A MIMO-OTFS system signal detection method based on least square minimum residual preprocessing and residual injection

Abstract

The application discloses a kind of MIMO-OTFS system signal detection methods based on least square minimum residual preprocessing and residual injection, belong to wireless communication technical field.The method includes: obtaining received signal vector, time delay-Doppler domain equivalent channel matrix and noise power;With and as input, least square minimum residual iteration is solved, and initial estimation vector and residual vector are obtained;According to residual energy ratio, injection factor is calculated;Enhanced observation vector and extended channel matrix are constructed;Based on residual correction noise precision initial value;With and as input, statistical quantity is used as priori initial value to execute unit approximate message passing iterative detection.The application accelerates iterative convergence and improves detection precision by high-quality initial estimation and residual injection mechanism, effectively suppresses residual interference in fractional Doppler channel.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a signal detection method suitable for multiple-input multiple-output orthogonal time-frequency spatial systems. Background Technology

[0002] In high-speed mobile communication scenarios, wireless channels exhibit time-varying and biselective characteristics, and orthogonal frequency division multiplexing (OFDM) modulation suffers from bit error rate degradation due to inter-carrier interference. Orthogonal time-frequency modulation (OTF) transforms the time-varying channel into a quasi-static sparse representation by placing information symbols in the delay-Doppler domain. Combining this modulation with multiple-input multiple-output (MIMO) technology can further improve spectral efficiency and resistance to channel fading.

[0003] In multiple-input multiple-output orthogonal time-frequency spatial systems, signal detection at the receiver requires handling inter-antenna spatial multiplexing interference and inter-symbol interference caused by fractional Doppler shift. The unit approximate message passing algorithm, by performing a unitary transformation on the channel matrix, improves the problem of insufficient adaptability of approximate message passing algorithms to general matrices and has been applied to signal detection in orthogonal time-frequency spatial systems.

[0004] In practical applications, this algorithm suffers from the problem that the convergence speed is affected by the quality of the initial estimate. The zero-mean initialization strategy cannot provide an effective starting point for iteration under low signal-to-noise ratio conditions, leading to an increase in the number of iterations required for convergence. The fractional Doppler offset term causes the channel matrix to lose its cyclic sparse structure, and residual interference between antennas and symbols gradually accumulates during iteration, causing error propagation when the fading differences between antenna paths are significant. Existing schemes using preprocessing-assisted detection directly use the coarse estimation result as the initial value for iteration, failing to utilize the residual vector generated in the preprocessing stage. The unrecovered signal energy and interference components contained in the residual are not effectively utilized. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a signal detection method that balances convergence speed and detection accuracy, addressing the issues of inaccurate initial estimation, slow convergence, and residual interference propagation in existing unit approximation message passing detection methods in multi-input multi-output orthogonal time-frequency spatial systems under fractional Doppler channels.

[0006] The technical solution is as follows: A signal detection method for a MIMO-OTFS system based on least squares minimum residual preprocessing and residual injection, such as... Figure 1 As shown, the specific steps include:

[0007] Step S1: Obtain the received signal vector, equivalent channel matrix, and noise power estimate. The specific operation is as follows:

[0008] Step S1-1: Obtain the time-domain received signals from each receiving antenna. In a multiple-input multiple-output orthogonal time-frequency space system, configure the transmitter... Antenna, receiver configuration Each antenna has q-th antenna. The transmitter maps the time-delay-Doppler domain symbols corresponding to each antenna to the time-frequency domain using an inverse symplectic finite Fourier transform, and then generates the time-domain transmitted signal using a Heisenberg transform. After transmission through a time-varying multipath channel, the time-domain received signal on the q-th receiving antenna is... It is composed of signals transmitted by each transmitting antenna, which are fading and superimposed through the corresponding channel, and then supplemented with additive white Gaussian noise.

[0009] Step S1-2: Perform matched filtering and symplectic finite Fourier transform on the time-domain received signal to obtain the time-delay-Doppler domain received symbol, and then process the time-domain received signal of the q-th receiving antenna. By sequentially performing the Wigner transform and the symplectic finite Fourier transform, the signal is converted from the time domain to the time-delay-Doppler domain, yielding the time-delay-Doppler domain received symbol matrix corresponding to the antenna. The matrix dimension is M×N, where M is the number of subcarriers and N is the number of symbols per frame. This process can be viewed as the inverse operation of the transmitter's inverse symplectic finite Fourier transform and Heisenberg transform;

