A precoding method combining quantum variation in millimeter wave massive MIMO system

Abstract

A precoding method combined with quantum variation in millimeter-wave massive MIMO systems. For millimeter-wave massive MIMO systems, this method aims at system reachability and maximum rate. By modeling the optimization problem in the communication system as the Hamiltonian in the quantum system, the design problem of optimal precoding is transformed into the problem of obtaining the ground state of the Hamiltonian of the quantum system. Then, the variational quantum eigensolver is used in combination with the optimization algorithm of classical machine learning to obtain the optimal parameterized quantum circuit through training. Finally, the ground state is extracted from the quantum circuit, which corresponds to the optimal precoding matrix. After verification and analysis by the tensorflow‑quantum quantum machine learning platform, this method can achieve exponential acceleration, and its performance is close to that of the classical SVD-based precoding scheme.

Description

Technical Field

[0001] The present invention belongs to the field of communication systems, and in particular relates to a precoding method combined with quantum variation in a millimeter wave large-scale MIMO system. Background Art

[0002] Millimeter wave and massive MIMO technology are the key technologies for current 5G and next-generation communications. Millimeter wave has the characteristics of short wavelength, high loss and wide frequency band. Massive MIMO technology is an extension of MIMO technology in the fourth-generation wireless communication technology. It improves the system capacity in space and improves the high loss of millimeter wave. There is no doubt that millimeter wave massive MIMO technology has become the inevitable direction and demand for the development of current 5G and future next-generation wireless communication technology. In MIMO systems, in order to suppress the influence of signal interference, precoding technology becomes the key to solving the problem. In the precoding scheme, all-digital precoding can simultaneously control the phase and amplitude of the transmitted signal, which can be used in both single-user and multi-user systems. However, as the number of antennas increases, the algorithm complexity and the difficulty of implementation will also increase significantly. The focus of current research is on how to reduce the algorithm complexity and how to reduce the overhead. On the other hand, after nearly four decades of development, quantum computing has gradually become a key area of ​​concern for current researchers. The combination of quantum computing and machine learning has become a new cross-disciplinary research field.

[0003] With the continuous development of quantum technology, major business giants, academic institutions and government strategies are turning their attention to quantum computing, and it is regarded as the main development direction in the next few decades. At the same time, with the rapid development of wireless communication technology, the number of wireless users is increasing, and the ability to process and analyze data is higher. Therefore, the application of quantum computing to the field of wireless communication is considered to be a promising direction to promote the development of wireless communication technology in the future 6G and post-6G era. Summary of the invention

[0004] This invention innovatively proposes to apply quantum computing to the precoding design of millimeter-wave massive MIMO systems, proposes a precoding method combined with quantum variation in millimeter-wave massive MIMO systems, and conducts experimental simulations on the Google quantum machine learning platform, using the high parallelism of quantum computing to improve the performance of the entire communication system.

[0005] A precoding method combined with quantum variation in a millimeter wave massive MIMO system, characterized in that the method comprises the following steps:

[0006] Step 1: Generate channel matrix based on Saleh-Valenzuela channel model , with the goal of system reachability and maximum speed, the optimal precoding matrix design problem is transformed into The characteristic decomposition of

[0007] Step 2: Construct a variational quantum system. First, prepare the initial quantum state. ,Will As the system Hamiltonian; then construct a parameterized quantum neural network and train it in the parameterized quantum circuit; get the output state ;

[0008] Step 3: Based on the parameters in the output state obtained after training in step 2 , taking the expected value as the optimized loss function L, according to the gradient descent method ,right Make updates;

[0009] Step 4: Based on the trained quantum circuit , get its corresponding matrix expression, extract the maximum eigenvector V corresponding to the maximum eigenstate m , f n =V m ;f n represents the precoding matrix; V m Indicated by M m Decomposed vector;

[0010] Step 5: Generate precoding matrix , applied in millimeter-wave massive MIMO systems.

[0011] Furthermore, in step 1, the Saleh-Valenzuela channel model is used:

[0012]

[0013] in, is the number of transmitting antennas of the base station, The number of receiving antennas for the user; is the millimeter wave scattered beam, represents the gain of the i-th scattering beam path, respectively , represents the departure angle of the ith path, represents the arrival angle of the ith path, and , represents the user antenna array response vector, represents the base station antenna array response vector, , It is expressed as follows, where j represents an imaginary number:

[0014]

[0015] in, represents the wavelength, Indicates the distance between antennas.

