CN116346164B - Maximum likelihood detection method for continuous parallel interference elimination in OTFS system - Google Patents
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Abstract
The invention discloses a maximum likelihood detection method for continuous parallel interference cancellation in an OTFS (optical transport stream system), belonging to the technical field of OTFS signal detection; inserting a null in the delay-doppler domain according to the magnitude of the maximum multipath delay; the delay Doppler domain obtains a receiving signal matrix, and single path superposition data and delay amount are determined according to the channel state informationThe method comprises the steps of carrying out a first treatment on the surface of the In the time delay amountRemoving the influence of a channel along the Doppler frequency shift direction at the corresponding index, detecting data by using a maximum likelihood detection algorithm, and recording; delay amount at multi-path superpositionCalculating an interference component according to the channel state information and the detected signal; and removing the influence of the channel along the Doppler direction after removing the interference component, and finishing the estimation of all the received signals. The invention realizes signal detection by changing MP algorithm and ML algorithm, and utilizes channel state information and detected signals to realize high-accuracy signal detection in delay Doppler domain, thereby reducing complexity of maximum likelihood detection algorithm.
Description
Technical Field
The invention belongs to the technical field of signal detection of an OTFS (optical transport stream system), and particularly relates to a maximum likelihood detection method for continuous parallel interference cancellation in an OTFS.
Background
One goal of future wireless communications is to support reliable communications in high speed mobile scenarios, with the dominant modulation technique of current 5G being orthogonal frequency division multiplexing (Orthogonal Frequency Division Multiplexing, OFDM). A large doppler shift occurs in a high-speed mobile scenario so that the channel has a fast time-varying characteristic, resulting in OFDM symbols experiencing severe interference. The novel modulation technique orthogonal time-frequency space (OTFS) modulation can achieve time-frequency domain full diversity, exhibiting significant performance advantages over OFDM. OTFS systems transmit signals in the Delay Doppler (DD) domain where the channel has time invariant properties, so that the signal transmission in the Delay Doppler domain can avoid the effects of channel time variability.
The OTFS system channel modeling is more in line with the actual physical channel, has remarkable performance advantages in a high-speed moving scene, but a signal detection algorithm with excellent performance is required to be developed to exert the advantages, and the signal detection problem is an important research direction of the OTFS system. Therefore, the research and design of the OTFS system signal detection problem have important significance for improving the OTFS system performance.
Common algorithms for signal detection by OTFS systems include Message Passing (MP) algorithms and modifications thereof, LMMSE, MMSE, ZF, and the like. The method utilizes the characteristic of sparsity of the time-delay Doppler domain channel, but does not fully utilize the detected signal in the signal detection process, and has high algorithm complexity. The ML algorithm is a classical method of signal detection, and is used for an OTFS system to perform exponential increase in complexity of the signal detection algorithm, and the more paths, the faster the increase. The delay Doppler domain channel has orthogonal characteristics, different paths can be separated, and the ML algorithm cannot be directly used for signal detection by an OTFS system obviously. Aiming at the problem, the invention fully utilizes the form of two-dimensional convolution of the transmitted signal and the channel state information and the detected signal, and proposes a method for reducing the complexity of a maximum likelihood detection algorithm by using a parallel interference elimination method. On the basis, the OTFS frame structure is improved and zero values are inserted, so that continuous parallel interference elimination is realized, and the algorithm complexity is further reduced.
Disclosure of Invention
The invention aims to provide a maximum likelihood detection method for continuous parallel interference cancellation in an OTFS system, so as to solve the problems in the background technology.
