OTFS system channel estimation method based on hybrid multi-pilot frequency combination

Abstract

The OTFS system channel estimation method based on hybrid multi-pilot frequency combination comprises the following steps: setting an OTFS transmitting frame which comprises a data symbol and a pilot frequency symbol which are simultaneously modulated to a DD domain; a DD domain sending signal is modulated by the OTFS and then reaches a receiving end through a channel, and a signal received by the receiving end is demodulated by the OTFS and then is converted into a DD domain receiving signal; the method comprises the following steps: receiving a signal based on a DD domain, and estimating time delay and integer Doppler of a channel by utilizing related characteristics of a pilot frequency sequence to obtain estimated values of the time delay and the integer Doppler; estimating decimal Doppler according to time invariance of a DD domain channel and adjustability of Doppler, and finally obtaining an estimated value of Doppler; performing LMMSE estimation on the attenuation coefficient according to the estimation values of the time delay and the Doppler to obtain an estimation value of the attenuation coefficient, and completing channel estimation of the OTFS system; according to the method, the pilot symbols and the data symbols are mixed, joint estimation is carried out, and accurate estimation of the OTFS decimal Doppler channel is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and particularly relates to a hybrid multi-pilot joint-based OTFS system channel estimation method. BACKGROUND

[0002] The International Mobile Telecommunications-2030 (6G) Promotion Group points out in the "6G Overall Vision and Potential Key Technology White Paper" that in the future, a three-dimensional grid of space-ground integration will be built, including ground cellular networks and high-orbit satellite networks, medium and low-orbit satellite networks, high-altitude platforms, and unmanned aerial vehicles. High mobility has become a typical feature of future communication scenarios. Currently, orthogonal frequency division multiplexing (OFDM) is widely used in fourth-generation mobile communication technology. However, with the modeling and use of typical high-speed mobile scenarios in fifth-generation and sixth-generation mobile communication technology, the time delay and Doppler shift caused by the transmission of communication signals in high-mobility scenarios will produce serious inter-symbol interference and inter-carrier interference, and will produce carrier frequency offset. The signal received at the receiving end is affected by the Doppler effect, which causes the frequencies of the transmitter and receiver oscillators to be unable to match. In OFDM and other multi-carrier modulation systems, the receiving carrier frequency offset will destroy the orthogonality between subcarriers, introduce serious inter-subcarrier interference, and thus have a serious impact on the performance of the OFDM system, severely reduce the data transmission quality, and make it difficult to achieve reliable communication requirements.

[0003] The existing orthogonal time frequency space modulation (OTFS) technology can effectively resist the time and frequency selective fading caused by Doppler shift. By converting the time-varying multipath channel to the time-delay-Doppler domain, all symbols experience almost the same and slowly changing sparse channels. And all symbols in the time-delay-Doppler domain are uniformly expanded to the entire time-frequency domain to achieve joint diversity gain, providing reliable communication in time-frequency dispersion channels and achieving reliable data transmission in high-speed mobile scenarios. Based on the above advantages, OTFS technology has broad application prospects in satellite communication, Internet of Vehicles communication and other scenarios, and has shown important application potential in 6G and future communication systems.

[0004] Since OTFS modulation was proposed, many scholars at home and abroad have tried many methods; among them, the commonly used channel estimation method in OTFS system is the estimation scheme based on embedded single pilot (Raviteja P, Phan K, Hong Y, et al. Embedded pilot-aided channel estimation for OTFS in delay doppler channels[J]. IEEE Transactions on Vehicular Technology, 2019, 68(5): 4906-4917.). The pilot structure of this kind is usually composed of a single pulse signal and a plurality of guard intervals arranged around it, and under the condition that the Doppler resolution is sufficient, the inter-Doppler interference caused by fractional Doppler is reconstructed as an independent term, but the influence of inter-Doppler interference on estimation performance cannot be fundamentally eliminated, and a large number of guard intervals are set in this pilot structure, which limits the effective use of the frequency band, wastes a lot of resources, and significantly reduces the spectral efficiency. In addition, the single pilot-based channel estimation may cause path detection missing and excessive estimation error of fading coefficient in channels with severe white noise or severe fading. Literature (Shao Jialiang. Channel estimation and signal detection technology research for 6G fast time-varying channel[D]. Nanjing University of Posts and Telecommunications, 2023.) proposes to use constant envelope zero autocorrelation sequence (CAZAC) as pilot in time-delay-Doppler domain and set guard interval for channel estimation, but this scheme does not consider the inter-Doppler interference caused by fractional Doppler, which causes high OTFS system channel estimation error. SUMMARY

