Auxiliary direction of arrival estimation and communication method based on dynamically rotatable space-based intelligent reflecting surface

Abstract

The invention discloses an auxiliary direction of arrival estimation and communication method based on a dynamically rotatable space-based intelligent reflecting surface, and belongs to the field of wireless communication. The method specifically comprises the following steps: firstly, a user periodically sends a positioning pilot signal, and the positioning pilot signal is reflected to a base station by an IRS to preliminarily and roughly estimate a direction of arrival from the user to the IRS; then, the IRS is adjusted to turn to the maximum reflection efficiency, and the theoretical rough estimation incoming wave angle of the user is calculated; the IRS direction and the value of a measurement matrix are adjusted according to the rough estimation result, the signal-to-noise ratio of a receiving end is improved, and a more accurate estimation result is obtained; the fine estimation is repeated a plurality of times until the error reaches a specified threshold. After the direction of arrival of the user is estimated, the direction of the IRS is adjusted according to a final estimated angle value so that the reflection efficiency of the system can be maximized, the beam coverage range is reduced to a direction of arrival estimation error threshold value, and the optimal phase shift matrix theta of the IRS is solved by taking the worst signal-to-noise ratio of the maximized beam coverage area as an optimization target. According to the invention, the performance of the intelligent reflecting surface in assisting the wireless communication system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology, and specifically relates to a method for angle of arrival estimation and communication assisted by a dynamically rotatable airborne intelligent reflecting surface. Background Art

[0002] In wireless communication, non-line-of-sight (NLoS) transmission is usually used in emergency communication scenarios where the direct link between a user and a nearby base station is blocked or cut off. In this case, using existing LoS-based solutions will result in a significant performance degradation.

[0003] As one of the key enabling technologies for the next-generation cellular network, an intelligent reflecting surface (IRS) can be carried by a drone as an aerial relay node to establish a virtual LoS link in the presence of obstacles, thereby restoring or enhancing wireless communication.

[0004] The IRS consists of a large number of low-cost passive reflecting elements. By setting the phase parameters of the reflecting units, the incident signal can be reflected in a specified direction and the reliability of the signal can be improved. Compared with the traditional amplify-and-forward (AF) relay system, the IRS fine-tunes the incident signal by controlling the phase shift of each reflecting element without high-power-consuming components such as radio frequency (RF) links and power amplifiers. Therefore, compared with the relay system in AF, the RIS-assisted system has higher energy efficiency and environmental friendliness.

[0005] The setting of the passive reflection phase shift matrix of the intelligent reflecting surface needs to be based on the instantaneous cascaded channel state information (CSI) of the system, and the acquisition of the instantaneous CSI will result in a large pilot overhead, especially in the case of multiple users, where the number of parameters to be estimated is even more.

[0006] To reduce the complexity of channel estimation, a passive beamforming design based on user location information is usually considered, reducing the parameters to be estimated to the angle information of the users. However, existing angle estimation algorithms are all established for the LoS propagation scenario and are not suitable and have reduced accuracy in the NLoS transmission scenario.

[0007] On the other hand, although current research has explored the improvement of system performance by optimizing the IRS location deployment, few studies have deeply explored the potential for improving the reflection efficiency brought by the mechanical orientation of the IRS in the system. Summary of the Invention

[0008] To solve the problem of user angle of arrival (AoA) estimation under non-line-of-sight conditions and the low reflection efficiency caused by the fixed position and orientation of the intelligent reflecting surface (IRS), the present invention proposes a method for AoA estimation and communication assisted by a dynamically rotatable space-based intelligent reflecting surface, which improves the performance of the intelligent reflecting surface when assisting a wireless communication system.

[0009] The method for AoA estimation and communication assisted by the dynamically rotatable space-based intelligent reflecting surface specifically comprises the following steps:

[0010] Step 1: Build a space-based intelligent reflecting surface communication system composed of a single-antenna user, an IRS, and a base station.

[0011] There are several single-antenna users. The intelligent reflecting surface IRS consists of N sub-units, and the base station is equipped with M antennas.

[0012] The IRS is installed on a rotatable mechanical device under the unmanned aerial vehicle and rotates and swings in azimuth and elevation angles according to the requirements of the actual scenario. The direct link between the base station and the user is blocked.

[0013] Step 2: The user periodically and repeatedly sends positioning pilot signals to the IRS, which are reflected by the IRS to the base station. The IRS randomly changes the phase shift matrix. The base station preliminarily and roughly estimates the AoA from the user to the IRS through the MUSIC algorithm based on the periodic sampling signals.

[0014] The specific estimation process is as follows:

[0015] Step 201: Calculate the spatial response channel steering vector from the user x to the IRS through the signal r(t) received by the receiving sensor of the base station.

