diagram of frequency offset estimation MSE under AWGN channel and exponential fading multipath channel according to the embodiment of the present invention;
fig. 10 is a structural diagram of an embodiment of a synchronization apparatus of a mimo-ofdm system according to an embodiment of the present invention;
fig. 11 is a structural diagram of another specific embodiment of a synchronization apparatus of a mimo-ofdm system according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the disclosure, the invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The terms "first," "second," "third," "fourth," and the like in the description and claims of this application and in the foregoing drawings are used for distinguishing between different objects and not necessarily for describing a particular sequential order. Furthermore, the terms "comprising" and "having," as well as any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those steps or elements but may include other steps or elements not expressly listed.
Having described the technical solutions of the embodiments of the present invention, various non-limiting embodiments of the present application are described in detail below.
Referring to fig. 1, fig. 1 is a schematic flow chart of a synchronization method of a mimo ofdm system according to an embodiment of the present invention, where the embodiment of the present invention includes the following:
s101: and training a timing error estimation model and a residual frequency offset estimation model by using a delay sample set in advance.
In this embodiment, the delayed sample set may include a plurality of sets of training sample pairs consisting of known timing offsets and pilots with known timing offsets; the frequency offset sample set comprises a plurality of groups of training sample pairs consisting of known frequency offsets and pilot frequencies containing the known frequency offsets; the pilots in each training sample pair comprise 2 OFDM symbols, one being a first OFDM symbol for initial estimation of timing and fractional frequency offset and the other being a second OFDM symbol for integer frequency offset estimation and channel estimation. For the generation of the pilot with known timing offset and the pilot with known frequency offset, the following steps may be performed: firstly, a plurality of pilot frequencies are obtained, and known timing synchronization deviation or known residual frequency deviation is added to each pilot frequency according to the requirement so as to synthesize the pilot frequency with known timing deviation or the pilot frequency with known frequency deviation.
Adding known delay into the pilot frequency, forming a training sample pair by the generated pilot frequency containing the delay and the corresponding delay thereof as input, inputting a timing error estimation model for timing synchronization, and training the timing error estimation model for timing synchronization; adding known frequency offset into the pilot frequency, forming a training sample pair by the generated pilot frequency containing the frequency offset and the frequency offset corresponding to the pilot frequency as input, inputting a residual frequency offset estimation model for frequency offset estimation, and training the residual frequency offset estimation model. In this embodiment, based on machine learning, any machine learning model, such as an extreme learning machine, a neural network model, for example, a convolutional neural network, etc., may be trained by using a training sample set to obtain a timing error estimation model and a residual frequency offset estimation model, and a person skilled in the art may select a type of the training model according to an actual application scenario, which is not limited in this application.
S102: and respectively inputting the frequency domain signals of the pilot frequency sequence subjected to the initial synchronization processing into a timing error estimation model and a residual frequency offset estimation model to obtain a timing synchronization error estimation value and a residual frequency offset estimation value of the pilot frequency sequence.
Before a communication system carries out communication, two model frames which are respectively used for timing error estimation and residual frequency offset estimation are trained by utilizing the last step, and the purpose of the training is to enable the trained model to establish a mapping relation between pilot frequency containing timing error and residual frequency offset and the corresponding timing error and residual frequency offset, namely to establish the mapping relation between the pilot frequency containing the timing error and the corresponding timing error by utilizing a timing error estimation model; and establishing a mapping relation between the pilot frequency containing the residual frequency offset and the corresponding residual frequency offset by using a residual frequency offset estimation model. After the timing error estimation model and the residual frequency offset estimation model are trained offline, they can be configured to the MIMO-OFDM system for use, that is, the transmitter transmits the pilot sequence first, for example, the pilot sequence can be transmitted in a time orthogonal manner. The pilot sequence is received by the receiver after passing through the wireless channel. The receiver can utilize the traditional method to carry out initial timing synchronization and initial frequency offset estimation according to the received pilot frequency signal, and carry out initial compensation on the pilot frequency signal according to the results of the initial timing synchronization and the frequency offset estimation, thereby completing the initial synchronization of the communication system. Because the synchronization precision in the initial synchronization process is lower than the precision of performing secondary estimation on the used pilot frequency by using the model obtained by training in S101, the initial synchronization can be called coarse synchronization, and the pilot frequency signal is processed by using the timing error estimation model and the residual frequency offset estimation model, so that the timing synchronization position and the carrier frequency offset with higher precision can be obtained, and the synchronization precision of the communication system is improved.
