Receiving method of amplitude limiting orthogonal time-frequency air conditioning system

Abstract

The invention discloses a receiving method for amplitude limiting orthogonal time-frequency air conditioning, and belongs to the field of multi-carrier mobile communication. According to the method, the sparsity of the delay-Doppler domain channel and the piecewise linear characteristic of the amplitude limiting amplitude are utilized, the joint iterative estimation of the channel and the amplitude limiting amplitude is realized by adopting an estimation method based on sparse Bayesian learning, the accurate estimation of the amplitude limiting amplitude enables the observation of the pilot frequency after amplitude limiting to be more accurate, the accuracy of channel estimation is improved, and the accuracy of channel estimation is improved. More accurate channel estimation also enables the amplitude limiting amplitude estimation of the next iteration to be more accurate. According to the invention, the detected data segment signal is used as a new known sequence, and prediction, filtering and smoothing processing are carried out in combination with effective observation results of a plurality of data blocks, so that the error of channel tracking is reduced, and the pilot frequency overhead can be reduced at the same time. According to the method, the coefficient of equalization and distortion elimination of next iteration is optimized by using the result of effective judgment on the data symbols, the influence of inter-symbol interference and amplitude limiting distortion is eliminated, and the bit error rate of signal detection is further reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi - carrier mobile communication, and relates to an optimization method for a receiver of limited - amplitude orthogonal time - frequency space modulation. Background Art

[0002] In high - speed mobile communication scenarios, multipath effects and Doppler frequency shifts cause time - frequency doubly selective fading in the channel, resulting in a serious degradation in the performance of traditional orthogonal frequency division multiplexing (OFDM) waveforms. Specifically, the doubly selective fading makes the channel gains on each sub - carrier uneven, and the effective signal - to - noise ratio (SNR) on individual sub - carrier symbols is extremely low, leading to an increase in the overall bit error rate. To make up for the deficiencies of OFDM, the academic community has proposed using orthogonal time - frequency space (OTFS) modulation as a new candidate waveform. OTFS modulates symbols in the delay - Doppler (DD) domain, making all symbols experience the same channel gain in both the time domain and the frequency domain. By designing appropriate equalization, full diversity in the time - frequency domain can be achieved. In addition, the sparsity and relatively slow - changing characteristics of the DD - domain channel make channel estimation and equalization simpler and more reliable. These advantages make OTFS more attractive in high - speed mobile communication. On the other hand, the power amplifier (PA) is also an important part of the radio - frequency mobile communication system. Both OTFS and OFDM belong to multi - carrier waveforms and have the problem of high peak - to - average power ratio (PAPR). When applied to the uplink, or systems such as high - speed Internet of Things (IoT) and machine - type communication (MTC), in order to improve the efficiency of the power amplifier, the power amplifier needs to operate near the saturation region. The actual output signal has non - linear distortion, causing signal constellation points to be distorted, which in turn affects the performance of signal detection. Even using ideal pre - distortion methods cannot compensate for the impact of saturation clipping distortion. In addition, considering factors such as changes in environmental temperature and humidity, device aging, and high measurement and calibration costs, the clipping amplitude (CA) is usually unknown to the receiving end.

[0003] In recent years, many OTFS receiving methods have been proposed in the academic community, mainly including two aspects: channel estimation and signal detection. Among them, channel estimation methods include DD-domain channel estimation methods based on thresholds and various compressive sensing methods, and signal detection methods include minimum mean square error (MMSE) block equalization, various message passing algorithms, and OTFS signal detection methods in the transform domain. However, these existing designs assume an ideal linear power amplifier model and do not consider the clipping distortion effect. If directly applied to a clipped OTFS system, it will lead to a serious decline in the accuracy of channel estimation and signal detection. To solve the above problems, not only new estimation methods need to be designed to simultaneously estimate the DD-domain channel response and the clipping amplitude, but also new signal detection methods need to be designed to eliminate the influence of inter-symbol interference and clipping distortion. Summary of the Invention

[0004] The purpose of the present invention is to provide a receiving method for clipped orthogonal time-frequency space modulation, which uses the sparse Bayesian learning (SBL) algorithm to realize the joint iterative estimation of the channel and the clipping amplitude. The accurate estimation of the clipping amplitude makes the observation of the clipped pilot more accurate; using the detected data segment signal as a new known sequence, and jointly performing prediction, filtering, and smoothing processing on the effective observation results of multiple data blocks to further reduce the channel tracking error and also reduce the pilot overhead; using the result of the effective decision on the data symbol to optimize the coefficients of the next iteration of equalization and distortion cancellation to further eliminate the influence of inter-symbol interference and clipping distortion, thereby being able to further reduce the bit error rate of signal detection.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A receiving method for clipped orthogonal time-frequency space modulation disclosed by the present invention includes the following steps:

[0007] Step 1: Generate K OTFS data symbol blocks s1,..., s K And add a cyclic prefix (CP), and add a pilot symbol block s0 in front to form a transmitted signal frame.

[0008] Randomly generate K consecutive symbol sequences of length MN and map them to the M×N DD-domain lattice points to generate OTFS symbol block vectors X1,..., X k . Each symbol is first transformed through the inverse symplectic finite Fourier transform (ISFFT) to obtain the time-frequency domain symbol block S k , which is expressed as:

[0009]

[0010] where F M is an M-dimensional discrete Fourier transform (DFT) matrix, is an N-dimensional inverse discrete Fourier transform (IDFT) matrix. After the Heisenberg transform, the time-domain signal s k is obtained. The whole process is specifically expressed as:

[0011]

[0012] where is the vectorized form of X k . is the transmit pulse shaping diagonal matrix.

[0013] The time-domain symbol blocks s1,..., s K are obtained, and the amplitude and phase are split and expressed in the following form:

[0014]

[0015] where a k = [a k (1),..., a k (MN)] T and are column vectors representing the amplitude and phase, respectively. After adding the pilot block s0 and CP, a transmit signal frame is formed.