[0016] The received signal is:

[0017]

[0018] α is the path loss factor from the IRS to the base station, a R is the spatial response channel steering vector between the receiving sensor and the IRS, is the known angle of arrival from the IRS to the receiving sensor, and the diagonal matrix Θ(t) represents the operation of the intelligent reflecting surface IRS on the incoming wave signal from the transmitting end at time t. is the path loss factor from the user x to the IRS, X is the total number of single-antenna users, p x represents the transmission power of the user x, s x (t) represents the message sent by the user x at time t, and n(t) is the Gaussian random noise of the base station at time t. are the unknown azimuth and elevation angles of arrival; The spatial response channel steering vector from user x to the IRS is calculated as follows:

[0019]

[0020] N is the total number of elements of the dimensional IRS, λ is the signal wavelength, and D is the side length of each IRS element;

[0021] Step 202: Set the IRS measurement matrix as a random phase shift matrix, which varies K times (K > X) within one period, and repeat L periods to obtain the reconstructed spatial response channel steering vector matrix from user x to the IRS:

[0022]

[0023] where,

[0024]

[0025] Step 203: Use the reconstructed spatial response channel steering vector matrix to obtain the spatial spectrum function:

[0026]

[0027] is the noise subspace after eigenvalue decomposition of the autocorrelation matrix of the received signal.

[0028] Step 204: By finding the peak value of the spatial spectrum function the preliminary estimated angle of arrival is obtained, that is

[0029] Step three: Adjust the IRS steering to the maximum reflection efficiency according to the angle of arrival obtained by the rough estimation, and calculate the theoretically rough estimated incoming wave angle of the user after the IRS steering

[0030]

[0031] θ z are the angles of the IRS rotating counterclockwise along the positive x-axis and z-axis respectively.

[0032] Step four: Calculate the value of the passive phase shift matrix when the IRS beam focuses on the incoming wave direction of the user with a coverage radius of R, randomly change several phase shift values among them as the measurement matrix for the next-stage angle of arrival estimation, repeat the estimation of the angle of arrival from the user to the IRS, and obtain the first fine estimation value and the estimation error from the theoretical value

[0033] Wherein:

[0034] Step 5: Return to Step 4, and repeat the calculation of the refined estimated value and the error between each refined estimated value and the previous one multiple times until the error reaches the specified threshold to obtain the final estimated value.

[0035] Step 6: For users with known azimuth, according to the relative positions of the base station - IRS - user, adjust the mechanical pointing of the IRS according to the final estimated angle value to maximize the system reflection efficiency, reduce the beam coverage range to the arrival angle estimation error threshold, and take the worst signal-to-noise ratio of the maximized beam coverage area as the optimization target to solve for the optimal phase shift matrix Θ of the IRS.

[0036] The optimization objective of IRS beamforming is as follows:

[0037]

[0038] s.t. |g h (Θ,Δ)| 2 ≥t

[0039]

[0040] 0 ≤ ψ n ≤ 2π, n = 1, 2, …, N

[0041] represents the corresponding IRS - user channel without considering the user direction uncertainty, i.e., the estimated channel; e h represents the signal error function considering the user direction error; Δθ represents the three-dimensional uncertainty vector of the arrival angle, and ψ, δ represent the specified error thresholds. ψ n represents the passive reflection phase shift value of the nth IRS unit;

[0042] Use the SDR technology to transform this optimization objective into a series of convex problems, and solve the optimal phase shift problem through a convex optimization tool (CVX).

[0043] The present invention has the following advantages:

[0044] 1. By reasonably designing the IRS reflection mode, measuring multiple times, and progressively estimating the arrival angle direction, the present invention gradually reduces the noise error, solves the problem that the performance of traditional arrival direction estimation algorithms deteriorates due to non-line-of-sight transmission caused by obstacles and scatterers, and the positioning mismatch problem in communication scenarios lacking LoS paths.

[0045] 2. By finely adjusting the azimuth and elevation angles of the IRS at specific positions, the present invention improves the system reflection efficiency, reduces power loss, enhances the focusing energy efficiency of the beam, and reduces energy waste, thereby achieving more efficient energy utilization and signal reception quality.

[0046] 3. The present invention designs the measurement matrix as a robust beamforming with an angular error range, solves the problem of unstable received signals caused by inaccurate user position estimation or IRS vibration and drift, and improves the accuracy of estimation and the stability of communication.

[0047] 4. Under the condition of constant transmit power at the transmitter, the present invention realizes precise control of the angle of incidence of the transmitted signal on the intelligent reflecting surface. The performance gain brought by the improved reflection efficiency can effectively reduce the performance loss caused by discrete phases. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flowchart of a method for angle-of-arrival estimation and communication assisted by a dynamically rotatable space-based intelligent reflecting surface according to the present invention;

[0049] Figure 2 is a schematic diagram of a space-based intelligent reflecting surface communication scenario constructed according to the present invention;

[0050] Figure 3 is a diagram of the system unit composition provided by the present invention.