S103: and determining a timing synchronization position and frequency offset estimation according to the timing synchronization error estimation value and the residual frequency offset estimation value.
In the technical solution provided in the embodiment of the present invention, a timing error estimation model and a residual frequency offset estimation model are trained to establish a mapping relationship between a pilot frequency containing a timing error and a corresponding timing error, and a mapping relationship between a pilot frequency containing a residual frequency offset and a corresponding residual frequency offset. Firstly, carrying out initial synchronization processing on a pilot frequency signal, then estimating a timing deviation contained in the pilot frequency according to the input pilot frequency signal, and carrying out fine timing synchronization on the pilot frequency by utilizing the estimated timing deviation; estimating residual frequency offset contained in the pilot frequency according to the input pilot frequency signal, and realizing fine frequency synchronization of the signal by using the estimated residual frequency offset; and performing secondary synchronous estimation on the pilot frequency output by the transmitter to estimate a timing synchronous position and carrier frequency offset with higher precision, thereby effectively improving the synchronous precision of the MIMO OFDM system.
In the foregoing embodiment, how to perform step S102 is not limited, and an implementation manner of the initial calibration of the pilot signal by the communication system in this embodiment may include the following steps:
for each pilot frequency in the pilot frequency sequence, determining an initial timing position, estimating frequency offset and compensating the frequency offset according to a first OFDM symbol and a second OFDM symbol of each pilot frequency;
carrying out frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence;
and respectively inputting the pilot frequency sequences after frequency domain equalization to a timing error estimation model and a residual frequency offset estimation model.
As an optional implementation manner of this embodiment, the process of initial timing estimation and initial frequency offset estimation may include:
for each pilot in the pilot sequence, a timing metric function is calculated from the first OFDM symbol of the current pilot to obtain an initial timing position.
After the initial timing position is obtained, fractional and integer frequency offset estimation is carried out by utilizing a first OFDM symbol and a second OFDM symbol of the current pilot frequency;
and performing frequency offset compensation on the current pilot frequency after initial timing by using the frequency offset estimation value.
In this embodiment, the receiver may calculate a timing metric function according to the correlation characteristic of the first OFDM symbol itself in the received signal, to obtain a coarse timing position; after the coarse timing position is obtained, the two OFDM symbols are comprehensively utilized to carry out fractional and integer frequency offset estimation, and frequency offset compensation is carried out on the pilot frequency after coarse timing by utilizing the frequency offset estimation value.
As another optional implementation manner of this embodiment, the implementation process of the frequency domain equalization process may include:
performing Fast Fourier Transform (FFT) operation on the compensated current pilot frequency to obtain a frequency domain signal of the current pilot frequency;
estimating a channel by using a second OFDM symbol of the current pilot frequency to obtain channel response information;
and performing frequency domain equalization on the current pilot frequency by utilizing the channel response information.
In this embodiment, FFT operation is performed on the compensated pilot frequency to obtain a frequency domain signal of the pilot frequency; estimating a channel by using a second OFDM symbol in the pilot frequency, and performing frequency domain equalization on the pilot frequency signal by using the channel response obtained by estimation; and respectively inputting the pilot frequency after frequency domain equalization into a timing error estimation model for timing synchronization and a residual frequency offset estimation model for frequency offset estimation to respectively obtain the estimation of a timing synchronization error and a residual frequency offset, and predicting the obtained timing synchronization error and the residual frequency offset estimation error by the communication system according to the residual frequency offset estimation model to obtain a final timing synchronization position and frequency offset estimation.
In the foregoing embodiment, how to perform step S101 is not limited, and a training implementation of the timing error estimation model and the residual frequency offset estimation model in this embodiment may include the following steps:
training an extreme learning machine frame by using a delay sample set to obtain a timing error estimation model so as to establish a mapping relation between pilot frequency containing timing deviation and corresponding timing deviation;
and training an extreme learning machine frame by using a frequency offset sample set to obtain a residual frequency offset estimation model so as to establish a mapping relation between the pilot frequency containing the residual frequency offset and the corresponding residual frequency offset.