[0010] Step S1-3: Stack the delay-Doppler domain symbols of all receiving antennas column-wise to form the received signal vector. ,Will Delay-Doppler domain symbol matrix of the root receiving antenna Stretch each column into a vector of length M·N, then... The vectors are concatenated vertically to form the received signal vector y, which has dimensions of . ;

[0011] Step S1-4: Obtain the time-delay-Doppler domain equivalent channel matrix Based on the channel impulse response parameters, a time-delay-Doppler domain channel submatrix is ​​constructed between the p-th transmit antenna and the q-th receive antenna. It is represented by the product of a cyclic delay matrix, an integer Doppler diagonal matrix, and a fractional Doppler matrix. The sub-matrices corresponding to all transmit and receive antenna pairs are arranged into blocks by transmit antenna index (column blocks) and blocks by receive antenna index (row blocks), and assembled into a block-structured MIMO-OTFS equivalent channel matrix. Its dimensions are The presence of the fractional Doppler offset term causes the matrix to lose its cyclic sparse structure;

[0012] Step S1-5: Obtain the noise variance through the noise power estimation module. The receiver noise power estimation module performs statistical analysis on the pilot symbols or silent period signals in the received signal to calculate the power estimate of additive white Gaussian noise. This serves as the noise parameter input for subsequent detection algorithms.

[0013] Step S2: Using the received signal vector and the channel matrix Using the input as input, perform least squares minimum residual iteration to obtain the initial estimation vector, and calculate the residual vector. The least squares minimum residual algorithm obtains an approximate solution in the Krylov subspace by minimizing the residual norm. Its monotonically decreasing residual sequence is suitable for solving ill-conditioned channel matrices. This step specifically includes the following sub-steps:

[0014] Step S2-1: Initialize the iteration count k=0, and initialize the solution vector. Zero vector, residual vector For the channel matrix The first column is normalized to obtain the initial basis vectors. ;

[0015] Step S2-2: For Perform the Golub-Kahan bidiagonalization process to generate orthogonal basis vectors sequentially. and , where K is the preset maximum number of preprocessing iterations;

[0016] Step S2-3: Perform recursive QR decomposition on the constructed double diagonal matrix to solve for the intermediate variables;

[0017] Step S2-4: Update the solution vector Make the residual norm 2 of the current iteration step It reaches its minimum in the generated Krylov subspace;

[0018] Step S2-5: Terminate the iteration when the residual norm is less than the preset tolerance or the maximum number of iterations K is reached, and output the initial estimation vector. And calculate the residual vector. .

[0019] Step S3: Based on the residual vector Calculate the injection factor This includes the following sub-steps:

[0020] Step S3-1: Calculate the received signal vector Total energy For the received signal vector The total energy of the received signal is obtained by summing the squares of the moduli of each component. This energy value reflects the overall power level of the signal observed at the receiver.

[0021] Step S3-2: Calculate the residual vector energy The residual vector obtained in step S2 The residual energy is obtained by summing the squares of the moduli of each component. Residual vector Its energy representation, after least squares minimum residual preprocessing, has not yet been included in the initial estimated vector. The power of the remaining signal components as explained;

[0022] Step S3-3: Calculate the injection factor based on the energy ratio Injection factor Determine using the following formula:

[0023] .because and Injection factor The range of values ​​is When the accuracy of least squares minimum residual estimation is high, the residual energy... Much less than the total energy of the received signal , Approaching 1; when the estimation accuracy is low, and comparable, The corresponding decrease. Injection factor. The adaptive value of the value enables the subsequent construction of enhanced observation vectors to dynamically adjust the weights based on the reliability of the preprocessing estimation.

[0024] Step S4: Using the initial estimation vector The injection factor and the channel matrix Constructing enhanced observation vectors This includes the following sub-steps:

[0025] Step S4-1: Calculate the channel response weighting term of the initial estimation vector, and then apply the initial estimation vector... Left multiplying the channel matrix The estimated observation vector under noise-free conditions is obtained. This vector represents the signal components that the receiver should observe after the channel effect, assuming the initial estimate is completely accurate.

[0026] Step S4-2: Apply injection weights to the estimated observation vector and calculate the weighting coefficients. Combine it with the estimated observation vector Multiplying them together yields the weighted observation term. Weighting coefficients The introduction of this factor makes the contribution of the weighted observation term to the enhanced observation vector subject to the injection factor. control;

[0027] Step S4-3: Vertically stack the original received signal vector with the weighted observation term, and stack the original received signal vector... With weighted observations Vertical stitching along the row direction to construct an enhanced observation vector :

[0028] ;

[0029] Step S4-4: Construct an extended channel matrix that matches the enhanced observation vector, and combine the original channel matrix... Vertically stacked with the channel matrices weighted by the same weights, an extended channel matrix is ​​formed. :

[0030] .