[0051] Figure 4 is a simulation example diagram of the steering optimization of an IRS at a given position given by the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0052] The following further elaborates on the specific implementation method of the present invention in conjunction with the drawings.

[0053] The present invention combines an intelligent reflecting surface with a drone to flexibly build a virtual link in an emergency scenario where the direct communication link between the base station and the user is blocked, studies the user direction estimation under NLoS conditions, and then conducts low-complexity beamforming design based on the direction angle information; deeply studies the specific impact of the effective incident area of the signal on the system cascaded channel gain, and minimizes the power loss of the received signal by precisely adjusting the direction of the intelligent reflecting surface.

[0054] The present invention proposes a method for angle-of-arrival estimation and communication assisted by a dynamically rotatable space-based intelligent reflecting surface, as Figure 1 shown, and the specific steps are as follows:

[0055] Step 1: Build a space-based intelligent reflecting surface communication system composed of a single-antenna user, an IRS, and a base station;

[0056] There are several single-antenna users, the intelligent reflecting surface (IRS) consists of N sub-units, and the base station is equipped with M antennas;

[0057] The IRS is installed on a rotatable mechanical device under the unmanned aerial vehicle (UAV) and rotates and swings in azimuth and elevation according to the requirements of the actual scenario; the direct link between the base station and the users is blocked.

[0058] Step 2: The users periodically and repeatedly send positioning pilot signals to the IRS, which are reflected to the base station by the IRS. The IRS randomly changes the phase shift matrix periodically. The receiving end uses a single antenna. According to the received periodic sampling signals, the angle of arrival (AoA) from the user to the IRS is initially and roughly estimated through the MUSIC algorithm.

[0059] The specific estimation process is as follows:

[0060] Step 201: Calculate the spatial response channel steering vector from the user x to the IRS through the signal r(t) received by the receiving sensor of the base station.

[0061]

[0062] α is the path loss factor from the IRS to the base station, a R is the spatial response channel steering vector between the receiving sensor and the IRS, is the known angle of arrival from the IRS to the positioning receiving sensor, and the diagonal matrix Θ(t) represents the operation of the intelligent reflecting surface IRS on the incoming wave signal from the transmitting end at time t. is the path loss factor from the user x to the IRS, X is the total number of single-antenna users, is the spatial response channel steering vector from the user x to the IRS, are the unknown azimuth and elevation angles of arrival, p x represents the transmit power of the user x, s x (t) represents the message sent by the user x at time t, and n(t) is the BS Gaussian random noise at time t. Among them:

[0063]

[0064] N is the total number of units of the IRS with size, λ is the signal wavelength, and D is the side length of each IRS unit;

[0065] Step 202: Set the IRS measurement matrix as a random phase shift matrix, which changes K times (K > X) within one period to simulate one snapshot data; repeat L periods. Obtain the reconstructed steering vector matrix.

[0066]

[0067] Among them,

[0068]

[0069] Step 203: Using the reconstructed spatial response channel steering vector matrix, the finally obtained spatial spectrum function is:

[0070]

[0071] is the noise subspace after eigenvalue decomposition of the autocorrelation matrix of the received signal.

[0072] Step 204: By finding the peak value of the spatial spectrum function the preliminary estimated angle of arrival is obtained That is

[0073] Step 3: Use the angle of arrival obtained from the rough estimation to adjust the IRS steering to the maximum reflection efficiency. Assume that the IRS rotates counterclockwise by angles θ z along the positive x-axis and z-axis respectively, and calculate the theoretical rough estimated incoming wave angle of the user after the IRS steering

[0074]

[0075] Step 4: Calculate the value of the passive phase shift matrix when the IRS beam is focused on a center with the user's incoming wave direction and a coverage radius of R. Randomly change several phase shift values among them as the measurement matrix for the next stage of angle of arrival estimation, repeat Step 2 to estimate the incoming wave angle, and obtain the first fine estimated value and the estimation error with the theoretical value

[0076]

[0077] Step 5: Return to Step 4, repeatedly calculate the fine estimated value and the error between each fine estimated value and the previous fine estimated value multiple times until the error reaches the specified threshold to obtain the final estimated value.

[0078] Step 6: For users with known azimuth, according to the relative positions of the base station - IRS - user, adjust the mechanical pointing of the IRS according to the final estimated angle value to maximize the system reflection efficiency, reduce the beam coverage range to the angle of arrival estimation error threshold, and take the worst signal-to-noise ratio of the maximized beam coverage area as the optimization objective to solve for the optimal phase shift matrix Θ of the IRS.

