A multi-user beam tracking method for millimeter wave array communication based on auxiliary beam

Abstract

The present invention provides a millimeter wave array communication multi-user beam tracking method based on auxiliary beams, comprising the following steps: constructing a millimeter wave multi-user downlink communication signal receiving model and a millimeter wave communication downlink channel model; constructing a beam tracking optimization problem model; solving the constructed optimization problem using a beam tracking method based on auxiliary beams to obtain an estimated value of the channel departure angle. The present invention provides two solution methods, one of which is to improve the angle judgment accuracy by transmitting left and right detection beams, multiplexing communication beams, and constructing a small-dimensional sparse model, while achieving high-precision beam tracking, expanding the beam tracking range, and solving the problem of a small beam tracking range in existing algorithms; the other is to estimate the channel departure angle by transmitting a differential beam as an auxiliary beam and introducing a sum-difference ratio, which can obtain a larger beam tracking range and provide high-precision beam tracking results with lower tracking overhead compared to existing algorithms.

Description

Technical Field

[0001] The invention relates to a millimeter wave array communication multi-user beam tracking method based on auxiliary beams, belonging to the technical field of millimeter wave wireless communications. Background Art

[0002] Millimeter wave communication, due to its abundant high-quality spectrum resources, can provide high-speed data transmission rates for wireless networks and is one of the key technologies for 5G and sub-6G. The millimeter wave band above the 20GHz band can provide a channel bandwidth of 1-2GHz and a data transmission rate of up to 20Gb / s, but the high path fading inherent in the millimeter wave band and the low diffraction ability around obstacles will have a certain impact on the communication performance of the system. Beamforming technology can provide high-gain communication beams to compensate for millimeter wave path fading, providing a solution to overcome the millimeter wave path loss problem.

[0003] In order to achieve accurate beamforming, it is necessary to obtain accurate channel state information (CSI) through channel estimation. However, in the current application scenario of large-scale multiple input and multiple output (MIMO) antenna array technology, the size of the channel matrix including CSI will become extremely large. At this time, the traditional channel estimation scheme will bring unacceptable estimation overhead, and the method of obtaining CSI by reducing the estimation overhead through beam training is widely adopted. The so-called beam training is for the user end to find the transceiver beam combination that best matches the channel between the user and the base station, that is, by adjusting the transceiver beam sequence of the base station and the user end, the user's received signal power is maximized, thereby avoiding the huge estimation overhead caused by estimating the complete channel matrix.

[0004] However, for CSI acquisition in mobile communication scenarios, if beam training is continued, a large training overhead will still be generated. This is because the target user is in a mobile state, and the base station needs to continuously obtain CSI in real time and select the best beam pointing to the user based on the real-time CSI. Therefore, the base station needs to frequently perform beam training procedures, resulting in high training overhead. Therefore, in order to reduce the channel estimation overhead in mobile communication scenarios, the actual millimeter wave massive MIMO system requires an effective beam tracking solution, that is, to track and obtain the best transmit and receive beam sequence after the user moves.

[0005] Reference [1] proposed an estimation algorithm for channel estimation using auxiliary beams under the millimeter wave massive MIMO communication architecture. Compared with the traditional grid beam scanning method, this algorithm can provide high-precision channel arrival angle (AoA) and channel departure angle (AoD) estimation. Reference [2], based on reference [1], proposed a beam tracking scheme supported by auxiliary beams in the millimeter wave broadband mobile communication scenario. This algorithm does not rely on the established angle change model and can provide high-precision angle tracking results. However, due to the inherent limitations of the auxiliary beam algorithm, the tracking range of this algorithm is fixed and it is not possible to effectively track high-speed moving objects.

[0006] [1]Zhu D, Choi J, Heath R W.Auxiliary Beam Pair Enabled AoD and AoAEstimation in Closed-loop Large-scale mmWave MIMO Systems[J]. IEEETransactions on Wireless Communications, 2017, 16(7): 4770-4785.

[0007] [2] Zhu D, Choi J, Qian C, et al. High-Resolution Angle Tracking for Mobile Wideband Millimeter-Wave Systems with Antenna Array Calibration[J]. IEEE Transactions on Wireless Communications, 2018, 17(11): 7173-7189. Summary of the invention

[0008] Technical problem: For multi-user beam tracking in millimeter wave mobile communication scenarios, in order to reduce beam tracking overhead and obtain high-precision channel AoD estimation, the present invention provides a millimeter wave array communication multi-user tracking method based on auxiliary beams. By multiplexing communication beams and constructing a small-dimensional sparse model to improve the angle judgment accuracy, a larger beam tracking range can be obtained compared to the method in document [2] without a large performance loss. At the same time, the present invention discloses a beam tracking method when the auxiliary beam is a differential beam. Compared with the method in document [2], a larger beam tracking range can be obtained with lower overhead, while the tracking performance is similar.

