Grating lobe suppression and angle estimation method for OFDM systems

Abstract

The application relates to a grating lobe suppression and angle estimation method for an OFDM system and belongs to the technical field of wireless communication. The method comprises the following steps: constructing an OFDM signal-based receiving model, receiving signals through a uniform linear array and converting the signals into baseband signals; constructing an equivalent frequency array by using OFDM subcarriers, selecting an arbitrary subcarrier as a frequency normalization reference, and mapping the frequency difference between the subcarriers to the element interval of the uniform linear array; reconstructing the receiving signal model based on the equivalent frequency array; simultaneously constructing a differential frequency array based on the equivalent frequency array; calculating the covariance matrix of the reconstructed receiving signal model, obtaining the equivalent receiving signal of the differential frequency array based on the covariance matrix; considering the covariance matrix error and transforming the equivalent receiving signal into a general receiving signal form; and performing angle estimation by using a parameter estimation algorithm. The application can improve the precision and robustness of angle measurement in indoor environment personnel positioning and other scenes.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology and relates to a method for grating lobe suppression and angle estimation for OFDM systems. Background Technology

[0002] In recent years, with the emergence and rapid development of Integrated Sensing and Communication (ISAC) technology, researchers have increasingly focused on building sensing systems based on communication devices such as WiFi. By reusing existing communication infrastructure, these systems have been widely applied in scenarios such as indoor positioning, human tracking, and behavior recognition. Most systems are built based on Channel State Information (CSI), utilizing multidimensional parameters extracted from CSI, such as Angle of Arrival (AoA), Time of Flight (ToF), and Doppler Frequency Shift (DFS), combined with predefined positioning or sensing models and supplemented by intelligent optimization algorithms, to achieve high-precision sensing. Therefore, accurately estimating these parameters is a key prerequisite for the effective operation of the system.

[0003] However, existing methods typically assume that the system operates under ideal conditions, such as an antenna array spacing of half a wavelength, in parameter estimation. But in real-world communication devices (such as most WiFi and 5G terminals), the antenna array spacing often exceeds half a wavelength for performance optimization. This large-spacing discrete array is prone to spatial aliasing during direction estimation, causing beams from non-target directions to coherently overlap at certain visible angles, forming grating lobes and leading to direction estimation errors. Therefore, to achieve ISAC sensing capabilities based on existing communication devices, it is crucial to address the angle estimation distortion problem caused by excessively large antenna spacing. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a grating lobe suppression and angle estimation method for orthogonal frequency division multiplexing (OFDM) systems, which solves the problem of grating lobe interference caused by the antenna array spacing being greater than half a wavelength in existing direction estimation systems based on communication equipment. This invention can improve the accuracy of angle estimation in large-spacing arrays without changing the antenna hardware structure, and is applicable to target localization and sensing tasks in ISAC systems.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for grating lobe suppression and angle estimation in OFDM systems, the method comprising:

[0007] A receiving model based on OFDM signals is constructed, which receives OFDM signals through a uniform linear array and converts them into baseband signals;

[0008] An equivalent frequency array is constructed using OFDM subcarriers. An arbitrary subcarrier is selected as the reference for frequency normalization, and the frequency difference between subcarriers is mapped onto the element spacing of a uniform linear array.

[0009] The received signal model is reconstructed based on the equivalent frequency array; at the same time, a differential frequency array is constructed based on the equivalent frequency array.

[0010] Calculate the covariance matrix of the reconstructed received signal model, and obtain the equivalent received signal of the differential frequency array based on the covariance matrix;

[0011] Considering the covariance matrix error and transforming the equivalent received signal into a general received signal form, angle estimation is performed using a parameter estimation algorithm.

[0012] Furthermore, for a subcarrier containing I subcarriers with a frequency of f... i The OFDM signal is received through a uniform linear array of N elements, where the spacing between elements is d; the frequency is f. i The received signal of the subcarrier is represented as:

[0013]

[0014] In the formula, ρ (k) (t) represents the amplitude of the multipath signal, K represents the number of far-field targets, and n i (t) represents additive white Gaussian noise, a i (θ k ) represents the steering vector, θ k Let k be the direction angle of the far-field target.

[0015] The received signal vector is converted into a baseband signal, and then low-pass filtered to obtain:

[0016]

[0017] In the formula, A i =[a i (θ1),...,a i (θ K )],

[0018] Furthermore, an equivalent frequency array is constructed using OFDM subcarriers, including:

[0019] Choose any one subcarrier as the reference for frequency normalization, normalize the frequencies of other subcarriers to obtain the equivalent frequency, calculate the frequency difference between adjacent subcarriers based on the equivalent frequency, and obtain the spacing Δd = 2(f) between adjacent subcarriers based on the frequency difference. i ′-f′ i-1 )d0d / c, f′、f′ i-1 The equivalent frequency is used. Based on each antenna of the uniform linear array and the subcarrier signal received by each antenna, N subarrays are constructed. Subarray 0 has 1 element, and subarrays 1 to N-1 each have 1 element. The interval between elements in subarrays 1 to N-1 is Δd = 2(f i ′-f′ i-1 )d0d / c; d0 is half wavelength in the sense of normalized frequency, representing the spacing between each subarray; N subarrays are merged to obtain an equivalent frequency array.