[0079] The solution of IRS beamforming is an optimization problem

[0080]

[0081] s.t. |g h (Θ,Δ)| 2 ≥t

[0082]

[0083] 0 ≤ ψ n ≤ 2π, n = 1, 2, …, n

[0084] denotes the IRS-user channel corresponding to the case without considering the user direction uncertainty, i.e., the estimated channel, e h denotes the signal error function considering the user direction error. The actual channel is expressed as the Hadamard product of the estimated channel and the channel error function; by optimizing the IRS phase shift matrix Θ, the worst signal-to-noise ratio within the region covered by the user direction error threshold is maximized, that is, to ensure that the variance of the beam radiation power within the beam coverage area is as small as possible. ψ n denotes the passive reflection phase shift value of the nth IRS element, Δθ denotes the three-dimensional uncertainty vector of the angle of arrival, and φ, δ denote the specified error thresholds.

[0085] Using the SDR technique, this optimization problem is transformed into a series of convex problems, and then the optimal phase shift problem is solved by a convex optimization tool (CVX).

[0086] Embodiment:

[0087] As Figure 2 shown, the space-based intelligent reflecting surface communication system built consists of multiple single-antenna users, a UPA (Uniform Planar Array) intelligent reflecting surface composed of N sub-elements, and a UPA base station equipped with M antennas. Among them, the airborne intelligent reflecting surface IRS is installed on a special mechanical device that can rotate under the unmanned aerial vehicle and can perform precise rotational swinging of the azimuth angle and elevation angle according to the actual scenario requirements; the direct link between the base station and the user is blocked.

[0088] The specific process of the method is as follows:

[0089] S1: Angle of arrival estimation stage:

[0090] The system first estimates the azimuth information of the user: using the IRS as an anchor point, the user sends a positioning pilot signal to the receiving end of the base station, and roughly estimates the angle of arrival from the user to the IRS;

[0091] The user periodically and repeatedly sends a positioning pilot signal to the IRS, which is reflected by the IRS to the base station receiver. Assume that one period is divided into K time slots and there are a total of L periods. Within one period, the IRS randomly adjusts the passive reflection phase shift matrix in each time slot to generate K sets of measurement matrices. The base station receiver samples the received signal and performs extraction, filtering, and transformation on the received signal through the MUSIC algorithm to preliminarily analyze the approximate azimuth of the user.

[0092] S2: Progressive estimation stage:

[0093] Perform beamforming design: Adjust the mechanical pointing and phase matrix of the IRS according to the angle of arrival information obtained from the rough estimation to maximize the received signal-to-noise ratio at the user end. Considering the errors existing in the angle of arrival estimation, a robust beamforming design with a certain width coverage range is carried out for the IRS centered on the user position, and the optimal phase shift matrix Θ0 of the IRS at this time and the azimuth of the user relative to the IRS are calculated. Randomly change several of the phase values based on Θ0 to obtain a new set of K measurement matrices, and estimate the user azimuth. The estimation error from the theoretical value is

[0094] Specifically, the base station side changes the passive reflection phase shift matrix of the IRS periodically through time division multiplexing. At the same time, the target user repeatedly sends a positioning pilot signal, uses the periodically changed reflection phase shift matrix as the positioning measurement matrix, sends the positioning signal to the positioning receiving sensor of the base station, and performs user direction estimation. This estimation result is used as the reference value in the rough estimation stage. Due to the randomness of the IRS phase shift matrix, the signal-to-noise ratio of the received signal at the receiving end is relatively small, resulting in errors in the estimation result.

[0095] Next, perform fine estimation. Adjust the pointing of the IRS and the value of the measurement matrix according to the rough estimation result to improve the signal-to-noise ratio at the receiving end and obtain a more accurate estimation result.

[0096] S3: Repeat the fine estimation step multiple times until the error reaches or is less than the specified threshold to obtain the final estimated value;

[0097] S4: After the angle of arrival estimation is completed, for a user with a known azimuth, the IRS calculates and adjusts its mechanical pointing to the optimal azimuth pointing according to the relative position of the base station - IRS - user to maximize the system reflection efficiency. At the same time, adjust the passive reflection phase shift matrix to the optimal, and reduce the coverage range according to the measurement results to focus the beam and achieve the maximum average received signal-to-noise ratio.

[0098] In S1, first, the principle of angle-of-arrival (AoA) estimation of the IRS-assisted user is analyzed: The target user sends a positioning pilot signal, which is reflected by the IRS and received by the positioning receiving sensor at the base station. The positioning receiving sensor includes a filter, a low-noise amplifier, a mixer, an ADC, and a baseband processor, and has the ability to process the received signal. Since the signals received by the receiving sensor all come from the direction of the IRS, the information between the receiving sensor elements reflects the angle information between the IRS and the receiving sensor, rather than the angle information between the user and the IRS. Therefore, an array antenna is not required at the receiving sensor, and a single antenna is sufficient.