In this embodiment, in order to further improve the performance of timing synchronization and frequency offset estimation, the generation process of the model training samples does not depend on the channel model, that is, the delay sample set includes a plurality of training sample pairs which do not contain channel fading and noise and are formed by known timing offset and pilot frequency containing known timing offset; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset. That is, the training samples for training the extreme learning machine are generated by adding known timing or frequency offsets to the pilots, and without adding channel fading and noise.
The training of the extreme learning machine of the embodiment does not depend on a channel model, the training complexity is low, high-precision timing synchronization and frequency offset estimation can be realized, and the performance of the MIMO-OFDM system is improved.
In order to make the technical solutions of the present application more clearly apparent to those skilled in the art, the present application also provides an illustrative example in conjunction with fig. 2, which may include the following:
a1: before a communication system carries out communication, two extreme learning machines which are respectively used for timing error estimation and residual frequency offset estimation need to be trained, and the purpose of training is to enable the extreme learning machines to establish a mapping relation between pilot frequency containing timing error and residual frequency offset and corresponding timing error and residual frequency offset.
The process of generating the pilot sequence for synchronization in this step may include: fig. 3 and fig. 4 show pilot structures adopted in the present embodiment, which take a2 × 2MIMO-OFDM system as an example, where TX1 and TX2 respectively represent transmit antenna 1 and transmit antenna 2, and pilots are transmitted in a time orthogonal manner. The pilot is of length N for all transmit antennas train =2(N g +N c ) In which N is g And N c Respectively indicate the length of a CP (Cyclic Prefix) and the length of one OFDM symbol. c. C p,1 And c p,2 Are two different PN sequences transmitted by the pth transmit antenna. First part c of pilot p,1 The structure is composed of two identical parts in time domain, and is used for estimating timing synchronization and fractional carrier frequency offset. This time domain structure is implemented by loading the PN sequence to even subcarriers of an OFDM symbol and nulling out on odd subcarriers. Second part c of the pilot p,2 The PN sequence on the odd subcarriers can be used for channel estimation, and the even subcarriersAnother PN sequence on the wave is used to assist in the estimation of the carrier frequency offset.
In this embodiment, the principle of the timing error estimation limit learning machine and the residual carrier frequency offset estimation limit learning machine is explained with reference to fig. 5 and 6:
FIG. 5 is a block diagram of the timing error extreme learning machine estimator in which the number of input neurons is 2N r N t N c The number of neurons in the hidden layer is
Figure BDA00029276573000001112
Number of output neurons is N o . The input, output, and weights and offsets of the extreme learning machine are complex numbers. Input to the prediction phase extreme learning machine of FIG. 5
Figure BDA0002927657300000111
Indicating that the qth receiving antenna receives signals from the pth transmitting antenna and c p,i The corresponding equalized signal. The real (-) function will return the real part of the input, and argmax (-) will return the index corresponding to the maximum in the vector of inputs. In the extreme learning machine training phase, training set
Figure BDA0002927657300000112
Needs to be generated first, wherein the input data of the n-th training sample
Figure BDA0002927657300000113
The representation contains an index vector O n The received pilot signal of the corresponding timing error is the frequency domain signal after FFT transformation. The index vector denoted by "index" in fig. 5 includes different timing errors. Index = [ -N ] in this embodiment g ,…,N g ]. Target output in training set O n Is a one-hot vector, is defined by the corresponding timing error τ R,n Obtained by one-hot coding. In this example, [1,0, \8230;, 0] T Corresponding timing error is τ R =-N g ,[0,…,0,1] T Corresponding timing error is τ R =N g . The specific process of training set generation is as follows:
Figure BDA0002927657300000114
Figure BDA0002927657300000115
Figure BDA0002927657300000116
Figure BDA0002927657300000117
Figure BDA0002927657300000118
wherein,
Figure BDA0002927657300000119
the pseudo functions "RemoveCP" and "FFT" in the above equation represent removing all CP and performing N, respectively c Fast fourier transform of the points. Note that, δ [ k- τ ] R,n ]Representing a delay of τ R,n The kronecker dirac function of (a),
Figure BDA00029276573000001110
and [ k- τ ] R,n ]When kronecker product is performed, the deficient elements are zero-filled. Input weight alpha of extreme learning machine k And offset b k Randomly generated by uniformly distributing U (-0.1, 0.1), wherein