[0020] Furthermore, the received signal model is reconstructed based on the equivalent frequency array. According to the number of elements P in the equivalent frequency array, the reconstructed received signal model is as follows:

[0021]

[0022]

[0023] n(t) = [n1(t), n2(t), ..., n P (t)] T

[0024] In the formula, s k (t) represents the narrowband signal; n(t) is the unknown noise vector; a(θ) k ) is the transpose vector; Let r be the phase of the p-th element. p It is the p-th element of the equivalent frequency array.

[0025] Constructing a differential frequency array based on an equivalent frequency array includes: first, performing a forward difference operation on all adjacent subarrays in the equivalent frequency array; then, for two adjacent subarrays, performing a forward difference operation between each element of the latter subarray and each element of the former subarray to obtain I. 2 By removing duplicate element spacing values ​​from each element spacing, we obtain 2I elements corresponding to the element spacings, which form the positive subarray in the differential frequency array. Similarly, we perform negative differential operations on all adjacent subarrays in the equivalent frequency array to obtain the negative subarray in the differential frequency array. Then, we perform a differential operation between subarray 1 in the equivalent frequency array and itself to obtain subarray 0 in the differential frequency array. The differential frequency array is formed by the positive subarray, the negative subarray, and subarray 0.

[0026] Furthermore, based on the reconstructed received signal model and the differential frequency array, the equivalent received signal of the differential frequency array is constructed, including:

[0027] Calculate the covariance matrix of the reconstructed received signal model:

[0028]

[0029] In the formula, E{·} represents the expectation operator, and I P Denotes the identity matrix of P×P. This represents the power of the k-th signal. R represents the noise variance. s The covariance matrix represents the received signal;

[0030] The equivalent received signal of the differential frequency array is obtained by vectorizing the covariance matrix:

[0031]

[0032] In the formula, and Let A represent the Khatri-Rao product and the Kronecker product, respectively. * Let a be the conjugate of the transpose matrix A. * (θ k ) is the transpose vector a(θ) k The conjugate of ); o p Let p represent the zero vector, where all elements except the p-th element are 0, and ρ is the signal power.

[0033] Furthermore, considering the covariance matrix error and transforming the equivalent received signal into a general received signal form, this includes first estimating the covariance matrix based on a finite number of snapshots. T represents the number of snapshots; then through R... x and After calculating and vectorizing the covariance matrix error, the equivalent received signal considering the error term is obtained as follows: Equivalent received signal Transform into a general signal model:

[0034]

[0035] In the formula, ε represents the vectorized covariance matrix error.

[0036] The beneficial effects of this invention are as follows:

[0037] (1) To address the spatial aliasing effect caused by antenna spacing exceeding half a wavelength in existing communication equipment, this invention constructs a two-level virtual array model consisting of an equivalent frequency array (EFA) and a differential frequency array (DFA), utilizing the multi-subcarrier characteristics of OFDM for signal reconstruction. Through frequency normalization and subcarrier differential operations, the physical large-spacing array is transformed into a high-density virtual array, expanding the array aperture and eliminating the coherence conditions caused by grating lobes. Furthermore, the DFA model achieves a multiple expansion of the array aperture through positive / negative differential operations, thereby suppressing coherent superposition of grating lobes at the signal level, solving the problem of direction estimation distortion, and improving the accuracy and robustness of angle measurement in scenarios such as personnel positioning in indoor environments.

[0038] (2) This invention is based on signal processing algorithms and does not require modification of the hardware structure of existing communication equipment. By reusing the inherent multi-subcarrier resources of OFDM system, this invention transforms frequency domain information into virtual space dimension and makes full use of the physical characteristics of the communication signal itself. This can greatly reduce the deployment threshold of ISAC system and enable existing commercial equipment (such as ordinary routers or terminals) to be directly transformed into sensing nodes, thus promoting the large-scale application of integrated sensing technology.

[0039] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0041] Figure 1 This is a schematic flowchart of a grating lobe suppression and angle estimation method for OFDM systems provided in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of a uniform linear array structure;

[0043] Figure 3 A schematic diagram illustrating the principle of constructing an EFA array;

[0044] Figure 4 A schematic diagram illustrating the principle of constructing a DFA array;

[0045] Figure 5 This is a diagram showing the results of grating lobe suppression in this invention;

[0046] Figure 6 This is a diagram showing the angle estimation results of this invention. Detailed Implementation

[0047] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0048] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0049] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0050] like Figure 1 As shown, this invention provides a method for grating lobe suppression and angle estimation in an OFDM system, which is described below:

[0051] I. Construct a receiving model based on OFDM signals, receive OFDM signals through a uniform linear array, and convert them into baseband signals.