[0031] Step S5: Based on the residual vector Correcting the initial value of noise accuracy This includes the following sub-steps:

[0032] Step S5-1: Determine the dimension of the received signal vector and obtain the received signal vector. The dimension is the product of the total number of transmitted symbols and the number of received antennas;

[0033] Step S5-2: Calculate the residual average energy, and use the residual energy obtained in step S3-2. Divide by the dimension of the received signal vector The residual average energy is obtained. This value reflects the average residual signal power per observation dimension that was not explained by the initial estimate;

[0034] Step S5-3: Construct an equivalent noise variance, converting the original noise variance... With residual average energy Add them together to obtain the equivalent noise variance. After a finite number of least squares minimum residual iterations, the residual vector still contains unrecovered signal energy. If we directly use... As noise parameters in subsequent message passing, they will cause the algorithm to over-rely on the accuracy of observations, thereby leading to excessively large iterative update step sizes or deviations in the convergence direction.

[0035] Step S5-4: Calculate the initial value of the corrected noise accuracy. Noise accuracy is defined as the reciprocal of the noise variance. Take the reciprocal of the equivalent noise variance: .

[0036] Step S6: Using the enhanced observation vector The extended channel matrix and the corrected noise accuracy The input is used to perform approximate message-passing iterative detection by the execution unit, and the output is the final detected symbol.

[0037] This step uses the statistics of each component of the least squares minimum residual estimation vector as the initial values ​​of the prior mean and prior variance to initiate the message passing iteration. A single iteration of the unit approximation message passing includes the following sub-steps:

[0038] Step S6-1: Based on the current prior mean and prior variance, calculate the predicted mean and predicted variance of the noiseless observation estimate;

[0039] Step S6-2: Calculate the observation residuals based on the difference between the enhanced observation vector and the predicted observation mean, and update the posterior distribution of the intermediate variables in combination with the corrected noise accuracy;

[0040] Step S6-3: Using the singular value decomposition results of the channel matrix, perform scalar message passing in the unitary transform domain and calculate the posterior mean and posterior variance;

[0041] Step S6-4: Combine the set of modulation symbol constellations to perform posterior probability mapping, and output the symbol decision for the current iteration and the external information for the next iteration.

[0042] Repeat the above sub-steps until the preset iteration stop condition is met, and output the final detection symbol.

[0043] Through the above steps, least squares minimum residual preprocessing provides a physically meaningful non-zero initial estimate for subsequent iterations, the residual injection mechanism reconstructs unrecovered signal components into enhanced observations, and noise accuracy correction provides more reasonable statistical assumptions in the early stages of iteration. The synergistic effect of these three factors enables the unit approximate message passing to achieve accelerated convergence and residual interference suppression in the fractional Doppler channel. Attached Figure Description

[0044] Figure 1 This is a flowchart of the detection method of the present invention;

[0045] Figure 2 Block diagram of MIMO-OTFS system;

[0046] Figure 3 This is a schematic diagram comparing the bit error rate performance under different MIMO configurations in an embodiment of the present invention;

[0047] Figure 4 This is a schematic diagram comparing the number of iterations to convergence in an embodiment of the present invention; Detailed Implementation

[0048] The present invention will be further described in detail below with reference to specific embodiments. This embodiment provides a signal detection process applied to a multi-input multi-output orthogonal time-frequency spatial system, with a number of transmitting antennas. Number of receiving antennas , the number of subcarriers Number of symbols per frame The modulation method uses quaternary quadrature amplitude modulation, and the constellation symbol set... The channel model adopts the extended vehicle channel model, which includes... Multipath propagation, maximum Doppler frequency shift determined by moving speed Decision, carrier frequency Subcarrier spacing .

[0049] Step S1: Obtain the received signal vector, equivalent channel matrix, and noise power estimate.

[0050] Step S1-1: Obtain the time-domain received signal from each receiving antenna. For example... Figure 2 As shown, the transmitter will The time-domain transmission signal is generated by the inverse symplectic finite Fourier transform and Heisenberg transform of the path delay-Doppler domain transmission symbol matrix. After transmission through the extended vehicle channel, the th... Time-domain received signal on the root receiving antenna It consists of two transmitted signals that have been fading and superimposed through their corresponding channels, with the addition of additive white Gaussian noise.