[0009] Technical solution: To achieve the purpose of the present invention, the technical solution adopted by the present invention is a millimeter wave array communication multi-user beam tracking method based on auxiliary beams, and the method comprises the following steps:

[0010] (1) Construct a millimeter-wave multi-user downlink communication signal reception model and a millimeter-wave communication downlink channel model;

[0011] (2) Construct an optimization model for beam tracking;

[0012] (3) The optimization problem constructed in (2) is solved by using a beam tracking method based on an auxiliary beam to obtain an estimated value of the channel AoD; two solution methods are included. The first method is that the base station transmits left and right detection beams and multiplexes the communication beams, and the user solves the problem by constructing a small-dimensional sparse model; the second method is that the base station transmits a differential beam as an auxiliary beam to solve the problem; the first method or the second method is used to solve the optimization problem.

[0013] Furthermore, consider a downlink communication scenario where a base station serves K users. Both the base station and the user end use uniform linear antenna arrays and the distance between two adjacent antennas is half the wavelength. The user end uses an analog beamforming architecture. Each user communicates with N users through one RF link. r Root receiving antennas are connected; the base station is equipped with N t transmit antennas and adopt a fully connected hybrid beamforming architecture. RF The RF links are connected to the N t Antennas connected and satisfying N t >>N RF ≥K, the method for constructing the millimeter wave multi-user communication downlink signal receiving model and the millimeter wave communication downlink channel model in step (1) is as follows:

[0014] Step (1.1), the millimeter wave multi-user communication downlink signal reception model is established as

[0015]

[0016] where y k represents the received signal of the kth user; and They represent the analog beamforming matrix and the digital beamforming matrix at the base station end respectively; represents the simulated beamforming vector used by the kth user to receive the base station signal; represents the millimeter wave downlink MIMO channel between the base station and the kth user; Represents the transmission signal vector, satisfying P is the total transmit power of the base station; represents the zero-mean additive complex Gaussian white noise vector received by the kth user and satisfies (·) H Represents the conjugate transpose operation.

[0017] Step (1.2), assuming that there is L between the base station and the kth user equipment k The following channel model is used to model the millimeter wave communication downlink channel:

[0018]

[0019] where α l，k represents the channel gain of the lth path, θ l，k ∈[-1, 1] is the channel AoD of the lth path, v l，k ∈[-1, 1] represents the channel AoA of the lth path; a(N t , θ) represents the array steering vector, and the specific expression is

[0020]

[0021] In the above formula, (·) T Represents a transpose operation.

[0022] Furthermore, the method for establishing the optimization problem model of beam tracking in step (2) is as follows:

[0023] Step (2.1), define f k =F RF [F BB ] ：，k represents the hybrid beamforming vector of the base station pointing to the kth user, where [F BB ] ：，k Indicates F BB The kth column of the base station is designed to best match H k f k and w k , the optimization problem is established as follows:

[0024]

[0025]

[0026] where ||·||2 represents the l2 norm of the vector.

[0027] In step (2.2), consider the beam tracking of the channel AoD at the base station end, and use time division multiple access to perform beam tracking for multiple users separately, so the subscript k can be omitted. If the line-of-sight path of the channel is much stronger than the non-line-of-sight path, the impact of the non-line-of-sight path on beam tracking can be ignored, and only the line-of-sight path is considered. The millimeter wave downlink channel model is simplified to

[0028]

[0029] Where α, v and θ represent the line-of-sight path gain, channel AoA and channel AoD respectively; L represents the number of paths between the base station and the user.

[0030] Furthermore, the method for solving the optimization problem constructed in step (2.1) using the first method is as follows:

[0031] Step (3.1.1), define the communication beam direction of the base station at time t as η, define the channel AoD of the user at time t+1 as θ, and define an auxiliary beam pair as two beams pointing to η-δ and η+δ respectively. These two beams are expressed as

[0032]

[0033]

[0034] The parameters The spatial angle domain pointing difference of a pair of auxiliary beams is determined to be 2 / N t .