Figure BDA00029276573000001111
Is the weight that connects the input neuron with the kth hidden layer neuron,
Figure BDA0002927657300000121
Figure BDA0002927657300000122
when the input weights and input biases are generated, the output of the hidden layer is
Figure BDA0002927657300000123
Wherein
Figure BDA0002927657300000124
In order to make the output of the extreme learning machine as close as possible to the target output, i.e. β D training And (c) = O. In general terms, the amount of the solvent to be used,
Figure BDA0002927657300000125
wherein, beta k Representing the output weight vector connecting the kth hidden layer neuron with the output layer, N o Denotes the number of output neurons, N in this embodiment o =2N g +1. Under the Least Squares (LS) criterion, the output weight is
Figure BDA0002927657300000126
The equalized pilot signal may be represented as an estimate or extreme learning machine prediction
Figure BDA0002927657300000127
The output of the hidden layer may be
Figure BDA0002927657300000128
Wherein
Figure BDA0002927657300000129
Since the input, output, weight and offset of the extreme learning machine are complex numbers, the real part of the output of the extreme learning machine is written as
Figure BDA00029276573000001210
The estimated timing error can be expressed as:
Figure BDA00029276573000001211
FIG. 6 is a block diagram of an estimator of a residual frequency offset limit learning machine, in which the number of input neurons is 2N r N t N c The number of neurons in the hidden layer is
Figure BDA00029276573000001212
The output layer has only one neuron, and records the residual frequency deviation epsilon R Is composed of
Figure BDA00029276573000001213
In order to make the residual frequency offset limit learning machine learn the relationship between the pilot frequency containing residual frequency offset and the corresponding residual frequency offset, firstly, it is necessary to generate a pilot frequency training set containing residual frequency offset, which is used here
Figure BDA00029276573000001214
Representing the input of the nth input residual frequency offset limit learning machine, and the corresponding residual frequency offset is epsilon R =O n The specific generation process is as follows:
Figure BDA00029276573000001215
Figure BDA0002927657300000131
Figure BDA0002927657300000132
Figure BDA0002927657300000133
Figure BDA0002927657300000134
the hidden layer outputs are
Figure BDA0002927657300000135
Wherein
Figure BDA0002927657300000136
Also, it is desirable that the output of the residual frequency offset limit learning machine coincide as much as possible with the target output O, i.e., β D training = O, then the output weight based on LS criteria is
Figure BDA0002927657300000137
Similar to the timing error extreme learning machine, the estimation of the residual frequency offset is
Figure BDA0002927657300000138
A2: after the training is completed off line, the extreme learning machine can be configured to the MIMO-OFDM system for use, namely, the transmitter transmits a pilot sequence firstly, and the pilot sequence is received by the receiver after passing through a wireless channel. The receiver firstly carries out coarse timing synchronization and coarse frequency offset estimation by using a traditional method according to the received pilot frequency signal, and carries out coarse compensation on the pilot frequency signal according to the result of the coarse timing synchronization and the frequency offset estimation. And performing FFT on the pilot signals subjected to the coarse compensation to obtain the pilot signals in the frequency domain. The channel can be estimated and equalized according to the frequency domain signal of the pilot.
In this step, the transmitter sends a pilot frequency, and the receiver implements coarse timing synchronization and carrier frequency offset estimation according to the received pilot frequency. Here, assuming the symbol timing offset to be estimated is τ, the estimation of the coarse timing offset
Figure BDA0002927657300000139
Can be expressed as:
Figure BDA00029276573000001310
wherein the discrete variable d represents the lengthIs N c First sample point in the window of (1), N t Number of transmitting antennas, d p =d-(N t -p)N train Calculated is the first part c of the pilot 1 The expression of (2) can be expressed as:
Figure BDA0002927657300000141
wherein, N r To receive the number of antennas, r q (i) Is the ith sampling point of the qth receiving antenna. And c 1 The received energy P (d) corresponding to the latter half is defined as:
Figure BDA0002927657300000142
after the coarse timing is completed, coarse carrier frequency offset estimation can be performed. Defining a normalized carrier frequency offset epsilon as epsilon = f offset A,/Δ f, wherein f offset For carrier frequency offset, Δ f is the OFDM subcarrier spacing. Marking normalized carrier frequency deviation epsilon as integral part epsilon i With a fractional part epsilon f I.e. epsilon = epsilon if Wherein
Figure BDA0002927657300000143
When | epsilon | is less than or equal to 1, the coarse carrier frequency offset can be directly estimated
