Mrc signal detection method with zp-otfs stage-wise weight regulation

Abstract

This invention discloses a staged weight-controlled MRC signal detection method for ZP-OTFS, mainly addressing the problem of high iteration counts in existing MRC detection algorithms due to fixed weight coefficients. The implementation scheme involves: constructing a time-delay-Doppler (DD) domain zero-filling orthogonal time-frequency space ZP-OTFS transmission signal and performing a signal domain transformation to generate a time-domain transmission signal suitable for wireless channel transmission; the receiving end reconstructs the time-domain received signal into a time-delay-time (DT) domain received signal; subsequently, MRC detection based on staged weight control is performed on the DT domain received signal to obtain an estimate of the DD domain transmission signal vector. This invention, by rationally setting weight coefficients at different iteration stages to progressively optimize the MRC detection process, effectively reduces system computational complexity and achieves better bit error rate performance under the same complexity, making it applicable to ZP-OTFS systems in high-speed mobile scenarios.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and specifically relates to a low-complexity MRC signal detection method, which can be used in zero-fill orthogonal time-frequency-space ZP-OTFS systems in high-speed mobile scenarios. Background Technology

[0002] The next-generation wireless communication system, 6G, needs to support various highly mobile scenarios, including low-Earth orbit satellites, high-speed trains, and drones. However, Orthogonal Frequency Division Multiplexing (OFDM) technology, widely used in 4G and 5G, faces severe inter-carrier interference in high-speed mobile environments, making it difficult to provide stable and reliable communication services. Orthogonal Time-Frequency Space-Time (OTFS) modulation, due to its adaptability to rapidly time-varying wireless channels, has become one of the candidate technologies for 6G. Unlike the time-frequency (TF) domain modulation scheme used in OFDM, OTFS modulates information in the delay-Doppler (DD) domain, distributing information symbols across the entire time-frequency resource through a set of two-dimensional transformations, thus achieving full diversity in the time-frequency domain. Furthermore, the rapidly changing channel in the time domain is transformed into a time-invariant sparse channel in the DD domain to combat Doppler shift and achieve reliable communication. ZP-OTFS is a variant of the OTFS system that zeros some symbols at the end of the DD grid, allowing them to participate in the signal processing at both the transmitter and receiver ends of the entire OTFS system. This scheme effectively resists inter-block interference generated during transmission, and compared with other frame structures, the input-output relationship of ZP-OTFS is mathematically simpler and relatively easier to implement. Signal detection algorithms for ZP-OTFS are currently a major research focus.

[0003] Currently, signal detection methods for ZP-OTFS can be broadly categorized into linear and nonlinear approaches. Linear detection methods primarily include the Linear Least Mean Square Error (LMMSE) algorithm. While relatively simple to implement, this method has limited error performance and suffers from high complexity due to the need for matrix inversion calculations. Nonlinear detection algorithms commonly include the Message Passing (MP) algorithm. This algorithm reduces complexity by approximating the interference term using a Gaussian distribution. However, since the MP algorithm relies on sparse channels, complex channel environments negatively impact its performance, especially as the modulation order increases, leading to a more significant increase in complexity.

[0004] In their paper "Low Complexity Iterative RakeDecision Feedback Equalizer for Zero-Padded OTFS Systems" (IEEE Transactions on Vehicular Technology, 2020), Thaj T, Viterbo E, et al., proposed a signal detection method for ZP-OTFS systems based on MRC. This method extracts and combines the received multipath components of transmitted symbols in the DD domain using maximum ratio combining to improve the signal-to-noise ratio (SNR) of the combined signal. Since this algorithm provides better performance than the MP algorithm while reducing complexity, the MRC algorithm has a significant advantage in low-complexity OTFS detection. However, the symbol vector estimation in the time delay-time (DT) domain typically relies on hard decision or soft estimation. For ZP-OTFS systems with high-order quadrature amplitude modulation (QAM), hard decision alone has low reliability and poor bit error rate performance in the initial stage; while soft estimation alone requires multiple iterations to achieve convergence, significantly increasing the system complexity.