[0099] Assume that a single-antenna receiving sensor is used, and the received signal is:

[0100]

[0101] where \(a\) R is the spatial response channel steering vector between the receiving sensor and the IRS, expressed as:

[0102]

[0103] The diagonal matrix represents the operation of the intelligent reflecting surface (IRS) on the incoming wave signal from the transmitting end at time \(t\). \(\Psi\) i,t \(\in[0, 2\pi]\) represents the phase shift of the \(i\)-th reflecting element on the IRS. \(p\) k represents the transmit power of user \(k\), and \(s\) k (\(t\)) represents the message sent by user \(k\) at time \(t\). is the Gaussian random noise at the base station (BS) at time \(t\), is the angle of arrival (AoA) from the IRS to the positioning receiving sensor, which is a known parameter, is the angle of arrival (AoA) from user \(k\) to the IRS, which is an unknown parameter to be solved. \(\alpha\) is the path loss factor from the IRS to the BS, is the path loss factor from user \(k\) to the IRS, is the Gaussian random noise.

[0104] For simplicity, define:

[0105]

[0106] Denote the correlation matrix of \(q(t)\) as Then the correlation matrix of \(t(r)\) is

[0107]

[0108] where:

[0109]

[0110] Denote the user-IRS-BS cascaded channel steering vector, which contains the set of angle-of-arrival parameters to be solved

[0111]

[0112] The pilot signal sent by the positioning user remains unchanged within a period. The IRS periodically changes the reflection coefficient matrix Θ(t) at a frequency of 1 / KT, and the specific setting is obtained from the aforementioned passive beamforming algorithm. Therefore, the received signal within a period is a vector with K (K>X) time slots, and we get

[0113]

[0114] where

[0115]

[0116] where

[0117]

[0118] The eigenvalue decomposition of the positive semi-definite Hermitian matrix always exists and can be expressed as:

[0119]

[0120] where the diagonal elements of D contain real-valued positive eigenvalues arranged in descending order, and the columns of

[0121] are the corresponding unit-length eigenvectors.

[0122]

[0123] matrix has rank X, so X eigenvalues of R are strictly greater than σ 2 , and the remaining K-X eigenvalues are exactly σ 2 . Index the eigenvalues in descending order, and decompose as where contains the eigenvectors corresponding to the non-zero eigenvalues of

[0124] . The X eigenvectors span the signal subspace of R, which contains all received signals and additive noise. The columns of 2 contain the eigenvectors corresponding to the zero eigenvalues of

[0125] Since the eigenvector in corresponds to the zero eigenvalue of

[0126]

[0127] According to the knowledge of linear algebra, if is a full-rank matrix, then

[0128]

[0129] That is

[0130]

[0131] Finally, the spatial spectrum of a single snapshot is obtained as:

[0132]

[0133] By finding the peak value of , the angle of arrival

[0134] The present invention considers a single-user scenario. Using the above algorithm, the arrival angle of the user is initially roughly estimated However, since the IRS is a random phase shift matrix, the signal-to-noise ratio of the positioning pilot signal at the receiving end is relatively low, resulting in inaccurate estimation. Next, according to the rough estimation result, beam focusing is performed by designing IRS beamforming to increase the signal-to-noise ratio of the received signal, thereby improving the estimation accuracy.

[0135] Specifically, according to the system cascaded channel gain model, using the angle of arrival of the user obtained by rough estimation the IRS is turned to the maximum reflection efficiency, and the theoretical rough estimation angle of arrival of the user after the IRS is turned is calculated Then, the value of the passive phase shift matrix when the IRS beam is focused on the user arrival direction area is calculated, and the operation of estimating the angle of arrival is repeated to obtain the first refined estimation value and the estimation error from the theoretical value Measurements are made multiple times until the error converges to a specified threshold.

[0136] In S2, analyze the system cascaded channel gain model and optimal active and passive beamforming: In the base station-IRS-user downlink, the signal received by the single-antenna receiving end is:

[0137]

[0138] Wherein, is the cascaded channel amplitude gain of the system, Denote the amplitude-normalized channel matrix between the IRS and the user, and the diagonal matrix Denote the operation of the IRS on the incident wave signal from the transmitter, Ψ i ∈[0,2π] represents the phase shift of the i-th reflecting element on the IRS, Denote the amplitude-normalized channel matrix between the transmitter and the IRS, v represents the active beamforming vector of the transmitter, and n represents Gaussian random noise. When the position and orientation of the IRS in the system are fixed, ρ IRS can be regarded as a constant. When the IRS is regarded as dynamically adjustable in direction, ρ IRS can then be regarded as a variable that can be optimized.

[0139] Among them,

[0140]

[0141] Among them,

[0142]

[0143] First, consider the rotation characteristics of the IRS. By adjusting the IRS steering to maximize the system cascaded channel gain, the expression of ρ IRS is as follows:

[0144]

[0145] Among them, G t is the transmitting antenna gain, G r is the receiving antenna gain, N is the total number of units of the IRS with size, λ is the signal wavelength, d G is the distance from the base station to the IRS, d h is the distance from the IRS to the user, θ t is the angle between the incident signal and the IRS normal, θ r is the angle between the reflected signal and the IRS normal.