[0005] In order to solve the problem that the fractional Doppler phenomenon affects the channel estimation accuracy of the OTFS system in the prior art, the purpose of the present application is to provide an OTFS system channel estimation method based on hybrid multi-pilot combination, which realizes accurate estimation of the OTFS fractional Doppler channel by mixing pilot symbols with data symbols and performing joint estimation.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is: The OTFS system channel estimation method based on hybrid multi-pilot combination comprises the following steps: Step 1: Set the OTFS transmission frame , containing data symbols and a pilot symbol with relatively high power and length L superimposed on it, the data symbols and the pilot symbol are modulated onto the DD domain at the same time to obtain the DD domain transmission signal; Step 2: Modulate the DD domain transmitted signal with OTFS to obtain the OTFS signal, and transmit it; the OTFS signal reaches the receiving end through the time-frequency dual-select multipath fading channel, and the received signal at the receiving end is demodulated with OTFS and transformed into the DD domain received signal; Step 3: Based on the received signal in the DD domain, utilize the correlation characteristics of its pilot sequence to estimate the channel delay and integer Doppler, obtaining the estimated values ​​of the delay and integer Doppler, respectively. , ; Step 4: Based on the time invariance and Doppler adjustability of the DD domain channel, estimate the fractional Doppler to obtain the final Doppler estimate. ; Step 5: Based on the estimated time delay and Doppler values, adjust the channel attenuation coefficient. Perform LMMSE estimation to obtain the channel attenuation coefficient. The estimated value This completes the channel estimation for the OTFS system.

[0007] In step 1, the pilot symbol Power ratio data symbols At least 5 times higher.

[0008] In step 1, the transmission frame The symbols in the DD field are arranged as follows:

[0009] in, This indicates the transmitted signal in the DD domain, where L is the length of the pilot sequence.

[0010] In step 1, the pilot symbol It is a ZC pilot sequence.

[0011] In step 2, the specific process of obtaining the DD domain received signal is as follows: a signal is sent to the DD domain. Converted to TF domain signal via ISFFT ; For TF domain signals After Heisenberg transform, it is converted into a continuous signal in the time domain. That is, the OTFS signal, which is transmitted; a continuous signal in the time domain. After being transmitted through a time-frequency dual-select multipath fading channel to the receiving end, a continuous signal in the time domain is obtained. For continuous signals in the time domain After Wegener transform, it is converted into a discrete signal in the TF domain. For discrete signals in the TF domain SFFT converted to DD domain received signal .

[0012] The DD domain received signal in step 2 The pilot response The data interference And the noise interference The three parts are superimposed, as shown in the following formula:

[0013] Wherein, the pilot response And the data interference The representation is as follows:

[0014]

[0015] Wherein, The pilot symbol, The data symbol, And The pilot placement position on the Doppler axis and the delay axis respectively, And The data placement position on the Doppler axis and the delay axis respectively, The effective channel response of the DD domain.

[0016] In step 2, the DD domain transmitted signal And the DD domain channel are two-dimensional circular convolution operation, the DD domain received signal As shown in the following formula:

[0017] Wherein, The phase information related to the channel, The attenuation coefficient, The noise interference.

[0018] In step 3, the estimation process of the channel delay and integer Doppler is: taking , As the search range, in the search range, taking the sequence length L as the sliding matching window, the DD domain received signal And the pilot sequence Correlation operation is carried out to find all the correlation values satisfying ; wherein, The correlation coefficient represents the amplitude ratio of the pilot symbol And the data symbol , The maximum value of the correlation operation in the search range; the formula of the correlation operation is as follows:

[0019] in, pilot sequence The complex conjugate value; At this point, the time delay estimated in the DD domain is... Doppler for At that time, Yan A certain path corresponds to multiple related values Preserve delay during Doppler operation The corresponding maximum correlation value That is, the starting position is A sliding window of length L is used; at this point, the estimated values ​​of time delay and integer Doppler are obtained as follows: , .

[0020] In step 4, the estimation process for the decimal Doppler is as follows: Step 4.1: Based on the time-invariance of the DD domain channel, use a complex exponential signal to input the time-domain pilot signal at the receiving end. Frequency offset compensation is performed to obtain the frequency offset compensated time-domain continuous pilot signal. ; Step 4.2: Decimal Doppler and its corresponding compensation factor It has the following relationship: ,

[0021] in, Represents the integer field; Under the influence of time-frequency dual-selection multipath fading channels with time delay and fractional Doppler, for For each value, all paths are monitored in parallel within the DD domain; once satisfied... Then the Doppler representation is:

[0022] in, The channel's first The actual Doppler in the path, Represents the integer part of the actual Doppler. Represents the fractional part of the actual Doppler. This represents the portion of the Doppler observed in the DD field that lies at integer lattice points. Indicates the compensation factor; Divide the two integer grid points in the DD field into A unit, i.e., a discretization step size, with a resolution of . Therefore, compensation factor The scope is: ; Step 4.3: Define a sequence , containing integer Doppler And the nearest integer grid point, ,in, ; Step 4.4: Based on the time-domain continuous pilot signal after frequency offset compensation Calculate the time domain of the receiving end and the compensation function. Related frequency offset compensation signal Its representation is as follows:

[0023] Among them, the compensation function , ; Step 4.5: Convert the frequency offset compensation signal Converted to DD domain signal via ZAK ; Step 4.6: Based on the estimated delay value , in sequence As the starting position, the pilot sequence With time delay located on the Doppler axis Corresponding DD domain signal The cross-correlation operation is shown in the following expression:

[0024] Find the Under this path, the compensation function The corresponding sequence The sequence Make The maximum value is represented as follows: ; Calculate all One corresponding The average value is used to obtain the Doppler estimate. .

[0025] In step 5, the channel attenuation coefficient The LMMSE estimation process is as follows: Step 5.1: Process the time-domain discrete received signal vector Perform ZAK transform to obtain the discrete received signal vector in the DD domain. As shown in the following formula:

[0026] in, , representing the noise vector, , representing the effective channel matrix, For the normalized discrete Fourier transform matrix, express An identity matrix of dimension 1 Represents Kronecker; The matrix Each can be determined by the forward cyclic shift matrix corresponding to the time delay. The diagonal matrix corresponding to Doppler It is represented in the following form: ,in ,

[0027] Therefore, the effective channel matrix It can be represented as:

[0028] in, , , ; Therefore, the discrete received signal vector in the DD domain It can be represented as: ;in, ; Simplifying, we get ; Among them, matrix , represents a matrix associated with the pilot sequence; matrix , represents a matrix associated with data symbols; Step 5.2: The channel in the DD domain is a zero-mean vector. Its representation is as follows: ; Therefore, the channel attenuation coefficient in the DD domain covariance matrix Its representation is as follows: ; Step 5.3: For the matrix Each column, ,in, It is a data symbol vector, with elements set to independent and identically distributed QPSK symbols. Therefore, ; For noise vector Their expectations Covariance Matrix They are represented as follows: , ; in, The variance of the noise signal is represented. express An identity matrix of 3D; For data symbols covariance matrix Its expression is as follows: ; in, Data symbols The variance; For the discrete received signal vector in the DD domain Its expression is as follows: ; in, Represents data symbols and noise generated on pilot symbols The interference vector; then its covariance matrix The representation of is as follows: ; For a random matrix satisfy Then for any Hermitian matrix They all ; Therefore, for the covariance matrix Its representation can be simplified to:

[0029] in, Then there is ; Therefore, the covariance matrix The representation of is as follows: ; in, Indicates the attenuation coefficient The variance; Step 5.4: Adjust the channel attenuation coefficient Perform LMMSE estimation, and its estimated value .

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The present invention constructs a transmission frame structure based on the fractional Doppler channel by superimposing pilot and data in step 1. By eliminating the restriction of the guard interval, it can reduce resource overhead and improve spectrum efficiency.

[0031] 2. This invention establishes the conversion relationship between the signal in the time domain and the DD domain by applying the time invariance and Doppler tunability of the DD domain channel in the OTFS system. Then, it uses a complex exponential signal to compensate for the frequency offset of the time domain signal and selects a compensation factor with appropriate accuracy within the range. This can effectively solve the fractional estimation problem of the time delay-Doppler dimension and improve the estimation accuracy.

[0032] 3. This invention treats data symbols as interference from pilot symbols and uses linear minimum mean square error (LMMSE) to estimate the received signal in the DD domain. It fully considers the influence of interference terms and uses prior information such as the variance of the noise signal and the covariance matrix of the attenuation coefficient for linear estimation. This can effectively combat interference in the channel, reduce the complexity of channel estimation, and improve the accuracy and stability of channel estimation.

[0033] In summary, compared with the prior art, the present invention eliminates the restriction of the guard interval, mixes pilot symbols and data symbols, and performs joint estimation to achieve accurate estimation of the OTFS fractional Doppler channel. Attached Figure Description

[0034] Figure 1 A schematic diagram of the arrangement of pilot and data symbols in the time-delay-Doppler domain in a frame transmitted by the OTFS system.

[0035] Figure 2 Comparison of normalized mean square error (NMSE) for channel estimation of different pilot sequences.

[0036] Figure 3 This refers to the entire modulation process of the OTFS system.

[0037] Figure 4 This image shows a performance comparison between the proposed method and the embedded single-pilot channel estimation scheme. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains.