[0035] To estimate θ, the base station first transmits auxiliary beam a(N t ,η-δ), the user adopts the steering vector a(N r , v) as the receiving beam, ignoring the impact of non-line-of-sight on beam tracking and only considering the line-of-sight path, the received signal is expressed as

[0036]

[0037] Where x is the pilot signal sent by the base station to the user, satisfying The power constraint of the received signal is expressed as

[0038]

[0039] After noise averaging, x Δ Simplified expression:

[0040]

[0041] The base station transmits auxiliary beam a(N t ,η+δ), the user adopts beam a(N r , v) as the receiving beam, ignoring the impact of non-line-of-sight on beam tracking and only considering the line-of-sight path, the received signal is expressed as

[0042]

[0043] The corresponding received signal power is approximately expressed as

[0044]

[0045] Step (3.1.2), based on the received signal power strength x Δ and x ∑ , define the metric ratio ζ as

[0046]

[0047]

[0048] definition Differentiating ζ with respect to z gives

[0049]

[0050] Use derivatives to divide the interval: when |θ-η|≤δ, It shows that the metric ratio ζ is a monotonically decreasing function when θ-η∈(-δ, δ), then the estimated value of θ is obtained according to the inverse function of v

[0051]

[0052] When |θ-η|>δ, This shows that the metric ratio ζ is a monotonically increasing function when θ-η<-δ and θ-η>δ. At this time, the estimated values ​​of θ obtained by performing inverse function operations in the two monotonic intervals are

[0053]

[0054] In the auxiliary beam tracking algorithm in the literature [2], in order to ensure that the metric ratio ζ remains monotonic within a fixed interval, only the interval θ-η∈(-δ, δ) is used for beam tracking, so the beam tracking range is only 2δ.

[0055] Furthermore, the process of solving the problem using the first method further includes step (3.1.3) by multiplexing the communication beam a(N t , n) to expand the beam tracking range, the subdivision steps are as follows:

[0056] (a) Define the beam a(N) pointing to η-2δ t , η-2δ) is the left detection beam, and the beam a(N t ,η+2δ) is the right detection beam; the user uses beam a(N r ,v) as the receiving beam, the received signals corresponding to the base station transmitting the left detection beam, communication beam and right detection beam are defined as y L ,y C and R .

[0057] Note that the left detection beam and the communication beam can form an auxiliary beam pair. L | 2 and |y C | 2 As x Δ and x ∑ Substitute into step (3.1.2) to calculate the metric ratio ζ at this time L , and calculate and To simplify the notation, we define and Similarly, the communication beam and the right detection beam can form an auxiliary beam pair, which will C | 2 and |y R | 2 As x Δ and x ∑ Substitute into (3.1.2) to calculate the metric ratio ζ at this time R , and calculate and To simplify the notation, we define and In fact, It constitutes a possible value vector of θ estimate.

[0058] (b) Let y = [y L ,y C ,y R ] H , define the dictionary matrix Defining the Matrix Then a small-dimensional sparse model of downlink signal transmission is constructed

[0059]

[0060] in is a vector with sparsity of 1; It is the matrix composed of the received noise vector when the base station transmits the left detection beam, communication beam and right detection beam; definition is a constant related to the line-of-sight path gain, pilot symbol, and user-side beam gain. Therefore, the estimated value of θ can be obtained by solving the following optimization problem:

[0061]

[0062]

[0063] Where ||·||0 represents the l0 norm of the vector;

[0064] (c) Define the matrix Compute the projection of y on each column of A and select the largest column index i opt , specifically expressed as

[0065]

[0066] Then the estimated value of θ is

[0067] Furthermore, the method for solving the optimization problem constructed in step (2) using the second method is as follows:

[0068] Step (3.2.1), define the left beam as a(M, η), where η is the communication beam direction transmitted by the base station at time t, and define the right beam as e jMπη a(M, η), then the communication beam a(N t , η) is the superposition of the left beam and the right beam, that is,

[0069]

[0070] in Using the left and right beam expressions, we can define the difference beam

[0071]

[0072] Step (3.2.2), at time t, the base station transmits the communication beam a (N t ,η), the user end uses a(N r , v) as the receiving beam, the received signal under the condition of ignoring noise is expressed as

[0073] f C =p1(θ, η)+p2(θ, η)=(1+e -jπM(θ-η) )p1(θ,η)

[0074] in,

[0075]

[0076] p2(θ,η)=e -jπM(θ-η) p1(θ,η)

[0077] In the above formula, L represents the number of paths between the base station and the user.

[0078] The base station then transmits differential beam a Δ (N t ,η), the user end uses a(N r , v) as the receiving beam, the received signal under the condition of ignoring noise is expressed as

[0079] f D =p1(θ, η)-p2(θ, η) = (1-e -jπM(θ-η) )p1(θ,η)

[0080] Step (3.2.3), based on f C and f D The calculation expression of the sum and difference ratio r is defined

[0081]

[0082] Then the estimated value of θ is

[0083]

[0084] where Imag{·} represents the imaginary part of the complex number; r is guaranteed to be a monotonic function, that is,

[0085]

[0086] This means that the tracking range of the beam tracking method is 2 / M or 4δ.

