A precoding optimization method for a 6G-oriented MIMO-OTFS system

Abstract

The application discloses a pre-coding optimization method for a 6G-oriented MIMO-OTFS system, which is based on a maximum signal-to-noise ratio criterion and constraints the total power of a base station to save resources and achieve the purpose of designing an optimal pre-coder.The implementation steps are as follows: firstly, a channel matrix is determined according to a system model; secondly, a delay-Doppler domain input-output relationship is obtained; thirdly, a target function problem with a pre-coding matrix as a variable is established according to the input-output relationship; and finally, the Dinkelbach algorithm is used to convert the target function into a form of subtraction of auxiliary variables, fix a variable, convert the original non-convex optimization problem into a semi-definite programming (SDP) problem, and obtain an optimal pre-coding matrix.The optimal pre-coder designed in this way not only eliminates the inter-user interference, but also eliminates the inter-symbol interference of the same user.The communication performance between different users is effectively ensured through the design and optimization of the pre-coding matrix, and the bit error rate of the MIMO-OTFS system is further reduced.

Description

Technical Field

[0001] This invention relates to a precoding optimization method for a 6G MIMO-OTFS system, belonging to the field of communication technology. By optimizing the design of the precoding matrix, the method effectively ensures the communication performance between different users and further improves the bit error rate performance of the MIMO-OTFS system. Background Technology

[0002] With the rapid development of communication technology, the Orthogonal Frequency Division Multiplexing (OFDM) technology widely used in 4G and 5G mobile communication systems is no longer suitable for the newly proposed 6G mobile communication systems. This is because 6G mobile communication systems are often used in many high-speed mobile scenarios, such as satellite communication. The relative motion between the earth station and the satellite generates severe Doppler frequency shift, leading to severe interference between OFDM subcarriers, thus destroying the orthogonality of the subcarriers and affecting the system's communication performance. Therefore, the emergence of the new Orthogonal Time Frequency Space (OTFS) modulation technology solves the subcarrier interference problem that traditional OFDM modulation cannot overcome. Furthermore, OTFS modulation does not aim to eliminate interference, but rather to minimize the interference experienced by the data itself. This technology is not only suitable for high-speed mobile scenarios but also supports Multiple-Input Multiple-Output (MIMO) technology.

[0003] Multiple-input multiple-output (MIMO) technology, as one of the key technologies in 5G wireless communication, can better utilize spatial resources and improve spectrum efficiency. Therefore, this technology has been applied to over-the-air (OTFS) systems, and MIMO-OTFS systems have begun to receive widespread attention and research. However, in multi-user MIMO-OTFS systems, how to eliminate inter-user interference, inter-antenna interference, and inter-symbol interference to improve system performance has become an urgent problem to be solved. Summary of the Invention

[0004] The purpose of this invention is to provide a precoding optimization scheme for MIMO-OTFS systems for 6G, to obtain the optimal precoding matrix and design the optimal precoder, so as to solve the communication performance that traditional precoding techniques cannot achieve.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A precoding optimization scheme for a 6G MIMO-OTFS system includes the following steps: determining the delayed Doppler domain channel matrix of the MIMO-OTFS system; obtaining the input-output relationship of the delayed Doppler domain signal; calculating the signal-to-leakage-noise ratio (SNR) based on the input-output relationship expression, maximizing the SNR under a certain total base station transmit power, thereby establishing an objective function problem regarding the precoding matrix; using the Dinkelbach algorithm to transform the objective function into a form of subtraction of auxiliary variables, assuming a certain variable is fixed, transforming the original non-convex optimization problem into a convex optimization problem, and using the positive semidefinite programming (SDP) method to solve this convex optimization problem, finally obtaining the optimal precoding matrix.

