Downlink beam method for removing cellular mMIMO system based on non-ideal calibration

Abstract

The invention discloses a method for removing a downlink beam of a cellular mMIMO (multiple input multiple output) system based on non-ideal calibration, which comprises the following steps of: firstly, giving a mapping relation between an uplink channel and a downlink channel under non-ideal calibration based on a Rician fading channel model, and then, according to an expression of data received by a downlink user under a non-ideal calibration condition, calculating a downlink beam of the cellular mMIMO system based on the non-ideal calibration. According to the method, a downlink rate expression of a cellular-removed large-scale MIMO system is deduced, and finally, a downlink sum rate maximization optimization problem is iteratively solved by using a Lagrangian dual transformation method and a scaling type alternating direction multiplier method with a purpose of maximizing the downlink sum rate, so that an optimal downlink beam sequence is obtained. According to the method, the negative influence of a reciprocity calibration error on the system performance is reduced, the performance loss caused by non-ideal calibration is reduced, and the downlink rate of the cellular-removed large-scale MIMO system under the non-ideal calibration is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a downlink beam method for a cellular mMIMO system based on non-ideal calibration. Background Art

[0002] In recent years, as a derivative technology of coordinated multi-point cooperative communication, decellularized massive MIMO technology has been widely studied. On the one hand, decellularized networks abandon the concept of cells in cellular architectures. By deploying a large number of access points (APs) around users, the communication distance between APs and users is greatly shortened, the path loss of signal propagation is reduced, and the interference and handover between cells caused by cell division are avoided. On the other hand, due to the introduction of massive MIMO technology, by configuring multiple antennas or antenna arrays on APs, a higher macro diversity gain is provided for the entire system. In addition, with the increase in the number of antennas, channel hardening and favorable propagation effects are more significant. In this case, the decellularized massive MIMO system can obtain higher communication capacity and better service quality even with a relatively simple signal reception scheme.

[0003] In wireless communication, channel state information is very important for the entire communication process, which determines the quality of signal detection and reception. In general, uplink channel information can be estimated by channel estimation methods, such as blind channel estimation and estimation based on pilot transmission. Using the channel reciprocity characteristics of the time division duplex mode, downlink channel information can be directly given by the uplink channel estimation. Therefore, current research on decellularized large-scale MIMO systems assumes that they work in time division duplex mode to reduce channel estimation operations. However, the transceiver RF links of the AP and the user end are two independent circuits. Due to the random fluctuations in the transceiver frequency response caused by the random influence of circuit thermal noise, channel reciprocity cannot be established in the actual system, and the uplink and downlink channels cannot be considered to be completely equal. Although some existing reciprocity calibration methods can improve the above problems, the existing calibration methods are heavily dependent on the characteristics of channel estimation, resulting in residual errors in the calibration process, causing uplink and downlink channel mismatches, thereby reducing the accuracy of downlink beam design and causing a serious decrease in downlink communication rate. In this context, the present invention proposes a downlink beam method for decellularized mMIMO systems based on non-ideal calibration. Summary of the invention

[0004] The present invention aims to provide a downlink beam method for a cellular mMIMO system based on non-ideal calibration, which reduces the influence of the calibration error and improves the downlink rate by designing a downlink beam sequence based on the residual error caused by the non-ideal calibration process.

[0005] In order to achieve the above object, the technical solution of the present invention is as follows: A downlink beam method for a cellular mMIMO system based on non-ideal calibration comprises the following steps: Step 1: Based on the decellularized massive MIMO system under non-ideal calibration conditions, considering the errors in the calibration process of uplink and downlink channel reciprocity, a functional relationship between the uplink and downlink channels is given; Step 2: Based on the functional relationship and the Rice fading channel model, an expression for the data received by the user in the downlink phase is given, and an expression for the downlink rate is derived; Step 3: Based on the downlink rate expression, taking the downlink sum rate as the objective function, the problem of maximizing the downlink sum rate of the AP with power constraints is proposed; Step 4: Use the Lagrange dual transformation method to reconstruct the original optimization problem, and then use the scaled alternating direction multiplier method to iteratively solve the reconstruction problem, and then output the optimal downlink beam sequence.