[0146] From the above formula, the amplitude gain of the IRS is essentially a function of the position and orientation of the IRS. Therefore, rotating the IRS at a fixed position will affect the value of ρ IRS .

[0147] The optimization problem can be transformed into:

[0148]

[0149] Among them, θ t is the angle between the signal incident direction and the IRS normal direction, θ r is the angle between the signal outgoing direction and the IRS normal direction, is the azimuth angle of arrival formed by the electromagnetic wave transmitted by the base station and the IRS, is the azimuth angle at which the electromagnetic wave reflected by the IRS reaches the receiving end. are the angles of rotation of the IRS along the x and z axes respectively. F(θ) is the normalized power radiation pattern of the intelligent reflecting surface, which reveals the incidence / reflection law of the signal passing through the intelligent reflecting surface and the dependence on the incidence / reflection angle:

[0150]

[0151] Based on the received power at the receiving end given the position and orientation of the IRS, when the power of the transmitting end is constant, by jointly adjusting the azimuth angle and elevation angle of the IRS, θ can be changed t and θ r values, to obtain the maximum reflection efficiency at a given position, and complete the space-based intelligent reflecting surface reflection structure and its joint passive beamforming design method.

[0152] Corollary 1: To maximize the objective function, it is first necessary to make the normal direction of the IRS, the signal incident direction, and the outgoing direction lie in the same plane, that is: is the elevation angle of arrival formed by the electromagnetic wave transmitted by the base station and the IRS.

[0153] Corollary 2: Calculate such that the normal of the IRS is parallel to the angle bisector of θ0, and at this time the objective function reaches the maximum value.

[0154] First, calculate the angle θ0 between the signal incident direction and the outgoing direction:

[0155]

[0156] When , the signal-to-noise ratio at the receiving end reaches the maximum.

[0157] Next, perform the IRS passive beamforming design. Due to the angle-of-arrival estimation error, the position of the receiving end may be unstable, introducing uncertainty to the AoA and AoD. To model the uncertainty of the receiving end position, this example considers a unified, bounded uncertainty model:

[0158]

[0159] where, Δθ represents the three-dimensional uncertainty vector of the angle of arrival, and φ, δ represent the error thresholds. Therefore, the true angle of arrival of the receiving end can be modeled as

[0160]

[0161] Project the beam range involved due to the angle of arrival (AoA) uncertainty of the user onto the ground receiving end, and calculate the stable coverage area range of the beam:

[0162] Let represent the estimated value of the user's angle of arrival, represent the estimated value of the corresponding user location coordinates, Δθ represent the angle estimation error, (w x ,w y ) represent the true value of the corresponding user coordinates. There is the following relationship:

[0163]

[0164]

[0165] Therefore, the elevation angle θ and the azimuth angle have the following relationship with the location coordinates between the IRS and the user:

[0166]

[0167] q z = d h cosθ (33)

[0168] Then the error between the user's expected location and the actual location is:

[0169]

[0170] Let Δ = [Δx, Δy] T represent the user location coordinate estimation error, then:

[0171]

[0172] The relationship between the spatial frequency of the signal from the IRS to the user along the IRS array direction and the user's location is:

[0173]

[0174] Therefore, the true spatial frequencies corresponding to the AoA and AoD of the ARIS can be given by the following formula:

[0175]

[0176] Where

[0177]

[0178] From the perspective of the perturbed spatial frequency, the steering vector affected by the user's angle of arrival uncertainty can be expressed as:

[0179]

[0180] where \( \mathbf{h} \) represents the true channel steering vector of the IRS-user, \( \hat{\mathbf{h}} \) represents the estimated channel steering vector of the IRS-user, and \( \mathbf{e} \) h represents the error function.

[0181] \( \mathbf{e} \) h \( = \mathbf{a} \) T (f x-I2U \( \Delta, f \) z-I2U \( \Delta) \ (48) \)

[0182] Based on the AIRS uncertainty model, the received SNR can be expressed as a function of the error vector:

[0183]

[0184] Then, considering the angular uncertainty, the goal is to maximize the worst SNR in the target region by jointly designing the BS active beam \( \mathbf{v} \) and the IRS passive beam \( \boldsymbol{\Theta} \) under the maximum transmit power constraint. This optimization problem can be formulated as

[0185]

[0186] \( \| \mathbf{v} \| \) 2 \( \leq P \) t \( \ (50b) \)

[0187] \( 0 \leq \psi \) n \( \leq 2 \pi, n = 1, 2, \ldots, N \ (50c) \)