The invention aims at realizing the following steps: the maximum likelihood detection method for continuous parallel interference elimination in the OTFS system is characterized in that: the maximum likelihood detection method comprises the following steps:
step S1: the transmitting end inserts zero value along the delay direction in the delay Doppler domain according to the maximum multipath delay to generate a transmitting signal matrix of the delay Doppler domain；
Step S2: the receiving end obtains a receiving signal matrix in a delay Doppler domainAccording to known channel state informationDetermining single path superimposed data and delay amount +.>；
Step S3: delay amount determined according to S2The influence of the removal channel along the Doppler shift direction at the corresponding index is +.>，/>Representing a receiving-side data matrix->Is>Go (go)/(go)>Indicate->Channel matrix of strip path->Is>A row; detecting +.>And recording; />Is maximum likelihood detection;
step S4: delay amount at multi-path superpositionCalculating interference component +.>The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Representing the transmit signal +.>Is>The rows are cyclically shifted in the direction of the Doppler shift>A detected result; />Representing the Hadamard product;
step S5: removing the interference component, i.e. based on the result of the calculation in step S4The influence of the channel is then removed in the Doppler direction +.>Then the data are detected by using a maximum likelihood detection algorithm>And recording data; wherein (1)>Representing the received signal +.>Matrix->The result after the detected signal is removed is retained only by the +.>Data of the paths;
step S6: the estimation of all received signals is completed.
Preferably, in step S1, zero values are inserted in the delay-doppler domain along the delay direction to generate a transmission signal of the delay-doppler domainThe specific operation is as follows:
step S1-1: based on channel state informationDetermine->Maximum delay of channel in the path +.>The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Indicating channel gain, +.>Modeling phase distortion generated by frequency offset +.>Modeling cyclic shifts;
step S1-2: in a discrete gridIn (2) delay amount->Satisfy the following requirementsConditional position insertion QAM symbol, delay amount +.>Satisfy->Zero value is inserted to finally form a transmission signal matrix of a delay Doppler domain>；
Wherein,represents the total number of paths>Representing carrier spacing and +.>，/>Discrete grid representing delay Doppler domain>Middle delay index, ++>Maximum value representing the delay direction index, +.>Discrete grid representing delay Doppler domain>Middle Doppler index>Indicating the index maximum in the doppler direction.
Preferably, the step S2 determines the data of the single path superposition and the delay amount specifically operates as follows:
step S2-1: after the transmission signal is transmitted through the channel, the transmission signal in the delay Doppler domain and the channel state information are two-dimensional convolution results, and an analysis formula is adoptedThe method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Representing +.>First->Line->Column element->Representing the transmit signal matrix->First->Line->Element(s) of->Representing additive noise->Indicating channel gain, +.>Representing Path i GenerationIs a phase noise of (a);
step S2-2: determination ofMinimum two delay amounts in the strip path +.>And->， />；
Step S2-3: determining a receiving end delay Doppler domain discrete grid planeIn, when the delay amount +.>Satisfy->In the receiving end delay Doppler signal matrix +.>Can obtain->+.>The single paths superimpose the data.
Preferably, in the step S3, a maximum likelihood detection algorithm is used for detectionAnd record the specific operations as follows:
step S3-1: delay amount at receiving endSatisfy->When the +.>+.>The data sequentially removes the influence of the channel along the doppler shift, i.e +.>，/>Representing a receiving-side data matrix->Is>Go (go)/(go)>Indicate->The>A row;
step S3-2: detecting data with channel effects removed by using maximum likelihood detection algorithmAnd recording the detection result as initial data of the subsequent parallel interference cancellation.
Preferably, in the step S4, an interference component is calculated based on the channel state information and the detected signalThe specific operation is as follows:
step S4-1: according to the formulaClearly at the current delay amountA plurality of interference paths are arranged, and required data is extracted from the result of the single-path detection in the last step according to the delay amount of the selected interference paths;
step S4-2: calculating interference components from channel state information and detected data of selected interference pathsWherein->Indicating that a signal has been detected.
Preferably, the step S5 removes the interference component, i.eMiddle->The method comprises the following steps:
，
，
wherein,representing the acceptance signal matrix +.>Is>Go (go)/(go)>Representing the path->Channel momentMatrix->Is>Go (go)/(go)>Representing channel matrix->Middle->Line->Column element->Representing the transmit signal +.>Is>The rows are cyclically shifted in the direction of the Doppler shift>Detected result,/->Representing the hadamard product.