[0006] Furthermore, in step 1, the functional relationship between the uplink and downlink channels is: , , in, Indicates AP and The downlink channel sequence between users is Indicates AP and The uplink channel sequence between users is Indicates The frequency response mismatch coefficient of each user is Indicates the calibration The frequency response mismatch coefficient of each user is Indicates The calibration error of the frequency response mismatch coefficient of each user, Indicates The frequency response mismatch coefficient matrix of APs is: Indicates the calibration The frequency response mismatch coefficient matrix of APs is: Indicates The calibration error matrix of the frequency response mismatch coefficients of the APs.

[0007] Furthermore, after the uplink channel estimation process, the uplink channel includes two parts: the uplink channel estimation and the estimation error. At this time, the downlink channel is expressed as in, Indicates AP and The uplink channel estimation sequence between users is: Indicates AP and The uplink channel estimation error sequence between users is: Indicates AP and The downlink channel estimation sequence between users is: Indicates AP and The downlink channel estimation error sequence between users.

[0008] Furthermore, in step 2, the data received by the user in the downlink phase The expression is: in, Indicates the total number of APs. Indicates the total number of users. represents the normalized downlink data transmission signal-to-noise ratio, Indicates AP and The downlink beam sequence between users, Indicates AP and The downlink beam sequence between users, Indicates The data symbol of each user satisfies and , Indicates The data symbol of each user, Indicates The additive complex Gaussian random noise received by each user has a mean of 0 and a variance of 1. Indicates AP and The downlink channel estimation sequence between users is: Indicates AP and The downlink channel estimation error sequence between users is: represents the conjugate transpose operation, represents the conjugate operation, Represents the expectation operation.

[0009] In step 2, the derived The downlink rate expression of a user is: in, Indicates The signal-to-interference-noise ratio of each user is Indicates that all APs and The downlink channel estimation sequence between users is: Indicates that all APs and The downlink beam sequence between users, Indicates that all APs and The downlink beam sequence between users, matrix , Indicates that all APs and The downlink channel estimation error sequence between users is the matrix , Indicates that all APs and The downlink channel estimation error sequence between users is: Represents a transpose operation.

[0010] Furthermore, in step 3, the downlink and rate maximization problem is expressed as: in, represents the Euclidean norm squared.

[0011] Furthermore, in step 4, the objective function is reconstructed using the Lagrange dual transformation method as follows: in, and Represents the sequence of auxiliary variables introduced.

[0012] In step 4, the reconstruction problem is expressed as: .

[0013] Furthermore, in step 4, the optimization problem is iteratively solved using the first-order condition and the scaling alternating direction multiplier method. The specific steps are as follows: Step 4-1: Based on the first-order condition, let the objective function About and The first-order partial derivative of is equal to 0, and we get , in, and Respectively, in each iteration and The optimal solution of Step 4-2: Based on the scaled alternating direction multiplier method, the Lagrangian augmented function of the reconstruction problem can be expressed as: in, An indicator function representing the AP power constraint, express Auxiliary variable sequence, represents the scaled dual variable sequence, represents the penalty factor, Step 4-3, in In the iterations, for a given value and , based on the first-order condition, let the function about The first-order partial derivative of is equal to 0, and all APs are The downlink beam sequence between users is The expression in the iteration is expressed as in, , The dimension is The identity matrix of is the number of antennas for each AP, Step 4-4: Given and , based on the KKT condition, solve the following sub-problems get In the The expression in the iteration is in, , Step 4-5: Given and , dual variable In the The expression in the iteration is updated to Step 4-6: Repeat steps 4-1 to 4-5 until the downlink and rate converge, end the loop and output the optimal downlink beam solution, i.e. , Refers to AP and The optimal beam sequence among users.

[0014] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the downlink beam method based on non-ideal calibration to decellularize the mMIMO system is implemented.