[0087] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0088] (1) Compared with the existing beam tracking scheme, the present invention proposes a beam tracking method based on auxiliary beams by multiplexing communication beams and constructing a small-dimensional sparse model, which can obtain a larger beam tracking range and solve the problem of fixed and small beam tracking range in the existing algorithm, thus providing the possibility for tracking high-speed moving targets.

[0089] (2) The present invention proposes another beam tracking method based on the auxiliary beam by designing the auxiliary beam as a differential beam. Compared with the existing algorithm, it can obtain a larger beam tracking range with lower beam tracking overhead and achieve high-precision beam tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 is a schematic diagram of a millimeter wave multi-user communication system model used in an embodiment of the present invention;

[0091] Figure 2 When the variation of channel AoD follows a uniform distribution between [-2δ, 2δ], the average sum rate of users of the beam tracking scheme proposed in step (3.1) of the present invention, the beam tracking scheme proposed in step (3.2) of the present invention, and the scheme in reference [2] are compared;

[0092] Figure 3is the mean square error comparison of the beam tracking results of the beam tracking scheme proposed in step (3.1) of the present invention, the beam tracking scheme proposed in step (3.2) of the present invention, and the beam tracking scheme of the literature [2] when the change in channel AoD obeys a uniform distribution between [-2δ, 2δ];

[0093] Figure 4 When the variation of channel AoD follows a uniform distribution between [-3δ, 3δ], the average sum rate of users of the beam tracking scheme proposed in step (3.1) of the present invention, the beam tracking scheme proposed in step (3.2) of the present invention, and the scheme in reference [2] are compared;

[0094] Figure 5 When the variation of channel AoD obeys uniform distribution between [-3δ, 3δ], the mean square error of the beam tracking results of the beam tracking scheme proposed in step (3.1) of the present invention is compared with the beam tracking scheme proposed in step (3.2) of the present invention and the beam tracking scheme in reference [2]. DETAILED DESCRIPTION

[0095] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0096] (1) Figure 1 As shown, the communication system model used in the present invention is described as follows:

[0097] (1.1) Consider a downlink communication scenario where a base station serves K users. Both the base station and the user end use uniform linear antenna arrays and the distance between two adjacent antennas is half the wavelength. The user end uses an analog beamforming architecture. Each user communicates with N r The base station is equipped with N receiving antennas. t transmit antennas and adopt a fully connected hybrid beamforming architecture. RF The RF links are connected to the N t Antennas connected and satisfying N t >>N RF ≥K and N t ≥4, then the downlink receiving signal model of the kth user can be established as

[0098]

[0099] where y k represents the received signal of the kth user; represents the simulated beamforming matrix at the base station, represents the digital beamforming matrix at the base station, and both satisfy the constraints represents the simulated beamforming vector used by the kth user to receive the base station signal; represents the millimeter wave downlink MIMO channel between the base station and the kth user; Represents the transmitted signal vector and satisfies the power constraint Where P represents the signal transmission power at the base station; represents the zero-mean additive complex Gaussian white noise vector received by the kth user and satisfies (·) H represents the conjugate transpose operation, ||·|| F Represents the F-norm of the matrix.

[0100] (1.2) Assume that there is L between the base station and the kth user equipment k The following channel model is used to model the millimeter wave communication downlink channel between the base station and the kth user equipment in step (1.1):

[0101]

[0102] where α l，k represents the channel gain of the lth path, θ l，k ∈[-1, 1] is the channel AoD of the lth path, v l，k ∈[-1, 1] represents the channel AoA of the lth path; a(N t , θ) represents the array steering vector, and the specific expression is

[0103]

[0104] In the above formula, (·) T Represents a transpose operation.

[0105] (2) Establish an optimization problem model for beam tracking and simplify the channel model.

[0106] (2.1) Definition represents the hybrid beamforming vector of the base station pointing to the kth user, where [F BB ] ：，k Indicates F BB The kth column of the channel matrix H is the kth user's beam tracking target. k The best matching transmit and receive beam f k and w k To maximize the received signal power of the kth user, it can be established as the following optimization problem:

[0107]

[0108]

[0109] where ||·||2 represents the l2 norm of the vector.

[0110] (2.2) Assuming that the base station knows the changes in the user-side channel AoA, consider the beam tracking of the base station-side channel AoD, and use time division multiple access to perform beam tracking on multiple users separately. Therefore, the user subscript k can be ignored, and only the beam tracking process of one user is described.

[0111] Due to the huge gap between the millimeter wave line-of-sight path gain and the non-line-of-sight path gain, we can ignore the impact of the non-line-of-sight path on beam tracking and only consider the line-of-sight path. Then the downlink channel between the base station and the user established in (1.2) can be simplified to

[0112]

[0113] Where α, v and θ represent the line-of-sight path gain, channel AoA and channel AoD respectively; L represents the number of paths between the base station and the user.