[0016] Furthermore, in step 1, it is assumed that the number of transmitted symbols, the number of transmitting antennas, and the number of receiving antennas are equal, that is, ; The signal sent by the transmitter is expressed as

[0017]

[0018] Wherein, F represents the precoding matrix of the transmitting end, and s represents the symbol sent by the transmitting end;

[0019] The signal received by the receiving end is expressed as

[0020]

[0021] Where n represents an additive complex Gaussian white noise vector with a mean of 0 and a variance of , the signal after being processed by the receiving matrix W is expressed as

[0022]

[0023] In mmWave massive MIMO systems, assuming , the system reachability and rate are expressed as follows, where I represents the identity matrix;

[0024]

[0025] The optimization problem with the goal of system reachability and maximum rate is described as follows, where Tr represents the trace of the matrix and P represents the power

[0026]

[0027] The channel matrix Recorded as ,in, ,

[0028] but , so the above formula is converted to

[0029]

[0030] Among them, , The SVD decomposition of , U m and V m Represents the left and right singular vectors of SVD decomposition, and the largest eigenvector is the optimal solution.

[0031] Furthermore, in step 2, As the system Hamiltonian, in order to successfully map the Hamiltonian to the quantum bit in the quantum circuit during quantum simulation, the Hamiltonian needs to be decomposed into a form composed of Pauli operators. The theoretical decomposition form is as follows: ,in , , n represents the number of Pauli operators in this term; Pauli operators are identified by Greek letters, represents the Pauli X-gate, represents the Pauli Y gate, and i and j represent the subspace on which the Hamiltonian quantum term acts.

[0032] Furthermore, in step 3, the training parameters , define the loss function about Expected value: ,right Make updates;

[0033] In the formula, Represented by the Pauli matrix on n qubits , , The tensor product combination composed of Find partial derivatives ,renew , and then input the updated parameters into the quantum computer to update the parameterized quantum circuit , and calculate the expected value. If the expected value is not reached, the optimization is continued until the optimal parameterized quantum circuit is obtained. .

[0034] The beneficial effects achieved by the present invention are:

[0035] (1) The high parallelism of quantum computing can reduce the complexity of traditional machine learning algorithms and greatly reduce the amount of computation;

[0036] (2) The accuracy of quantum computing is consistent with that of traditional algorithms;

[0037] (3) Verification and analysis show that this method can achieve exponential acceleration and its performance is close to that of the classic SVD-based precoding scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a system model diagram in an embodiment of the present invention.

[0039] Figure 2 It is a basic flow chart of the variational quantum eigenvalue solver in the embodiment of the present invention.

[0040] Figure 3is a quantum neural network diagram in an embodiment of the present invention.

[0041] Figure 4 This is a diagram of a precoding algorithm combined with a quantum variational algorithm in an embodiment of the present invention.

[0042] Figure 5 In the embodiment of the present invention , A graph showing the relationship between the system achievable rate and signal-to-noise ratio.

[0043] Figure 6 In the embodiment of the present invention , The relationship between the system reachability and rate and signal-to-noise ratio.

[0044] Figure 7 In the embodiment of the present invention The relationship between the achievable rate and the transmitting antenna of each algorithm system. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0046] The traditional MIMO channel model is not suitable for millimeter wave MIMO systems due to the high path loss and the obvious sparsity of the millimeter wave channel. The number of effective propagation paths in the channel is much smaller than that of the microwave channel. The millimeter wave large-scale MIMO system channel model in this method adopts the Saleh-Valenzuela channel model:

[0047]

[0048] in, is the number of transmitting antennas of the base station, The number of receiving antennas for the user; is the millimeter wave scattered beam, represents the gain of the i-th scattering beam path, respectively , represents the departure angle of the ith path, represents the arrival angle of the ith path, and , represents the user antenna array response vector, represents the base station antenna array response vector, , It is expressed as follows, where j represents an imaginary number:

[0049]

[0050] in, represents the wavelength, Indicates the distance between antennas.

[0051] Figure 1 The millimeter wave massive MIMO system model is shown, with the transmitter equipped with Antenna, the receiving end is equipped with antennas, the number of symbols sent is d, and the precoding matrix at the transmitter is The receiving matrix at the receiving end is The channel matrix is .