[0015] Compared with the prior art, the present invention has the following beneficial effects: (1) Most existing works assume perfect channel reciprocity, while the present invention takes into account the residual error caused by imperfect channel reciprocity and non-ideal calibration, which is a performance influencing factor that cannot be ignored for the actual design of wireless communication systems, making the present invention more practical; (2) Based on the non-ideal calibration decellularized massive MIMO system, the present invention combines the Lagrangian dual transformation method and the scaled alternating direction multiplier method for the first time to design the downlink beam sequence for such a system, thereby reducing the performance loss caused by calibration errors and solving technical problems that have not been solved in most existing works. (3) The present invention has low computational complexity, requires fewer iterations, and has a fast convergence speed, thus having high feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is the cumulative distribution function diagram of downlink rate for different downlink beam methods; Figure 2 Graph showing the number of iterations for the downlink beam design method. DETAILED DESCRIPTION

[0017] The technical means and effects of the present invention are further described below in conjunction with the accompanying drawings to make the present invention easy to understand. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and cannot be used to limit the protection scope of the present invention.

[0018] Embodiment: This embodiment provides a downlink beam method for a cellular mMIMO system based on non-ideal calibration, which aims to reduce the degradation of system performance caused by non-ideal calibration and improve the downlink rate. The method includes the following steps: Step 1: Based on the decellularized massive MIMO system under non-ideal calibration conditions, considering the errors in the calibration process of uplink and downlink channel reciprocity, a functional relationship between the uplink and downlink channels is given; Step 2: Based on the functional relationship and the Rice fading channel model, an expression for the data received by the user in the downlink phase is given, and an expression for the downlink rate is derived; Step 3: Based on the downlink rate expression, taking the downlink sum rate as the objective function, the problem of maximizing the downlink sum rate of the AP with power constraints is proposed; Step 4: Use the Lagrange dual transformation method to reconstruct the original optimization problem, and then use the scaled alternating direction multiplier method to iteratively solve the reconstruction problem, and then output the optimal downlink beam sequence.

[0019] Furthermore, the present invention considers a decellularized massive MIMO system under non-ideal calibration conditions, the system comprising Access Points AP and single antenna users, each AP uses Antennas. Due to the imperfect channel reciprocity, the functional relationship between the uplink and downlink channels is: , , in, Indicates AP and The downlink channel sequence between users is Indicates AP and The uplink channel sequence between users is Indicates The frequency response mismatch coefficient of each user is Indicates the calibration The frequency response mismatch coefficient of each user is Indicates The calibration error of the frequency response mismatch coefficient of each user, Indicates The frequency response mismatch coefficient matrix of APs is: Indicates the calibration The frequency response mismatch coefficient matrix of APs is: Indicates The calibration error matrix of the frequency response mismatch coefficients of the APs.

[0020] Furthermore, after the uplink channel estimation process, the uplink channel includes two parts: the uplink channel estimation and the estimation error. At this time, the downlink channel is expressed as in, Indicates AP and The uplink channel estimation sequence between users is: Indicates AP and The uplink channel estimation error sequence between users is: Indicates AP and The downlink channel estimation sequence between users is: Indicates AP and The downlink channel estimation error sequence between users.

[0021] Furthermore, in step 2, the data received by the user in the downlink phase The expression is: in, Indicates the total number of APs. Indicates the total number of users. represents the normalized downlink data transmission signal-to-noise ratio, Indicates AP and The downlink beam sequence between users, Indicates AP and The downlink beam sequence between users, Indicates The data symbol of each user satisfies and , Indicates The data symbol of each user, Indicates The additive complex Gaussian random noise received by each user has a mean of 0 and a variance of 1. Indicates AP and The downlink channel estimation sequence between users is: Indicates AP and The downlink channel estimation error sequence between users is: represents the conjugate transpose operation, represents the conjugate operation, Represents the expectation operation.