[0007] Methods for determining the delay-Doppler domain channel matrix of a MIMO-OTFS system include: assuming a two-dimensional delay-Doppler domain channel (τ, ν represent the delay dimension and Doppler dimension, respectively), where h(τ, ν) is in the range [0, τ] on the delay axis. max The range on the Doppler axis is [-ν]. max ,ν max ], τ max and ν max Let represent the maximum delay and maximum Doppler shift across all channel paths, respectively. Typically, only a small number of reflectors in the channel have associated delays and Doppler shifts; therefore, only a small number of parameters are needed to build the channel model in the delay-Doppler domain. Then, the base station's q-th antenna (total equipped with N...) tx The sparse representation of the channel from the root antenna to the k-th user at the receiver is as follows:

[0008]

[0009] Among them, L k Let δ(·) represent the total number of subpaths in the channel between the base station and the k-th user, and let h be the impulse function. k,q,i τ represents the channel complex gain along the i-th sub-path from the q-th base station antenna to the k-th user. k,i ν represents the delay between the k-th users along the i-th sub-path. ki Let h represent the Doppler effect between the k-th users along the i-th sub-path. Define the channel gain h in the above equation. k,q,i Represented as:

[0010]

[0011] Where d represents the distance between uniformly distributed antennas, λ represents the carrier wavelength of the system, and g k,i Φ represents the channel gain along the i-th subpath between the base station and the k-th user. k,i Let represent the azimuth deviation angle of the i-th path from the base station to the k-th user. Additionally, define l...k,i ,p k,i These are the delay taps and Doppler taps between the k-th users along the i-th sub-path, respectively:

[0012]

[0013] Here, Δf represents the subcarrier spacing, T represents the duration of the multicarrier symbol (i.e., the OTFS information symbol transmitted by the base station), N is the number of delay dimension grids, M is the number of Doppler dimension grids, MΔf represents the bandwidth of the transmitted signal frame, and NT represents the total duration of the transmitted signal frame.

[0014] Based on the MIMO-OTFS system model diagram, the time-domain signal received by the k-th user is represented as:

[0015]

[0016] Among them, s k,q τ(t) represents the time-domain signal transmitted from the q-th antenna of the base station to the k-th user. i ν represents the delay under the i-th sub-path. i Let s represent the Doppler flow under the i-th sub-path. k,q (t-τ i ) indicates that the time-domain signal transmitted from the q-th antenna to the k-th user is delayed by τ. i n k (t) represents the time-domain noise term, and the matrix form of the above equation can be further expressed as:

[0017] y k =H k s k +n k

[0018] Among them, S k This represents the time-domain transmitted signal of the k-th user, n. k Let represent the noise vector of the k-th user. The delay-Doppler domain channel matrix... With H k Satisfying the relational equation:

[0019]

[0020] in, F represents the Kronecker product. N and Let I represent the N-point DFT and IDFT respectively. M It is an M-dimensional identity matrix. Given H... k Thus, the channel matrix is ​​determined. Right now

[0021]

[0022] The method for determining the input-output relationship of the delayed Doppler domain signal includes: combining the time-domain representation of the input-output relationship obtained above, after the user receives the time-domain signal, it first undergoes a Wigner transform (the inverse of the Heisenberg transform), then is filtered through a receiving window and converted to a delayed Doppler domain signal using a sine four-factor transform (SFFT). Represented as:

[0023]

[0024] Among them, w k This represents the precoding matrix of the k-th user. This represents the delayed Doppler domain information symbol transmitted from the q-th antenna of the base station to user k. The above equation, representing the noise term for the k-th user, is further expressed as:

[0025]

[0026] The first term in the above equation represents the signal received by the k-th user, the second term represents the interference signal from other users, and the third term... It is vectorized noise.

[0027] Methods for establishing the objective function of the precoding matrix include: firstly, calculating the signal-to-leakage-to-noise ratio (SLNR) based on the input-output relationship expression. k :

[0028]

[0029] Among them, P n It is noise power. The numerator of the fraction represents the effective signal power received by user k, while the denominator represents the signal interference generated by other users to user k and the noise interference power in the channel.

[0030] Given the constraint that the total transmit power of the base station should be maximized to achieve the signal-to-leakage-to-noise ratio, the objective function problem is as follows:

[0031]

[0032] stSLNR k ≥γ0

[0033]

[0034] γ0 is the minimum threshold value of the signal-to-leakage-to-noise ratio, P total This represents the total transmit power of the base station.

