Angle estimation method for antenna spacing exceeding half a wavelength

Abstract

The present invention proposes a method for estimating angles when the antenna spacing exceeds half a wavelength, which is used for angle measurement when the antenna spacing exceeds half a wavelength. The method comprises the following steps: 1) constructing an OFDM-based angle measurement system; 2) initializing a transmitter to send an OFDM signal to a receiver; 3) constructing a signal reception model at the receiving end; 4) introducing a reference angle to iteratively project the signal; 5) using the proposed power-based matching pursuit algorithm to perform parameter estimation; and 6) determining the angle of the direct path. The present invention effectively solves the problem that the angle cannot be accurately measured when the antenna spacing exceeds half a wavelength, and improves the angle measurement accuracy, and is suitable for scenarios such as personnel positioning in indoor environments.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communications, and in particular to a method for estimating an incoming wave angle of a communication device with an antenna spacing greater than half a wavelength. Background Art

[0002] In recent years, driven by the proposal and development of Integrated Sensing and Communication (ISAC) technology, researchers have paid extensive attention to the development of sensing systems based on communication devices such as WiFi. By leveraging existing communication equipment, these systems have promoted a wide range of sensing applications, including indoor positioning, human tracking, and human activity recognition. Most of these systems are developed based on channel state information (CSI). Specifically, these systems are implemented by integrating multi-dimensional parameters obtained through CSI (including angle of arrival (AoA), time of flight (ToF), and Doppler frequency shift (DFS)) into pre-developed positioning or sensing models, supplemented by advanced intelligent optimization algorithms. Therefore, accurate acquisition of channel parameter information has become a basic prerequisite for the successful implementation of these systems.

[0003] However, channel parameter estimation in existing systems is typically limited to relatively ideal conditions. For example, it is often assumed that the antenna array spacing is half a wavelength. However, in existing communication devices (such as most WiFi devices), the antenna array is often wider than half a wavelength, forming a uniform or non-uniform array. For discrete aperture antennas with element spacing greater than half a wavelength, spatial aliasing causes plane waves incident on the array from visible angles other than the desired direction to coherently add, resulting in grating lobes and ultimately incorrect angle measurements. Therefore, if ISAC is to be implemented using existing communication equipment, the problem of antenna spacing greater than half a wavelength, which prevents accurate angle measurements, must be addressed. Summary of the Invention

[0004] The purpose of the present invention is to provide an angle estimation method when the antenna spacing exceeds half a wavelength, so as to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides a method for estimating an angle when the antenna spacing exceeds half a wavelength, comprising the following steps:

[0006] Step 1: Construct an OFDM-based angle measurement system, including a receiver R and a transmitter T. Receiver R is equipped with N antennas for receiving OFDM signals, and the spacing between antennas is greater than half the wavelength corresponding to the frequency of the transmitted and received electromagnetic wave signals. The transmitter is also equipped with an antenna for transmitting OFDM signals.

[0007] Step 2: Initialize the transmitter to send an OFDM signal to the receiver. The bandwidth of the transmitted electromagnetic wave signal is B and the center frequency is f c ;

[0008] Step 3: (3a) Construct a signal model. Assume there are I paths. The multipath signal received by the receiver is expressed as:

[0009]

[0010] Where w(t) is Gaussian white noise, α i is the attenuation coefficient of the i-th path, y(t) represents the total received signal of the receiver, s(t) represents the transmitted signal of the transmitter, a(θ i ) is the steering vector of the i-th path signal, θ i represents the arrival azimuth of the i-th path;

[0011] (3b) The receiving antenna array forms a planar array, a(θ i ) can be expressed as:

[0012] a(θ i )=[a1(θ i ),…,a n (θ i ),…,a N (θ i )] T ,

[0013] in, x n and y n They represent the relative horizontal and vertical coordinates of the nth antenna in the coordinate system formed by the receiver antenna, with a total of N antennas. λ represents the center frequency f c The wavelength of the electromagnetic wave corresponding to the electromagnetic wave;

[0014] (3c) The channel state information A obtained by superimposing the multipath steering vectors can be expressed as:

[0015]

[0016] Step 4: Project the signal model constructed in step 3, introduce a reference angle θ′ within the angle range [0°, 180°] where the signal may arrive, and iteratively project the channel state information in step (3c) according to different reference angle values θ′. The projected channel state information A′ can be expressed as:

