Downlink Beamforming Method for Non-Ideal Calibrated Decellularized mMIMO Systems

Abstract

The present invention discloses a downlink beamforming method for a non-ideal calibration-based cellular mMIMO system. First, based on the Rice fading channel model, the mapping relationship between the uplink channel and the downlink channel under non-ideal calibration is given. Then, according to the data expression received by the downlink user under non-ideal calibration conditions, the downlink rate expression of the cellular massive MIMO system is derived. Finally, aiming at maximizing the downlink sum rate, the Lagrangian dual transformation method and the scaled alternating direction multiplier method are used to iteratively solve the optimization problem of maximizing the downlink sum rate, and the optimal downlink beam sequence is obtained. The present invention reduces the negative impact of reciprocity calibration error on the system performance, reduces the performance loss caused by non-ideal calibration, and effectively improves the downlink rate of the cellular massive MIMO system under non-ideal calibration.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a downlink beamforming method for a non-ideal calibration-based cellular mMIMO system. Background Art

[0002] In recent years, as a derivative technology of coordinated multi-point cooperative communication, the cellular massive MIMO technology has been widely studied. On the one hand, the cellular network abandons the cell concept in the cellular architecture. By deploying a large number of access points (APs) around users, the communication distance between the AP and the user is greatly shortened, the path loss of signal propagation is reduced, and the inter-cell interference and handover caused by cell division are avoided. On the other hand, due to the introduction of the massive MIMO technology, by configuring multiple antennas or antenna arrays at the AP, a higher macro-diversity gain is provided for the entire system. In addition, as the number of antennas increases, the channel hardening and favorable propagation effects become more significant. In this case, the cellular massive MIMO system can obtain a higher communication capacity and better quality of service 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. Generally, the uplink channel information can be estimated by channel estimation methods, such as channel blind estimation and pilot-based estimation. By using the channel reciprocity characteristic of the time-division duplex mode, the downlink channel information can be directly given by the uplink channel estimation. Therefore, the current research on the cellular massive MIMO system assumes that it operates in the time-division duplex mode to reduce the channel estimation operation. However, the transmit and receive radio frequency links at the AP and the user terminal are two independent circuits. Due to the random fluctuation of the transceiver frequency response caused by the random influence of the circuit thermal noise, the channel reciprocity does not hold in the actual system, and the uplink and downlink channels cannot be considered completely equal. Although some existing reciprocity calibration methods can improve the above problems, the existing calibration methods rely heavily on the characteristics of channel estimation, resulting in residual errors still existing in the calibration process, causing uplink and downlink channel mismatch, further reducing the accuracy of downlink beamforming design, and causing a serious decline in the downlink communication rate. Against this background, the present invention proposes a downlink beamforming method for a non-ideal calibration-based cellular mMIMO system. Summary of the Invention

[0004] The object of the present invention is to provide a downlink beamforming method for a non-ideal calibration-based cellular mMIMO system. On the basis of considering the residual error caused by the non-ideal calibration process, by designing the downlink beam sequence, the influence of the calibration error is reduced, and the downlink rate is improved.

[0005] To achieve the above object, the technical solution of the present invention is as follows: A downlink beamforming method for a non-ideal calibration-based cellular mMIMO system, comprising the following steps:

[0006] Step 1: Based on the cellular massive MIMO system under non-ideal calibration conditions, considering the errors existing in the uplink and downlink channel reciprocity calibration process, give the functional relationship between the uplink and downlink channels;

[0007] Step 2: Based on the functional relationship and the Rice fading channel model, give the data expression received by the user in the downlink phase, and derive the downlink rate expression;

[0008] Step 3: Based on the downlink rate expression, with the downlink sum rate as the objective function, propose a downlink sum rate maximization problem with power constraints for the AP;

[0009] Step 4: Use the Lagrangian dual transformation method to reconstruct the original optimization problem, and then use the scaled alternating direction method of multipliers to iteratively solve the reconstructed problem, and then output the optimal downlink beam sequence.