Figure BDA0002927657300000144
Comprises the following steps:
Figure BDA0002927657300000145
wherein,
Figure BDA0002927657300000146
representing the sum of the phases of the complex autocorrelations from the pilots of different transmit antennas. When ε > 1, then c needs to be used 2 And (4) finishing the estimation of the integer carrier frequency offset in an auxiliary manner. Suppose that
Figure BDA0002927657300000147
Wherein g is an integer. Before estimating integral carrier frequency deviation, firstly utilizing the estimation
Figure BDA0002927657300000148
Correcting the pilot frequency, and then performing FFT operation on the pilot frequency to obtain the sum c p,1 And c p,2 Corresponding frequency domain signal x q,p,1 And x q,p,2 Then estimation of g
Figure BDA00029276573000001413
Can be expressed as:
Figure BDA0002927657300000149
wherein X Even A subset of even-numbered frequency indices is indicated,
Figure BDA00029276573000001410
finally, estimation of carrier frequency offset
Figure BDA00029276573000001411
Can be expressed as
Figure BDA00029276573000001412
A3: the pilot signal after channel equalization is input to the timing offset estimation limit learning machine, and the timing offset estimation limit learning machine estimates the timing offset contained in the pilot signal according to the input pilot signal, and at this time, the estimated timing offset can be used for carrying out fine timing synchronization on the pilot signal. Inputting the pilot frequency subjected to fine timing synchronization into a residual frequency offset estimation limit learning machine, estimating residual frequency offset contained in the pilot frequency by the residual frequency offset limit learning machine according to the input pilot frequency signal, and finally realizing fine frequency synchronization of the signal by utilizing the estimated residual frequency offset.
In this embodiment, column vectors are represented using the lower case letter x in bold, and upper case letters in bold are usedThe parent X represents a matrix. Upper label -1*TH And
Figure BDA0002927657300000151
respectively, an inversion operation, a conjugate operation, a transposition operation, a conjugate transposition operation, and a Moore-Penrose generalized inverse operation.
Figure BDA0002927657300000152
⊙、
Figure BDA0002927657300000153
E{·}、
Figure BDA0002927657300000154
And
Figure BDA0002927657300000155
respectively representing the kronecker product, the hadamard product, the cyclic convolution, the mathematical expectation operation, the floor function, and the imaginary unit. The angle (·) function is used to output the phase angle of the complex input. repmat (a, m, n) is used to output a matrix that repeats matrix a m and n times in the row and column directions, respectively.
In order to verify the validity of the technical scheme of the present application, the present application further provides a verification experiment, the verification results can be shown in fig. 7 to 9, fig. 7 is a timing deviation diagram under gaussian channel AWGN channel and exponential fading multipath channel respectively, and 3 × 10 is performed in total 5 A secondary channel realization. It can be seen that under AWGN channel conditions, the proposed method of the present invention can achieve error-free timing synchronization when the signal-to-noise ratio is greater than 3 dB. FIG. 8 is a diagram of the timing estimation MSE (Mean Square Error) for AWGN channel and exponential fading multipath channel, which is performed by 3 × 10 5 A secondary channel realization. It can be seen from fig. 8 that the MSE performance of the timing synchronization of the proposed method is better than that of the conventional method under both AWGN and fading channel conditions. FIG. 9 is a diagram of frequency offset estimation MSE under AWGN channel and exponential fading multipath channel, which is performed by 3 × 10 5 Sub-channel implementation, as can be seen in FIG. 9In addition, the MSE performance of the frequency offset estimation of the method provided by the application is superior to that of the traditional method under the AWGN channel condition or the fading channel condition.
It should be noted that, in the present application, there is no strict sequential execution order among the steps, and as long as a logical order is met, the steps may be executed simultaneously or according to a certain preset order, and fig. 1 to fig. 2 are only schematic manners, and do not represent only such an execution order.
The embodiment of the invention also provides a corresponding device for the synchronization method of the MIMO OFDM system, thereby further ensuring that the method has higher practicability. Wherein the means can be described separately from the functional module point of view and the hardware point of view. The following describes a synchronization apparatus of a mimo ofdm system according to an embodiment of the present invention, and the synchronization apparatus of the mimo ofdm system described below and the synchronization method of the mimo ofdm system described above may be referred to in correspondence to each other.