[0016] Step 2: Pass all the symbol blocks in the transmit signal frame generated in Step 1 through a soft limiter with a limiting amplitude of A to obtain the symbol vectors z0,..., z k .

[0017] Introduce a binary column vector c k = [c k (1),..., c k (MN)] T , where c k (n) is used to represent whether the nth sampling point of s k is limited, expressed as

[0018]

[0019] Then the output signal vector of the limiter is further expressed as:

[0020]

[0021] Step 3: After amplitude-limiting all the symbols in a frame using the method of Step 2, pass them through a randomly generated channel and add Gaussian white noise. Remove the CP from the received signal and perform serial-to-parallel conversion to obtain symbol vectors y0,..., y K , and convert the model expression of y0,..., y K into a form where the DD-domain sparse channel and the amplitude-limiting amplitude are linear and piecewise-linear functions respectively.

[0022] Step 3.A: For p = 1,..., P, randomly generate the complex gains of each path of the channel corresponding to the pilot symbol block according to the known channel fading parameter statistical model Normalized multipath delay l p and normalized Doppler shift o p , and then calculate the complex gains of each path of the channel corresponding to the data symbol block of k = 1,..., K according to the relationship between the phase of each path and the Doppler shift After amplitude-limiting all the symbols in a frame using the method of Step 4, pass them through a randomly generated channel and add a Gaussian white noise vector v with variance k , remove the CP from the received signal and perform serial-to-parallel conversion to obtain symbol vectors y0,..., y K , where y k is expressed in the following form:

[0023] y k = H k z k + v k (6)

[0024] where H k is the equivalent channel response in the time-delay domain, and the specific calculation method is:

[0025]

[0026] where Π is a permutation matrix, expressed as:

[0027]

[0028] Δ p is a diagonal matrix, expressed as:

[0029]

[0030] where

[0031] Step 3.B: Reconstruct with a delay dimension of G τ and a Doppler dimension of G νThe DD domain two-dimensional grid, where G τ >l P , G ν >o P Then the DD domain channel response is re-expressed on this grid point as:

[0032]

[0033] in is the complex gain of a path with a delay of m grid units and a Doppler shift of n grid units, and δ(·) is the Dirac delta function. The channel matrix in the time-delay domain is reformulated as follows:

[0034]

[0035] where Π is the same permutation matrix as in (7), Δ m,n It is expressed as:

[0036]

[0037] in In formula (11), all G τ G ν indivual There are only P non-zero ones in Extract to a sparse vector h k In this paper, equation (6) is reformulated as:

[0038]

[0039] Where W is a constant matrix expressed as:

[0040]

[0041] h k is a column vector containing the complex gains of each path on the DD domain grid point, expressed as:

[0042]

[0043] make Then when s k When constant, Φ(s k ,A) is piecewise linear with respect to A. (13) is remodeled as:

[0044] y k =Φ(s k ,A)h k +v k (16)

[0045] Step 4: Extract the pilot block y0 required for channel estimation, input the known transmitted non-clipped pilot sequence s0, the maximum number of iterations i max , and the estimation accuracy ∈, calculate the values of the intermediate variables required for channel estimation, and initialize the clipping amplitude and the hyperparameter matrix.

[0046] Extract the pilot block y0, input the known transmitted non-clipped pilot sequence s0, the maximum number of iterations i max , and the estimation accuracy ∈, and let denote the pilot amplitude vector sorted from small to large, be the q-th non-repeated value in The total number of possible values is finite, denoted as Q; P s is the sorting matrix; then the sorted pilot sequence, binary vector, and phase vector are respectively denoted as and Furthermore, note that is a vector with multiple consecutive elements 0 in the front and all elements 1 in the back, and the total number of possible values is also finite. Denote the possible value of the q-th as Initialize the hyperparameter matrix representing the variance of the sparse channel vector h0 The initial clipping amplitude A (0) = max(a0), the number of iterations i = 1.

[0047] Step 5: Update the posterior mean μ (i-1) and variance Σ (i-1) of the sparse channel vector h0 with respect to A (i) and γ (i) in the i-th iteration.

[0048] The posterior distribution of h0 is expressed as where

[0049]

[0050] Step 6: Let h0 = μ (i) , update the estimated result A (i) of the clipping amplitude and the hyperparameter matrix Γ (i) in the i-th iteration. Determine whether the iteration stop condition is satisfied. If satisfied, output the initial channel estimation result of the pilot and the estimated result of the clipping amplitude as well as the hyperparameter matrix Γ SBL = Γ (i) ; otherwise, let i = i + 1 and return to Step 5.

[0051] Step 6.A: Let h0 = μ (i), the optimization objective is to calculate A that maximizes the target log-likelihood ratio (i) and Γ (i) , that is

[0052]

[0053] where

[0054]

[0055] For the intervals corresponding to q = 1,..., Q, that is in the case of, removing the terms unrelated to A, the objective function is transformed into

[0056]

[0057] where in all the corresponding intervals, that is in the case of, calculate the extreme point of the target log-likelihood ratio with respect to A. The specific method is:

[0058]

[0059] Compare to obtain the optimal value in the interval:

[0060]

[0061] Compare the extremes of all intervals and take the minimum to obtain the optimal A (i) value:

[0062]

[0063] Step 6.B: γ that maximizes the target log-likelihood ratio (i) The calculation method is specifically:

[0064]

[0065] where is a vector composed of all the diagonal elements of Σ (i) . Finally, let Γ (i) = diag(γ (i) ). When the number of iterations reaches the maximum (i ≥ i max ) or satisfies the convergence condition then stop the iteration and output the initial pilot channel estimation result and the estimation result of the clipping amplitude as well as the hyperparameter matrix Γ SBL = Γ (i) ; otherwise, continue the iteration, let i = i + 1, and return to Step 5.