[0005] In their paper "General I / O Relations and Low-Complexity Universal MRC Detection for All OTFS Variants" (IEEE Access, 2022), Thaj T, Viterbo E, and others attempted to select the optimal weight coefficients by weighting the soft value estimation and hard decision. Although this method compensated for some of the shortcomings of the above algorithms and improved system performance through iteration, it still required a large number of iterations due to the fixed optimal weight coefficients during the iteration process, which increased the complexity. Summary of the Invention

[0006] This invention aims to address the shortcomings of existing technologies by proposing a staged weight control method for MRC signal detection in ZP-OTFS, thereby accelerating system convergence, reducing computational complexity, and further improving the bit error rate performance of the ZP-OTFS system under the same complexity.

[0007] The technical idea of ​​this invention is to gradually optimize the existing detection algorithm by reasonably introducing different weight factors at different iteration stages of the existing DT domain MRC algorithm, so that the weight selection at each iteration stage is more in line with the needs of the current system state. This reduces the system computational complexity while maintaining the same bit error rate performance as the existing technology, or achieves better bit error rate performance under the same complexity.

[0008] Based on the above ideas, the implementation steps of the present invention include the following:

[0009] (1) Given an M-row, N-column time-delay-Doppler DD domain grid, set the grid ends l max Set ×N symbols to zero, and place M′×N QAM symbols in the first M′ rows of the grid to obtain the two-dimensional DD domain transmitted signal X, where the m-th row of X is the DD domain transmitted signal vector x. m transpose vector Where m is the row index of the DD domain grid, m = 0, 1, ..., M-1, M′ = Ml max , l max This is the maximum delay tap of the channel;

[0010] (2) Perform an inverse symptotic Fourier transform (ISFFT) on the DD domain transmitted signal X to transform it into a time-frequency TF domain transmitted signal X. tf Then, after Heisenberg transformation, a time delay-time (DT) domain signal is generated and transmitted. The m-th row is the DT domain transmitted signal vector. transpose vector Sending signals to the DT domain The signal is vectorized into a column domain to obtain the time-domain transmission signal s, which is then transmitted via a wireless channel.

[0011] (3) After the time-domain transmitted signal s is transmitted through the wireless channel, the time-domain received signal r is obtained at the receiving end. The time-domain received signal r is then reconstructed into a matrix to obtain the DT domain received signal.

[0012] (4) Receiving signals in the DT domain The detection yields the estimated value of the transmitted symbol vector in the DD domain.

[0013] (4a) Initialize the estimated value of the DT domain transmission symbol vector at the start of the iteration. Calculate the initial residual noise and interference RNPI vector And set the maximum number of iterations ite, where 0 N Let N be the zero vector. Sending signals to the DT domain The estimated value of the column vector of the m-th row symbols, where i is the iteration number, i = 0;

[0014] (4b) Calculate the transmitted signal vector x containing the DD domain under different time delays l. m Maximum ratio merge result of RNPI combination of all delay branches Soft value estimation results combined with maximum ratio in is a set of different time delays for P propagation paths in the DD domain, where 0 ≤ l ≤ l max ;

[0015] (4c) Use phased weight coefficient regulation to calculate the estimated value of the transmitted symbol vector in the DT domain at the i-th iteration

[0016] Set an intermediate iteration number mid-ite, making mid-ite slightly less than the maximum iteration number ite, and compare the current iteration number i with the intermediate iteration number mid-ite:

[0017] If i ≤ mid-ite, use the first weight coefficient ω1 to calculate the estimated value of the transmitted symbol vector in the DT domain at the i-th iteration

[0018]

[0019] If mid-ite < i ≤ ite, use the second weight coefficient ω2 to calculate the estimated value of the transmitted symbol vector in the DT domain at the i-th iteration

[0020]

[0021] where is to judge (·) as its constellation point value, and F N is the normalized N-point DFT matrix, and (·) H is the conjugate transpose of the matrix;

[0022] (4d) At different row indices m, and ensuring that the value of l satisfies m + l ≤ M - 1, use each estimated value of the transmitted symbol vector in the DT domain to update the RNPI vector

[0023] (4e) Compare the norm of the RNPI vector at the i-th iteration with the norm of the RNPI vector at the previous iteration as follows:

[0024] If then stop the iteration and output the estimated value of the transmitted symbol vector in the DT domain at the i-th iteration

[0025] Otherwise, execute step (4f);

[0026] (4f) Compare the current iteration number i with the maximum iteration number ite:

[0027] If i < ite, then set i = i + 1 and return to step (4b);

[0028] Otherwise, output the estimated value of the DT field sent symbol vector for the t-th iteration.