[0017] A′=A·H(θ′),

[0018] where H(θ′)=[1,h2(θ′),…,h N-1 (θ′),1] T is the projection vector, where x n ′ and y n ′ respectively represent the horizontal and vertical coordinate differences between the projected nth virtual antenna position and the original antenna position, a′(θ)=a(θ i )·H(θ′), is the steering vector of A′ after projection, only when θ′ is equal to θ i When , the change of a′(θ) is linearly related to a(θ), that is, if and only if in this case, the angle calculated by the antenna array composed of virtual antennas can correspond to the reference angle;

[0019] Step 5: (5a) Based on the super-resolution estimation method in the power domain, in order to obtain the power of the signal at a certain angle to the received signal, a certain weight can be applied to the signal of each antenna to achieve constructive superposition of the signal of this path, while other signals achieve destructive superposition. By arranging and accumulating these signals, the power of other angles is successfully reduced, and the angle θ is obtained. i The signal power of , the weight value applied to the i-th path is:

[0020]

[0021] Among them, d n The distance between the nth antenna and the first antenna, d n Indicates the distance between the Nth antenna and the first antenna, with a total of N antennas;

[0022] (5b) Assume that the signal of the kth multipath is identified, and its power is p k , in θ k In the angular direction, the signal weighted sum Y p It can be expressed as:

[0023]

[0024] Among them, Y p The received signal is at θ k The weighted sum expression in the direction, y nrepresents the received signal of the nth antenna. From (5a), let Indicates that the nth antenna has a projection angle of θ k The weight term, e jε(n,θi) Indicates that the nth antenna has a real path angle of θ i The weight value of Indicates the projection angle θ at the nth antenna k Angle θ with the true path i Therefore, only when i=k, That is, when the projection angle is the same as the true path angle, constructive superposition is achieved, while the others are canceled out;

[0025] (5c) Combined with the projected channel state information described in step 4, after introducing the reference angle θ′, Y in (5b) p It can be expressed as:

[0026]

[0027] (5d) According to (5b) and (5c), only when θ′ and the multipath angle θ i When the signal powers are equal, constructive superposition is possible. Then the power at the reference angle θ′ is expressed as:

[0028]

[0029] (5e) A power orthogonal matching pursuit algorithm based on power domain and compressed sensing theory is proposed, where the constructed atomic set is represented as The received signal is projected at θ′ and expressed as y′ θ′ , which is expressed as follows:

[0030]

[0031] in, To estimate the angle, Nor represents normalization, |<·>| represents the inner product operation, and max represents the maximum value operation when taking different θ′;

[0032] (5f) The angle calculation can be expressed as:

[0033]

[0034] Where Δθ i is the angular difference between the estimated angle and the projection angle, min(.) is the representation of the minimization optimization problem, st is the abbreviation of the satisfied condition, and |.| represents the absolute value operation;

[0035] Step 6: Determine the direct path angle. According to steps 4 and 5, after projection and the power orthogonal matching pursuit algorithm based on power domain and compressed sensing theory, Δθ can be obtained.i and The combination of , setting the step size of the reference angle to 1°, can obtain 180 groups of the above combinations. Therefore, a direct path judgment method based on maximum likelihood is proposed, which can be expressed as:

[0036]

[0037] Where S i represents the score of each path, ω p and ω e Represents the weight, i.e., a constant. As described in step (3a), each path has different attenuation, and the attenuation of the direct path is the smallest. Therefore, the direct path is determined to be S i The path with the largest value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart for the implementation of the present invention;

[0039] Figure 2 This is a phase projection model diagram of the present invention;

[0040] Figure 3 Iteration diagram introduced for the reference angle of the present invention;

[0041] Figure 4 This is a schematic diagram based on the power domain and orthogonal matching principle proposed by the present invention;

[0042] Figure 5 This is the layout diagram of the antenna array used in the experiment of the present invention;

[0043] Figure 6 This is a diagram of the experimental results of the present invention. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below with reference to specific embodiments.

[0045] Reference Figure 1 , the present invention comprises the following steps:

[0046] Step 1: Construct an OFDM-based angle measurement system, including a receiver R and a transmitter T. Receiver R is equipped with N antennas for receiving OFDM signals, and the spacing between antennas is greater than half the wavelength corresponding to the frequency of the transmitted and received electromagnetic wave signals. The transmitter is also equipped with an antenna for transmitting OFDM signals.