Preferably, the step S5 removes an interference componentThe influence of the channel is then removed in the Doppler direction +.>In the current delay amount +.>The basis of->Removing interference from the detected signal, i.e. matrix +.>Is>The line only retains +>Data ∈of the strip path>；
Representing the received signal matrix>First->The result after the detected signal is removed is shown in the row, where only the +.>Data of the strip path.
Preferably, the maximum likelihood detection algorithm in step S3 and step S5 is:
；
wherein,representing the effective channel matrix of the delay-doppler domain, +.>To accept the signal; />Representation and reception signal->Related->Vector of individual transmitted signals, vector->Together (S)/(S)>Species, the resulting solution space is denoted +.>Q is the QAM symbol addition order; />Representation->Medium and receive signal->Correlated channel state information; the maximum likelihood detection is noted +.>。
Compared with the prior art, the invention has the following improvement and advantages: 1. zero values are inserted into the delay Doppler domain signal matrix of the transmitting end, single-path overlapped data are monitored at the receiving end, then detected signal interference is removed during multi-path strong overlapped data monitoring, continuous parallel interference elimination is achieved, and complexity of a maximum likelihood detection algorithm is reduced.
2. The invention changes the ML algorithm to realize signal detection based on the basic principles of the MP algorithm and the ML algorithm, fully utilizes the channel state information and the detected signal, and further reduces the complexity of the maximum likelihood detection algorithm.
Drawings
Fig. 1 is a flow chart of the present invention.
Fig. 2 is a system model diagram of the present invention.
Fig. 3 is a schematic diagram of information transfer in MP algorithm.
Fig. 4 is a schematic diagram of the positional relationship of input and output signals in the DD domain.
Fig. 5 is a diagram showing the structure of a DD domain frame.
Fig. 6 is a graph showing comparison of error rate performance of MMSE algorithm, MP algorithm, ML algorithm signal detection.
Fig. 7 is a graph comparing bit error rate performance of the maximum likelihood detection algorithm and its modified algorithm.
Fig. 8 is a graph of bit error rate performance versus different doppler frequency shifts.
Detailed Description
The invention is further summarized below with reference to the drawings.
As shown in fig. 1, the maximum likelihood detection method for continuous parallel interference cancellation in an OTFS system includes the following steps:
step S1: the transmitting end inserts zero value along the delay direction in the delay Doppler domain according to the maximum multipath delay to generate a transmitting signal matrix of the delay Doppler domain；
The specific operation is as follows:
step S1-1: based on channel state informationDetermine->Maximum delay amount of channel in the path +.>；
Wherein,is a permutation matrix,/->Is a diagonal momentThe array is as follows:
wherein the method comprises the steps ofI.e. Path->Is a delay of the transmitted signal vector->The cyclic shift produced is modeled as +.>The phase distortion caused by the frequency offset is modeled as +.>；
Step S1-2: in a discrete gridIn (2) delay amount->Satisfy the following requirementsConditional position insertion QAM symbol, delay amount +.>Satisfy->Zero value is inserted to finally form a transmission signal matrix of a delay Doppler domain>。
Step S2: the receiving end obtains a receiving signal matrix in a delay Doppler domainAccording to known channel state informationDetermining single path superimposed data and delay amount +.>；
The data of the single path superposition and the specific operation of the delay measuring tool are determined in the step S2 as follows:
step S2-1: after the transmission signal is transmitted through the channel, the transmission signal in the delay Doppler domain and the channel state information are two-dimensional convolution results, and an analysis formula is adopted；
Step S2-2: determination ofMinimum two delay amounts in the strip path +.>And->；
Step S2-3: determining a receiving end delay Doppler domain discrete grid planeIn, when the delay amount +.>Satisfy->In the receiving end delay Doppler signal matrix +.>Can obtain->+.>The single paths superimpose the data.