[0029] (4g) The receiver transmits the symbol vector estimate from the output DT domain. The transmitted signal vector in the DD domain is recovered.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] Firstly, this invention addresses the limitations of fixed weight coefficients in existing MRC detection methods by introducing different weight coefficients at different iteration stages. This makes the weight selection at each iteration stage more aligned with the system state requirements, and this phased weight coefficient approach is used to regulate the estimation of the sign vector in the DT domain. It not only optimizes the existing MRC detection process, but also reduces the system's computational complexity while maintaining the same bit error rate performance as existing technologies, or achieves better bit error rate performance with the same complexity, especially under high-order QAM modulation.

[0032] Secondly, because the selection strategy of the first weight coefficient ω1 and the second weight coefficient ω2 determined by this invention has strong universality, it can be stably applied under different scenarios and channel conditions, without being limited by specific environments. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the implementation process of the present invention;

[0034] Figure 2 This is a schematic diagram of the DD domain transmitting signal X in this invention;

[0035] Figure 3 This is a flowchart illustrating the implementation of detecting the received signal Y in the DT domain in this invention.

[0036] Figure 4 The graph shows the bit error rate curves of the received signal detected by the present invention and the existing MRC algorithm under the conditions of signal-to-noise ratio range of 20dB to 30dB and modulation mode of 16-QAM, with the maximum number of iterations set to 10, 11 and 14 respectively.

[0037] Figure 5 The graph shows the bit error rate curves of the present invention and the existing MRC algorithm for detecting the received signal under the conditions of signal-to-noise ratio range of 27.5dB to 37.5dB and modulation mode of 64-QAM, with the maximum number of iterations set to 20, 24 and 35 respectively.

[0038] Figure 6This is a comparison of the bit error rate curves of the received signal detected by the present invention, the existing MP algorithm, and the LMMSE linear detection algorithm under the conditions of signal-to-noise ratio range of 20dB to 30dB and modulation mode of 16-QAM, with the maximum number of iterations of the present invention set to 14 and the maximum number of iterations of the existing MP algorithm set to 30. Detailed Implementation

[0039] The specific embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings.

[0040] Reference Figure 1 The implementation steps for this example are as follows:

[0041] Step 1: Construct the delay-Doppler DD domain ZP-OTFS to transmit signal X.

[0042] The zero-filled orthogonal time-frequency space ZP-OTFS signal is a variant of the orthogonal time-frequency space OTFS signal. It participates in the signal processing of the entire OTFS system transmitter and receiver by setting some symbols to zero at the end of the DD domain grid.

[0043] The specific implementation of this step is as follows:

[0044] (1.1) Given an M-row, N-column time-delay-Doppler DD domain grid, set the grid ends l max Set ×N symbols to zero, and place M′×N QAM symbols in the first M′ rows of the grid to obtain the two-dimensional DD domain transmitted signal X, where the m-th row of X is the DD domain transmitted signal vector x. m transpose vector like Figure 2 As shown, where Represents an M×N dimensional matrix space, where N is the total number of symbol blocks, M is the total number of subcarriers, and M′=Ml max , l max is the maximum delay tap of the channel, and m is the row index of the DD domain grid, m = 0, 1, ..., M-1;

[0045] (1.2) Set the duration of transmitting a single symbol block to T, then the total duration of transmitting signal X in the DD domain is NT. In order to satisfy the orthogonality between subcarriers, set the subcarrier interval Δf to 1 / T, then the total bandwidth is MΔf.