[0047] Step 2: Initialize the transmitter to send an OFDM signal to the receiver. The bandwidth of the transmitted electromagnetic wave signal is B and the center frequency is f c ;

[0048] Step 3: (3a) Construct a signal model. Assume there are I paths. The multipath signal received by the receiver is expressed as:

[0049]

[0050] Where w(t) is Gaussian white noise, α i is the attenuation coefficient of the i-th path, y(t) represents the total received signal of the receiver, s(t) represents the transmitted signal of the transmitter, a(θ i ) is the steering vector of the i-th path signal, θ i represents the arrival azimuth of the i-th path;

[0051] (3b) The receiving antenna array forms a planar array, a(θ i ) can be expressed as:

[0052] a(θ i )=[a1(θ i ),…,a n (θ i ),…,a N (θ i )] T ,

[0053] in, x n and y n They represent the relative horizontal and vertical coordinates of the nth antenna in the coordinate system formed by the receiver antenna, with a total of N antennas. λ represents the center frequency f c The wavelength of the electromagnetic wave corresponding to the electromagnetic wave;

[0054] (3c) The channel state information A obtained by superimposing the multipath steering vectors can be expressed as:

[0055]

[0056] Step 4: Project the signal model constructed in step 3, introduce a reference angle θ′ within the angle range [0°, 180°] where the signal may arrive, and iteratively project the channel state information in step (3c) according to different reference angle values θ′. The projected channel state information A′ can be expressed as:

[0057] A′=A·H(θ′),

[0058] where H(θ′)=[1,h2(θ′),…,h N-1 (θ′),1] T is the projection vector, where x n ′ and y n′ respectively represent the horizontal and vertical coordinate differences between the projected nth virtual antenna position and the original antenna position, a′(θ)=a(θ i )·H(θ′), is the steering vector of A′ after projection, only when θ′ is equal to θ i When , the change of a′(θ) is linearly related to a(θ), that is, if and only if in this case, the angle calculated by the antenna array composed of virtual antennas can correspond to the reference angle;

[0059] Step 5: (5a) Based on the super-resolution estimation method in the power domain, in order to obtain the power of the signal at a certain angle to the received signal, a certain weight can be applied to the signal of each antenna to achieve constructive superposition of the signal of this path, while other signals achieve destructive superposition. By arranging and accumulating these signals, the power of other angles is successfully reduced, and the angle θ is obtained. i The signal power of , the weight value applied to the i-th path is:

[0060]

[0061] Among them, d n The distance between the nth antenna and the first antenna, d n Indicates the distance between the Nth antenna and the first antenna, with a total of N antennas;

[0062] (5b) Assume that the signal of the kth multipath is identified, and its power is p k , in θ k In the angular direction, the signal weighted sum Y p It can be expressed as:

[0063]

[0064] Among them, Y p The received signal is at θ k The weighted sum expression in the direction, y n represents the received signal of the nth antenna. From (5a), let Indicates that the nth antenna has a projection angle of θ k The weight term, e jε(n,θi) Indicates that the nth antenna has a real path angle of θ i The weight value of Indicates the projection angle θ at the nth antenna k Angle θ with the true path i Therefore, only when i=k, That is, when the projection angle is the same as the true path angle, constructive superposition is achieved, while the others are canceled out;

[0065] (5c) Combined with the projected channel state information described in step 4, after introducing the reference angle θ′, Y in (5b) p It can be expressed as:

[0066]

[0067] (5d) According to (5b) and (5c), only when θ′ and the multipath angle θ i When the signal powers are equal, constructive superposition is possible. Then the power at the reference angle θ′ is expressed as:

[0068]

[0069] (5e) A power orthogonal matching pursuit algorithm based on power domain and compressed sensing theory is proposed, where the constructed atomic set is represented as The received signal is projected at θ′ and expressed as y′ θ′ , which is expressed as follows:

[0070]

[0071] in, To estimate the angle, Nor represents normalization, |<·>| represents the inner product operation, and max represents the maximum value operation when taking different θ′;

[0072] (5f) The angle calculation can be expressed as:

[0073]

[0074] Where Δθ i is the angular difference between the estimated angle and the projection angle, min(.) is the representation of the minimization optimization problem, st is the abbreviation of the satisfied condition, and |.| represents the absolute value operation;