[0188] The optimization problem \( \mathcal{P}3 \) is difficult to solve directly. First, the objective function is the worst-case SNR over a two-dimensional (2D) region, which is not an explicit representation of the optimization variables. Second, this optimization problem is highly non-convex because \( \Delta \) contains three-dimensional continuous variables, resulting in an infinite number of constraints. To handle \( \mathcal{P}3 \) with reasonable complexity, note that the contributions of \( \boldsymbol{\Theta} \) and \( \mathbf{v} \) to the objective function can be separated as:

[0189]

[0190] where,

[0191]

[0192] \( \mathbf{g} \) G \( = \mathbf{G} \mathbf{v} \ (53) \)

[0193] By separately designing \( | \mathbf{g} \) h \( | \) and \( | \mathbf{g} \) G \( | \) corresponding to the reflection array gain and the active array gain to maximize \( \gamma \) Δ \( (\boldsymbol{\Theta}, \mathbf{v}) \).

[0194] For the active array gain \( | \mathbf{g} \)G , by exploiting the cascaded channel h H ΘGv's special structure, the optimal transmit beamforming vector v corresponds to the simple MRT of AIRS and is independent of the reflection link from AIRS to the target area.

[0195] The base station's active beamforming is obtained according to the MRT principle:

[0196]

[0197] The problem is transformed into:

[0198]

[0199] 0 ≤ ψ n ≤ 2π, n = 1, 2, …, N (55b)

[0200] Then, the objective function is explicitly transformed for easy solution:

[0201]

[0202] s.t. |g h (Θ, Δ)| 2 ≥ t (56a)

[0203]

[0204] 0 ≤ ψ n ≤ 2π, n = 1, 2, …, N (56c)

[0205] The constraint (56b) is non-convex because |g h (Θ, Δ)| 2 is a function of Δ and is subject to infinitely many inequality constraints. Next, the SDR technique is used to transform the non-convex problem into a series of convex problems, and then the optimal phase shift problem is solved by some convex optimization tools (CVX).

[0206] As Figure 3 shown, the present invention proposes an air-based intelligent reflecting surface-assisted positioning and communication system with dynamically rotatable directions. The system mainly consists of two core parts: an airborne intelligent reflecting surface air relay platform and a ground emergency communication base station. Among them, the unmanned aerial vehicle is tightly connected to the intelligent reflecting surface through a specially designed mechanical device, enabling the intelligent reflecting surface to achieve flexible and precise angular rotation to adapt to different communication requirements.

[0207] The deployment location of the intelligent reflecting surface is at any position between the base station and the user, ensuring the continuity and stability of signal transmission. The beam direction of the ground base station is accurately pointed at the intelligent reflecting surface to achieve high-efficiency signal relaying. The ground base station is equipped with antennas, including but not limited to horn antennas, array antennas, omnidirectional antennas, for transmitting beams to the intelligent reflecting surface carried on the tethered drone.

[0208] The uniqueness of this system lies in the dynamic rotation characteristic of its airborne intelligent reflecting surface, which can not only improve the flexibility and adaptability of the communication system, but also achieve better communication effects in complex environments. Overall, the present invention provides an innovative and efficient solution for the wireless communication field.

[0209] For an airborne intelligent reflecting surface-assisted positioning and communication system with dynamically rotatable direction, both the deployment location and direction selection of the intelligent reflecting surface have a profound impact on the power gain of the received signal. In practical applications, compared with frequently changing the deployment location of the intelligent reflecting surface, flexibly adjusting its direction to adapt to the changes in different user positions can more effectively save the power consumption of the drone. This strategy not only improves the energy utilization efficiency of the system, but also helps to extend the working time of the entire system, providing more reliable and lasting support for wireless communication.

[0210] As Figure 4 shown, through the proposed dynamically rotatable airborne intelligent reflecting surface-assisted communication system of the present invention, the optimal rotation angle of the IRS can be calculated under any drone and user positions that meet the requirements of the actual scenario. In the example, the base station is located at the origin of the coordinate system, the coordinates of the RIS are [15, 5, 10] T , and the user coordinates are [100, 0, 0] T . The simulation diagrams respectively show the variation of the signal-to-noise ratio at the receiving end with the number of IRS units when the IRS adopts the optimal phase shift matrix configuration under four conditions: continuous phase shift-fixed steering, continuous phase shift-optimal steering, discrete phase shift-fixed steering, and discrete phase shift-optimal steering. Among them, continuous phase shift is an assumption under ideal conditions. In fact, the phase of the actual IRS can only take a limited number of discrete values, and 1-bit discrete phase shift is adopted in the simulation example. The simulation results show that by rotating the azimuth angle of the IRS, the power loss caused by discrete phase shift can be effectively compensated, achieving almost the same received signal-to-noise ratio as the continuous phase shift assumption, and the system performance is improved by about 33.9%.

[0211] In an airborne intelligent reflecting surface-assisted angle-of-arrival estimation and communication system with dynamically rotatable direction in the present invention, within each period, first estimate the angle of arrival of the user to determine the user's azimuth, and then adjust the mechanical pointing of the IRS and the passive reflection phase shift matrix according to the user's position to maximize the signal-to-noise ratio at the user end.