[0046] Although the above zeroing operation will reduce the communication rate of the system, these empty symbols can effectively serve as an interleaving guard band for the time-domain transmitted signals, thereby avoiding interference between the received signal blocks in the time domain. At the same time, compared with other OTFS variants, it is the simplest in terms of mathematical expressions for input and output and is easier to implement in practical applications.

[0047] Step 2: Perform signal domain conversion on the DD domain signal X and transmit it through the wireless channel.

[0048] The signal domain conversion refers to performing inverse symmetric Fourier transform (ISFFT), Heisenberg transform, and matrix vectorization sequentially on the DD domain transmitted signal X to obtain a time-domain transmitted signal s suitable for transmission in a wireless channel.

[0049] The specific implementation of this step is as follows:

[0050] (2.1) Perform an inverse symptotic Fourier transform (ISFFT) on the DD domain transmitted signal X to transform it into a time-frequency TF domain transmitted signal X. tf :

[0051]

[0052] in, F M F is the normalized M-point Discrete Fourier Transform (DFT) matrix. N For the normalized N-point DFT matrix, (·) H This is the conjugate transpose of a matrix;

[0053] (2.2) Send signal X to the TF domain tf Perform a Heisenberg transform to generate a time-delay-time (DT) domain transmitted signal.

[0054]

[0055] in, The m-th row is the DT domain transmitted signal vector. transpose vector The Heisenberg transform can be seen as a generalization of the IFFT in OFDM systems. When a rectangular wave of duration T is used, it is equivalent to the IFFT.

[0056] (2.3) Sending signals to the DT domain Perform matrix column vectorization to obtain the time-domain transmitted signal s:

[0057]

[0058] in, Representing an MN×1 dimensional matrix space, vec(·) denotes the matrix column vectorization, and the signal is subsequently transmitted via a wireless channel.

[0059] Step 3: Obtain the time-domain received signal r.

[0060] The time-domain transmitted signal s can be considered as being transmitted on the time-domain equivalent channel H, thus obtaining the time-domain received signal r at the receiving end:

[0061] r = Hs + w

[0062] in, w is the time-domain noise vector.

[0063] P is the number of propagation paths, Δ = diag{α} 0 ,α 1 ,α 2 ,...,α MN-1} is a diagonal matrix, where α = e j2π / MN h q Let l be the channel gain of the q-th path. q and k q These represent the time delay component and Doppler frequency shift of the q-th path, respectively. It is a forward cyclic matrix.

[0064] Step 4, obtain the DT domain received signal

[0065] The receiver performs matrix reconstruction on the time-domain received signal r to obtain the DT-domain received signal.

[0066]

[0067] in,

[0068] It is the inverse operation of vec(·), which reconstructs a vector into an M-row N-column matrix.

[0069] Step 5, receive the signal in the DT domain. Perform detection to obtain the estimated value of the transmitted symbol vector in the DD domain.

[0070] Reference Figure 3 The specific implementation steps of this step include the following:

[0071] (5.1) Initialize the estimated value of the DT domain transmitted symbol vector at the start of the iteration. Set the maximum number of iterations (ite), and calculate the initial residual noise and interference RNPI vector.

[0072]

[0073] Where i is the iteration number, i = 0;

[0074] 0 N It is a zero vector of length N;

[0075] DT domain signal reception The column vector of symbols in the m-th row;

[0076] The discrete Doppler spread vector of the DT domain channel. Let l be the set of different time delays for P propagation paths in the DD domain, 0 ≤ l ≤ l max ;

[0077] Sending signals to the DT domain The estimated value of the column vector of the m-th row symbols, the value of l should ensure that ml≥0;

[0078] (5.2) Calculate the transmitted signal vector x containing the DD domain. m Maximum ratio merge result of RNPI combination of all delay branches

[0079]

[0080] in,(·) * Let denote the complex conjugate matrix. Let denote the Hadamard product, where the value of l should ensure that m + l ≤ M - 1;

[0081] (5.3) Calculate the soft value estimation results of the maximum ratio merging.