[0114] (3) Regarding the acquisition of channel state information in mobile communication scenarios, due to the rapid change of user spatial angles, if beam training is continued to be used to obtain real-time CSI, it will bring huge overhead. Therefore, the present invention proposes two millimeter wave array communication multi-user tracking methods based on auxiliary beams. The first method is to transmit left and right detection beams, and solve the optimization problem constructed in step (2.1) by multiplexing communication beams and constructing a small-dimensional sparse model, which is included in step (3.1); the second method is to solve the optimization problem constructed in step (2.1) by transmitting a differential beam as an auxiliary beam by the base station, which is included in step (3.2).

[0115] (3.1) The specific method for solving the optimization problem constructed in step (2.1) using the first method is as follows.

[0116] (3.1.1) Define the communication beam direction of the base station at time t as η, define the channel AoD of the user at time t+1 as θ, and define an auxiliary beam pair as two beams pointing to η-δ and η+δ respectively. These two beams are expressed as

[0117]

[0118]

[0119] The parameters The spatial angle domain pointing difference of a pair of auxiliary beams is determined to be 2 / N t .

[0120] To estimate θ, the base station first transmits auxiliary beam a(N t ,η-δ), the user adopts the steering vector a(N r, v) as the receiving beam. If the influence of non-line-of-sight path on beam tracking is ignored and only line-of-sight path is considered, the received signal can be expressed as

[0121]

[0122] Where x is the pilot signal sent by the base station to the user, satisfying The power constraint of the received signal is expressed as

[0123]

[0124] After noise averaging, x Δ Simplified expression:

[0125]

[0126] The base station transmits auxiliary beam a(N t ,η+δ), the user adopts beam a(N r , v) as the receiving beam, if the influence of non-line-of-sight path on beam tracking is ignored and only line-of-sight path is considered, the received signal is expressed as

[0127]

[0128] The corresponding received signal power is approximately expressed as

[0129]

[0130] (3.1.2) Based on the received signal power strength x Δ and x ∑ , define the metric ratio ζ as

[0131]

[0132] As can be seen from the above equation, the metric ratio ζ is closely related to the difference between the shifted channel AoDθ and the current transmit beam pointing η. Definition Differentiating ζ with respect to z gives

[0133]

[0134] From the derivative of ζ with respect to z, we know that when |θ-η|≤δ, It shows that the metric ratio ζ is a monotonically decreasing function when θ-η∈(-δ, δ), then the estimated value of θ is calculated based on the inverse function of ζ

[0135]

[0136] When |θ-η|>δ, This shows that the metric ratio ζ is a monotonically increasing function when θ-η<-δ and θ-η>δ. At this time, the estimated values ​​of θ obtained by performing inverse function operations in the two monotonic intervals are

[0137]

[0138] (3.1.3) In order to further expand the beam tracking range to 6δ, the present invention multiplexes the communication beam a(N t ,η) and construct a small-dimensional sparse model, thereby using the non-monotonic interval to expand the tracking range. The subdivision steps are as follows:

[0139] (a) Define the beam a(N) pointing to η-2δ t , η-2δ) is the left detection beam, and the beam a(N t ,η+2δ) is the right detection beam; the user uses beam a(N r ,v) as the receiving beam, the received signals corresponding to the base station transmitting the left detection beam, communication beam and right detection beam are defined as y L ,y C and R .

[0140] Note that the left detection beam and the communication beam can form an auxiliary beam pair. L | 2 and |y C | 2 As x Δ and x ∑ Substitute into (3.1.2) to calculate the metric ratio ζ at this time L , and calculate and To simplify the notation, we define and Similarly, the communication beam and the right detection beam can form an auxiliary beam pair, which will C | 2 and |y R | 2 As x Δ and x ∑ Substitute into (3.1.2) to calculate the metric ratio ζ at this time R , and calculate and To simplify the notation, we define and In fact, It constitutes a possible value vector of the estimated value of θ.

[0141] (b) Let y = [y L ,y C,y R ] H , define the dictionary matrix Defining the Matrix Then a small-dimensional sparse model of downlink signal transmission is constructed

[0142]

[0143] in is a vector with sparsity of 1; It is the matrix composed of the received noise vector when the base station transmits the left detection beam, communication beam and right detection beam; definition is a constant related to the line-of-sight path gain, pilot symbol, and user-side beam gain. Therefore, the estimated value of θ can be obtained by solving the following optimization problem:

[0144]

[0145]

[0146] where ||·||0 represents the l0 norm of the vector.