[0066] Step 7: Extract data blocks y1,...,y K , input the maximum number of iterations j max and the result of pilot estimation in Step 6 to initialize the tracking result Initial decision symbol Let the number of iterations j = 1, and then let the posterior channel mean and variance be respectively and

[0067] Step 8: In the j-th iteration, use the DD-domain channel tracking method based on Kalman filtering to update the channel tracking result of the data block

[0068] Step 8.A: Channel prediction to obtain the prior channel mean and variance corresponding to each symbol block for k = 1,...,K:

[0069] h k|k-1 = Th k-1|k-1 (26)

[0070] P k|k-1 = TP k-1|k-1 T H (27)

[0071] where h k-1|k-1 and P k-1|k-1 are respectively the posterior mean and variance of the previous block. T is the transition matrix that correlates the channel phases of the (k - 1)-th block and the k-th block:

[0072]

[0073] Step 8.B: Filtering, calculate the Kalman gain G k 、posterior mean and variance of the current block, which are specifically expressed as:

[0074]

[0075] h k|k = h k|k-1 + G k (y k - E k h k|k-1 ) (30)

[0076]

[0077] where the calculation method of E k is

[0078]

[0079] Through the above prediction and filtering processes, calculate the posterior mean h k|kSum of variances P k|k .

[0080] Step 8.C: Smoothing, apply the observations of all K symbols to each block, expressed as:

[0081] h k-1|K = T -1 h k|K (33)

[0082] P k-1|K = P k|K (34)

[0083] For k = 1, ..., K, let the tracking result h ( k j) = h k-1|K .

[0084] Step 9: In the j-th iteration, use the clipping OTFS signal detection method based on minimum mean square error - decision feedback block-wise equalization (MMSE-DFBE) to equalize, cancel distortion, make decisions, and provide feedback for the signal, and update the decision result and the feedback signal If the number of iterations reaches the maximum, output the channel tracking result and the signal detection result Otherwise, continue the iteration, let j = j + 1, and return to Step 8.

[0085] Step 9.A: The equalization part includes a block feed-forward equalizer and a block feedback equalizer whose output signal is expressed as:

[0086]

[0087] where the k that minimizes the mean square error between the equalized output and the actual clipped signal z is calculated as:

[0088]

[0089]

[0090] where represent the transmitted signal power and the signal power after the decision in the previous iteration, respectively. is the estimated result of their correlation value, and the calculation method is:

[0091]

[0092] where η is a scaling factor introduced to avoid the performance degradation of the feedback iteration caused by an overly large estimated value; according to the estimated and Equation (7), the estimated time-delay domain channel H is calculated ; k ;

[0093] When j = 1, since there is no decision result, the block feedback equalizer is At this time, the block feedforward equalizer is the same as the linear MMSE block equalizer.

[0094] Step 9.B: Distortion cancellation in the time domain is performed on the equalized signal. The specific method is as follows:

[0095]

[0096] where represents the normalized cross-correlation value between the clipped distortion signal and the unclipped signal, while represents the distortion part in the clipped distortion signal that is uncorrelated with the unclipped signal, and is calculated according to the previous iteration decision result as:

[0097]

[0098] Step 9.C: The signal after time-domain distortion cancellation is transformed to the DD domain for hard decision, which is expressed as:

[0099]

[0100] Finally, the signal after the decision is transformed back to the time domain to obtain the unclipped signal after the decision. Then, the signal is clipped using a soft clipper with an amplitude of to obtain the clipped signal after the decision, which is used for subsequent iterative tracking and equalization. This process is specifically expressed as:

[0101]

[0102]

[0103] When the number of iterations reaches the maximum (j ≥ j max ), the iteration stops, and for k = 1,..., K, the channel tracking result and the signal detection result are output. Otherwise, the iteration continues, let j = j + 1, and return to Step 8.

[0104] Beneficial effects:

[0105] 1. The existing DD-domain channel estimation method is only applicable to the linear power amplifier output model and is not applicable to the clipped OTFS pilot signal. A receiving method for clipped orthogonal time-frequency space modulation disclosed by the present invention utilizes the sparsity of the DD-domain channel and the piecewise linear characteristic of the clipping amplitude, and adopts the SBL algorithm based on expectation maximization to realize the joint iterative estimation of the channel and the clipping amplitude. The accurate estimation of the clipping amplitude makes the observation of the clipped pilot more accurate, and can further improve the accuracy of channel estimation compared with the existing channel estimation method. Moreover, the more accurate channel estimation also makes the estimation of the clipping amplitude in the next iteration more accurate.

[0106] 2. The number of observations of the pilot block is limited and the channel multipath phase changes rapidly with time, resulting in a large error in directly predicting the DD-domain channel of the data block based on the channel estimation result. A receiving method for clipped orthogonal time-frequency space modulation disclosed by the present invention is based on the DD-domain channel tracking of Kalman filtering, which can use the detected data segment signal as a new known sequence, and perform prediction, filtering and smoothing processing by combining the effective observation results of multiple data blocks, further reducing the error of channel tracking and also reducing the pilot overhead.

[0107] 3. The ability of the linear equalization method to eliminate inter-symbol interference is limited and it cannot eliminate the clipping distortion, resulting in a high bit error rate. A receiving method for clipped orthogonal time-frequency space modulation disclosed by the present invention performs OTFS detection based on the minimum mean square error-decision feedback block equalization and time-domain distortion cancellation, which can optimize the coefficients of the next iteration of equalization and distortion cancellation by using the result of the effective decision on the data symbol, further eliminating the influence of inter-symbol interference and clipping distortion, and further reducing the bit error rate of signal detection. Description of the Drawings

[0108] Figure 1 It is the flow chart of the clipped OTFS receiving method of the present invention;

[0109] Figure 2 It is the OTFS frame structure diagram based on block pilots;

[0110] Figure 3 It is the OTFS iterative detector framework of the minimum mean square error-decision feedback block equalization and time-domain distortion cancellation proposed by the present invention;

[0111] Figure 4 It is the relationship diagram between the channel estimation NMSE and SNR of different methods when the clipping amplitude is 1 dB in the simulation of the example scenario;