[0010] Further, in Step 1, the functional relationship between the uplink and downlink channels is:

[0011] ,

[0012] ,

[0013] where, represents the downlink channel sequence between the th AP and the th user, represents the uplink channel sequence between the th AP and the th user, represents the frequency response mismatch coefficient of the th user, represents the calibrated frequency response mismatch coefficient of the th user, represents the calibration error of the frequency response mismatch coefficient of the th user, represents the frequency response mismatch coefficient matrix of the th AP, represents the calibrated frequency response mismatch coefficient matrix of the th AP, represents the calibration error matrix of the frequency response mismatch coefficient of the th AP.

[0014] Further, after the uplink channel estimation process, the uplink channel consists of two parts: uplink channel estimation and estimation error. At this time, the downlink channel is expressed as

[0015]

[0016] where represents the uplink channel estimation sequence between the -th AP and the -th user, represents the uplink channel estimation error sequence between the -th AP and the -th user, represents the downlink channel estimation sequence between the -th AP and the -th user, represents the downlink channel estimation error sequence between the -th AP and the -th user.

[0017] Further, in step 2, the data received by the user in the downlink phase is expressed as:

[0018]

[0019] where represents the total number of APs, represents the total number of users, represents the normalized downlink data transmission signal-to-noise ratio, represents the downlink beam sequence between the -th AP and the -th user, represents the downlink beam sequence between the -th AP and the -th user, represents the data symbol of the -th user, which satisfies and , represents the data symbol of the -th user, represents the additive complex Gaussian random noise received by the -th user, with a mean of 0 and a variance of 1, represents the downlink channel estimation sequence between the -th AP and the -th user, represents the downlink channel estimation error sequence between the -th AP and the -th user, denotes the conjugate transpose operation, denotes the conjugate operation, denotes the expectation operation.

[0020] In step 2, the derived downlink rate expression for the -th user is:

[0021]

[0022]

[0023] where, denotes the signal-to-interference-plus-noise ratio (SINR) of the -th user, denotes the downlink channel estimation sequence between all APs and the -th user, denotes the downlink beamforming sequence between all APs and the -th user, denotes the downlink beamforming sequence between all APs and the -th user, matrix ,

[0024] denotes the downlink channel estimation error sequence between all APs and the -th user, matrix , denotes the downlink channel estimation error sequence between all APs and the -th user, denotes the transpose operation.

[0025] Furthermore, in step 3, the downlink sum-rate maximization problem is expressed as:

[0026]

[0027] where, denotes the square of the Euclidean norm.

[0028] Furthermore, in step 4, the objective function is reconstructed using the Lagrangian dual transformation method as:

[0029]

[0030]

[0031] where, and denote the introduced auxiliary variable sequences.

[0032] In step 4, the reconstructed problem is expressed as:

[0033]

[0034] 。

[0035] Furthermore, in step 4, the first-order condition and the scaled alternating direction method of multipliers are used to iteratively solve the optimization problem, and the specific steps are as follows:

[0036] Step 4-1: Based on the first-order condition, let the objective function with respect to and be equal to 0 respectively, and we get

[0037] ,

[0038] where and represent the optimal solutions of and in each iteration respectively,

[0039] Step 4-2: Based on the scaled alternating direction method of multipliers, the augmented Lagrangian function of the reconstructed problem can be expressed as:

[0040]

[0041]

[0042] where represents the indicator function of the AP power constraint, represents the sequence of auxiliary variables of represents the sequence of scaled dual variables, represents the penalty factor,

[0043] Step 4-3: In the -th iteration, for the given values and , based on the first-order condition, let the first-order partial derivative function of the function with respect to be equal to 0, and the expression of the downlink beam sequence between all APs and the -th user in the -th iteration is expressed as

[0044]

[0045] where

[0046] , represents the dimension of The identity matrix, is the number of antennas for each AP,

[0047] Step 4-4, Given and , solve the following sub-problem based on the KKT conditions

[0048]

[0049] Obtain The expression in the th iteration is

[0050]

[0051] where ,

[0052] Step 4-5, Given and , the dual variable in the th iteration is updated to

[0053]

[0054] Step 4-6, Repeat Steps 4-1 to 4-5 until the downlink sum rate converges, end the loop and output the optimal downlink beamforming solution, i.e., , denotes the optimal beam sequence between the th AP and the th user.