[0051] Step S1-2: Perform matched filtering and symplectic finite Fourier transform on the time-domain received signal to obtain the time-delay-Doppler domain received symbol. For the... root antenna By sequentially performing the Wigner transform and the symplectic finite Fourier transform, the time-delay-Doppler domain received symbol matrix is ​​obtained. ,in , .

[0052] Step S1-3: Stack the delay-Doppler domain symbols of all receiving antennas column-wise to form the received signal vector. .Will and Stretch each column to a length of The vector is then concatenated perpendicularly to obtain the received signal vector. .

[0053] Step S1-4: Obtain the time-delay-Doppler domain equivalent channel matrix Based on the extended vehicle channel parameters, construct the first... root transmitting antenna to the first Channel submatrix between root receiving antennas Its expression is:

[0054] .

[0055] in For the first The fading coefficient of the path, For delay index, Integer Doppler index, This is the fractional Doppler offset. It is a cyclic delay matrix. It is an integer Doppler diagonal matrix. This is a fractional Doppler matrix. Assembling all submatrices into a block-structured matrix yields... .

[0056] Step S1-5: Obtain the noise variance through the noise power estimation module. The receiver statistically analyzes the silent periods in the received signal to obtain an estimate of the power of the additive white Gaussian noise. In this embodiment, the signal-to-noise ratio range is set to... to ,correspond .

[0057] Step S2: Using the received signal vector and channel matrix Using the input as input, perform least squares minimum residual iteration to obtain the initial estimated vector. And calculate the residual vector. .

[0058] Step S2-1: Initialization. Set the maximum number of iterations. tolerance Iteration counting Initial solution vector residual vector Calculate the initial basis vectors:

[0059] .

[0060] Step S2-2: For Perform the Golub-Kahan bidiagonalization process:

[0061] .

[0062] Step S2-3: For the... , The constructed double-diagonal matrix is ​​used for recursive QR decomposition, and the intermediate variables and solution vectors are updated using Givens rotation. .

[0063] Step S2-4: Check convergence conditions If satisfied or Then terminate the iteration and output. If the tolerance is not met but the maximum number of iterations is reached, output... .

[0064] Step S2-5: Calculate the residual vector:

[0065] .

[0066] Step S3: Based on the residual vector Calculate the injection factor .

[0067] Step S3-1: Calculate the total energy of the received signal:

[0068] .

[0069] Step S3-2: Calculate the residual energy:

[0070] .

[0071] Step S3-3: Calculate the injection factor:

[0072]

[0073] Step S4: Using the initial estimated vector Injection factors and channel matrix Constructing enhanced observation vectors .

[0074] Step S4-1: Calculate the estimated observation vector:

[0075] .

[0076] Step S4-2: Calculate the weighted observations:

[0077] .

[0078] Step S4-3: Vertically stack to construct enhanced observation vectors:

[0079] .

[0080] Step S4-4: Construct the extended channel matrix:

[0081]

[0082] Step S5: Based on residual vector Correcting the initial value of noise accuracy .

[0083] Step S5-1: Determine the dimension of the received signal vector .

[0084] Step S5-2: Calculate the residual average energy:

[0085] .

[0086] Step S5-3: Construct the equivalent noise variance. Assume the current signal-to-noise ratio is... The equivalent noise variance is:

[0087] .

[0088] Step S5-4: Calculate the initial value of the corrected noise accuracy:

[0089] .

[0090] Step S6: Enhance the observation vector Extended channel matrix and the corrected noise accuracy The input is used to perform approximate message-passing iterative detection by the execution unit, and the output is the final detected symbol.

[0091] Step S6-1: Prior information initialization. Initialize the prior mean vector... Each component is taken as Corresponding component values; prior variance vector Each component is initialized as follows:

[0092] .

[0093] Step S6-2: Set the maximum number of iterations The convergence threshold is defined as the number of symbols differing between two consecutive hard-decision iterations being less than the total number of symbols. .

[0094] Step S6-3: Execute the unit's approximate message-passing iteration. A single iteration is as follows:

[0095] Calculate the predicted mean and predicted variance:

[0096] ,

[0097] in This indicates element-wise multiplication.

[0098] Calculate the observed residuals and update the intermediate variables:

[0099] ,

[0100] in This indicates element-wise division.

[0101] right Perform singular value decomposition Scalar message passing is performed element-wise in the transform domain to compute the posterior mean. and posterior variance .