[0147] (c) Since we do not need to estimate the The complete information of θ is only needed for the information associated with the main path AoDθ, so the optimization problem constructed in (b) is equivalent to

[0148]

[0149] stθ=[u] j , j = 1, 2, 3, 4

[0150] An effective solution to the above optimization problem is to make the vector After normalization, the projection on y is the largest, so the matrix is ​​defined as Compute the projection of y on each column of A and select the largest column index i opt , specifically expressed as

[0151]

[0152] Then the estimated value of θ is

[0153] (3.2) Furthermore, the present invention provides a second method, which is a beam tracking method when the auxiliary beam is designed as a differential beam. Compared with the existing algorithm, it is possible to obtain a larger beam tracking range while reducing the beam tracking overhead. The specific steps are as follows:

[0154] (3.2.1) The traditional auxiliary beam-based beam tracking algorithm needs to use the left beam a(N) in two time slots.t ,η-δ) and the right beam a(N t ,η+δ) for transmission, which leads to the question of whether the left beam and the right beam can be transmitted at the same time to save a time slot. The left beam is defined as a(M,η), η is the communication beam direction transmitted by the base station at time t, and the right beam is defined as e jMπη a(M, η), then the communication beam a(N t , η) is the superposition of the left beam and the right beam, that is,

[0155]

[0156] in Define the differential beam as

[0157]

[0158] (3.2.2) At time t, the base station transmits the communication beam a(N t ,η), the user end uses a(N r , v) as the receiving beam, the received signal under the condition of ignoring noise is expressed as

[0159] f C =p1(θ, η)+p2(θ, η)=(1+e -jπM(θ-η) )p1(θ,η)

[0160] in,

[0161]

[0162] p2(θ,η)=e -jπM(θ-η) p1(θ,η)

[0163] Where L represents the number of paths between the base station and the user.

[0164] The base station then transmits differential beam a Δ (N t ,η), the user end uses a(N r , v) as the receiving beam, the received signal under the condition of ignoring noise is expressed as

[0165] f D =p1(θ, η)-p2(θ, η) = (1-e -jπM(θ-η) )p1(θ,η)

[0166] (3.2.3) Based on f C and f D The calculation expression of the sum and difference ratio r is defined

[0167]

[0168] The estimated value of θ based on the above formula is

[0169]

[0170] where Imag{·} represents the imaginary part of the complex number; r is guaranteed to be a monotonic function, that is,

[0171]

[0172] This means that the tracking range of the beam tracking method is 2 / M or 4δ. Multi-user beam tracking can be performed by using time division multiple access to perform beam tracking on multiple users in different time periods. It is noted that compared with the traditional beam tracking algorithm based on auxiliary beams, this method can save one time slot while expanding the beam tracking range and providing high-precision beam tracking results.

[0173] The present invention is further described below in combination with simulation parameter settings and simulation results. The simulation parameters are set as follows: the number of base station antennas N t =128, the base station serves 4 users in total, each user is equipped with N r = 16 antennas. Assume that the total number of transmission paths between the kth user and the base station is L k is equal to 3, including one main path and two slave paths, where the channel gain of the main path obeys the complex Gaussian distribution, that is The channel gain of the slave path also obeys the complex Gaussian distribution, and the energy is 1 / 10 of that of the main path, that is, Set the number of Monte Carlo simulations to 10 5 .

[0174] Figure 2 The comparison of user average and rate under different beam tracking schemes is described when the change Δθ of the channel AoD from time t to time t+1 obeys the uniform distribution between [-2δ, 2δ], that is, Δθ~U[-2δ, 2δ] (U[a, b] represents the uniform distribution in the interval [a, b]). The ideal CSI refers to the accurate channel AoD information that can be obtained by the base station. The first method of the present invention refers to the beam tracking method proposed in step (3.1), and the second method of the present invention refers to the beam tracking scheme proposed in step (3.2). From Figure 2It can be seen that the user average and rate of the first method and the second method of the present invention are significantly better than those of the literature [2], and can approach the performance of the ideal CSI under high signal-to-noise ratio (SNR) conditions. This is because the beam tracking range of the two methods proposed in the present invention is greater than or equal to 4δ, while the beam tracking range of the method proposed in the literature [2] is only 2δ. Therefore, when Δθ ~ U [-2δ, 2δ], the performance of the method in the literature [2] must have a certain performance gap with the solution proposed in the present invention. Note that at low SNR, the first method and the second method proposed in the present invention still have a certain performance gap with the ideal CSI. This is because at low SNR, the effective information stored in the received signal for tracking the channel AoD will be submerged by noise, which has a certain impact on the performance of the beam tracking method proposed in the present invention.