Based on the angle of the functional module, referring to fig. 10, fig. 10 is a structural diagram of a synchronization apparatus of a mimo-ofdm system according to an embodiment of the present invention in a specific implementation, where the synchronization apparatus may include:
a model pre-training module 1001 for training a timing error estimation model and a residual frequency offset estimation model in advance by using a delay sample set; the delay sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known timing deviation and pilot frequency containing the known timing deviation; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset; the pilot includes a first OFDM symbol for initial estimation of timing and fractional frequency offset and a second OFDM symbol for integer frequency offset estimation and channel estimation.
An initial synchronization processing module 1002, configured to perform initial synchronization processing on the received pilot sequence.
A secondary synchronization processing module 1003, configured to input the frequency domain signal of the pilot sequence subjected to the initial synchronization processing into a timing error estimation model and a residual frequency offset estimation model, respectively, so as to obtain a timing synchronization error estimation value and a residual frequency offset estimation value of the pilot sequence; and determining a timing synchronization position and frequency offset estimation according to the timing synchronization error estimation value and the residual frequency offset estimation value.
Optionally, in some embodiments of this embodiment, the initial synchronization processing module 1002 may include:
the coarse synchronization sub-module is used for determining the initial timing position, estimating the frequency offset and compensating the frequency offset of each pilot frequency in the pilot frequency sequence according to the first OFDM symbol and the second OFDM symbol of each pilot frequency;
and the equalization processing submodule is used for carrying out frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence.
As an optional implementation manner of this embodiment, the coarse synchronization sub-module may further be configured to:
for each pilot frequency in the pilot frequency sequence, calculating a timing measurement function according to a first OFDM symbol of the current pilot frequency to obtain an initial timing position; after the initial timing position is obtained, fractional and integer frequency offset estimation is carried out by utilizing a first OFDM symbol and a second OFDM symbol of the current pilot frequency; and performing frequency offset compensation on the current pilot frequency after the initial timing by using the frequency offset estimation value.
As another optional implementation manner of this embodiment, the equalization processing sub-module may be further configured to:
performing fast Fourier transform operation on the compensated current pilot frequency to obtain a frequency domain signal of the current pilot frequency; estimating a channel by using a second OFDM symbol of the current pilot frequency to obtain channel response information; and performing frequency domain equalization on the current pilot frequency by utilizing the channel response information.
Optionally, in another implementation manner of this embodiment, the model pre-training module 1001 is further configured to train an extreme learning machine framework by using a delay sample set to obtain a timing error estimation model, so as to establish a mapping relationship between a pilot frequency containing a timing offset and a corresponding timing offset; and training the extreme learning machine frame by using the frequency offset sample set to obtain a residual frequency offset estimation model so as to establish a mapping relation between the pilot frequency containing the residual frequency offset and the corresponding residual frequency offset.
The functions of the functional modules of the synchronization apparatus of the mimo-ofdm system according to the embodiments of the present invention may be specifically implemented according to the method in the foregoing method embodiments, and the specific implementation process may refer to the description related to the foregoing method embodiments, which is not described herein again.
Therefore, the embodiment of the invention improves the precision of the timing synchronization position and the carrier frequency offset and effectively improves the synchronization precision of the MIMO OFDM system.
The above mentioned synchronization device for mimo ofdm system is described from the perspective of functional modules, and further, the present application also provides a synchronization device for mimo ofdm system, which is described from the perspective of hardware. Fig. 11 is a structural diagram of a synchronization apparatus of another mimo-ofdm system according to an embodiment of the present application. As shown in fig. 11, the apparatus includes a memory 110 for storing a computer program;
a processor 111, configured to implement the steps of the synchronization method of the mimo-ofdm system as mentioned in any of the above embodiments when executing the computer program.
The processor 111 may include one or more processing cores, such as a 4-core processor, an 8-core processor, and the like. The processor 111 may be implemented in at least one hardware form of a DSP (Digital Signal Processing), an FPGA (Field-Programmable Gate Array), and a PLA (Programmable Logic Array). The processor 111 may also include a main processor and a coprocessor, where the main processor is a processor for Processing data in an awake state, and is also called a Central Processing Unit (CPU); a coprocessor is a low power processor for processing data in a standby state. In some embodiments, the processor 111 may be integrated with a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content required to be displayed on the display screen. In some embodiments, the processor 111 may further include an AI (Artificial Intelligence) processor for processing computing operations related to machine learning.