[0039] The channel estimation method for OTFS systems based on hybrid multi-pilot joint estimation improves the overall system performance and achieves accurate estimation of channel parameters by starting from the pilot structure and eliminating the restriction of guard interval. It utilizes multiple pilots and superimposed data symbols for joint channel estimation. Specifically, it includes the following steps: Step 1: In the OTFS system, specify the data symbols to be sent. Modulated onto the gridded delay-Doppler domain (DD domain), at the starting position ( , ) data symbols Superimposed pilot sequence symbols with relatively high power and length L This constitutes a transmit frame in the DD domain. The transmission frame Includes data symbols And a pilot sequence symbol of relatively high power and length L superimposed on it. ,like Figure 1 As shown; Step 1.1: In the OTFS system, the time and frequency axes are divided into virtual resource grids. The number of OTFS symbols is N, and the number of subcarriers is M, thus constructing a dimension-... Virtual resource grid The grid It contains M units in the time delay dimension and N units in the Doppler dimension; The DD domain resources are divided into: grid As shown in the following formula:

[0040] in, For frame length, For subcarrier spacing, The duration of a single symbol in the time-frequency domain (TF domain); Discretize the DD domain into a grid. As shown in the following formula:

[0041] in, For bandwidth.

[0042] Step 1.2: Set the data symbols to be sent Place into the grid In each unit, for the starting position ( , ) data symbols A pilot sequence of relatively high power and length L is superimposed on top. This constitutes the entire transmit frame in the DD domain. The pilot sequence symbol Power ratio data symbols At least 5 times higher.

[0043] Using pilot symbols When performing channel estimation, it is usually necessary to consider the balance between the type and arrangement of pilots in the transmitted frame and the performance of channel estimation. For existing single-pilot-based embedded pilot designs, given the maximum channel delay... and maximum Doppler The arrangement of symbols in the DD field is shown in the following formula:

[0044] in, The pilot signal is positioned along the Doppler axis. This indicates the placement position of the pilot signal on the time delay axis.

[0045] This invention eliminates the numerical symbols. and pilot symbols The guard interval between them, the time delay corresponding to each symbol and the integer Doppler part can be obtained from... The arrangement of symbols for the transmitted frames in the DD domain is now confirmed as follows:

[0046] in, This indicates that the DD domain is sending a signal. Data symbols The arrangement, Indicates pilot symbol The arrangement of the pilots, where L is the length of the pilot sequence.

[0047] like Figure 2 As shown, in order to select the most suitable pilot type for application in this invention, the normalized mean square error (NMSE) of several common pilot sequences during channel estimation was compared. The results show that the ZC pilot sequence has a smaller normalized mean square error and is more suitable for the pilot structure designed in this invention.

[0048] Based on this, a ZC pilot sequence of length L is established, and it is placed in the DD domain. , Insert ZC pilot sequences within the specified range, and insert data symbols at other positions. The ZC pilot sequence is represented as follows: ; Step 2: The DD domain transmitted signal is modulated using OTFS to obtain an OTFS signal, which is then transmitted. The OTFS signal reaches the receiver via a time-frequency dual-select multipath fading channel. The received signal is then demodulated using OTFS to transform it into a DD domain received signal with superimposed interference, such as... Figure 3 As shown; Step 2.1: Send signal to DD domain Perform inverse symplectic finite Fourier transform (ISFFT) to convert it into a signal in the TF domain. The inverse symplectic finite Fourier transform is shown in the following equation:

[0049] in, and These represent the magnitudes of time delay and Doppler dimension, respectively. and Indicates the time-frequency domain index. and Indices representing Doppler and time delay, respectively. The imaginary unit, This represents an exponential function, where π is a constant. Step 2.2: For TF domain signals Perform a Heisenberg transform to convert it into a continuous signal in the time domain. This is the OTFS signal, which is transmitted through a transmitter; the Heisenberg transform is shown in the following equation:

[0050] in, This represents the shaping filter function for the transmitted pulse. Indicates frame length, Indicates the subcarrier spacing, and has .

[0051] Step 2.3: Continuous signal in the time domain The signal is transmitted to the receiving end through a time-frequency dual-selection multipath fading channel, and the receiving end receives a continuous time-domain signal. The expression is:

[0052] in, For the DD domain channel impulse response, each delay amount and Doppler frequency shift Corresponding to a complex channel attenuation coefficient, Indicates noise.

[0053] Typically, the number of reflectors in a channel is finite, therefore fewer parameters are required for channel modeling in the DD domain. The channel exhibits sparsity, and the DD domain channel impulse response... It can be represented in the following form:

[0054] in, It is the total number of transmission paths. Denotes the Dirac function, the first... The path can be determined by the attenuation coefficient. Delay and Doppler frequency shift Joint representation. Considering integer lattice points in DD dimensions, their mapping relationship is as follows: ,

[0055] Step 2.4: Continuously receive signals in the time domain Perform a Wigner transform to convert it into a discrete signal in the TF domain. As shown in the following formula:

[0056] Among them, continuous signals in the TF domain , It is a receiving pulse filter.