[0112] Figure 5 It is the relationship diagram between the channel estimation NMSE and SNR of different methods when the clipping amplitude is 3 dB in the simulation of the example scenario;

[0113] Figure 6Channel estimation NMSE vs. SNR relationship diagrams of different methods with a simulation clipping amplitude of 5 dB in the example scenario;

[0114] Figure 7 For the relationship diagram of the clipping amplitude estimation NMSE and SNR of different methods with a simulation clipping amplitude of 1 dB in the example scenario;

[0115] Figure 8 For the relationship diagram of the clipping amplitude estimation NMSE and SNR of different methods with a simulation clipping amplitude of 3 dB in the example scenario;

[0116] Figure 9 For the relationship diagram of the clipping amplitude estimation NMSE and SNR of different methods with a simulation clipping amplitude of 5 dB in the example scenario;

[0117] Figure 10 For the relationship diagram of the BER and SNR of different methods with a simulation clipping amplitude of 1 dB in the example scenario;

[0118] Figure 11 For the relationship diagram of the BER and SNR of different methods with a simulation clipping amplitude of 3 dB in the example scenario;

[0119] Figure 12 For the relationship diagram of the BER and SNR of different methods with a simulation clipping amplitude of 5 dB in the example scenario. Detailed implementation method

[0120] To better illustrate the purpose and advantages of the present invention, the following further describes the content of the invention in conjunction with the accompanying drawings and examples.

[0121] Example 1:

[0122] As Figure 1 shown. The clipping orthogonal time-frequency space modulation receiving method disclosed in this embodiment is specifically implemented as follows:

[0123] Step 1: Generate 14 OTFS data symbol blocks s1,..., s 14 and add a cyclic prefix, add a pilot symbol block s0, and form a transmitted signal frame according to the frame structure as Figure 2 shown;

[0124] Randomly generate 14 consecutive symbol sequences of length 32×32 = 1024 and map them to the 32×32 DD-domain lattice points to generate OTFS symbol block vectors X1,..., X 14 . First, pass each symbol through the inverse symplectic finite Fourier transform (ISFFT) to obtain the time-frequency domain symbol block S k , expressed as:

[0125]

[0126] where F 32 is a 32-dimensional discrete Fourier transform (DFT) matrix, and is a 32-dimensional inverse discrete Fourier transform (IDFT) matrix. After the Heisenberg transform, the time-domain signal s k is obtained. The whole process is specifically expressed as:

[0127]

[0128] where is the vectorized form of X k . is the transmit pulse shaping diagonal matrix.

[0129] The time-domain symbol blocks s1,..., s 14 are obtained. The amplitude and phase are split and expressed in the following form:

[0130]

[0131] where a k = [a k (1),..., a k (1024)] T and are column vectors representing the amplitude and phase, respectively. After adding the pilot block s0 and the cyclic prefix, a transmit signal frame is formed.

[0132] Step 2: All the symbol blocks in the transmit signal frame generated in Step 1 are passed through a soft limiter with a limiting amplitude of A to obtain the symbol vectors z0,..., z 14 ; In the example, the average energy of the OTFS signal is fixed at 1, and the limiting amplitude is expressed in decibels as 20log 10 (A) [dB]. In the example, three different limiting amplitudes are considered, namely 1 dB, 3 dB, and 5 dB, corresponding to the scenarios of severe, relatively severe, and mild limiting distortion.

[0133] A binary column vector c k = [c k (1),..., c k (1024)] T is introduced, where c k (n) is used to represent s kWhether the n-th sampling point is clipped, denoted as

[0134]

[0135] Then the output signal vector of the clipper is further denoted as:

[0136]

[0137] Step 3: After clipping and outputting all the symbols in a frame using the method of Step 2, pass them through a randomly generated channel, and add Gaussian white noise with a variance of The signal-to-noise power ratio (SNR) is expressed in decibels as Remove the CP from the received signal and perform serial-to-parallel conversion to obtain the symbol vectors y0,..., y 14 , and convert the model expressions of y0,..., y 14 into a form where the sparse channel in the DD domain and the clipping amplitudes are linear and piecewise linear functions respectively;

[0138] Step 3.A: For p = 1,..., P, randomly generate the complex gains of each path of the channel corresponding to the pilot symbol block according to the known channel fading parameter statistical model The normalized multipath delay l p and the normalized Doppler shift o p , and then calculate the complex gains of each path of the channel corresponding to the data symbol blocks of k = 1,..., 14 according to the relationship between the phases of each path and the Doppler shift After clipping all the symbols in a frame using the method of Step 4, pass them through a randomly generated channel, and add Gaussian white noise. Remove the CP from the received signal and perform serial-to-parallel conversion to obtain the symbol vectors y0,..., y 14 k where y k is expressed in the following form:

[0139] y k = H k z k + v k (50)

[0140] where H k is the equivalent channel response in the time-delay domain, and the specific calculation method is:

[0141]

[0142] where Π is a permutation matrix, denoted as:

[0143]

[0144] Δ p is a diagonal matrix, expressed as:

[0145]

[0146] where

[0147] Step 3.B: Reconstruct the two-dimensional lattice in the DD domain with a delay dimension of G τ and a Doppler dimension of G ν , where G τ > l P , G ν > o P . Then the channel response in the DD domain is re-expressed at this lattice point as:

[0148]

[0149] where is the complex gain of the path with a delay of m lattice units and a Doppler shift of n lattice units, and δ(·) is the Dirac δ function; the channel matrix in the time-delay domain is re-expressed in the following form:

[0150]

[0151] where Π is the same permutation matrix as in equation (51), and Δ m,n is expressed as:

[0152]

[0153] where In equation (55), only P out of all 128 are non-zero. Extract all the into a sparse vector h k , and equation (50) is re-expressed as:

[0154]

[0155] where W is a constant matrix, expressed as:

[0156] W = [Π 0 Δ 0,0 ,..., Π 0 Δ 0,7 , Π 1 Δ 1,0 ,..., Π 15 Δ 15,7 (58)

[0157] h k is a column vector containing the complex gains of each path at the DD domain lattice points, expressed as:

[0158]

[0159] Let Then when s k is constant, Φ(s k , A) is piecewise linear with respect to A. (56) is remodelled as:

[0160] y k = Φ(s k , A)h k + v k (60)

[0161] Step 4: Extract the pilot block y0 required for channel estimation, input the known transmitted unclipped pilot sequence s0, the maximum number of iterations, and the estimation accuracy, calculate the values of each intermediate variable required for channel estimation, initialize the hyperparameter matrix and the clipping amplitude, and set the iteration number i = 1.