[0035] Methods for solving objective function problems include: Let W k =wk w k H , λ k =SLNR k (Constant), using the Dinkelbach algorithm for fractional programming, the objective function is transformed into a form of subtraction of auxiliary variables:

[0036]

[0037]

[0038] tr(W k )≤P total k = 1, 2, ..., K

[0039] Assuming λ is known k Since is a constant, the above equation satisfies the conventional form of a semidefinite programming (SDP) problem. Therefore, the original non-convex optimization problem is solved using the SDP method, and the optimal precoding matrix is ​​obtained by running the CVX toolbox in MATLAB.

[0040] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The present invention proposes a precoding optimization method for MIMO-OTFS systems for 6G. Compared with the traditional precoding method based on the MMSE criterion, the method of the present invention has better communication performance, effectively reduces the bit error rate, and is more suitable for precoding design in the context of 6G mobile communication. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the multi-user MIMO-OTFS system model in this invention;

[0042] Figure 2 This is a flowchart of the present invention;

[0043] Figure 3 This is a performance comparison chart of the precoding optimization method for 6G MIMO-OTFS system provided by this invention with the precoding schemes used in the prior art at different signal-to-noise ratios. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings.

[0045] Multi-user MIMO-OTFS system model such as Figure 1 As shown. The base station transmitter is equipped with N txOne antenna serves K single-antenna users. The delayed Doppler domain transmitted signal first passes through a pre-encoder, then undergoes inverse symplectic finite Fourier transform (ISFFT) and windowing, followed by Heisenberg transform to convert it into a time-domain signal. The user end receives the time-domain signal and performs Wigner transform, finally filtering and using symplectic Fourier transform (SFFT) to convert the signal back into a delayed Doppler domain signal for output.

[0046] definition in 1≤q≤N tx Let s be the delayed Doppler domain signal vector transmitted from the q-th antenna to the k-th user by the base station. k,q (t) represents the time-domain signal transmitted by the k-th user on the q-th antenna, y k (t) represents the time-domain signal received by the k-th user, n k (t) represents the time-domain noise term. w is the delayed Doppler domain received signal vector received by the k-th user receiver. k ∈C MN×1 This is the vectorized noise term.

[0047] Figure 2 The diagram shown is a flowchart of the present invention. Specifically, it includes the following steps:

[0048] a. Determine the delay Doppler domain channel matrix of the MIMO-OTFS system

[0049] Assume that h(τ,ν) has a range of [0,τ] on the delay axis. max The range on the Doppler axis is [-v]. max ,v max ], τ max and v max Let represent the maximum delay and maximum Doppler shift across all channel paths, respectively. Typically, only a small number of reflectors in the channel have associated delays and Doppler shifts; therefore, only a small number of parameters are needed to build the channel model in the delay-Doppler domain. Then, the base station's q-th antenna (total equipped with N...) tx The sparse representation of the channel from the root antenna to the k-th user at the receiver is as follows:

[0050]

[0051] Among them, L k Let δ(·) represent the total number of subpaths in the channel between the base station and the k-th user, and let h be the impulse function. k,q,i τ represents the channel complex gain along the i-th sub-path from the q-th base station antenna to the k-th user. k,iv represents the delay between the k-th users along the i-th sub-path. k,i Let h represent the Doppler effect between the k-th users along the i-th sub-path. Define the channel gain h in the above equation. k,q,i Represented as:

[0052]

[0053] Where d represents the distance between uniformly distributed antennas, λ represents the carrier wavelength of the system, and g k,i Φ represents the channel gain along the i-th subpath between the base station and the k-th user. k,i Let represent the azimuth deviation angle of the i-th sub-path from the base station to the k-th user. Additionally, define l... k,i ,ν k,i These represent the delay and Doppler tap of the i-th sub-path, respectively:

[0054]

[0055] Here, MΔf represents the bandwidth of the transmitted signal frame, and NT represents the total duration of the transmitted signal frame. Based on the MIMO-OTFS system model diagram, the transmitted information symbols are processed by a pre-encoder, and then transformed into the time-frequency domain by inverse symplectic Fourier transform (ISFFT), represented as x. k,q [n,m]:

[0056]

[0057] n=0,1,...,N-1,m=0,1,...,M-1

[0058] Among them, the transmitted signal vector After precoding, it is represented as Then, the Heisenberg transform is used to transform the time-frequency signal x. k,q [n,m] is converted into a time-domain signal s k,q (t):