[0022] In step 2, the derived The downlink rate expression of a user is: in, Indicates The signal-to-interference-noise ratio of each user is Indicates that all APs and The downlink channel estimation sequence between users is: Indicates that all APs and The downlink beam sequence between users, Indicates that all APs and The downlink beam sequence between users, matrix , Indicates that all APs and The downlink channel estimation error sequence between users is the matrix , Indicates that all APs and The downlink channel estimation error sequence between users is: Represents a transpose operation.

[0023] Furthermore, taking the downlink and rate as the objective function and considering that each AP has a maximum power limit, the downlink and rate maximization problem is expressed as: in, represents the Euclidean norm squared.

[0024] Furthermore, in order to separate the signal-to-interference-noise ratio function from the logarithmic function, an auxiliary variable is introduced and , the objective function is reconstructed using the Lagrange dual transformation method as follows: in, and Represents the sequence of auxiliary variables introduced.

[0025] Furthermore, the original objective function is replaced by the reconstruction function, and the reconstruction problem of the original optimization problem is expressed as: Furthermore, the reconstruction problem is iteratively solved using the first-order condition and the scaled alternating direction multiplier method.

[0026] Step 4-1: Based on the first-order condition, let the objective function About and The first-order partial derivative of is equal to 0, and the solution is , in, and Respectively, in each iteration and The optimal solution of Step 4-2: Based on the scaled alternating direction multiplier method, the Lagrangian augmented function of the above reconstruction problem can be expressed as: in, An indicator function representing the AP power constraint, express Auxiliary variable sequence, represents the scaled dual variable sequence, represents the penalty factor, Step 4-3, in In the iterations, for a given value and , based on the first-order condition, let the function about The first-order partial derivative of is equal to 0, and all APs are The downlink beam sequence between users is The expression in the iteration is expressed as in, , The dimension is The identity matrix of For the number of antennas for each AP, step 4-4, given and , based on the KKT condition, solve the following sub-problems get In the The expression in the iteration is in, , Step 4-5: Given and , dual variable In the The expression in the iteration is updated to Step 4-6: Repeat steps 4-1 to 4-5 until the downlink and rate converge, end the loop and output the optimal downlink beam solution, i.e. , Refers to AP and The optimal beam sequence among users.

[0027] Furthermore, the obtained optimal downlink beam sequence is substituted into the downlink rate expression to calculate the downlink rate of each user.

[0028] See also Figure 1It can be found that when the vertical coordinate is equal to 0.5, the corresponding downlink sum rate value under ideal calibration is 51.60 (bit / s / Hz), the downlink sum rate of the maximum ratio transmission scheme under non-ideal calibration is 27.38 (bit / s / Hz), and the downlink sum rate of zero-forcing precoding is 34.19 (bit / s / Hz), which are respectively reduced by 46.94% and 33.74% compared with ideal calibration. This is because the calibration error caused by non-ideal calibration seriously reduces the system performance. Under the same circumstances, the downlink sum rate of the method of the present invention is 37.63 (bit / s / Hz), which is 37.43% and 10.06% higher than that of maximum ratio transmission and zero-forcing precoding, which fully verifies that the beam design scheme proposed by the method of the present invention can effectively reduce the impact of calibration errors, compensate for the performance loss caused by non-ideal calibration, and improve system performance.

[0029] See also Figure 2 It can be found that with the increase of the number of iterations, the downlink rate gradually increases and converges. Even for a large-scale system, that is, the number of APs is 80 and the number of users is 30, the method of the present invention can still converge in about 4 iterations, which effectively illustrates that the method of the present invention has good feasibility.

[0030] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A downlink beamforming method for a cellular mMIMO system based on non-ideal calibration, characterized in that: The method comprises the following steps: Step 1: Based on the decellularized massive MIMO system under non-ideal calibration, considering the errors in the calibration process of uplink and downlink channel reciprocity, a functional relationship between the uplink and downlink channels is given; Step 2: Based on the functional relationship and the Rice fading channel model, the data expression received by the user in the downlink phase is given, and the downlink rate expression is derived; Step 3: Based on the downlink rate expression, taking the downlink sum rate as the objective function, the problem of maximizing the downlink sum rate of the AP with power constraints is proposed; Step 4: Use the Lagrange dual transformation method to reconstruct the original optimization problem, and then use the scaled alternating direction multiplier method to iteratively solve the reconstruction problem, and then output the optimal downlink beam sequence.