[0162] Extract the pilot block y0, input the known transmitted unclipped pilot sequence s0, the maximum number of iterations i max = 50, and the estimation accuracy ∈ = 10 -5 . Let denote the pilot amplitude vector sorted from small to large, be the q-th non-repeated value in . The total number of possible values is finite, denoted as Q; P s is the sorting matrix; then the sorted pilot sequence, binary vector, and phase vector are respectively denoted as and Furthermore, note that is a vector with multiple consecutive elements 0 in the front and all elements 1 in the back. Denote the possible value of the q-th as Initialize the hyperparameter matrix Γ representing the variance of the sparse channel vector h0 (0) = I 128 ; the initial clipping amplitude A (0) = max(a0), and the iteration number i = 1.

[0163] Step 5: Update the posterior mean μ (i-1) and variance Σ (i-1) of the sparse channel vector h0 with respect to A (i) and γ (i) in the i-th iteration;

[0164] The posterior distribution of h0 is expressed as where

[0165]

[0166] Step 6: Let \(h_0 = \mu\) (i) , update the estimation result \(A\) of the clipping amplitude in the \(i\)-th iteration (i) and the hyperparameter matrix \(\Gamma\) (i) , determine whether the iteration stop condition is satisfied. If the number of iterations reaches the maximum (\(i\geq50\)) or the convergence condition is satisfied, then stop the iteration and output the initial pilot channel estimation result and the estimation result of the clipping amplitude as well as the hyperparameter matrix \(\Gamma\) SBL \(=\Gamma\) (i) ; otherwise, let \(i = i + 1\) and return to Step 5;

[0167] Step 6.A: Let \(h_0 = \mu\) (i) , calculate \(A\) that maximizes the target log-likelihood ratio (i) and \(\Gamma\) (i) , that is

[0168]

[0169] where

[0170]

[0171] For the intervals corresponding to \(q = 1,...,Q\), that is in the case of, remove the terms independent of \(A\), and the objective function is transformed into

[0172]

[0173] where Calculate its extreme point with respect to \(A\). The specific method is as follows:

[0174]

[0175] Compare to obtain the optimal value in the interval:

[0176]

[0177] Compare the extremes of all intervals and take the minimum to obtain the optimal \(A\) (i) value:

[0178]

[0179] Step 6.B: \(\gamma\) that maximizes the target log-likelihood ratio (i) The calculation method is specifically as follows:

[0180]

[0181] where is a vector composed of all diagonal elements of Σ (i) . Finally, let Γ (i) = diag(γ (i) ). When the number of iterations reaches the maximum (i ≥ i max ) or satisfies the convergence condition , stop the iteration and output the initial channel estimation result of the pilot and the estimation result of the clipping amplitude as well as the hyperparameter matrix Γ SBL = Γ (i) ; otherwise, continue the iteration, let i = i + 1, and return to step 5

[0182] Step 7: Extract data blocks y1,..., y 14 , input the maximum number of iterations j max = 4 and the result of pilot estimation in step 6, and initialize the tracking result Initial decision symbol Let the number of iterations j = 1, and then let the posterior channel mean and variance be and

[0183] Step 8: In the jth iteration, use the DD-domain channel tracking method based on Kalman filtering to update the channel tracking result of the data block

[0184] Step 8.A: Channel prediction to obtain the prior channel mean and variance corresponding to each symbol block for k = 1,..., 14

[0185] h k|k-1 = Th k-1|k-1 (70)

[0186] P k|k-1 = TP k-1|k-1 T H (71)

[0187] where h k-1|k-1 and P k-1|k-1 are the posterior mean and variance of the previous block respectively. T is the transition matrix that relates the channel phases of the (k - 1)th block and the kth block

[0188]

[0189] Step 8.B: Filtering, calculate the Kalman gain G k of the current block, the posterior mean and variance, which are specifically expressed as

[0190]

[0191] h k|k= h k|k-1 + G k (y k - E k h k|k-1 ) (74)

[0192]

[0193] where E k is calculated as

[0194]

[0195] Through the above prediction and filtering process, calculate the posterior mean h k|k and variance P k|k .

[0196] Step 8.C: Smoothing, apply the observations of all 14 symbols to each block, expressed as:

[0197] h k-1|14 = T -1 h k|14 (77)

[0198] P k-1|14 = P k|14 (78)

[0199] For k = 1,..., 14, let the tracking result

[0200] Step 9: In the j-th iteration, use the MMSE-DFBE-based clipped OTFS signal detection method as Figure 3 shown to equalize, cancel distortion, make decisions, and provide feedback on the signal, updating the decision result and the feedback signal If the number of iterations reaches the maximum (j ≥ j max ), then output the channel tracking result and the signal detection result Otherwise, continue the iteration, set j = j + 1, and return to Step 8.

[0201] Step 9.A: The equalization part includes a block feedforward equalizer and a block feedback equalizer whose output signal is expressed as:

[0202]

[0203] where the k that minimizes the mean square error between the equalization output and the actual clipped signal z is calculated as:

[0204]

[0205] wherein respectively represent the transmitted signal and the signal power after the previous iteration decision. is the estimated result of their correlation value, and the calculation method is:

[0206]

[0207] where η = 0.7 is a scaling factor introduced to avoid the deterioration of the feedback iteration performance caused by too large an estimated value; according to the estimated and Equation (7), the estimated time-delay domain channel H k ;

[0208] When j = 1, since there is no decision result, so the block feedback equalizer is At this time, the block feedforward equalizer is the same as the linear MMSE block equalizer.