Step S3: delay amount determined according to S2The influence of the removal channel along the Doppler shift direction at the corresponding index is +.>Detecting +.>And recording;
in step S3, the data is detected by using a maximum likelihood detection algorithmAnd record the specific operations as follows:
step S3-1: delay amount at receiving endSatisfy->When the +.>+.>The individual data are sequentially freed from the influence of the channel, i.e. +.>，/>Representing a receiving-side data matrix->Is>Go (go)/(go)>Indicate->The>A row;
step S3-2: detecting data with channel effects removed by using maximum likelihood detection algorithmAnd recording the detection result as initial data of the subsequent parallel interference cancellation.
Step S4: delay amount at multi-path superpositionCalculating interference component +.>；
In step S4, an interference component is calculated based on the channel state information and the detected signalThe specific operation is as follows:
step S4-1: according to the formulaClearly at the current delay amountA plurality of interference paths are arranged, and required data is extracted from the result of the single-path detection in the last step according to the delay amount of the selected interference paths;
step S4-2: calculating interference components from channel state information and detected data of selected interference pathsWherein->Indicating that a signal has been detected.
Step S5: removing the interference component, i.e. based on the result of the calculation in step S4The influence of the channel is then removed in the Doppler direction +.>Then the data are detected by using a maximum likelihood detection algorithm>And recording data;
the interference component is removed in the step S5The influence of the channel is then removed in the Doppler direction +.>The specific operation is as follows:
at the current delay amountThe basis of->Removing interference from the detected signal, i.e. matrix +.>Is>The line only retains +>Data ∈of the strip path>。
Step S6: the estimation of all received signals is completed.
Working principle: when the maximum likelihood detection algorithm is used for signal detection, the algorithm complexity rises rapidly along with the increase of the number of paths. The ML algorithm is improved here to reduce the algorithm complexity.
In OTFS modulation, information symbols, i.e. QAM symbols,q is the modulation order; directly mapped to the DD domain. Inverse octyl Fourier transform (Inverse Symplectic Finite Fourier Transform, ISFFT) is performed at the transmitting end to map DD-domain data signals to the time-frequency domain, i.e
OFDM modulation is performed in the frequency domain, converting the frequency domain signal into a time domain signal,
wherein,is a transmitting-end pulse waveform, when rectangular wave is adopted +.>Is a unitary matrix->，/>Representing a fourier transform matrix, ">And->Representing the inverse fourier transform matrix. />Respectively represent DD domain signals, time-frequency domain signals, and time-domain signals generated by OFDM modulation. Preference of matrix by column>Expanded into vector->The transformation is as follows:
wherein the method comprises the steps ofRepresenting the matrix +.>By serial-parallel conversion into vectors->，/>Representing the Cronecker product, time-domain signal before transmission +.>And adding a cyclic prefix, wherein the length of the cyclic prefix is determined according to the maximum multipath delay of the channel.
After adding the cyclic prefix, the data signal undergoes a bidirectional selective fading channel, the cyclic prefix is removed at the receiving end, and the following expression can be obtained in a discrete time domain:
wherein,representing the acceptance signal +.>Vector>Element(s)>Express vector->The number of elements, P is the total number of propagation paths, +.>Indicating channel gain, +.>Representing a modulo operation, +.>Representing additive noise->And->Respectively representing integer multipath delay and Doppler shift, the invention does not consider fractional situations. The form of writing equation (4) as a vector is as follows:
wherein,，/>is a permutation matrix,/->Is a diagonal matrix, as follows:
is a permutation matrix,/->Is a diagonal matrix, as follows:
，
wherein the method comprises the steps ofI.e. Path->Is a delay of the transmitted signal vector->The cyclic shift produced is modeled as +.>The phase distortion caused by the frequency offset is modeled as +.>。
Then, the reverse operation corresponding to the transmitting end is carried out, and the received signal is converted into serial-parallel conversionAnd then sequentially converting the signals into a time frequency domain and a DD domain, wherein the time frequency domain and the DD domain are as follows:
wherein the method comprises the steps ofRespectively represent DD domain signals, time-frequency domain receiving signals, < >>Corresponding matched filtering, when rectangular wave is used, is identity matrix +.>。
To embody the effect of the actual channel, the matrix of the received signals is writtenVectorized form:
（8）
wherein,representing the received signal matrix>Vectorized result,/->Representing the effective channel, i.e. the delay-doppler-domain channel matrix,/->Representing noise vectors, when rectangular waves are used, the channel is represented as follows:
（9）
wherein the method comprises the steps ofThe result is related to the delay and doppler shift of each path, and the calculation process takes advantage of the block-cycle characteristics of the matrix:
wherein,respectively represent matrix->Row and column indices of>. According to->The result of (2) can be written into a two-dimensional convolution relation of DD domain input and output:
wherein,representing additive noise->Representing the path->The phase noise generated.