[0082]

[0083] in, This represents Hadamard division, where the value of l should ensure that m + l ≤ M - 1;

[0084] (5.4) The estimated value of the DT domain transmitted symbol vector in the i-th iteration is calculated by using phased weight coefficient adjustment.

[0085] (5.4.1) Set an intermediate iteration number mid-ite, such that mid-ite is slightly less than the maximum iteration number ite, and compare the current iteration number i with the intermediate iteration number mid-ite:

[0086] If i ≤ mid-ite, then proceed to step (5.4.2);

[0087] If mid-ite < i ≤ ite, then proceed to step (5.4.3);

[0088] (5.4.2) Calculate the estimated value of the DT domain transmitted symbol vector in the i-th iteration using the first weighting coefficient ω1.

[0089]

[0090] (5.4.3) The estimated value of the DT domain transmitted symbol vector in the i-th iteration is calculated using the second weighting coefficient ω2.

[0091]

[0092] Based on existing MRC algorithms with fixed weight coefficients, it is known that selecting the optimal weight coefficient ω... opt The system achieves the best performance when ω=1, but requires multiple iterations to converge. While choosing ω=1 allows for rapid convergence, the performance is poor. Therefore, this invention uses ω... opt This is combined with ω=1. For different modulation schemes, the first weighting coefficient ω1 is set as the optimal weighting coefficient ω for that modulation scheme. opt Specifically, for 16QAM modulation, the first weight coefficient ω1 is set to 0.2, and for 64QAM modulation, the first weight coefficient ω1 is set to 0.1. This prevents the algorithm from over-adjusting in the early stages of iteration, so that the system performance reaches a state that is not converged but has approached the optimal solution. The second weight coefficient ω2 is set to 1. This is because a reliable foundation has been established for the system in the early stages, and a large weight can be used in the later stages to enable the algorithm to converge quickly and reach the final stable state.

[0093] In the above formula To determine the value of (·) as its constellation point, This can be viewed as a hard-decision estimation. The hard-decision method first performs an N-point FFT transform on the MRC soft-value estimation result, then remodulates the transformed result (i.e., demodulates and remodulates), and then performs another N-point IFFT transform. Finally, it is compared with the MRC soft-value estimation result. A weighted average is then performed to obtain the final DT domain estimated sign vector.

[0094] (5.5) Under different row indices m, and ensuring that the value of l is m+l≤M-1, use each DT field to send the symbol vector estimate. Update RNPI vector

[0095]

[0096] (5.6) The norm of the RNP1 vector in the i-th iteration The norm of the RNPI vector from the previous iteration Comparison:

[0097] like Then stop iterating and output the estimated value of the DT field sent symbol vector for the i-th iteration.

[0098] Otherwise, proceed to step (5.7);

[0099] (5.7) Compare the current iteration number \(i\) with the maximum iteration number \(ite\):

[0100] If \(i < ite\), then let \(i = i + 1\) and return to step (5.2);

[0101] Otherwise, output the estimated value of the DT-domain transmitted symbol vector for the \(ite\) -th iteration

[0102] (5.8) The receiving end obtains the DD-domain transmitted signal vector from the output estimated value of the DT-domain transmitted symbol vector and recovers it

[0103] The effects of the present invention can be further illustrated by the following simulations:

[0104] 1. Simulation conditions:

[0105] The simulation uses the MATLAB R2021a simulation software. The total number of sub - carriers \(M\) of the ZP - OTFS system used in the simulation experiment is 64, the total number of symbol blocks \(N\) is 16, the carrier frequency is 4 GHz, the maximum moving speed is 500 km / h, the sub - carrier spacing is 15 KHz, and the typical extended vehicular channel model EVA is used as the wireless channel model of the system of the present invention. Its multipath delays are [0, 30, 150, 310, 370, 710, 1090, 1730, 2510] ns, and the relative powers are [0, - 1.5, - 1.4, - 3.6, - 0.6, - 9.1, - 7.0, - 12.0, - 16.9] dB. For low - order 4QAM modulation, as analyzed and verified by relevant literature, when the fixed optimal weight coefficient \(\omega\) opt = 1, the optimal bit - error performance and the least number of iterations can be obtained. Therefore, 16QAM and 64QAM are selected as the digital modulation methods for transmission in this paper. To ensure the generality and statistical significance of the results, 5000 ZP - OTFS signals are transmitted for each data point of the bit - error rate performance curve for simulation.