[0075] Step 6: Determine the direct path angle. According to steps 4 and 5, after projection and the power orthogonal matching pursuit algorithm based on power domain and compressed sensing theory, Δθ can be obtained. i and The combination of , setting the step size of the reference angle to 1°, can obtain 180 groups of the above combinations. Therefore, a direct path judgment method based on maximum likelihood is proposed, which can be expressed as:

[0076]

[0077] Where S i represents the score of each path, ω p and ω e Represents the weight, i.e., a constant. As described in step (3a), each path has different attenuation, and the attenuation of the direct path is the smallest. Therefore, the direct path is determined to be Si The path with the largest value.

[0078] The following is a further explanation of the technical effectiveness of the present invention in conjunction with experimental data:

[0079] (1) The present invention was simulated and tested under the following conditions: OFDM signal, 2.8GHz center frequency, 100MHz bandwidth, 64 subcarriers, a signal-to-noise ratio of 10dB, and antenna spacings of 0.6, 0.8, and 1 wavelength. Furthermore, the present invention was compared with an antenna array with an antenna spacing of 0.5 wavelengths and a signal-to-noise ratio of 10dB. The 90% error results are shown in Table 1.

[0080] Table 1

[0081] Antenna spacing 0.5λ 0.6λ 0.8λ 1λ Angular error (°) 5.8 5.1 3.4 2.3

[0082] The calculation formula for angle measurement error is:

[0083]

[0084] in, Represents the error between the true angle value and the angle estimated by the algorithm, θ t and θ e The values are the true angle value and the algorithm-estimated angle value, respectively. As shown in Table 1, the present invention can effectively solve the problem of being unable to perform angle estimation when the antenna spacing is greater than half a wavelength. Furthermore, the larger the antenna spacing, the higher the angle estimation accuracy. This is consistent with the theory in array signal processing that a larger antenna array aperture results in higher angular resolution.

[0085] (2) The present invention conducted a real scene experiment with an experimental condition of 10×13m 2 The signal is an OFDM signal with a center frequency of 2.8 GHz, a bandwidth of 100 MHz, 64 subcarriers, and an antenna array layout as shown in the following figure. Figure 5 The experimental results are shown in Figure 6 As shown in FIG, the actual experimental results are consistent with the simulation results. As can be seen from the results, the present invention can effectively solve the problem of being unable to measure angles when the antenna spacing is greater than half a wavelength.

[0086] In summary, the present invention overcomes the phase ambiguity problem caused by the antenna spacing being greater than half a wavelength, and can effectively perform angle measurement when the antenna spacing is less than 1 wavelength.

[0087] (3) Compared with the existing invention, the existing invention provides a positioning system and positioning method based on the soft position information of a single base station. The system includes: a positioning base station for receiving positioning data sent by a user terminal and generating a positioning result based on the positioning data; a user terminal for sending positioning data to the positioning base station and receiving the positioning result; a positioning module for estimating the user position based on the soft position information and the inertial data of the user terminal. This invention overcomes the phase ambiguity caused by the antenna spacing being greater than half a wavelength by providing prior information based on the user's existing position information, and improves the angle measurement accuracy by increasing the antenna spacing, thereby improving the positioning accuracy. However, the present invention can obtain accurate angle information only through an algorithm, and also conforms to the theory that the larger the antenna array, the higher the angle accuracy. Therefore, the present invention has more advantages in application.