From the formula (11), it can be seen that the input and output in the DD domain show a two-dimensional convolution relationship, and the full diversity can be obtained in the delay Doppler domain. From equation (12) it can be found that the channel state information is time independent, i.e. the channel state information does not change with time.
The main idea of improving the maximum likelihood detection algorithm is illustrated by fig. 4, which assumes for simplicity of illustrationThere are two paths, path 1 parameters: />Path 2 parameters: />Only DD domain transmission is concerned without considering channel gainThe superimposed form of the signals at the receiving end is shown in fig. 4, (a) represents the transmitted signal, and (b) represents the received signal. The mathematical relationship corresponding to fig. 4 (b) is as follows:
the signal X can be obtained by adopting a maximum likelihood detection algorithm to the first row of signals at the receiving end 11 ，X 21 ，X 31 ，X 41 ，X 14 ，X 24 ，X 34 ，X 44 Is a function of the estimate of (2). At the right X 12 ，X 22 ，X 32 ，X 42 In the detection estimation, the influence of the detected signal can be removed by an interference elimination method, for example, the detection estimation is performed on X 22 Is estimated by (a):
wherein Y is 22 Is X 11 ，X 22 Is formed by superposition after the channels are passed,and->Respectively X 11 And X is 22 Corresponding channel information.
And (3) carrying out the operation of the formula (14) on each row of the received signals, and finally, detecting the transmitted signals. The scheme fully utilizes the correlation between the detected signal and the channel state information, and reduces the complexity of the ML detection algorithm.
The parallel interference elimination is mainly carried out by taking each row of the receiving and transmitting signals as a basic unit, and is different from the serial interference elimination adopted by common symbol-by-symbol detection, and in order to more intuitively embody the process, the input-output relationship of the delay Doppler domain is rewritten into the following form:
wherein,representing the acceptance signal matrix +.>Is>Go (go)/(go)>Representing the path->Channel matrix->Is>The number of rows of the device is,representing the transmit signal +.>Is>Lines, circularly shifted in Doppler shift direction +.>As a result of (a)>Representing the hadamard product.
In general, the number of rows in the initial stage that employ the maximum likelihood detection algorithm depends on the maximum multipath delay,assuming that the maximum multipath delay isThe main flow of the algorithm is as follows:
step one: when (when)At the time of receiving each signal +.>Based on the formula->Traversing +.>Performing seed solution, and solving and recording estimation of signals on each path; wherein (1)>Representing the effective channel matrix of the delay-doppler domain, +.>To accept the signal; />Representation and reception signal->Related->Vector of individual transmitted signals, vector->Together (S)/(S)>Species, the resulting solution space is denoted +.>Q is the QAM symbol addition order; />Representation->Medium and receive signal->Correlated channel state information; the maximum likelihood detection is noted +.>；
Step two: when (when)In the meantime, based on the detected data recorded in the first step and the channel information + ->For each row of signals to be detected, all detected signals are eliminated, i.e. +.>，/>Representing received signalsMatrix->The result after the detected signal is removed is retained only by the +.>Data of the paths;
step three: after eliminating the interference, toRemoving the influence of the channel and then performing maximum likelihood detection, i.e +.>Repeating the stepsStep two and step three;
step four: when receiving signal matrixWhen all lines of (a) complete interference cancellation signal detection, & gt is synthesized>The detection result of the paths gives an estimate of the data signal to be detected>
The algorithm is marked as a parallel interference cancellation maximum likelihood detection algorithm.