[0055] An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, it implements the downlink beamforming method for the non-ideal calibration-based cellular mMIMO system described above.

[0056] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0057] (1) Most of the current existing works assume perfect channel reciprocity. The present invention takes into account the imperfect channel reciprocity and the residual error caused by non-ideal calibration, which is an inignorable performance impact factor for the actual design of wireless communication systems, thus making the present invention more practical;

[0058] (2) Based on the non-ideal calibration-based cellular large-scale MIMO system, the present invention combines the Lagrangian dual transformation method and the scaled alternating direction method of multipliers for the first time to design the downlink beam sequence for such a system, reducing the performance loss caused by calibration errors and solving the technical problems that have not been solved by most of the existing works;

[0059] (3) The calculation complexity of the present invention is relatively low, the required number of iterations is small, and the convergence speed is fast. Therefore, it has high feasibility. Description of the Drawings

[0060] Figure 1 It is the cumulative distribution function graph of the downlink rate for different downlink beam methods;

[0061] Figure 2 It is the graph of the number of iterations of the downlink beam design method. Specific Embodiments

[0062] The technical means and effects of the present invention will be further described below in conjunction with the 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.

[0063] Embodiment: This embodiment provides a downlink beam method for a non-ideal calibration-based cellular mMIMO system, aiming to reduce the deterioration of system performance caused by non-ideal calibration and improve the downlink rate. The method includes the following steps:

[0064] Step 1: Based on the cellular massive MIMO system under non-ideal calibration conditions, considering the errors existing in the uplink and downlink channel reciprocity calibration process, the functional relationship between the uplink and downlink channels is given;

[0065] Step 2: Based on the functional relationship and the Rice fading channel model, the data expression received by the user in the downlink stage is given, and the downlink rate expression is derived;

[0066] Step 3: Based on the downlink rate expression, with the downlink sum rate as the objective function, the problem of maximizing the downlink sum rate with power constraints for the AP is proposed;

[0067] Step 4: Use the Lagrangian dual transformation method to reconstruct the original optimization problem, and then use the scaled alternating direction multiplier method to iteratively solve the reconstructed problem, and then output the optimal downlink beam sequence.

[0068] Further, the present invention considers a cellular massive MIMO system under non-ideal calibration conditions, and this system includes access points AP and single-antenna users, and each AP uses antennas. Due to imperfect channel reciprocity, the functional relationship between the uplink and downlink channels is:

[0069] ,

[0070] ,

[0071] Among them, Indicates the downlink channel sequence between the th AP and the th user, Indicates the uplink channel sequence between the th AP and the th user, Indicates the frequency response mismatch coefficient of the th user, Indicates the frequency response mismatch coefficient of the th calibrated user, Indicates the calibration error of the frequency response mismatch coefficient of the th user, Indicates the frequency response mismatch coefficient matrix of the th AP, Indicates the frequency response mismatch coefficient matrix of the th calibrated AP, Indicates the calibration error matrix of the frequency response mismatch coefficient of the th AP.

[0072] Furthermore, after the uplink channel estimation process, the uplink channel consists of two parts: uplink channel estimation and estimation error. At this time, the downlink channel is expressed as

[0073]

[0074] where Indicates the uplink channel estimation sequence between the th AP and the th user, Indicates the uplink channel estimation error sequence between the th AP and the th user, Indicates the downlink channel estimation sequence between the th AP and the th user, Indicates the downlink channel estimation error sequence between the th AP and the th user.