[0052] To simplify the analysis, it is assumed that the number of transmitted symbols, the number of transmitting antennas, and the number of receiving antennas are equal, that is, The signal sent by the transmitter can be expressed as

[0053]

[0054] Wherein, F represents the precoding matrix of the transmitting end, and s represents the symbol sent by the transmitting end.

[0055] The signal received by the receiving end can be expressed as

[0056]

[0057] Where n represents an additive complex Gaussian white noise vector with a mean of 0 and a variance of , the signal processed by the receiving matrix W can be expressed as

[0058]

[0059] In the millimeter wave massive MIMO system, this method is used to simplify the receiving end processing and assumes , the system reachability and rate can be expressed as follows, where I represents the identity matrix

[0060]

[0061] The optimization problem with the goal of system reachability and maximum rate can be described as follows, where Tr represents the trace of the matrix and P represents the power

[0062]

[0063] The channel matrix Recorded as ,in, ,

[0064] but , so the above formula is converted to

[0065]

[0066] Among them, , The SVD decomposition of , U m and V m Represents the left and right singular vectors, and the maximum eigenvector is the optimal solution. This method considers constructing a variational quantum system, taking M as the system Hamiltonian, and obtaining the maximum eigenvector of M, that is, the maximum eigenvector V, through the quantum eigensolver. m , the optimal solution of the above formula is f m , from which we can get the precoding matrix .

[0067] The variational quantum eigenvalue solver (VQE) algorithm is based on the variational principle. The variational principle means that for any initial state, when the Hamiltonian of a system is applied to it, the average energy of the system in this state can be obtained. , which will be greater than or close to the ground state energy of the system ,Right now

[0068]

[0069] From the above formula, we can see that if the prepared initial state is exactly the ground state of the system, then , directly get the ground state energy of the system; but often the initial state we prepare is very different from the ground state energy of the system, resulting in , at this time, a set of parameters needs to be introduced. By continuously adjusting the parameters and setting a threshold, the prepared quantum state can be infinitely close to the ground state of the system. To solve, we can use the VQE algorithm to find the eigenvalue of the Hamiltonian describing a system. , thus obtaining the feature vector.

[0070] The variational quantum eigenvalue solver (VQE) is a quantum-classical hybrid algorithm used to find the ground state of a system and can effectively find a larger matrix The algorithm can greatly reduce the requirement of coherence time. Therefore, in order to solve the precoding optimization problem of formula (9) above, this method proposes an algorithm that combines VQE with precoding. As the system Hamiltonian of the variational quantum eigenvalue solver (VQE), firstly, a parameterized quantum circuit is constructed to characterize the precoding vector that can be adjusted by parameters; then It is decomposed into sub-Hamiltonians composed of Pauli matrices, which are trained in quantum neural networks respectively. After the gradient optimization algorithm, the maximum singular vector is obtained, and finally the precoding matrix F is generated.

[0071] When performing quantum simulation, in order to successfully map the Hamiltonian to the quantum bit in the quantum circuit, the Hamiltonian needs to be decomposed into a form composed of Pauli operators. In general, any Hamiltonian can be expressed as:

[0072]

[0073] Represents the Hamiltonian can be expanded into the sum of multiple sub-Hamiltonians, where , , n is the number of Pauli operators in the term. Pauli operators are identified by Greek letters, for example represents the Pauli X-gate, represents the Pauli Y gate, i and j represent the subspaces acted upon by the Hamiltonian quantum term. Since the observable is linear, when calculating the average energy of the system:

[0074]

[0075] According to the above formula, the Hamiltonian can be expanded into the following form:

[0076]

[0077] Consider the Hamiltonian, written as a polynomial relative to the size of the system, which can be approximated as a matrix of sums of n-fold tensor products. Using a classical adder, The calculation is simplified to a quantum state The sum of the polynomial number of expectation values ​​of simple Pauli operators multiplied by some real constant. Quantum devices can efficiently obtain the expectation value of the tensor product of any number of simple Pauli operators. Using n qubits, we can get this The expectation value of the Hamiltonian.

[0078] Unitary Operator In this method, we first need to prepare the parameterized quantum initial state of the precoding vector, and then generate an all-zero quantum state. The action parameterized quantum circuit is as follows, and the parameterized quantum initial state corresponding to the precoding vector is prepared, which can be written as a combination of eigenstates. Among them, represents the probability amplitude, Represents the ground state.