[0057] Step 2.5: Discrete the signal in the TF domain Perform a symplectic finite Fourier transform (SFFT) to convert it into the received signal in the DD domain. As shown in the formula below: ; The ISFFT and SFFT transforms mentioned above establish the connection between the DD and TF domains. The ISFFT transform can be understood as performing an FFT transform along the time delay axis to obtain the frequency domain, and an IFFT transform along the Doppler axis to obtain the time domain. The DD domain receives signals. From pilot response Data interference and noise interference It consists of three superimposed parts, as shown in the following formula:

[0058] Among them, pilot response and data interference The representation is as follows:

[0059]

[0060] in, Pilot symbol, For data symbols, and These represent the placement positions of the pilot signals on the Doppler axis and the time delay axis, respectively. and These represent the placement of the data on the Doppler axis and the time delay axis, respectively. This is the effective channel response in the DD domain.

[0061] After passing through a time-frequency dual-selective multipath fading channel in the DD domain, the pilot sequence will inevitably be affected by surrounding data symbols due to time delay and Doppler effects. Since the pilot sequence, as a known signal, needs to reflect the unknown characteristic parameters of the channel, the pilot energy setting cannot be too low. The transmitted and received symbols in the DD domain have a two-dimensional convolution relationship with the channel, meaning the transmitted signal in the DD domain... Perform a two-dimensional circular convolution operation with the DD domain channel to obtain the DD domain received signal. As shown in the following formula:

[0062] in, For channel-related phase information, The attenuation coefficient; For OTFS systems, channel estimation mainly involves three physical quantities of the DD domain channel: the first... Attenuation coefficient of the path Delay And Doppler Make an estimate.

[0063] Step 3: Receive signal based on DD domain By utilizing the correlation characteristics of its pilot sequence, the channel delay and integer Doppler are estimated, yielding the estimated values ​​for the delay and integer Doppler, respectively. , ; by , As the search range, within this search range, the sequence length L is used as the sliding matching window to receive the DD domain signal. With pilot sequence Perform cross-correlation operations to find all that satisfy... The relevant values, among which, The correlation coefficient, The correlation coefficient represents the maximum value of the correlation operation within the search range; pilot symbol With data symbols The amplitude ratio; the formula for the correlation calculation is as follows:

[0064] in, pilot sequence The complex conjugate value.

[0065] At this point, the time delay estimated in the DD domain is... Doppler for Due to the presence of fractional Doppler, signal energy leaks to other integer lattice points, therefore This path may correspond to multiple Dopplers. At that time, Yan A certain path corresponds to multiple related values Preserve delay during Doppler operation The corresponding maximum correlation value That is, the starting position is A sliding window of length L is used; at this point, the estimated values ​​of time delay and integer Doppler are obtained as follows: , .

[0066] Step 4: Based on the time invariance of the DD domain channel and the adjustability of Doppler, estimate the fractional Doppler to obtain the final Doppler estimate. ; Step 4.1: Based on the time-invariance of the DD domain channel, use a complex exponential signal to input the time-domain pilot signal at the receiving end. Frequency offset compensation is performed to obtain the frequency offset compensated continuous pilot signal in the time domain at the receiver. ; The OTFS carrier in the time domain can be viewed as a frequency-modulated pulse sequence. In the time domain, time delay is represented as a translation on the time axis, introducing a time-shifted pulse train. The pulse train starts at time l, repeats every M sampling points, and is sampled N times. .

[0067] In digital signal processing, the length of the entire transmission block is considered as Each sampling point, the Doppler effect is manifested as a frequency shift, compared to integer Doppler values. corresponding frequency Therefore, Doppler is represented by a complex exponential signal. Frequency modulation is applied to the entire pulse train.

[0068] Time-domain pulse train Complex exponential signals By combining these, we obtain the time-domain waveform corresponding to the symbol in the DD domain. Its representation is as follows:

[0069] Therefore, the transmission frame The starting position in The time-domain representation of the pilot sequence is as follows: .

[0070] Considering the shape invariance of the OTFS carrier under time delay and Doppler shift, it can be quasi-periodically extended in the DD domain trellis. Therefore, the time-domain pilot signal at the transmitter... After passing through the channel After the path is established, the time-domain pilot signal at the receiving end is obtained. Its expression is as follows:

[0071] It has a time delay Doppler and attenuation coefficient The OTFS carrier signal at the receiving end generally retains its shape compared to the transmitting end. However, due to the effects of time delay and Doppler, the time-domain waveform of the OTFS carrier undergoes time delay and periodic changes.