[0075] Furthermore, in step 2, the data received by the user in the downlink phase has the following expression:

[0076]

[0077] where Indicates the total number of APs, Indicates the total number of users, Indicates the normalized downlink data transmission signal-to-noise ratio, Indicates the th downlink beam sequence between the th AP and the th user, Indicates the th downlink beam sequence between the th AP and the th user. The data symbol of the th user satisfies and Indicates the data symbol of the th user, Indicates the additive complex Gaussian random noise received by the th user, with a mean of 0 and a variance of 1. Indicates the th downlink channel estimation sequence between the th AP and the th user, Indicates the th downlink channel estimation error sequence between the th AP and the Indicates the conjugate transpose operation, Indicates the conjugate operation,

[0078] In step 2, the derived downlink rate expression for the th user is:

[0079]

[0080]

[0081] Among them, Indicates the th user's signal-to-interference-plus-noise ratio, Indicates the th downlink channel estimation sequence between all APs and the th user, Indicates the th downlink beam sequence between all APs and the th user, matrix ,

[0082] Indicates the th downlink channel estimation error sequence between all APs and the , Indicates the th downlink channel estimation error sequence between all APs and the Indicates the transpose operation.

[0083] Furthermore, with the following sum rate as the objective function and considering that each AP has a maximum power constraint, the downlink sum rate maximization problem is expressed as:

[0084]

[0085] where, represents the square of the Euclidean norm.

[0086] Furthermore, to separate the signal-to-interference-plus-noise ratio function from the logarithmic function, auxiliary variables and are introduced, and the objective function is reconstructed using the Lagrangian dual transformation method as:

[0087]

[0088]

[0089] where, and represent the introduced sequence of auxiliary variables.

[0090] Furthermore, by replacing the original objective function with the reconstructed function, the reconstructed problem of the original optimization problem is expressed as:

[0091]

[0092] Furthermore, the above reconstructed problem is iteratively solved using the first-order condition and the scaled alternating direction method of multipliers.

[0093] Step 4-1: Based on the first-order condition, let the objective function be respectively equal to 0 for the first-order partial derivative functions with respect to and , and the solutions are obtained as

[0094] ,

[0095] where, and respectively represent the optimal solutions of and in each iteration,

[0096] Step 4-2: Based on the scaled alternating direction method of multipliers, the Lagrangian augmented function of the above reconstructed problem can be expressed as:

[0097]

[0098]

[0099] where, An indicator function representing the AP power constraint, denoted as a sequence of auxiliary variables denoted as a sequence of scaled dual variables, denoted as a penalty factor,

[0100] Step 4-3: In the th iteration, for the given values and , based on the first-order condition, set the first-order partial derivative function of the function with respect to equal to 0. The expression of the downlink beam sequence between all APs and the th user in the th iteration is expressed as

[0101]

[0102] where

[0103] , denotes the identity matrix of dimension , is the number of antennas of each AP. Step 4-4: Given and , solve the following sub-problem based on the KKT condition

[0104]

[0105] to obtain The expression in the th iteration is

[0106]

[0107] where ,

[0108] Step 4-5: Given and , the expression of the dual variable in the th iteration is updated as

[0109]

[0110] Step 4-6: Repeat Steps 4-1 to 4-5 until the downlink sum rate converges, end the loop and output the optimal downlink beamforming solution, i.e., , where denotes the optimal beam sequence between the th AP and the ​

[0111] Further, substitute the obtained optimal downlink beam sequence into the downlink rate expression to calculate the downlink rate of each user.

[0112] Please refer to Figure 1 , it can be found that when the ordinate is equal to 0.5, the downlink sum rate value corresponding to the ideal calibration case 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). Compared with the ideal calibration, the two decrease by 46.94% and 33.74% respectively, because the calibration error caused by non-ideal calibration seriously degrades the system performance. Under the same conditions, the downlink sum rate of the method of the present invention is 37.63 (bit / s / Hz), which increases by 37.43% and 10.06% compared with the maximum ratio transmission and zero-forcing precoding, fully verifying that the beam design scheme proposed by the method of the present invention can effectively reduce the influence of calibration error, make up for the performance loss caused by non-ideal calibration, and improve the system performance.