[0175] Figure 3 The comparison of the mean square error (MSE) of beam tracking results of different schemes is described when the change of channel AoD from time t to time t+1 is Δθ~U[-2δ, 2δ]. Figure 3 It can be seen that when Δθ ~ U [-2δ, 2δ], the beam tracking range needs to reach 4δ to achieve ideal beam tracking, which has exceeded the beam tracking range of the method in reference [2]. Therefore, there will be a constant beam tracking error, which is reflected in the MSE. The MSE of the method in reference [2] is a constant value, while the MSE of the first method and the second method of the present invention decreases with the decrease of SNR. Note that the MSE of the first method is slightly inferior to that of the second method at low signal-to-noise ratio. This is because noise will affect the judgment accuracy of the small-dimensional sparse model of the first method on the angle information, resulting in a certain error between the estimated channel AoD and the true value.

[0176] Figure 4 The comparison of user average and rate under different beam tracking schemes is described when the channel AoD changes by Δθ to U[-3δ, 3δ]. Figure 4 It can be seen that the first method proposed in the present invention is significantly better than other beam tracking methods and can approach the upper limit of the ideal CSI when the SNR is greater than 0dB. This is because Δθ~U[-3δ, 3δ] requires a beam tracking range of 6δ to achieve ideal beam tracking, which has exceeded the beam tracking range of the method in reference [2] and the second method proposed in the present invention, which will lead to beam tracking errors within a constant range, thereby causing a decrease in user average and rate performance.

[0177] Figure 5The MSE comparison of beam tracking results of different schemes is described when the change of channel AoD is Δθ~U[-3δ, 3δ]. Figure 5 It can be seen that the MSE of the second method proposed in document [2] and the present invention is a constant. This is because the beam tracking range of the solution in document [2] and the second method proposed in the present invention is less than 6δ. When the user moves outside the beam tracking range of the second method, a theoretical constant beam tracking error of 4δ will be caused, which is significantly higher than the tracking error of the solution in document [2]. Therefore, even when Δθ~U[-2δ, 2δ], the beam tracking performance of the second method of the present invention can approach the ideal CSI upper limit. When Δθ~U[-3δ, 3δ], the MSE of the second method is still slightly higher than the method proposed in document [2]. Since the tracking range of the first method proposed in the present invention can reach 6δ, which can completely cover the situation of Δθ~U[-3δ, 3δ], the MSE of the first method of the present invention can be continuously reduced with the increase of SNR, and can reach 10 at 20dB. -7 This indicates that the first method proposed in this paper has a larger beam tracking range than the solution in reference [2], while the tracking accuracy is not significantly reduced.

[0178] In summary, compared with the traditional beam tracking method, the present invention proposes two beam tracking methods based on auxiliary beams. The first method obtains a larger beam tracking range by transmitting left and right detection beams, multiplexing communication beams, and constructing a small-dimensional sparse model, which solves the problem of fixed and small beam tracking range in the auxiliary beam algorithm, and can obtain high-precision beam tracking results. At the same time, the second method provided by the present invention transmits a differential beam as an auxiliary beam. Compared with the existing beam tracking algorithm, it can obtain a larger beam tracking range with lower beam tracking overhead and provide high-precision beam tracking results.