2. The downlink beamforming method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 1, the functional relationship between the uplink and downlink channels is: ， ， in, Indicates AP and The downlink channel sequence between users is Indicates AP and The uplink channel sequence between users is Indicates The frequency response mismatch coefficient of each user is Indicates the calibration The frequency response mismatch coefficient of each user is Indicates The calibration error of the frequency response mismatch coefficient of each user, Indicates The frequency response mismatch coefficient matrix of APs is: Indicates the calibration The frequency response mismatch coefficient matrix of APs is: Indicates The calibration error matrix of the frequency response mismatch coefficients of the APs.

3. The downlink beamforming method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 2, the data received by the user in the downlink phase The expression is: in, Indicates the total number of APs. Indicates the total number of users. represents the normalized downlink data transmission signal-to-noise ratio, Indicates AP and The downlink beam sequence between users, Indicates AP and The downlink beam sequence between users, Indicates The data symbol of each user satisfies and , Indicates The data symbol of each user, Indicates The additive complex Gaussian random noise received by each user has a mean of 0 and a variance of 1. Indicates AP and The downlink channel estimation sequence between users is: Indicates AP and The downlink channel estimation error sequence between users is: represents the conjugate transpose operation, represents the conjugate operation, Represents the expectation operation.

4. The downlink beamforming method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 2, the derived The downlink rate expression of a user is: in, Indicates The signal-to-interference-noise ratio of each user is Indicates that all APs and The downlink channel estimation sequence between users is: Indicates that all APs and The downlink beam sequence between users, Indicates that all APs and Downlink beam sequence between users Column, Matrix , Indicates that all APs and The downlink channel estimation error sequence between users is the matrix , Indicates that all APs and The downlink channel estimation error sequence between users is: Represents a transpose operation.

5. The downlink beam method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 3, the downlink and rate maximization problem is expressed as: in, represents the Euclidean norm squared.

6. The downlink beam method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 4, the objective function is reconstructed using the Lagrange dual transformation method as follows: in, and Represents the sequence of auxiliary variables introduced.

7. The downlink beam method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 4, the reconstruction problem is expressed as: 。 8. The downlink beamforming method for decellularized mMIMO system based on non-ideal calibration according to claim 1, characterized in that: In step 4, the optimization problem is iteratively solved using the first-order condition and the scaled alternating direction multiplier method. The specific steps are as follows: Step 4-1: Based on the first-order condition, let the objective function About and The first-order partial derivative of is equal to 0, and we get ， in, and Respectively, in each iteration and The optimal solution of Step 4-2: Based on the scaled alternating direction multiplier method, the Lagrangian augmented function of the reconstruction problem is expressed as: in, An indicator function representing the AP power constraint, express Auxiliary variable sequence, represents the scaled dual variable sequence, represents the penalty factor, Step 4-3, in In the iterations, for a given value and , based on the first-order condition, let the function about The first-order partial derivative of is equal to 0, and all APs are The downlink beam sequence between users is The expression in the iteration is expressed as: in, , The dimension is The identity matrix of is the number of antennas for each AP, Step 4-4: Given and , based on the KKT condition, solve the following sub-problems: get In the The expression in the iteration is in, , Step 4-5: Given and , dual variable In the The expression in the iteration is updated to Step 4-6: Repeat steps 4-1 to 4-5 until the downlink and rate converge, end the loop and output the optimal downlink beam solution, i.e. , Refers to AP and The optimal beam sequence among users.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the downlink beam method based on non-ideal calibration de-cellularized mMIMO system as described in any one of claims 1 to 8 above is implemented.

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