[0059]

[0060] In the formula, g t (·) represents a rectangular filter pulse, as follows:

[0061]

[0062] The time-domain signal received by the k-th user at the receiver is represented as:

[0063]

[0064] Among them, s k,q(t) represents the time-domain signal transmitted from the q-th antenna of the base station to the k-th user, and n(t) is the time-domain noise term. The matrix form of the above equation is further expressed as:

[0065] y k =H k s k +n k

[0066] Therefore, H is derived. k ∈C MN×MN :

[0067]

[0068] Where Π is the positive cyclic shift matrix:

[0069]

[0070] Δ is an MN×MN diagonal matrix:

[0071] Δ=diag[z 0 ,z 1 ,...,z MN-1 ]∈MN×MN

[0072] in The delayed Doppler domain channel matrix With H k Satisfying the relational equation:

[0073]

[0074] in, F represents the Kronecker product. N and Let I represent the N-point DFT and IDFT respectively. M It is an M-dimensional identity matrix. Given H... k Thus, the channel matrix is ​​determined.

[0075] b. Determine the input-output relationship of the delayed Doppler domain signal;

[0076] Combining the previous time-domain input-output relationship expression, we can obtain the input-output relationship of the delayed Doppler domain signal:

[0077]

[0078] Among them, w k This represents the precoding matrix of the k-th user. This represents the delayed Doppler domain information symbol transmitted from the q-th antenna of the base station to user k. Representing the noise term for the k-th user, we can simplify to obtain:

[0079]

[0080] In the above formula, the first term represents the valid signal received by the k-th user, the second term represents the interference signal from other users, and the third term... It is vectorized noise.

[0081] c. Calculate the signal-to-noise ratio (SNR) based on the input-output relationship expression, maximize the SNR under a certain total base station transmission power, and thus establish the objective function for the precoding matrix;

[0082] Define the signal-to-noise ratio (SNR) of user k as:

[0083]

[0084] Among them, P n Let $k$ be the noise power. The numerator of the fraction represents the effective signal power received by user $k$, while the denominator represents the signal interference generated by other users on user $k$ and the noise interference power in the channel. Therefore, the objective function problem is established as follows:

[0085]

[0086] stSLNR k ≥γ0

[0087]

[0088] γ0 is the minimum threshold value of the signal-to-leakage-to-noise ratio, P total This represents the total transmit power of the base station.

[0089] d. Use the Dinkelbach algorithm to transform the objective function into the form of subtracting auxiliary variables, and then use positive semidefinite programming (SDP) to solve the original non-convex optimization problem to obtain the optimal precoder matrix, i.e. the optimal precoder.

[0090] Let W k =w k w k H , λ k =SLNR k (Constant), using Dinkelbach's algorithm and fractional programming, the objective function problem can be rewritten as:

[0091]

[0092]

[0093] tr(W k )≤P total k = 1, 2, ..., K

[0094] The above equation satisfies the applicable problem form of semidefinite programming (SDP) and can be solved using the CVX toolbox in MATLAB.

[0095] Figure 3 The figure shows a performance comparison of the precoding optimization method described in this invention with the precoding schemes used in the prior art under different signal-to-noise ratios (SNRs). As can be seen from the simulation figures, the bit error rate performance of the precoding optimization scheme proposed in this invention improves with increasing SNR, consistently demonstrating better performance compared to traditional precoding techniques based on the MMSE criterion.

[0096] This invention provides a precoding optimization method for 6G MIMO-OTFS systems, used to design the optimal precoder, reduce the bit error rate, and improve communication performance. Compared with traditional precoding schemes, this method can not only effectively handle high-speed mobile scenarios in 6G mobile communication systems, but is also more suitable for signal processing in the context of large-scale MIMO systems. Compared with precoding schemes based on the MMSE criterion, the method described in this invention also has greater performance advantages.