[0209] Step 9.B: Distortion cancellation in the time domain is performed on the equalized signal, and the specific method is:

[0210]

[0211] where represents the normalized cross-correlation value between the clipped distortion signal and the unclipped signal, and represents the distortion part in the clipped distortion signal that is uncorrelated with the unclipped signal, and is calculated according to the previous iteration decision result as:

[0212]

[0213] Step 9.C: The signal after time-domain distortion cancellation is transformed to the DD domain for hard decision, which is expressed as:

[0214]

[0215] Finally, the signal after the decision is transformed back to the time domain to obtain the unclipped signal after the decision, and then the signal is clipped with a soft clipper with an amplitude of to obtain the clipped signal after the decision for subsequent iterative tracking and equalization. This process is specifically expressed as:

[0216]

[0217] When the number of iterations reaches the maximum (j ≥ 4), the iteration stops, and for k = 1,..., 14, the channel tracking result and the signal detection result Otherwise, continue iterating, set j=j+1, and return to step 8.

[0218] This concludes the example process. Table 1 summarizes the parameter settings for the example scenario.

[0219] Table 1 Example scenario parameter settings

[0220] Parameter Parameter setting <![CDATA[Carrier frequency f C > 4 GHz Number of OTFS symbol blocks K per frame 14 Subcarrier bandwidth Δf 15 kHz Number of subcarriers M 32 Number of symbols N per block 32 <![CDATA[CP length N CP > 16 Number of paths P 5 <![CDATA[Number of delayed lattice points G τ > 16 <![CDATA[Doppler grid number G ν > 8

[0221] MATLAB software is used to randomly generate 50,000 frames of transmission signals and simulate the receiving process. The signal peak amplitude is about 9dB, so in these three scenarios, additional backoff of 8dB, 6dB and 4dB is required to make the power amplifier output a distortion-free linear signal. The estimated error and the number of error bits each time are counted to obtain the normalized mean square error (NMSE) and the bit error rate (BER) of the channel and limiting amplitude estimation obtained by different methods under each limiting scenario and SNR. In order to simplify the representation and distinguish it from other methods, the tracking and detection methods of steps 8 and 9 of the present invention are collectively referred to as expectation maximization-based iterative tracking and detection (EM-ITD) methods in the subsequent results.

[0222] The relationship between channel estimation NMSE and SNR is obtained using different methods in three limiting scenarios Figures 4 to 6As shown. Among them, the curves "MMSE-CE" and "MMSE-JE" represent the performance of the existing MMSE channel estimation method and the MMSE channel clipping amplitude joint estimation method based on iterative alternating optimization, respectively; the curves "SBL-CE" and "Linear SBL-CE" represent the performance of the existing SBL channel estimation method under the current scenario of clipping distortion and the output signal of the linear power amplifier, respectively; the curves "SBL-JE" and "EM-ITD" represent the performance of the SBL-based channel and clipping amplitude joint estimation method and the data block-based EM iterative channel tracking and detection method proposed by the present invention, respectively. It can be observed that since the MMSE-based estimation method does not utilize the DD-domain sparsity characteristic of the channel, its estimation error is very high at each signal-to-noise ratio; the error of the SBL-based channel estimation method under clipping distortion first decreases and then increases with the signal-to-noise ratio. This is because the influence of clipping distortion can be equivalent to additional extra noise, and the SBL algorithm only brings in the noise power for iterative calculation and is very sensitive to the accuracy of the noise power. At low signal-to-noise ratios, since the proportion of clipping distortion in the total power of noise plus distortion is small, it can still converge. However, as the signal-to-noise ratio increases, the clipping distortion dominates in the total power, making the error between the noise power brought into the calculation and the actual total power larger and larger, and unable to converge to the correct result; while the joint channel and clipping amplitude estimation method proposed by the present invention uses the clipped pilot in the iterative estimation, greatly reducing the influence of clipping distortion, so its performance is far superior to the existing solutions. In addition, it can also be observed that the iterative channel tracking method based on Kalman filtering proposed by the present invention can utilize the effective observations of all data blocks to further reduce the influence of noise. For the three scenarios with clipping amplitudes of 1 dB, 3 dB, and 5 dB, the SNR required for the iterative channel tracking method proposed by the present invention to reach NMSE of 10 -3 is 5 dB, 6 dB, and 8 dB lower than that of the pilot block joint estimation method, respectively.

[0223] The relationship between NMSE and SNR of the clipping amplitude estimation obtained by different methods under three clipping scenarios is as Figures 7 to 9 shown. It can be observed that the SBL-based joint estimation performance proposed by the present invention is superior to the MMSE joint estimation based on alternating optimization. Both adopt the segmented clipping amplitude estimation method proposed by the present invention, and the channel estimation result used by the SBL-based joint estimation in the iterative process is more reliable, so the performance is better.