Experimental results:
the simulation parameter carrier frequency is 4GHz, the number of carriers is 256 (M), the number of symbols is 256 (N), the carrier interval is 15KHz, the maximum moving speed is 500KM/h, the cyclic prefix long queue 17 adopts 4-QAM symbols, and the number of paths is set to be 4. Consider the integer delay and doppler shift amounts.
Fig. 5 compares the bit error rate performance of MMSE algorithm, MP algorithm, ML algorithm signal detection algorithm. In the three algorithms, the MP algorithm has the best error code performance, and the ML algorithm has slightly better performance than the MMSE algorithm. When the signal-to-noise ratio is low, the MMSE algorithm and the ML algorithm slowly decrease along with the increase of the signal-to-noise ratio, and the error rate rapidly decreases from the vicinity of 12 db. The MP algorithm error rate curve is divided into two sections mainly by taking 14db as a boundary, the error rate of the latter section drops faster than that of the former section, and the two sections change approximately linearly. The ML algorithm can realize higher-precision signal detection.
Fig. 6 compares the maximum likelihood detection algorithm with the bit error rate performance of two ML-enhancement algorithms proposed by the present invention. It is readily apparent from the figure that the ML algorithm has significant differences from the other two algorithms, and while traversing all possible solutions for each point in the DD domain, the ML algorithm has no performance advantage over the other two algorithms, with the computational complexity increasing exponentially with the path. The main reason is that the number of solutions in the solution space isThe more pathsThe more the multiple solutions, the smaller the distance between the solutions, the lower the anti-noise performance, and the better the performance when the noise is smaller. And when the signal-to-noise ratio is lower than 14db, the CPICMLD algorithm is basically coincident with the bit error rate curve of the PICMLD algorithm, and the bit error rate is continuously reduced along with the reduction of the signal-to-noise ratio. After 14db the CPIC algorithm bit error rate rises slightly compared to EPIC 2. The main reason why the error rate of CPICMLD algorithm slightly increases is as follows: when some paths with larger fading exist in the channel, the channel gain is smaller, the CPICML algorithm adopts interference elimination in the initial stage, and the error probability is increased.
There is also a clear trend that the bit error rate of the ML algorithm decreases rapidly with increasing signal to noise ratio, while the other two algorithms decrease at a rate of about 14db after the signal to noise ratio. The main reason is that interference elimination is self, if error codes occur in the solving process, the error can be propagated backwards, each node in the ML algorithm is independently solved, and the phenomenon of backward propagation does not exist.
Fig. 7 compares the bit error rate performance of OTFS systems at different doppler frequency shifts, using a continuous parallel interference cancellation maximum likelihood detection algorithm. Wherein the maximum k values are respectively equal to 2, 8 and 16, and the relative speeds of the receiving and transmitting ends are 30 km/h, 120 km/h and 500km/h. The error rate curves of the three are basically coincident when the signal to noise ratio is between 10db and 14db, and the error rate performance of high Doppler frequency shift is slightly poorer than that of low Doppler frequency shift when the signal to noise ratio is between 14db and 20 db. At the position ofThe phase distortion caused by doppler shift changes faster when larger, and some small amount is produced when the channel response is multiplied with QAM symbols in the DD domain, resulting in some increase in bit error rate performance. However, it is not difficult to find that the signal-to-noise ratio is a main factor affecting the performance of the bit error rate, and as the signal-to-noise ratio increases, the bit error rate is continuously reduced, and some performance differences are only exhibited until the signal-to-noise ratio is high. The sending signal of DD domain passes through the constant channel, so that OTFS system has better error rate performance gain under high Doppler frequency shift.
The foregoing description is only illustrative of the invention and is not to be construed as limiting the invention. Various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, or the like, which is within the spirit and principles of the present invention, should be included in the scope of the claims of the present invention.