[0106] Based on the existing MRC algorithm with fixed weight coefficients, when only the optimal weight coefficient \(\omega\) opt is used, the average number of iterations of the algorithm shows an upward trend with the increase of SNR. Specifically, for the 16QAM modulation method, when \(\omega\) opt = 0.2, at 27.5 dB, the algorithm needs to iterate 12 times to converge, while at 30 dB, it needs to iterate 14 times to converge; for the 64QAM modulation method, when \(\omega\) opt=0.1. At 35dB, the algorithm needs 26 iterations to converge, while at 37.5dB, it needs 35 iterations to converge. Therefore, under higher-order modulation, the increase in the average number of iterations will significantly increase the computational complexity of the algorithm, which cannot be ignored in practical applications.

[0107] 2. Simulation content and result analysis:

[0108] Simulation 1: Under the simulation conditions described above, the parameters shown in Table 1 were set, and the received signal was detected using the detection algorithm of this invention and the existing MRC algorithm in 16QAM modulation mode. The results are as follows: Figure 4 As shown.

[0109] Table 1 16QAM Simulation Parameters

[0110]

[0111] Depend on Figure 4 It can be seen that:

[0112] Regardless of the maximum number of iterations, the method of this invention outperforms existing MRC algorithms in terms of bit error rate performance.

[0113] Under the conditions of a maximum iteration count of 11, a first weight coefficient ω1 = 0.2, a second weight coefficient ω2 = 1, and a midpoint of the iteration count mid-item of 9, the method of this invention, compared with the existing MRC algorithm, achieves better results with a fixed optimal weight coefficient ω1. opt =0.2 and has a comparable bit error rate performance after 14 iterations.

[0114] Simulation 2: Under the simulation conditions described above, the parameters shown in Table 2 were set, and the received signal was detected using the detection algorithm of this invention and the existing MRC algorithm in 64QAM modulation. The results are as follows: Figure 5 As shown.

[0115] Table 2 64QAM Simulation Parameters

[0116]

[0117] Depend on Figure 5 It can be seen that:

[0118] Regardless of the maximum number of iterations, the bit error rate performance of the method in this invention is superior to existing MRC algorithms.

[0119] Under the conditions of a maximum iteration count of ite = 24, a first weight coefficient ω1 = 0.1, a second weight coefficient ω2 = 1, and a midpoint of the iteration count mid-ite = 22, the method of this invention, compared with the existing MRC algorithm, achieves better results with a fixed optimal weight coefficient ω. opt=0.1 and has a bit error rate performance comparable to that of 35 iterations.

[0120] comprehensive Figure 4 and Figure 5 Simulation results show that, while maintaining the same bit error rate performance, the present invention reduces the number of iterations and the system computational complexity compared to existing MRC algorithms. Furthermore, the present invention achieves better bit error rate performance under the same complexity, especially under high-order QAM modulation.

[0121] Simulation 3: Under the above simulation conditions, the maximum number of iterations for the method of this invention was set to 14, while the maximum number of iterations for the existing MP algorithm was set to 30. The received signal was detected using the detection algorithm of this invention, the existing MP detection algorithm, and LMMSE linear detection under 16QAM modulation. The results are as follows: Figure 6 As shown. Since the complexity of the MP algorithm increases with the modulation order, such as in 64QAM where its computational complexity is too high to be effectively implemented in practical applications, this comparison only lists the performance results for the 16QAM modulation scheme.

[0122] Depend on Figure 6 It can be seen that when BER = 2 × 10 -4 At this time, the method of the present invention has a 3dB performance improvement compared to the existing MP algorithm, when BER = 1×10 -3 At the same time, the method of the present invention has a performance improvement of 6.3dB compared with the existing LMMSE algorithm. Overall, it shows that the present invention has superior convergence and detection performance.