[0224] The relationship between BER and SNR obtained by different pilot channel estimation and detection methods under three clipping scenarios is as Figures 10 to 12As shown. Among them, the curves "SBL-CE+LBE" and "SBL-JE+LBE" respectively represent the results of using the existing SBL channel estimation method and the SBL joint estimation proposed in the present invention, and the signal detection results of directly using linear MMSE equalization without channel tracking; the curves "EM-ITD+LBE" and "EM-ITD+DFBE" represent the results of using the iterative channel tracking and signal detection method based on expectation maximization proposed in the present invention, and respectively adopt linear equalization and the decision feedback block equalization proposed in the present invention during the iterative process; the curves "known channel & clipping amplitude" and "linear known channel" respectively represent the results of assuming known channel and distortion characteristics and using the decision feedback block equalization proposed in the present invention under the current scenario of clipping distortion and linear power amplifier output signal. It can be observed that if the channel obtained by using the existing SBL channel estimation method is used for subsequent signal detection, there will be a very high BER, while if the channel and clipping amplitude obtained by using the joint estimation proposed in the present invention are used for detection, the BER is greatly reduced. Therefore, it is very necessary to estimate the clipping amplitude. In addition, it can also be observed that the joint channel tracking and detection method based on expectation maximization of the present invention can further reduce the BER. Among them, using the decision feedback block equalization method of the present invention can better eliminate the interference between symbols by using the feedback result. Therefore, the BER is lower than that of linear equalization and is close to the BER when the channel and clipping amplitude are known, which verifies the superiority of the iterative tracking and detection method proposed in the present invention again. On the other hand, the BER obtained by using the receiver proposed in the present invention in three scenarios reaches 10 -4 The required SNR is about 4 dB, 2.5 dB and 0.5 dB higher than that assumed for the output of a linear distortionless power amplifier respectively, and is lower than the additional back-off required to make the power amplifier output linear under the corresponding clipping amplitude. Therefore, the clipping OTFS receiver of the present invention can support the transmitting device to work at a lower back-off, thereby improving the efficiency of the power amplifier.

[0225] The above specific description further details the purpose, technical solution and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A receiving method for amplitude-limited orthogonal time-frequency space modulation, characterized in that: including the following steps, Step 1: Generate K OTFS data symbol blocks s1,..., s K and add a cyclic prefix (CP), and add a pilot symbol block s0 in front to form a transmitted signal frame; Step 2: Pass all symbol blocks in the transmitted signal frame generated in Step 1 through a soft limiter with a limiting amplitude of A to obtain symbol vectors z0,..., z k ; Step 3: After amplitude-limiting and outputting all symbols in a frame using the method in Step 2, pass them through a randomly generated channel and add Gaussian white noise. Remove the CP from the received signal and perform serial-to-parallel conversion to obtain symbol vectors y0,..., y k , and convert the model expressions of y0,..., y k into forms where the DD-domain sparse channel and the amplitude-limiting amplitudes are linear and piecewise-linear functions, respectively; Step 4: Extract the pilot block y0 required for channel estimation, input the known transmitted unclipped pilot sequence s0, the maximum number of iterations i max , and the estimation accuracy ∈, calculate the values of the intermediate variables required for channel estimation, and initialize the clipping amplitude and the hyperparameter matrix; Step 5: Update the posterior mean μ (i-1) and γ (i-1) of the sparse channel vector h0 in the i-th iteration with respect to A (i) and the variance Σ (i) values; Step 6: Let \(h_0 = \mu\) (i) , update the estimation result \(A\) of the clipping amplitude in the \(i\)-th iteration (i) and the hyperparameter matrix \(\Gamma\) (i) , determine whether the iteration stop condition is satisfied. If satisfied, output the initial channel estimation result of the pilot and the estimation result of the clipping amplitude as well as the hyperparameter matrix \(\Gamma\) SBL \(=\Gamma\) (i) ; otherwise, let \(i = i + 1\) and return to Step 5 Step 7: Extract data blocks y1,..., y K , input the maximum number of iterations j max and the result of pilot estimation in Step 6 to initialize the tracking result Initial decision symbol Let the number of iterations j = 1, and then let the posterior channel mean and variance be respectively and Step 8: In the j-th iteration, update the channel tracking result of the data block using the DD-domain channel tracking method based on Kalman filtering Step 9: In the j-th iteration, use the clipping OTFS signal detection method based on minimum mean square error-decision feedback block-wise equalization (MMSE-DFBE) to equalize, eliminate distortion, make decisions, and provide feedback for the signal, and update the decision result. and the feedback signal If the number of iterations reaches the maximum, output the channel tracking result and the signal detection result Otherwise, continue the iteration, set j = j + 1, and return to Step 8.

2. The receiving method of the limited-amplitude orthogonal time-frequency space modulation according to claim 1, characterized in that: The implementation method of step 1 is,[[]] Randomly generate a sequence of K consecutive symbols of length MN and map them to the lattice points in the M×N DD domain to generate the OTFS symbol block vectors X1,..., X k ; First, pass each symbol through the inverse symplectic finite Fourier transform (ISFFT) to obtain the time-frequency domain symbol block S k , which is expressed as: where F M is an M-dimensional discrete Fourier transform (DFT) matrix, is an N-dimensional inverse discrete Fourier transform (IDFT) matrix; and then through the Heisenberg transform, the time-domain signal s k is obtained; the whole process is specifically expressed as: wherein is the vectorized form of X k ; and is the transmit pulse shaping diagonal matrix Obtain time-domain symbol blocks s1,..., s K , split the amplitude and phase and represent them in the following form: where a k = [a k (1),..., a k (MN)] T and are column vectors representing amplitude and phase respectively; after adding the pilot block s0 and the cyclic prefix (CP), a transmission signal frame is formed.

3. The receiving method of the limited amplitude orthogonal time-frequency space modulation according to claim 1, characterized in that: The implementation method of step 2 is,[[]] Introduce a binary column vector c k = [c k (1),..., c k (MN)] T , where c k (n) is used to represent whether the n-th sampling point of s k is clipped, expressed as: Then the output signal vector of the limiter is further expressed as:

4. The receiving method of amplitude-limited orthogonal time-frequency space modulation according to claim 1, wherein: The implementation method of step 3 is,[[]] Step 3.A: For p = 1, ..., P, randomly generate the complex gains of each path of the channel corresponding to the pilot symbol block according to the known channel fading parameter statistical model Normalized multipath delay l p and normalized Doppler shift o p , and then calculate the complex gains of each path of the channel corresponding to the data symbol blocks k = 1, ..., K according to the relationship between the phases of each path and the Doppler shift Limit all the symbols in a frame using the method in Step 4, pass them through the randomly generated channel, and add a Gaussian white noise vector v with variance . Remove the CP from the received signal and perform serial-to-parallel conversion to obtain symbol vectors y0, ..., y k , where y k is expressed in the following form: k ​ y k = H k z k + v k (6) where H k is the equivalent channel response in the time-delay domain, and the specific calculation method is as follows: where Π is a permutation matrix, expressed as: Δ p is a diagonal matrix, expressed as: Among them Step 3.B: Reconstruct the delay dimension to G τ , and the Doppler dimension to G ν of the two-dimensional lattice points in the DD domain, where G τ > l P , G ν > o P ; then the DD domain channel response is re-expressed at this lattice point as: where is the complex gain of a path with a delay of m grid units and a Doppler shift of n grid units, and δ(·) is the Dirac delta function; the channel matrix in the time-delay domain is re-expressed in the following form: where Π is the same permutation matrix as in Equation (7), and Δ m,n is expressed as: Among them In formula (11), all G τ G ν pieces Only P of them are non-zero. Extract all into a sparse vector h k In this case, formula (6) is re-expressed as: where W is a constant matrix, expressed as: h k is a column vector containing the complex gains of each path on the DD domain lattice points, expressed as: Let Then when s k is constant, Φ(s k , A) is piecewise linear with respect to A; (13) is remodelled as: y k = Φ(s k , A)h k + v k (16) 5. The receiving method of limited amplitude orthogonal time-frequency space modulation according to claim 1, wherein: The implementation method of step 4 is,[[]] Extract the pilot block y0, input the known transmitted unclipped pilot sequence s0, and the maximum number of iterations i max , and the estimation accuracy ∈, and let denote the pilot amplitude vector sorted from small to large, be the q-th non-repeated value among The total number of possible values is finite, denoted as Q, P s is the sorting matrix; then the sorted pilot sequence, binary vector, and phase vector are respectively denoted as and Furthermore, note that is a vector with consecutive elements 0 in the front and all 1 in the back. Denote the possible value of the q-th as Initialize the hyperparameter matrix representing the variance of the sparse channel vector h0 The initial clipping amplitude A (0) = max(a0), and the number of iterations i = 1.

6. The receiving method of amplitude-limited orthogonal time-frequency space modulation according to claim 1, wherein: In step 5, the posterior distribution of h0 is expressed as where 7. The receiving method of amplitude-limited orthogonal time-frequency space modulation according to claim 1, characterized in that: The implementation method of step 6 is,[[]] Step 6.A: Let h0 = μ (i) , and the optimization objective is to calculate A (i) and Γ (i) that maximize the target log-likelihood ratio, i.e., where For the intervals corresponding to q = 1,..., Q, that is in the case of, removing the terms unrelated to A, the objective function is transformed into Among them Calculate its extreme points with respect to A. The specific method is as follows: Compare to obtain the optimal value within the interval: Compare the extreme values of all intervals and take the minimum to obtain the optimal A (i) Value: Step 6.B: γ that maximizes the target log-likelihood ratio (i) The specific calculation method is as follows: Among them is a vector composed of all diagonal elements of Σ (i) ; finally, let Γ (i) = diag(γ (i) ). When the number of iterations reaches the maximum (i ≥ i max ) or satisfies the convergence condition then stop the iteration and output the initial pilot channel estimation result and the estimation result of the clipping amplitude as well as the hyperparameter matrix Γ SBL = Γ (i) ; otherwise, continue the iteration, let i = i + 1, and return to step 5.

8. The receiving method of limited-amplitude orthogonal time-frequency space modulation according to claim 1, characterized in that: The implementation method of step 8 is,[[]] Step 8.A: Channel prediction to obtain the prior channel means and variances for each symbol block corresponding to k = 1,..., K: h k|k-1 = Th k-1|k-1 (26) P k|k-1 = TP k-1|k-1 T H (27) where h k-1|k-1 and P k-1|k-1 are the posterior mean and variance of the previous block, respectively; T is the transition matrix that relates the channel phases of the (k - 1)-th block and the k-th block: Step 8.B: Filtering, calculating the Kalman gain G of the current block k , the posterior mean and variance, which are specifically expressed as: h k|k = h k|k-1 + G k (y k - E k h k|k-1 ) (30) Among which E k The calculation method is Through the above prediction and filtering processes, the posterior mean h is calculated up to k = K k|k and the variance P k|k ; Step 8.C: Smoothing, applying the observations of all K symbols to each block, expressed as: h k-1|K = T -1 h k|K (33) P k-1|K = P k|K (34) For k = 1, ..., K, let the tracking result 9. The receiving method of the limited-amplitude orthogonal time-frequency space modulation according to claim 1, characterized in that: The implementation method of step 9 is,[[]] Step 9.A: The equalization section includes a block feedforward equalizer and a block feedback equalizer The output signal thereof is expressed as: where the mean square error between the equalized output and the actual clipped signal z k is minimized The calculation method is as follows: wherein respectively represent the transmitted signal and the signal power after the previous iteration decision; is the estimated result of their correlation value, and the calculation method is: where η is a scaling factor introduced to avoid the deterioration of the feedback iteration performance caused by an excessively large estimated value; according to the estimated and the formula (7), calculate the estimated time-delay domain channel H ; k ; When j = 1, since there is no decision result, so The block feedback equalizer is At this time, the block feedforward equalizer is the same as the linear MMSE block equalizer; Step 9.B: Eliminate the time-domain distortion of the equalized signal, and the specific method is: where represents the normalized cross-correlation value between the clipped distortion signal and the unclipped signal, and represents the distortion part in the clipped distortion signal that is uncorrelated with the unclipped signal, and is calculated according to the previous iteration decision result as: Step 9.C: Transform the time-domain distortion-eliminated signal to the DD domain for hard decision, expressed as: The signal after the final decision is transformed back to the time domain to obtain the unclipped signal after the decision. Then, a soft limiter with an amplitude of is used to clip the signal to obtain the clipped signal after the decision, which is used for subsequent iterative tracking and equalization. This process is specifically expressed as: Stop the iteration when the number of iterations reaches the maximum (j≥j max ), and for k = 1,..., K, output the channel tracking result and the signal detection result Otherwise, continue the iteration, set j = j + 1, and return to step 8.

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