Claims (1)
- A maximum likelihood detection method for continuous parallel interference elimination in an OTFS system is characterized in that: the maximum likelihood detection method comprises the following steps:step S1: the transmitting end inserts zero value along the delay direction in the delay Doppler domain according to the maximum multipath delay to generate a transmitting signal matrix X of the delay Doppler domain DD ；Inserting null values in the delay-doppler domain along the delay direction, generating a transmit signal X of the delay-doppler domain DD The specific operation is as follows:step S1-1: based on channel state informationDetermining the maximum delay l of the channels in the P paths τ The method comprises the steps of carrying out a first treatment on the surface of the Wherein h is i Indicating channel gain, +.>Phase distortion generated for frequency offset, +.>Cyclic shift of the transmit signal vector for the amount of delay;step S1-2: in a discrete grid Λ= { (k/TN, l/Δfm), k=0,..m-1, l=0, in N-1, the delay amount l is more than or equal to 0 and less than or equal to M-1-l τ Inserting QAM symbols at positions of conditions, wherein the delay quantity l meets M-1-l τ Inserting zero value into M-1 less than or equal to l to form the transmitting signal matrix X of delay Doppler domain DD The method comprises the steps of carrying out a first treatment on the surface of the Wherein k only considers integers, k represents Doppler shift quantity, and k also represents index corresponding to Doppler shift quantity; considering only integer, l represents delay amount, l also represents index corresponding to delay amount, M-1 represents maximum value of index corresponding to Doppler shift amount, N-1 represents an index maximum corresponding to the delay amount; t represents one OFDM symbol duration; Δf represents a carrier spacing, and t=1/Δf, P represents a total number of paths;step S2: the receiving end obtains a receiving signal matrix Y in a delay Doppler domain DD According to the known channel state information H i Determining the ith pathSuperimposing data and delay amount l by a single path; wherein->And->Is the minimum two delay amounts in P paths,/for>Step S3: removing the influence of a channel along the Doppler frequency shift direction at the index corresponding to the delay amount l determined in the step S2, detecting and recording the data with the channel influence removed by adopting a maximum likelihood detection algorithm, and taking the data as initial data for the subsequent parallel interference elimination;step S4: calculating interference component according to channel state information and detected signal at delay amount of multipath superpositionWherein (1)>Representing the transmitted signal X DD [ l-l ] i′ ] M The rows are cyclically shifted by k along the Doppler shift direction i' A detected result; k (k) i' An index corresponding to the i' th Doppler shift amount; m represents the total number of Doppler shift direction indexes, and N represents the total number of delay direction indexes; [ l-l ] i′ ] M In [] M Indicating that the modulo operation is about to be [ l-l ] i′ ]Molding with M; />Representing the Hadamard product; i ' represents an i ' th path of the P paths, i represents an i ' th path of the P paths; l (L) i' Index value corresponding to i' th path delay amount is represented; [ k-k ] i′ ] N In [] N Indicating that the modulo operation is about to be [ k-k ] i′ ]Molding with N;step S5: obtaining by removing the interference component data based on the calculation result in step S4Removing the influence of the channel along the Doppler frequency shift direction, detecting and recording the data with the influence of the channel removed by adopting a maximum likelihood detection algorithm; wherein b l,i Representing the received signal Y DD The first row of the matrix only reserves the data of the ith path after removing the detected signals; y is Y l Representing a matrix Y of received signals DD Is the first row of (2);step S6: finishing the estimation of all the received signals;when receiving signal matrix Y DD When all lines of the (a) complete the detection of the interference elimination signal, synthesizing the detection results of the P paths to obtain the estimation of the data signal to be detected;the maximum likelihood detection algorithm in the step S3 and the step S5 is as follows:wherein H is eff Representing a delay Doppler domain effective channel matrix; y is the received signal; x epsilon C p×1 Representing a vector of P transmitted signals associated with received signal y, vector x being a total of Q P In a seed form, the formed solution space is marked as omega, and Q is the modulation order of the QAM symbol; h p ∈C p×p Represents H eff Neutralizing and receiving signalsy-related channel state information.
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