[0123] The complexity of this invention is analyzed using the above simulation parameters:

[0124] Taking 16QAM modulation as an example, the complexity and performance differences between the algorithm of this invention and the existing MRC algorithm are compared and analyzed. The total number of subcarriers M is 64, the total number of symbol blocks N is 64, the number of propagation paths P is 9, and the maximum number of iterations ite is 10, 11, and 14, respectively. Substituting the above values ​​into the complexity calculation formula, the complexity values ​​of each are calculated, and the results are shown in Table 3.

[0125] Table 3. Comparison of the complexity of the present invention and existing MRC methods under different iteration numbers of 16QAM.

[0126]

[0127]

[0128] As can be seen from the data in Table 3, under the same bit error rate performance, the method of the present invention reduces the number of iterations compared with the existing MRC algorithm, thereby effectively reducing the computational complexity of the system; in addition, under the same computational complexity, the method of the present invention can achieve better bit error rate performance compared with the existing MRC algorithm.

[0129] Given the total number of subcarriers, symbol blocks, and propagation paths mentioned above, the maximum number of iterations for the existing MP algorithm is set to 30, while the maximum number of iterations for the method of this invention and the existing MRC algorithm is set to 14. Based on the complexity calculation formula, the complexity of the method of this invention, the existing MRC algorithm, the MP algorithm, and the LMMSE linear detection algorithm are calculated and compared, and the results are shown in Table 4.

[0130] Table 4. Comparison of the complexity of different detection methods in 16QAM

[0131]

[0132] As can be seen from the data in Table 4, the method of the present invention exhibits lower computational complexity and lower computational overhead compared to the existing MP algorithm and the classic LMMSE linear detection method. Compared to the existing MRC algorithm, although the complexity is similar, the bit error rate performance is improved, as shown in Table 3.

[0133] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0134] It should be noted that the step numbers in the specification and claims of this invention are only for the purpose of clearly describing the embodiments of this invention and facilitating understanding, and their order is not limited.

Claims

1. A method for detecting MRC signals using ZP-OTFS staged weighted modulation, characterized in that, It includes the following steps: (1) Given an M-row, N-column time-delay-Doppler DD domain grid, set the grid ends l max Set ×N symbols to zero, and place M′×N QAM symbols in the first M′ rows of the grid to obtain the two-dimensional DD domain transmitted signal X, where the m-th row of X is the DD domain transmitted signal vector x. m transpose vector Where m is the row index of the DD domain grid, m = 0, 1, ..., M-1, M′ = Ml max , l max This is the maximum delay tap of the channel; (2) Perform an inverse symptotic Fourier transform (ISFFT) on the DD domain transmitted signal X to transform it into a time-frequency TF domain transmitted signal X. tf Then, after Heisenberg transformation, a time delay-time (DT) domain signal is generated and transmitted. The m-th row is the DT domain transmitted signal vector. transpose vector Sending signals to the DT domain The signal is vectorized into a column domain to obtain the time-domain transmission signal s, which is then transmitted via a wireless channel. (3) After the time-domain transmitted signal s is transmitted through the wireless channel, the time-domain received signal r is obtained at the receiving end. The time-domain received signal r is then reconstructed into a matrix to obtain the DT domain received signal. (4) Receiving signals in the DT domain The detection yields the estimated value of the transmitted symbol vector in the DD domain. (4a) Initialize the estimated value of the DT domain transmission symbol vector at the start of the iteration. Calculate the initial residual noise and interference RNPI vector And set the maximum number of iterations ite, where 0 N Let N be the zero vector. Sending signals to the DT domain The estimated value of the column vector of the m-th row symbols, where i is the iteration number, i = 0; (4b) Calculate the transmitted signal vector x containing the DD domain under different time delays l. m Maximum ratio merge result of RNPI combination of all delay branches Soft value estimation results combined with maximum ratio in Let l be the set of different time delays for P propagation paths in the DD domain, 0 ≤ l ≤ l max ; (4c) Calculate the estimated value of the DT domain transmitted symbol vector in the i-th iteration by using phased weight coefficient adjustment. Set an intermediate value of the iteration number mid-ite, such that mid-ite is less than the maximum iteration number ite, and compare the current iteration number i with the intermediate value of the iteration number mid-ite: If i ≤ mid-ite, then the first weighting coefficient ω1 is used to calculate the estimated value of the DT domain transmitted symbol vector in the i-th iteration. If mid-ite < i ≤ ite, the estimated value of the DT-domain transmission symbol vector for the i-th iteration is calculated using the second weight coefficient ω2 in, To determine the (·) as its constellation point value, F N For the normalized N-point DFT matrix, (·) H This is the conjugate transpose of a matrix; (4d) Under different row indices m, and ensuring that the value of l is m+l≤M-1, use each DT field to send the symbol vector estimate. Update RNPI vector (4e) The norm of the RNP1 vector in the i-th iteration The norm of the RNPI vector from the previous iteration Comparison: like Then stop iterating and output the estimated value of the DT field sent symbol vector for the i-th iteration. Otherwise, proceed to step (4f); (4f) Compare the current iteration number i with the maximum iteration number ite: If i < ite, then set i = i + 1 and return to step (4b); Otherwise, output the estimated value of the DT field sent symbol vector for the t-th iteration. (4g) The receiver transmits the symbol vector estimate from the output DT domain. The transmitted signal vector in the DD domain is recovered.