[0113] Please refer to Figure 2 , it can be found that as the number of iterations increases, the downlink sum rate gradually increases and converges. Even for a large-scale system, that is, when the number of APs is 80 and the number of users is 30, the method of the present invention can still converge after about 4 iterations, effectively demonstrating that the method of the present invention has good feasibility.

[0114] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope 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: Reconstruct the original optimization problem using the Lagrange dual transformation method, and then iteratively solve the reconstruction problem using the scaled alternating direction multiplier method to output the optimal downlink beam sequence; In step 2, the data r received by the user in the downlink phase k The expression is: Where M represents the total number of APs, K represents the total number of users, and ρ d represents the normalized downlink data transmission signal-to-noise ratio, w mk represents the downlink beam sequence between the mth AP and the kth user, W mk′ represents the downlink beam sequence between the mth AP and the k′th user, q k represents the data symbol of the kth user, which satisfies E{|q k | 2 }=1 and q k′ represents the data symbol of the k′th user, n k represents the additive complex Gaussian random noise received by the kth user, with a mean of 0 and a variance of 1. represents the downlink channel estimation sequence between the mth AP and the kth user, represents the downlink channel estimation error sequence between the mth AP and the kth user, (·) H represents the conjugate transpose operation, (·) * represents the conjugate operation, and E{·} represents the expectation operation; In step 2, the derived downlink rate expression of the kth user is: Among them, SINR k represents the signal-to-interference-noise ratio of the kth user, represents the downlink channel estimation sequence between all APs and the kth user, represents the downlink beam sequence between all APs and the kth user, represents the downlink beam sequence between all APs and the k′th user, and the matrix represents the downlink channel estimation error sequence between all APs and the kth user, and the matrix represents the downlink channel estimation error sequence between all APs and the kth user, (·) T Represents the transpose operation; In step 3, the downlink and rate maximization problem is expressed as: Among them, ||·|| 2 represents the Euclidean norm squared; In step 4, the objective function is reconstructed using the Lagrange dual transformation method as follows: Where γ=[γ1,...,γ K ] T and y = [y1, ..., y K ] T Represents the sequence of auxiliary variables introduced; In step 4, the reconstruction problem is expressed as:

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, represents the downlink channel sequence between the mth AP and the kth user, g m k represents the uplink channel sequence between the mth AP and the kth user, f k represents the frequency response mismatch coefficient of the kth user, represents the frequency response mismatch coefficient of the calibrated k-th user, represents the calibration error of the frequency response mismatch coefficient of the kth user, B m represents the frequency response mismatch coefficient matrix of the mth AP, represents the frequency response mismatch coefficient matrix of the calibrated m-th AP, The calibration error matrix representing the frequency response mismatch coefficients of the mth AP.

3. 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 f(w k , γ k ,y k ) respectively about γ k and k The first-order partial derivative of is equal to 0, and we get in, and Respectively represent the k and k 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: Among them, f(z mk ) represents the indicator function of AP power constraint, z mk Indicates w mk Auxiliary variable sequence, μ mk represents the scaled dual variable sequence, ε represents the penalty factor, Step 4-3: In the (i)th iteration, for a given value and Based on the first-order condition, let the function L(w k , z mk , μ mk )About w k The first-order partial derivative function of is equal to 0, and the expression of the downlink beam sequence between all APs and the k-th user in the (i+1)th iteration is expressed as: in, , I MN represents the unit matrix of dimension MN×MN, where N is the number of antennas of each AP, Step 4-4: Given and Based on the KKT condition, solve the following sub-problems get The expression in the (i+1)th iteration is in, Step 4-5: Given and Dual variable μ mk The expression in the (i+1)th 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 the optimal beam sequence between the mth AP and the kth user.

4. 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 3 above is implemented.

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