Claims

1. A method for angle-of-arrival estimation and communication assisted by a dynamically rotatable airborne intelligent reflecting surface, characterized in that The specific steps are as follows: Step 1: Build an air-based intelligent reflecting surface communication system composed of a single-antenna user, an intelligent reflecting surface (IRS), and a base station; Step 2: The user periodically and repeatedly sends a positioning pilot signal to the IRS, which is reflected by the IRS to the base station. The IRS periodically and randomly changes the phase shift matrix. The base station roughly estimates the angle of arrival of the user to the IRS through the MUSIC algorithm based on the periodically sampled signal. Step 3: According to the estimated angle of arrival Adjust the IRS steering to the maximum reflection efficiency, and calculate the theoretical rough estimated incoming wave angle of the user after the IRS steering θ z They are the angles of counterclockwise rotation of the IRS along the positive x-axis and z-axis respectively; Step 4: Calculate the value of the passive phase shift matrix when the IRS beam is focused with the user's incoming wave direction as the center and the coverage area radius is R. Randomly change several of the phase shift values as the measurement matrix for the next stage of angle-of-arrival estimation. Repeat the estimation of the angle of arrival from the user to the IRS to obtain the first refined estimation value and the estimation error from the theoretical value Wherein: Step 5: Return to Step 4, repeat the calculation of the refined estimated value and the error between each refined estimated value and the previous one multiple times until the error reaches the specified threshold to obtain the final estimated value; Step 6: For a user with a known azimuth, according to the relative positions of the base station - IRS - user, adjust the mechanical orientation of the IRS according to the final estimated angle value to maximize the system reflection efficiency, reduce the beam coverage range to the angle of arrival estimation error threshold, and take the worst signal-to-noise ratio of the maximized beam coverage area as the optimization objective to solve for the optimal phase shift matrix Θ of the IRS; The optimization objective of IRS beamforming is as follows: s.t. |g h (Θ, Δ)| 2 ≥ t 0 ≤ ψ n ≤ 2π, n = 1, 2, …, N |g h represents the reflection array gain, represents the estimated channel steering vector of the IRS-user corresponding to the case without considering the user direction uncertainty, e h represents the signal error function considering the user direction error; t is the variable to be optimized, representing |g h (Θ,Δ)| 2 the lower limit of the value within the target coverage area, and maximizing this value aims to maximize the worst signal-to-noise ratio within the area; Δθ represents the three-dimensional angle-of-arrival uncertainty vector, φ, δ represent the specified error thresholds; ψ n represents the passive reflection phase shift value of the nth IRS unit; Use the SDR technology to transform this optimization objective into a series of convex problems and solve the optimal phase shift problem through a convex optimization tool (CVX).

2. The method for angle of arrival estimation and communication assisted by a dynamically rotatable airborne intelligent reflecting surface according to claim 1, wherein In the above Step 1, the intelligent reflecting surface IRS is composed of N sub-units, and the base station is equipped with M antennas; The IRS is installed on a rotatable mechanical device under the unmanned aerial vehicle and rotates and swings in azimuth and pitch according to the requirements of the actual scenario; The direct link between the base station and the user is blocked.

3. A method for angle of arrival estimation and communication assisted by a dynamically rotatable airborne intelligent reflecting surface according to claim 1, characterized in that, The specific estimation process of the above Step 2 is as follows: Step 201: Calculate the spatial response channel steering vector from user x to the IRS based on the signal r(t) received by the receiving sensor of the base station The received signal is: α is the path loss factor from the IRS to the base station, a R is the spatial response channel steering vector between the receiving sensor and the IRS, is the known angle of arrival from the IRS to the receiving sensor. The diagonal matrix Θ(t) represents the operation of the intelligent reflecting surface IRS on the incoming wave signal from the transmitter at time t, is the path loss factor from user x to the IRS, X is the total number of single-antenna users, p x represents the transmit power of user x, s x (t) represents the message sent by user x at time t, and n(t) is the base station Gaussian random noise at time t; are the unknown azimuth and elevation angles; is the spatial response channel steering vector from user x to the IRS, and the calculation formula is: N is the total number of elements of the IRS with size, λ is the signal wavelength, and D is the side length of each IRS element; Step 202: Set the IRS measurement matrix as a random phase shift matrix, which changes K times within one period, and repeat L periods to obtain the reconstructed spatial response channel steering vector matrix from the user x to the IRS: where, Step 203: Use the reconstructed spatial response channel steering vector matrix to obtain the spatial spectrum function: is the noise subspace after eigen - value decomposition of the autocorrelation matrix of the received signal; Step 204, by finding the peak value of the spatial spectrum function to obtain the preliminary estimated angle of arrival That is

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