[0102] Combining 4QAM constellation collection Calculate the posterior probability of each symbol, output the hard decision of the symbol in the current iteration, and update the extrinsic information for the next iteration. and .

[0103] Step S6-4: Repeat step S6-3 until the convergence condition is met. In this embodiment, after the 4th iteration, the proportion of hard decision difference symbols between two adjacent iterations decreases to Stop the iteration and output the final detected symbol.

[0104] like Figure 3 The simulation results shown indicate that in this embodiment... Antenna configuration, signal-to-noise ratio Under these conditions, the bit error rate of this method reaches Compared to traditional unit-based approximate message passing algorithms (with the same bit error rate), This improves bit error rate performance by approximately an order of magnitude. For example... Figure 4 As shown, this method requires 4 iterations to converge, compared to 8 iterations for the traditional unit approximation message-passing algorithm, thus improving the convergence speed by approximately [percentage missing]. .

[0105] Those skilled in the art will understand that the maximum number of least squares minimum residual iterations in the above embodiments is... Parameters such as the maximum number of iterations for unit approximate message passing and the convergence judgment threshold can be adjusted according to the processing capacity and real-time requirements of the actual system. The injection factor can also be calculated using other mapping functions based on residual statistics, as long as they can characterize the reliability of the estimation in the preprocessing stage. These variations all fall within the protection scope of this invention.

[0106] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A signal detection method for a MIMO-OTFS system based on least squares minimum residual preprocessing and residual injection, characterized in that... Includes the following steps: Step S1: Obtain the received signal vector y and the time-delay-Doppler domain equivalent channel matrix. and noise power estimates ; Step S2: Using the received signal vector y and the channel matrix Using the input as input, perform least squares minimum residual iteration to obtain the initial estimated vector. And calculate the corresponding residual vector. ; Step S3: Based on the residual vector Calculate the injection factor The injection factor Characterizes the relative relationship between residual signal energy and total received signal energy; Step S4: Using the initial estimation vector The injection factor and the channel matrix Constructing enhanced observation vectors , making It includes both the original received signal components and the weighted initial estimated contribution components; Step S5: Based on the residual vector Correcting the initial value of noise accuracy The residual average energy is included in the equivalent noise term; Step S6: Using the enhanced observation vector The channel matrix and the corrected noise accuracy As input, with the initial estimated vector The statistical values ​​of each component are used as the initial values ​​of the prior mean and prior variance. The execution unit performs approximate message passing iterative detection and outputs the final detection symbol.

2. The method according to claim 1, characterized in that... The least squares minimum residual iteration solution in step S2 includes: Step S2-1: Initialize the iteration count Initial solution vector residual vector ,right The first column is normalized to obtain the initial basis vectors. ; Step S2-2: For Perform the Golub-Kahan bidiagonalization process to generate orthogonal basis vectors. and ; Step S2-3: Perform recursive QR decomposition on the constructed double diagonal matrix to solve for the intermediate variables; Step S2-4: Update the solution vector β_k such that the residual L2 norm of the current iteration step is... Minimize within the generated Krylov subspace; Step S2-5: Terminate the iteration when the residual norm is less than the preset tolerance or the maximum number of iterations K is reached, and output the initial estimation vector. .

3. The method according to claim 1, characterized in that... The injection factor mentioned in step S3 The calculation formula is: in This represents the square of the second norm of a vector.

4. The method according to claim 1, characterized in that... The method for constructing the enhanced observation vector ỹ in step S4 is as follows: in It is the square root of the injection factor.

5. The method according to claim 1, characterized in that... The corrected noise accuracy described in step S5 The initial value is set to: in For the received signal vector Dimensions.

6. The method according to claim 1, characterized in that... The single iteration of the unit approximate message passing iterative detection in step S6 includes the following sub-steps: Step S6-1: Calculate the mean and variance of the noiseless observation estimate; Step S6-2: Update the mean and variance of the intermediate variables based on the observed residuals; Step S6-3: Calculate the posterior mean and posterior variance through message passing in the unitary transform domain; Step S6-4: Combine the set of modulation symbol constellations to perform posterior probability mapping, and output the symbol decision for the current iteration and the external information for the next iteration.

7. The method according to claim 2, characterized in that... The maximum number of iterations K ranges from 3 to 10.

8. The method according to claim 1, characterized in that... The time-delay-Doppler domain equivalent channel matrix The channel matrix is ​​a block-structured MIMO-OTFS, and its sub-blocks are composed of the product of a cyclic delay matrix, an integer Doppler diagonal matrix, and a fractional Doppler matrix.

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