[0097] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for precoding optimization of a 6G-oriented MIMO-OTFS system, wherein OTFS information symbols transmitted by a base station are received by different users via a delay-Doppler domain channel, characterized in that, The method comprises the following steps: Step 1: determining a delay-Doppler domain channel matrix of a MIMO-OTFS system; Step 2: obtaining an input-output relationship of a delay-Doppler domain signal; Step 3: establishing an optimization problem with a maximum signal-to-leakage-and-noise ratio as an objective function according to the input-output relationship expression of step 2, wherein the objective function takes a precoding matrix as a variable; Step 4: solving the optimization problem of step 3 to obtain an optimal precoding matrix; The expression of the optimization problem in step 3 is: s.t. SLNR k ≥ γ0 wherein SLNR k is the signal-to-leakage-and-noise ratio (SLNR) of the kth user, n is the noise power, γ0is the minimum threshold value of the signal-to-leakage-and-noise ratio (SLNR), P total is the total power of the base station, K is the number of users, is the delay-Doppler domain channel matrix from the base station to the kth user, is the precoding matrix of the kth user, N tx is the number of antennas of the base station, N is the number of delay grids, and M is the number of Doppler grids, is the delay-Doppler domain channel matrix from the base station to the ith user; In step 4, the optimization problem of step 3 is converted into a convex optimization problem by using a Dinkelbach algorithm, and the convex optimization problem is solved by using a semi-definite programming (SDP) to obtain the optimal precoding matrix.

2. The precoding optimization method for a 6G-oriented MIMO-OTFS system according to claim 1, characterized in that, In the MIMO-OTFS system of step 1, the delay-Doppler domain channel matrix of a base station to a kth user is expressed as follows: where denotes the Kronecker product, F N and denotes the N-point DFT and IDFT, respectively, I M is the M-dimensional identity matrix; H k denotes the channel matrix from the base station to the kth user.

3. The precoding optimization method for a 6G-oriented MIMO-OTFS system according to claim 2, characterized in that, The sparse representation of the channel from the qth antenna of the base station to the kth user is: where τ denotes a delay variable, v denotes a Doppler variable, L k is the total number of sub-paths of the channel between the base station and the kth user, δ(·) denotes an impulse function, h k,q,i denotes the complex gain of the channel between the qth antenna of the base station and the kth user along the ith sub-path, τ k,i denotes the delay of the channel between the base station and the kth user along the ith sub-path, v k,i denotes the Doppler of the signal between the base station and the kth user along the ith sub-path; The time-domain signal received by the kth user is represented as: where s k,q (t) denotes the time-domain signal transmitted by the qth antenna of the base station to the kth user, τ i denotes the delay of the ith sub-path, ν i denotes the Doppler of the ith sub-path, s k,q (t-τ i ) denotes the time-domain signal transmitted by the qth antenna of the base station to the kth user delayed by τ i , n k (t) is the time-domain noise term of the kth user; The time-domain signal received by the kth user is represented in a matrix form as: y k = H k s k + n k where s k denotes the time-domain transmit signal of the kth user, n k denotes the noise vector of the kth user.

4. The precoding optimization method for a 6G-oriented MIMO-OTFS system according to claim 3, characterized in that, h k,q,i The expression is: wherein d represents the antenna spacing of the base station, λ represents the carrier wavelength of the system, g k,i represents the channel gain of the i-th sub-path between the base station and the k-th user, Φ k,i represents the azimuth angle of the i-th sub-path from the base station end to the k-th user.

5. The precoding optimization method for a 6G-oriented MIMO-OTFS system according to claim 3, characterized in that, l k,i ,p k,i respectively denote the delay taps along the i-th sub-path and the Doppler taps along the i-th sub-path between the base station and the k-th user, Δf denotes the subcarrier spacing, and T denotes the multi-carrier symbol duration.

6. The precoding optimization method for a 6G-oriented MIMO-OTFS system according to claim 1, characterized in that, The input-output relationship of the delay-Doppler domain in step 2 is represented as: wherein is a vectorized noise representation in delay-Doppler domain, denotes the delay-Doppler domain signal received by the kth user, denotes the delay-Doppler domain transmit signal sent by the base station to the kth user, w k' denotes the precoding matrix of the k'th user, denotes the delay-Doppler domain transmit signal sent by the base station to the k'th user.

7. The precoding optimization method for a 6G-oriented MIMO-OTFS system according to claim 1, characterized in that, In step 4: Let W k = w k w k H , λ k = SLNR k , the optimization problem in step 3 is rewritten as:

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