Memory 110 may include one or more computer-readable storage media, which may be non-transitory. Memory 110 may also include high speed random access memory, as well as non-volatile memory, such as one or more magnetic disk storage devices, flash memory storage devices. In this embodiment, the memory 110 is at least used for storing a computer program 1101, wherein after being loaded and executed by the processor 111, the computer program can implement the relevant steps of the synchronization method of the mimo-ofdm system disclosed in any of the foregoing embodiments. In addition, the resources stored in the memory 110 may also include an operating system 1102, data 1103, and the like, and the storage manner may be transient storage or permanent storage. Operating system 1102 may include Windows, unix, linux, etc. The data 1103 may include, but is not limited to, data corresponding to a synchronization result of a mimo ofdm system, and the like.
In some embodiments, the synchronization apparatus of the mimo-ofdm system may further include a display screen 112, an input/output interface 113, a communication interface 114, a power supply 115, and a communication bus 116.
Those skilled in the art will appreciate that the structure shown in fig. 11 does not constitute a limitation of the synchronization apparatus of the mimo ofdm system, and may include more or less components than those shown, for example, the sensor 117.
The functions of the functional modules of the synchronization apparatus of the mimo-ofdm system according to the embodiments of the present invention may be specifically implemented according to the method in the foregoing method embodiments, and the specific implementation process may refer to the related description of the foregoing method embodiments, which is not described herein again.
Therefore, the embodiment of the invention improves the precision of the timing synchronization position and the carrier frequency offset and effectively improves the synchronization precision of the multi-input multi-output orthogonal frequency division multiplexing system.
It is to be understood that, if the synchronization method of the mimo ofdm system in the above embodiments is implemented in the form of a software functional unit and sold or used as a separate product, it may be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the present application may be substantially or partially implemented in the form of a software product, which is stored in a storage medium and executes all or part of the steps of the methods of the embodiments of the present application, or all or part of the technical solutions. And the aforementioned storage medium includes: a U disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), an electrically erasable programmable ROM, a register, a hard disk, a removable magnetic disk, a CD-ROM, a magnetic or optical disk, and other various media capable of storing program codes.
Based on this, an embodiment of the present invention further provides a computer-readable storage medium, which stores a synchronization program of a mimo ofdm system, where the synchronization program of the mimo ofdm system is executed by a processor, and the synchronization method of the mimo ofdm system according to any one of the above embodiments includes the steps.
The functions of the functional modules of the computer-readable storage medium according to the embodiment of the present invention may be specifically implemented according to the method in the foregoing method embodiment, and the specific implementation process may refer to the related description of the foregoing method embodiment, which is not described herein again.
Therefore, the embodiment of the invention improves the precision of the timing synchronization position and the carrier frequency offset and effectively improves the synchronization precision of the multi-input multi-output orthogonal frequency division multiplexing system.
The embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same or similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the components and steps of the various examples have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the technical solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The present invention provides a synchronization method, apparatus and computer readable storage medium for mimo ofdm system. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present application.

Claims (8)

1. A synchronization method for a mimo-ofdm system, comprising:
training a timing error estimation model and a residual frequency offset estimation model by using a delay sample set in advance;
respectively inputting frequency domain signals of the pilot frequency sequence subjected to initial synchronization processing into the timing error estimation model and the residual frequency offset estimation model to obtain a timing synchronization error estimation value and a residual frequency offset estimation value of the pilot frequency sequence;
determining a timing synchronization position and frequency offset estimation according to the timing synchronization error estimation value and the residual frequency offset estimation value;
wherein the delayed sample set comprises a plurality of groups of training sample pairs consisting of known timing offsets and pilots containing known timing offsets; the frequency offset sample set comprises a plurality of groups of training sample pairs consisting of known frequency offsets and pilots containing the known frequency offsets; the pilot frequency comprises a first OFDM symbol used for initial estimation of timing and fractional frequency offset and a second OFDM symbol used for integral frequency offset estimation and channel estimation;
wherein, the training of the timing error estimation model and the training of the residual frequency offset estimation model by using the delay sample set in advance comprises:
training an extreme learning machine frame by using the delay sample set to obtain the timing error estimation model so as to establish a mapping relation between pilot frequency containing timing deviation and corresponding timing deviation;
training an extreme learning machine frame by using the frequency offset sample set to obtain the residual frequency offset estimation model so as to establish a mapping relation between a pilot frequency containing residual frequency offset and corresponding residual frequency offset;
wherein the set of delayed samples comprises a plurality of sets of training sample pairs which do not contain channel fading and noise and are composed of known timing offset and pilot frequency containing known timing offset; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset.