[0072] Therefore, based on the time-domain pilot signal at the transmitting end This time-invariance during channel travel can be addressed by modulating the OTFS carrier in the time domain to adjust the Doppler parameters of the signal. This can be achieved by utilizing the time-domain pilot signal at the transmitter. The time-domain tunable property of Doppler allows for the transformation of the OTFS carrier. One Doppler conversion, the conversion method is as follows: .

[0073] Therefore, for those who have experienced Doppler... The receiving end time-domain pilot signal Its relationship with the time-domain pilot signal at the transmitting end The mapping relationship is shown in the following formula:

[0074] in, .

[0075] Therefore, based on the time-domain pilot signal at the receiving end By utilizing the time invariance and Doppler tunability after channeling, a frequency-offset compensated time-domain continuous pilot signal is obtained. The expression is as follows:

[0076] in, , which is a noise signal.

[0077] Step 4.2: The Doppler is the sum of the integer and fractional parts, as shown in the following formula:

[0078] in, The resolution of the Doppler axis in the DD domain. .

[0079] The fractional part of Doppler and its corresponding compensation factor It has the following relationship: ,

[0080] in, Represents the integer field.

[0081] Under the influence of time-frequency dual-selection multipath fading channels with time delay and fractional Doppler, for For each value, all paths are monitored in parallel within the DD domain. Once satisfied... Then the Doppler representation is:

[0082] in, The channel's first The actual Doppler in the path, Represents the integer part of the actual Doppler. Represents the fractional part of the actual Doppler. This represents the portion of the Doppler observed in the DD field that lies at integer lattice points. This represents the compensation factor.

[0083] Divide the two integer grid points in the DD field into A unit, i.e., a discretization step size, with a resolution of . Therefore, compensation factor The scope is: .

[0084] Step 4.3: Considering channel noise and the spread of fractional Doppler in the DD domain, define a sequence It contains integer Dopplers And the nearest integer grid point, i.e. ,in, .

[0085] Step 4.4: Based on the time-domain continuous pilot signal after frequency offset compensation Calculate the time domain of the receiving end and the compensation function. Related frequency offset compensation signal Its representation is as follows:

[0086] Among them, the compensation function , .

[0087] Step 4.5: Convert the frequency offset compensation signal Perform a ZAK transform to convert the signal to the DD domain. ; Step 4.6: Based on the estimated delay value On the Doppler axis corresponding to the time delay axis, in sequence As the starting position, the pilot sequence With time delay located on the Doppler axis Corresponding DD domain signal The cross-correlation operation is shown in the following expression:

[0088] in, pilot sequence The complex conjugate value.

[0089] Find the Under this path, the compensation function The corresponding sequence The sequence Make The maximum value is represented as follows: ; Calculate all One corresponding The average value is used to obtain the Doppler estimates for the integer and decimal parts, which are expressed as follows: .

[0090] Step 5: Based on the estimated time delay and Doppler values, adjust the channel attenuation coefficient. Linear minimum mean square error (LMMSE) estimation is performed to obtain an estimate of the channel attenuation coefficient. Complete the channel estimation for the OTFS system; Step 5.1: Send a signal to the DD domain Perform IZAK transform to obtain the discrete transmitted signal vector in the DD domain. The IZAK transformation is shown in the following equation:

[0091] Among them, matrix The pulse shaping matrix at the transmitting end is obtained by uniformly sampling the transmitted pulse. The normalized discrete Fourier transform matrix is ​​represented as follows: .

[0092] For time-domain discrete received signal vector Perform ZAK transform to obtain the discrete received signal vector in the DD domain. As shown in the following formula:

[0093] Simplifying, we get ; in, , representing the noise vector, , representing the effective channel matrix, express An identity matrix of dimension 1 Represents Kronecker; Assuming the pulse filters at the transmitter and receiver are ideal rectangular window functions, then we have ,matrix This represents the pulse shaping matrix at the receiving end.

[0094] The matrix Each can be determined by the forward cyclic shift matrix corresponding to the time delay. The diagonal matrix corresponding to Doppler It is represented in the following form: ,in ,

[0095] Therefore, the effective channel matrix It can be expressed by the following formula:

[0096] in, , , .

[0097] Therefore, the discrete received signal vector in the DD domain It can be represented in the following form: ;in, ; Simplifying, we get ; Among them, matrix , represents a matrix associated with the pilot sequence; matrix , represents a matrix associated with data symbols.

[0098] Step 5.2: The channel in the DD domain is a zero-mean vector. Its representation is as follows: ; Channel attenuation coefficient in DD domain covariance matrix The channel remains stable across multiple consecutive transmission frames; based on this channel stationarity, the receiver can efficiently obtain the channel attenuation coefficient using observed samples. covariance matrix Its representation is as follows: .