[0079]

[0080]

[0081] Will As the system Hamiltonian , decomposed into sub-Hamiltonian forms according to the following formula, the system Hamiltonian exist The expected energy under

[0082]

[0083] In the process of implementing VQE, we first need to design and build a quantum neural network QNN, which can also be understood as a parameterized quantum circuit. , to construct a trial wave function such that . Quantum Neural Networks like Figure 2 As shown. Where D represents the depth of the quantum neural network.

[0084] By acting on quantum neural networks In the initial state On, get the output state In the VQE model, the global loss function is calculated by giving an analytical expression The gradient of the parameterized quantum circuit can be obtained by updating To estimate the gradient. The loss function The gradient depends on the parameters , taking the expected value as the optimized loss function, generally given by The expectation value of the Hamiltonian is given.

[0085]

[0086] in, Represented by the Pauli matrix on n qubits , , In classical computers, according to the gradient descent method, the loss function Find partial derivatives ,renew , and then input the updated parameters into the quantum computer to update the parameterized quantum circuit , and calculate the expected value. If the expected value is not reached, the optimization is continued in the classical computer until the optimal parameterized quantum circuit is obtained. Finally, we get the parameterized quantum circuit The unitary matrix is ​​the optimal precoding matrix under the objective of maximizing the sum rate. The specific algorithm is as follows Figure 4 shown.

[0087] A precoding method combined with quantum variation in a millimeter wave massive MIMO system comprises the following steps:

[0088] Step 1: Generate channel matrix according to Saleh-Valenzuela channel model , with the goal of system reachability and maximum speed, the optimal precoding matrix design problem is transformed into The characteristic decomposition of

[0089] Step 2: Construct a variational quantum system. First, prepare the initial quantum state. ,Will as the system Hamiltonian.

[0090] Step 3: Decompose according to the following form Decomposed into the form of Pauli operators:

[0091]

[0092] Step 4: Then construct a parameterized quantum neural network and train it in a parameterized quantum circuit. The output state is obtained .

[0093] Step 5: Based on the parameters in the output state obtained after training in step 2 , taking the expected value as the optimized loss function, the loss function is defined as:

[0094]

[0095] Step 6: According to the gradient descent method ,right to update.

[0096] Step 7: Based on the trained quantum circuit , get its corresponding matrix expression, extract the maximum eigenvector corresponding to the maximum eigenstate , .

[0097] Step 8: Generate precoding matrix: .

[0098] Next, we conduct experimental verification. The simulation environment used in this embodiment is a millimeter wave large-scale MIMO system model. The training parameters are set as follows: the quantum neural network depth D is set to 2, and the total number of iterations is set to 80. In order to verify the effectiveness of the method, we verify it on the Google quantum platform and use the quantum programming framework cirq to compare the system reachability and rate of the following algorithms under different signal-to-noise ratios and different numbers of transmitting antennas: 1) SVD precoding; 2) MMSE precoding. The simulation results are shown in Figure 2. Figure 5-7 shown.

[0099] Figure 5 and Figure 6 Respectively represent when the system is , Time and , The relationship between the reachability and rate of each algorithm system and the signal-to-noise ratio is as follows: Figure 5 and Figure 6 It can be seen that the system achievable sum rate increases with the increase of signal-to-noise ratio. The achievable sum rate performance of this method is similar to the traditional SVD precoding performance and is better than the MMSE precoding performance.

[0100] Figure 7 Indicates when The relationship between the reachability and rate of each algorithm system as the number of transmitting antennas changes from 16 to 196 is given by Figure 7 It can be seen that the reachable sum rate of each algorithm system increases with the increase of the number of transmitting antennas. The performance of this method is similar to that of the SVD precoding algorithm and is better than the MMSE precoding algorithm.

[0101] The precoding method combined with the variational quantum eigenvalue solver proposed in this invention aims at the system reachability and maximum rate. The variational quantum eigenvalue solver is used to transform the problem into solving the expectation of the system Hamiltonian and its corresponding quantum state. A parameterized trial wave function is prepared on the quantum machine learning platform, and then combined with the optimization algorithm of classical machine learning, a set of optimal parameters are trained to update the parameterized quantum circuit, thereby obtaining the optimal precoding matrix. After verification and analysis, the scheme proposed in this article can have exponential acceleration, and its performance is similar to that of the classical algorithm, but it has the advantage of computational complexity.