[0088] In summary, the present invention overcomes the problem of angle estimation ambiguity caused by the antenna spacing being greater than half a wavelength, and can realize angle measurement when the antenna spacing is greater than half a wavelength, and the measurement accuracy is higher than the scenario where the antenna spacing is half a wavelength.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for estimating angles when the antenna spacing exceeds half a wavelength, characterized in that: The following steps are involved: Step 1: Construct an OFDM-based angle measurement system, including a receiver R and a transmitter T. Receiver R is equipped with N antennas for receiving OFDM signals, and the spacing between antennas is greater than half the wavelength corresponding to the frequency of the transmitted and received electromagnetic wave signals. The transmitter is also equipped with an antenna for transmitting OFDM signals. Step 2: Initialize the transmitter to send an OFDM signal to the receiver. The bandwidth of the transmitted electromagnetic wave signal is B and the center frequency is f c ; Step 3: (3a) Construct a signal model. Assume there are I signal paths. The multipath signal received by the receiver is expressed as: Where w(t) is Gaussian white noise, α i is the attenuation coefficient of the i-th path, y(t) represents the total received signal of the receiver, s(t) represents the transmitted signal of the transmitter, a(θ i ) is the steering vector of the i-th path signal, θ i represents the arrival azimuth of the i-th path; (3b) The receiver antenna array forms a planar array, a(θ i ) is expressed as: a(θ i )=[a1(θ i ),…,a n (i i ),…,a N (i i )] T , in, x n and y n They represent the relative horizontal and vertical coordinates of the nth antenna in the coordinate system formed by the receiver antenna, with a total of N antennas. λ represents the center frequency f c The wavelength of the electromagnetic wave corresponding to the electromagnetic wave; (3c) The channel state information A obtained by superimposing the multipath steering vectors can be expressed as: Step 4: Project the channel state information constructed in step 3, introduce a reference angle θ′ within the angle range [0°, 180°] where the signal may arrive, and iteratively project the channel state information in step (3c) according to different reference angle values θ′. The projected channel state information A′ can be expressed as: A′=A·H(θ′), where H(θ′)=[1,h2(θ′),…,h N-1 (θ′),1] T is the projection vector, where x n ′ and y n ′ respectively represent the horizontal and vertical coordinate differences between the projected nth virtual antenna position and the original antenna position, a′(θ)=a(θ i )·H(θ′), is the steering vector of A′ after projection, only when θ′ is equal to θ i When , the change of a′(θ) is linearly related to a(θ), that is, if and only if in this case, the angle calculated by the antenna array composed of virtual antennas can correspond to the reference angle; Step 5: (5a) Based on the super-resolution estimation method in the power domain, in order to obtain the power of the signal at a certain angle to the received signal, a certain weight can be applied to the signal of each antenna to achieve constructive superposition of the signal of this path, while other signals achieve destructive superposition. By arranging and accumulating these signals, the power of other angles is successfully reduced, and the angle θ is obtained. i The signal power of , the weight value applied to the i-th path is: Among them, d n The distance between the nth antenna and the first antenna, d N Indicates the distance between the Nth antenna and the first antenna, with a total of N antennas; (5b) Assume that the signal of the kth multipath is identified, and its power is p k , in θ k In the angular direction, the signal weighted sum Y p It can be expressed as: Among them, Y p The received signal is at θ k The weighted sum expression in the direction, y n represents the received signal of the nth antenna. From (5a), let Indicates that the nth antenna has a projection angle of θ k The weight term, e jε(n,θi) Indicates that the nth antenna has a real path angle of θ i The weight value of Indicates the projection angle θ at the nth antenna k Angle θ with the true path i Therefore, only when i=k, That is, when the projection angle is the same as the true path angle, constructive superposition is achieved, while the others are canceled out; (5c) Combined with the projected channel state information described in step 4, after introducing the reference angle θ′, Y in (5b) p It can be expressed as: (5d) According to (5b) and (5c), only when θ′ and the multipath angle θ i When the signal powers are equal, constructive superposition is possible. Then the power at the reference angle θ′ is expressed as: (5e) A power orthogonal matching pursuit algorithm based on power domain and compressed sensing theory is proposed, where the constructed atomic set is represented as The received signal is projected at θ′ and expressed as y′ θ′ , which is expressed as follows: in, To estimate the angle, Nor represents normalization, |<·>| represents the inner product operation, and max represents the maximum value operation when taking different θ′; (5f) The angle calculation can be expressed as: Where Δθ i is the angular difference between the estimated angle and the projection angle, min(.) is the representation of the minimization optimization problem, st is the abbreviation of the satisfied condition, and |.| represents the absolute value operation; Step 6: Determine the direct path angle. According to steps 4 and 5, after projection and the power orthogonal matching pursuit algorithm based on power domain and compressed sensing theory, Δθ can be obtained. i and The combination of , setting the step size of the reference angle to 1°, can obtain 180 groups of the above combinations. Therefore, a direct path judgment method based on maximum likelihood is proposed, which can be expressed as: Where S i represents the score of each path, ω p and ω e Represents the weight, i.e., a constant. As described in step (3a), each path has different attenuation, and the attenuation of the direct path is the smallest. Therefore, the direct path is determined to be S i The path with the largest value.

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