[0099] Step 5.3: For the matrix Each column, ,in, It is a data symbol vector, with elements set to independent and identically distributed orthogonal phase shift keying (QPSK) symbols. Therefore, .

[0100] and They are independent of each other, therefore, For all columns Both are true. Therefore, .

[0101] For noise vector Their expectations Covariance Matrix They are represented as follows: , ; in, The variance of the noise signal is represented. express An identity matrix of 3D; For data symbols covariance matrix Its expression is as follows:

[0102] in, , Data symbols The variance; simplification yields, .

[0103] For the discrete received signal vector in the DD domain Its expression is as follows: ; in, Represents data symbols and noise generated on pilot symbols The interference vector; then its covariance matrix The representation of is as follows: ; For a random matrix satisfy Then for any Hermitian matrix They all .

[0104] Therefore, for the covariance matrix Its representation can be simplified to:

[0105] in, Then there is ; Therefore, the covariance matrix The representation of is as follows: ; in, This represents the variance of the attenuation coefficient; Step 5.4: Based on the Linear Least Mean Square Error (LMMSE) estimation formula, perform linear estimation using prior information such as the variance of the noise signal and the covariance matrix of the attenuation coefficient, to estimate the channel attenuation coefficient. The estimated value .

[0106] in, Represents the channel attenuation coefficient in the DD domain. The covariance matrix, This represents a matrix associated with the pilot sequence. Represents data symbols and noise generated on pilot symbols interference vector The covariance matrix, This represents the discrete received signal vector in the DD domain.

[0107] Figure 4 The estimation performance of the two schemes under different signal-to-noise ratios is compared. Compared with the embedded single-pilot scheme, the scheme of this invention eliminates data symbols. and pilot symbols By adjusting the guard interval between them, fractional-order Doppler frequency shift estimation was achieved, and channel estimation was performed using a multi-pilot joint approach, thus improving the accuracy of channel estimation.

[0108] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the scope of protection of this application. Various modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the inventive concept should be covered within the scope of the claims of the invention.

Claims

1. A channel estimation method for an OTFS system based on hybrid multi-pilot joint operation, characterized in that, Includes the following steps: Step 1: Configure OTFS transmit frames , containing data symbols And a pilot symbol of relatively high power and length L superimposed on it. Data symbols and pilot symbols They are simultaneously modulated onto the DD domain to obtain the DD domain transmitted signal; Step 2: Modulate the DD domain transmitted signal with OTFS to obtain the OTFS signal, and transmit it; the OTFS signal reaches the receiving end through the time-frequency dual-select multipath fading channel, and the received signal at the receiving end is demodulated with OTFS and transformed into the DD domain received signal; Step 3: Based on the received signal in the DD domain, utilize the correlation characteristics of its pilot sequence to estimate the channel delay and integer Doppler, obtaining the estimated values ​​of the delay and integer Doppler, respectively. , ; Step 4: Based on the time invariance and Doppler adjustability of the DD domain channel, estimate the fractional Doppler to obtain the final Doppler estimate. ; Step 5: Based on the estimated time delay and Doppler values, adjust the channel attenuation coefficient. Perform LMMSE estimation to obtain the channel attenuation coefficient. The estimated value This completes the channel estimation for the OTFS system.

2. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 1, the pilot symbol Power ratio data symbols At least 5 times higher.

3. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 1, the transmission frame The symbols in the DD field are arranged as follows: in, This indicates the transmitted signal in the DD domain, where L is the length of the pilot sequence.

4. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 1, the pilot symbol It is a ZC pilot sequence.

5. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 2, the specific process of obtaining the DD domain received signal is as follows: Sending signals to the DD domain Converted to TF domain signal via ISFFT ; For TF domain signals After Heisenberg transform, it is converted into a continuous signal in the time domain. That is, the OTFS signal, and transmit it out; Continuous signal in time domain After being transmitted through a time-frequency dual-select multipath fading channel to the receiving end, a continuous signal in the time domain is obtained. For continuous signals in the time domain After Wegener transform, it is converted into a discrete signal in the TF domain. ; Discrete signals in the TF domain SFFT converted to DD domain received signal .

6. The channel estimation method for an OTFS system according to claim 1 or 5, characterized in that: In step 2, the DD domain receives the signal. From pilot response Data interference and noise interference It consists of three superimposed parts, as shown in the following formula: Among them, pilot response and data interference The representation is as follows: in, Pilot symbol, For data symbols, and These represent the placement positions of the pilot signals on the Doppler axis and the time delay axis, respectively. and These represent the placement of the data on the Doppler axis and the time delay axis, respectively. This is the effective channel response in the DD domain.

7. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 2, the DD domain is sent with a signal. Perform a two-dimensional circular convolution operation with the DD domain channel to obtain the DD domain received signal. As shown in the following formula: in, For channel-related phase information, The attenuation coefficient is... This is due to noise interference.

8. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 3, the estimation process for channel delay and integer Doppler is as follows: by , As the search range, within this search range, the sequence length L is used as the sliding matching window to receive the DD domain signal. With pilot sequence Perform cross-correlation operations to find all that satisfy... The relevant values; among which, Represents the correlation coefficient, indicated by the pilot symbol. With data symbols amplitude ratio, This represents the maximum value of the correlation operation within the search range; the formula for the correlation operation is as follows: in, pilot sequence The complex conjugate value; At this point, the time delay estimated in the DD domain is... Doppler for At that time, Yan A certain path corresponds to multiple related values Preserve delay during Doppler operation The corresponding maximum correlation value That is, the starting position is A sliding window of length L is used; at this point, the estimated values ​​of time delay and integer Doppler are obtained as follows: , .

9. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 4, the estimation process for the decimal Doppler is as follows: Step 4.1: Based on the time-invariance of the DD domain channel, use a complex exponential signal to input the time-domain pilot signal at the receiving end. Frequency offset compensation is performed to obtain the frequency offset compensated time-domain continuous pilot signal. ; Step 4.2: Decimal Doppler and its corresponding compensation factor It has the following relationship: ， in, Represents the integer field; Under the influence of time-frequency dual-selection multipath fading channels with time delay and fractional Doppler, for For each value, all paths are monitored in parallel within the DD domain; once satisfied... Then the Doppler representation is: in, The channel's first The actual Doppler in the path, Represents the integer part of the actual Doppler. Represents the fractional part of the actual Doppler. This represents the portion of the Doppler observed in the DD field that lies at integer lattice points. Indicates the compensation factor; Divide the two integer grid points in the DD field into A unit, i.e., a discretization step size, with a resolution of . Therefore, compensation factor The scope is: ; Step 4.3: Define a sequence , containing integer Doppler And the nearest integer grid point, ,in, ; Step 4.4: Based on the time-domain continuous pilot signal after frequency offset compensation Calculate the time domain of the receiving end and the compensation function. Related frequency offset compensation signal Its representation is as follows: Among them, the compensation function , ; Step 4.5: Convert the frequency offset compensation signal Converted to DD domain signal via ZAK ; Step 4.6: Based on the estimated delay value , in sequence As the starting position, the pilot sequence With time delay located on the Doppler axis Corresponding DD domain signal The cross-correlation operation is shown in the following expression: Find the Under this path, the compensation function The corresponding sequence The sequence Make The maximum value is represented as follows: ; Calculate all One corresponding The average value is used to obtain the Doppler estimate. .

10. The channel estimation method for the OTFS system according to claim 1, characterized in that: In step 5, the channel attenuation coefficient The LMMSE estimation process is as follows: Step 5.1: Process the time-domain discrete received signal vector Perform ZAK transform to obtain the discrete received signal vector in the DD domain. As shown in the following formula: in, , representing the noise vector, , representing the effective channel matrix, For the normalized discrete Fourier transform matrix, express An identity matrix of dimension 1 Represents Kronecker; The matrix Each can be determined by the forward cyclic shift matrix corresponding to the time delay. The diagonal matrix corresponding to Doppler It is represented in the following form: ,in , Therefore, the effective channel matrix It can be represented as: in, , , ; Therefore, the discrete received signal vector in the DD domain It can be represented as: ;in, ; Simplifying, we get ; Among them, matrix , represents a matrix associated with the pilot sequence; matrix , represents a matrix associated with data symbols; Step 5.2: The channel in the DD domain is a zero-mean vector. Its representation is as follows: ； Therefore, the channel attenuation coefficient in the DD domain covariance matrix Its representation is as follows: ； Step 5.3: For the matrix Each column, ,in, It is a data symbol vector, with elements set to independent and identically distributed QPSK symbols. Therefore, ; For noise vector Their expectations Covariance Matrix They are represented as follows: ， ； in, The variance of the noise signal is represented. express An identity matrix of 3D; For data symbols covariance matrix Its expression is as follows: ； in, Data symbols The variance; For the discrete received signal vector in the DD domain Its expression is as follows: ； in, Represents data symbols and noise generated on pilot symbols The interference vector; then its covariance matrix The representation of is as follows: ； For a random matrix satisfy Then for any Hermitian matrix They all ; Therefore, for the covariance matrix Its representation can be simplified to: in, Then there is ; Therefore, the covariance matrix The representation of is as follows: ； in, Indicates the attenuation coefficient The variance; Step 5.4: Adjust the channel attenuation coefficient Perform LMMSE estimation, and its estimated value .

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