2. The method according to claim 1, characterized in that, In step (2), the time-frequency TF domain transmits the signal X. tf DT domain transmits signals The time-domain transmitted signal s is represented as follows: in, Representing an M×N dimensional matrix space, F M For the normalized M-point DFT matrix, F N This is the normalized N-point DFT matrix; Represents an MN×1 dimensional matrix space, and vec(·) denotes column vectorization.

3. The method according to claim 2, characterized in that, The time-domain received signal r and the DT-domain received signal in step (3) They are represented as follows: r = Hs + w, in, Representing an MN×1 dimensional matrix space, w is a time-domain noise vector. Represents an MN×MN dimensional matrix space, where P is the number of propagation paths, and Δ=diag{α 0 ,α 1 ,α 2 ,...,α MN-1 } is a diagonal matrix, where α = e j2π / MN h q Let l be the channel gain of the q-th path. q and k q These represent the time delay component and Doppler frequency shift of the q-th path, respectively. It is a forward circular matrix; Represents an M×N dimensional matrix space. It is the inverse operation of vec(·), which reconstructs the vector into an M-row N-column matrix.

4. The method according to claim 1, characterized in that, In step (4a), the initial residual noise and interference RNPI vector are calculated. The formula is as follows: in, DT domain signal reception The column vector of the symbols in the m-th row. Let l be the discrete Doppler spread vector of the DT domain channel, and the value of l should ensure that ml ≥ 0. It represents the Hadamardi (or Hadama) stack.

5. The method according to claim 1, characterized in that, In step (4b), the transmitted signal vector x containing the DD domain is calculated. m Maximum ratio merge result of RNPI combination of all delay branches The output vector merged with the maximum ratio The formulas are as follows: in, Let l be the discrete Doppler spread vector of the DT domain channel. The value of l should ensure that m+l≤M-1, (·) * Let denote a complex conjugate matrix. Let denote the Hadamard product. This represents the Hadama division.

6. The method according to claim 1, characterized in that, The first weight coefficient ω1 and the first weight coefficient ω2 in step (4c) are determined as follows: (3c1) When the current iteration number i is i ≤ the midpoint of the iteration number mid-ite, for different modulation schemes, the first weighting coefficient ω1 is set as the optimal weighting coefficient ω under that modulation scheme. opt That is, for 16QAM modulation, the first weighting coefficient ω1 is set to 0.2, and for 64QAM modulation, the first weighting coefficient ω1 is set to 0.1; (3c2) When the current iteration number i satisfies mid-ite < i ≤ the maximum iteration number ite, set the second weight coefficient ω2 to 1.

7. The method according to claim 1, characterized in that, In step (4d), each estimated symbol vector is used Update RNPI vector The formula is as follows: in, Let be the discrete Doppler spread vector of the DT domain channel. Let represent the Hadamard product.

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