[0102] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A precoding method combining quantum variation in a millimeter wave massive MIMO system, characterized by: The method comprises the following steps: Step 1: Generate the channel matrix H according to the Saleh-Valenzuela channel model. With the goal of maximum system reachability and speed, the optimal precoding matrix design problem is transformed into H m H H m The characteristic decomposition of Step 2: Construct a variational quantum system. First, prepare the initial quantum state and set M m =H m H H m , M m as the system Hamiltonian; then construct a parameterized quantum neural network and train it in a parameterized quantum circuit; obtain the output state |ψ(θ)>; Step 3: Based on the parameter θ in the output state obtained after training in step 2, the expected value is used as the optimized loss function L, and the gradient descent method is used to calculate the optimal loss function L. Update θ; In step 3, the training parameters θ are defined, and the expected value of the loss function with respect to |ψ(θ)> is defined as: Update θ; In the formula, Represented by the Pauli matrix σ on n qubits x , σ y , σ z The tensor product combination composed of ; According to the gradient descent method, the partial derivative of the loss function L(θ) is calculated Update θ, then input the updated parameters into the quantum computer, update the parameterized quantum circuit U(θ), ​​and calculate the expected value. If the expected value is not reached, continue to optimize until the optimal parameterized quantum circuit U(θ) is obtained. Step 4: According to the trained quantum circuit U(θ), ​​obtain its corresponding matrix expression and extract the maximum eigenvector V corresponding to the maximum eigenstate m , f n =V m ; fn represents the precoding matrix; V m Indicated by M m Decomposed vector; Step 5: Generate precoding matrix F opt =diag{f1,f2,...f n }, applied in millimeter-wave massive MIMO systems.

2. The precoding method combined with quantum variation in a millimeter wave massive MIMO system according to claim 1, characterized in that: In step 1, the Saleh-Valenzuela channel model is used: Among them, N t is the number of transmitting antennas of the base station, N r is the number of user receiving antennas; L is the millimeter wave scattering beam, δ i represents the gain of the ith scattering beam path, θ i denote the departure angle and arrival angle of the ith path respectively, and θ i ∈[0,2π], represents the user antenna array response vector, represents the base station antenna array response vector, α BS (θ i ) is expressed as follows, where j represents an imaginary number: Where λ is the wavelength and d is the distance between the antennas.

3. The precoding method combined with quantum variation in a millimeter wave massive MIMO system according to claim 2, characterized in that: In step 1, it is assumed that the number of transmitted symbols, the number of transmitting antennas, and the number of receiving antennas are equal, that is, d = N t =N r ; The signal sent by the transmitter is expressed as x=Fs Wherein, F represents the precoding matrix of the transmitting end, and s represents the symbol sent by the transmitting end; The signal received by the receiving end is expressed as y=HFs+n Where n represents an additive complex Gaussian white noise vector with a mean of 0 and a variance of σ 2 , the signal after being processed by the receiving matrix W is expressed as In the mmWave massive MIMO system, assuming W H W = 1, the system reachability and rate are expressed as follows, where I represents the identity matrix; The optimization problem with the goal of system reachability and maximum rate is described as follows, where Tr represents the trace of the matrix and P represents the power s.t.Tr(FF H )≤P Let the channel matrix H be H = [H1, H2, ..., H N ],in, Then HF=[H1H1,H2F2,…,H N F N ], so the above formula is converted to Among them, M m The SVD decomposition of W m =U m ∑V m H , U m and V m Represents the left and right singular vectors of SVD decomposition, and the largest eigenvector is the optimal solution.

4. The precoding method combined with quantum variation in a millimeter wave massive MIMO system according to claim 1, characterized in that: In step 2, M m As the system Hamiltonian, in order to successfully map the Hamiltonian to the quantum bit in the quantum circuit during quantum simulation, the Hamiltonian needs to be decomposed into a form composed of Pauli operators. The theoretical decomposition form is as follows: in n represents the number of Pauli operators in this term; Pauli operators are identified by Greek letters, σ x represents the Pauli X gate, σ y represents the Pauli Y gate, and i and j represent the subspace on which the Hamiltonian quantum term acts.

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