[0179] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-user beam tracking method for millimeter wave array communication based on auxiliary beams, characterized in that: The method comprises the following steps: (1) Construct a millimeter-wave multi-user downlink communication signal reception model and a millimeter-wave communication downlink channel model; (2) Construct an optimization model for beam tracking; (3) Solving the optimization problem by using a beam tracking method based on an auxiliary beam to obtain an estimated value of the channel departure angle AoD; specifically, there are two solving methods. The first method is that the base station transmits left and right detection beams and reuses the communication beam, and the user solves the problem by constructing a small-dimensional sparse model; the second method is that the base station transmits a differential beam as an auxiliary beam to solve the problem; The sub-steps of step (1) are as follows: (1.1) Consider a downlink communication scenario where a base station serves K users. Both the base station and the user end use uniform linear antenna arrays with a half-wavelength spacing between two adjacent antennas. The user end uses an analog beamforming architecture. Each user communicates with N r Root receiving antennas are connected; the base station is equipped with N t transmit antennas and adopt a fully connected hybrid beamforming architecture. RF The RF links are connected to the N t Antennas connected and satisfying N t >>N RF ≥K, then the millimeter wave communication multi-user downlink signal reception model is established as where y k represents the received signal of the kth user; and They represent the analog beamforming matrix and the digital beamforming matrix at the base station end respectively; represents the simulated beamforming vector used by the kth user to receive the base station signal; represents the millimeter wave downlink MIMO channel between the base station and the kth user; Represents the transmission signal vector, satisfying P is the total transmit power of the base station; represents the zero-mean additive complex Gaussian white noise vector received by the kth user; (·) H represents the conjugate transpose operation; (1.2) Assume that there is L between the base station and the kth user equipment k The following channel model is used to model the millimeter wave communication downlink channel: where α l,k represents the channel gain of the lth path, θ l,k ∈[-1,1] is the channel AoD of the lth path, v l,k ∈[-1,1] represents the channel arrival angle of the lth path; a(N t ,θ) represents the array steering vector, and the specific expression is In the above formula, (·) T Represents the transpose operation; The sub-steps of step (2) are as follows: (2.1) Considering the beam tracking of the channel AoD at the base station, the time division multiple access method is used to perform beam tracking for multiple users separately. Define f k =F RF [F BB ] :,k represents the hybrid beamforming vector of the base station pointing to the kth user, where [F BB ] :,k Indicates F BB The kth column of the base station is designed to best match H k f k and w k , the optimization problem is established as follows: Where ||·||2 represents the l2 norm of the vector; The sub-steps of solving the optimization problem constructed in step (2) using the first method are as follows: (3.1.1) Define the communication beam direction of the base station at time t as η, define the channel AoD of the user at time t+1 as θ, and define an auxiliary beam pair as two beams pointing to η-δ and η+δ respectively. These two beams are expressed as The parameters To estimate θ, the base station first transmits auxiliary beam a(N t ,η-δ), the user adopts the steering vector a(N r ,v) as the receiving beam, if the channel line-of-sight path is much stronger than the non-line-of-sight path, the received signal is expressed as Where α, v and θ represent the path gain, channel arrival angle and channel AoD of the channel line-of-sight path respectively; L represents the number of paths between the base station and the user; x is the pilot symbol sent by the base station to the user, satisfying The power constraint of the received signal is expressed as After noise averaging, x Δ Simplified expression: The base station transmits auxiliary beam a(N t ,η+δ), the user adopts beam a(N r ,v) as a receiving beam, if the channel line-of-sight path is much stronger than the non-line-of-sight path, the received signal is expressed as The corresponding received signal power is approximately expressed as (3.1.2) Define the metric ratio ζ as definition Differentiating ζ with respect to z gives When |θ-η|≤δ, Then the estimated value of θ based on the inverse function of ζ is When |θ-η|>δ, The estimated values ​​of θ obtained by performing inverse function operations in two monotonic intervals of θ-η<-δ and θ-η>δ are The step (3.1.3) further includes multiplexing the communication beam a(N t ,η) Expand the beam tracking range. The specific three subdivision steps are as follows: (a) Define the beam a(N) pointing to η-2δ t ,η-2δ) is the left detection beam, and the beam a(N t ,η+2δ) is the right detection beam; the user uses beam a (N r ,v) as the receiving beam, the received signals corresponding to the left detection beam, communication beam and right detection beam transmitted by the base station are defined as y L ,y C and R ; |y L | 2 and |y C | 2 As x Δ and x ∑ Substitute into (3.1.2) to calculate the metric ratio ζ at this time L , and calculate and definition and |y C | 2 and |y R | 2 As x Δ and x ∑ Substitute into (3.1.2) to calculate the metric ratio ζ at this time R , and calculate and definition and It constitutes the possible value vector of θ estimate; (b) Let y = [y L ,y C ,y R ] H , define the dictionary matrix Defining the Matrix Then a small-dimensional sparse model of downlink signal transmission is constructed in is a vector with sparsity 1; It is the matrix composed of the received noise vector when the base station transmits the left detection beam, communication beam and right detection beam; definition is a constant related to the line-of-sight path gain, pilot symbol, and user-side beam gain; the estimated value of θ can be obtained by solving the following optimization problem Where ||·||0 represents the l0 norm of the vector; (c) Define the matrix Compute the projection of y on each column of A and select the largest column index i opt , specifically expressed as Then the estimated value of θ is The sub-steps of solving the optimization problem constructed in step (2) using the second method are as follows: (3.2.1) Define the left beam as a(M,η), where η is the communication beam direction transmitted by the base station at time t, and define the right beam as e jMπη a(M,η), then the communication beam a(N t ,η) is the superposition of the left beam and the right beam, that is in Define the differential beam as (3.2.2) At time t, the base station transmits the communication beam a(N t ,η), the user end uses a(N r ,v) as the receiving beam, the received signal under the condition of ignoring noise is expressed as f C =p1(θ,η)+p2(θ,η)=(1+e -jπM(θ-η) )p1(θ,η) in, p2(θ,η)=e -jπM(θ-η) p1(θ,η) Where L represents the number of paths between the base station and the user; The base station then transmits differential beam a Δ (N t ,η), the user end uses a(N r ,v) as the receiving beam, the received signal under the condition of ignoring noise is expressed as f D =p1(θ,η)-p2(θ,η)=(1-e -jπM(θ-η) )p1(θ,η) (3.2.3) Define the sum and difference ratio r Then the estimated value of θ is Where Imag{r} represents the imaginary part of r.

Images