2. The synchronization method of mimo-ofdm according to claim 1, wherein the inputting of the frequency domain signals of the pilot sequences processed by the initial synchronization to the timing error estimation model and the residual frequency offset estimation model respectively comprises:
for each pilot frequency in the pilot frequency sequence, determining an initial timing position, estimating frequency offset and compensating frequency offset according to a first OFDM symbol and a second OFDM symbol of each pilot frequency;
carrying out frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence;
and respectively inputting the pilot frequency sequences after frequency domain equalization to the timing error estimation model and the residual frequency offset estimation model.
3. The synchronization method of mimo-OFDM according to claim 2, wherein the performing initial timing position determination, frequency offset estimation and frequency offset compensation according to the first OFDM symbol and the second OFDM symbol of each pilot comprises:
for each pilot frequency in the pilot frequency sequence, calculating a timing measurement function according to a first OFDM symbol of the current pilot frequency to obtain an initial timing position;
after the initial timing position is obtained, fractional and integer frequency offset estimation is carried out by utilizing a first OFDM symbol and a second OFDM symbol of the current pilot frequency;
and performing frequency offset compensation on the current pilot frequency after initial timing by using the frequency offset estimation value.
4. The synchronization method of mimo-ofdm system according to claim 2, wherein the performing the frequency domain equalization process on the frequency domain information of each pilot of the compensated pilot sequence comprises:
performing fast Fourier transform operation on the compensated current pilot frequency to obtain a frequency domain signal of the current pilot frequency;
estimating a channel by using a second OFDM symbol of the current pilot frequency to obtain channel response information;
and performing frequency domain equalization on the current pilot frequency by using the channel response information.
5. A synchronization apparatus for a mimo-ofdm system, comprising:
the model pre-training module is used for pre-training a timing error estimation model and a residual frequency offset estimation model by utilizing a delay sample set; the delay sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known timing deviation and pilot frequency containing known timing deviation; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset; the pilot frequency comprises a first OFDM symbol used for initial estimation of timing and fractional frequency offset and a second OFDM symbol used for integral frequency offset estimation and channel estimation;
the initial synchronization processing module is used for carrying out initial synchronization processing on the received pilot frequency sequence;
the secondary synchronization processing module is used for respectively inputting the frequency domain signals of the pilot frequency sequence subjected to the initial synchronization processing into the timing error estimation model and the residual frequency offset estimation model to obtain a timing synchronization error estimation value and a residual frequency offset estimation value of the pilot frequency sequence; determining a timing synchronization position and frequency offset estimation according to the timing synchronization error estimation value and the residual frequency offset estimation value;
wherein the model pre-training module is further to: training an extreme learning machine frame by using the delay sample set to obtain the timing error estimation model so as to establish a mapping relation between pilot frequency containing timing deviation and corresponding timing deviation; training an extreme learning machine frame by using the frequency offset sample set to obtain the residual frequency offset estimation model so as to establish a mapping relation between a pilot frequency containing residual frequency offset and corresponding residual frequency offset; the delay sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known timing deviation and pilot frequency containing known timing deviation; the frequency offset sample set comprises a plurality of groups of training sample pairs which do not contain channel fading and noise and are composed of known frequency offset and pilot frequency containing the known frequency offset.
6. The synchronization apparatus of mimo-ofdm according to claim 5, wherein the initial synchronization processing module comprises:
the coarse synchronization sub-module is used for carrying out initial timing position determination, frequency offset estimation and frequency offset compensation on each pilot frequency in the pilot frequency sequence according to a first OFDM symbol and a second OFDM symbol of each pilot frequency;
and the equalization processing submodule is used for carrying out frequency domain equalization processing on the frequency domain information of each pilot frequency of the compensated pilot frequency sequence.
7. A synchronization apparatus for a mimo-ofdm system, comprising a processor configured to implement the steps of the synchronization method of the mimo-ofdm system according to any one of claims 1 to 4 when executing a computer program stored in a memory.
8. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a synchronization program of a mimo-ofdm system, which when executed by a processor implements the steps of the synchronization method of the mimo-ofdm system according to any one of claims 1 to 4.
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