[0052] 1. Consider an OFDM signal with a bandwidth of M MHz and a subcarrier frequency of f. i It contains a total of I subcarriers. This signal is received through a linear array of N elements (e.g., ...). Figure 2 As shown in the figure, the element spacing is d.

[0053] For frequency f i The subcarriers, where i = 1, 2, ..., I, are multipath signals from K far-field targets located in the direction of arrival θ. kAt a point, where k∈{1,2,...,K}, it can be represented as:

[0054]

[0055] Where, ρ (k) (t) represents the amplitude of the multipath signal, which remains constant between the receiving antennas and is typically related to the material properties of the reflecting surface; n i (t) represents additive white Gaussian noise; a i (θ k ) represents the guide vector.

[0056] 2. Assume it is white noise in both space and time; steering vector a i (θ k (Corresponds to the direction of arrival θ) k , is represented as:

[0057]

[0058] Where, λ i =c / f i This indicates that it corresponds to f i The wavelength is denoted by λ, and c is the speed of wave propagation.

[0059] The received signal vector is converted into a baseband signal, and after low-pass filtering, we can obtain:

[0060]

[0061] Among them, A i =[a i (θ1),...,a i (θ K )], Let be the signal strength of the k-th path of the i-th subcarrier.

[0062] 2. Construct a virtual array, select any subcarrier as the reference for frequency normalization, divide the frequency of other subcarriers by the frequency of the reference subcarrier to obtain the equivalent frequency, which is independent of the actual frequency value, and then map the frequency difference between subcarriers onto the physical interval d.

[0063] Introducing L i = 2d / λ, the array position set after frequency normalization can be expressed as:

[0064]

[0065] Where d0 is the half-wavelength in the normalized frequency sense (i.e., not referring to a specific frequency), and represents the spacing between the subarrays in the constructed virtual array, Δd = 2(fi -f i-1 )d0d / c represents the spacing between elements in the subarray. Because this array It is obtained through frequency transformation, hence the name equivalent frequency array (EFA). For example... Figure 3 As shown, the EFA consists of N subarrays, corresponding to the number of physical sensors in the original array. Each subarray contains I elements, equal to the number of subcarriers. The I elements of subarray 0 overlap, so the constructed EFA has a total of P = I × (N-1) + 1 elements.

[0066] III. The received signal model can be reconstructed based on EFA as follows:

[0067]

[0068] Where x(t)=[x1(t),x2(t),...,x P (t)] T , s(t)=[s1(t),s2(t),...,s K (t)] T ,

[0069] A = [a(θ1), a(θ2), ..., a(θ)] K )], Narrowband signal s k (t)=ρ (k) exp(j2πft), λ is the wavelength of the signal source, r p express The p-th element. n(t) = [n1(t), n2(t), ..., n P (t)] T It is an unknown noise vector. d p a(θ) represents the spacing of the p-th element. k ) represents the transpose vector, ρ (k) Indicates the amplitude of the multipath signal. This represents the phase of the p-th element.

[0070] For each k∈{1,2,...,K}, the multipath signal s k All (t) are independent of each other and follow a complex Gaussian distribution with a mean of zero, and have a common variance. Each element of the noise vector n(t) is also independent and follows a complex Gaussian distribution with zero mean and variance.

[0071] IV. Construct a DFA received signal model with a covariance error term.

[0072] 1. Construct a differential frequency array (DFA) to further suppress grating lobes. Specifically, this can be achieved using... Construct a DFA.

[0073] like Figure 4 As shown, DFA subarray 1 (denoted as...) Let's take the construction of EFA as an example. The i-th element in the n-th subarray of EFA is represented as... Specifically, in order to obtain To perform a forward difference operation between EFA2 and EFA1, specifically, perform a forward difference operation between each element in EFA2 and each element in EFA1 to obtain I. 2 After removing duplicate element spacing values ​​from each element spacing interval, we obtain 2I elements corresponding to element spacing intervals, where the element spacing interval value is d0±iΔd. The maximum spacing is d0+iΔd (through...). and (obtained by difference operation between them), and the minimum spacing is d0-IΔd( and (Obtained through difference operations). From Figure 4 It can be seen that, compared with EFA1, the constructed The array width and number of elements are both doubled. Similarly, other subarrays of the DFA can be obtained through the same process. It's important to note that subarray EFA1 is subdivided by itself to obtain a DFA subarray, which becomes DFA subarray 0, or DFA0. Furthermore, performing negative difference operations between EFA subarrays will generate additional DFAs. - Subarray, final DFA - Subarray, DFA + The subarray and DFA0 together constitute the DFA array.

[0074] 2. To obtain the equivalent received signal of the DFA, the covariance of the reconstructed received signal model is first calculated. Assuming a stable source signal and noise, the covariance matrix of the output vector x(t) can be written as:

[0075]

[0076] Where E{·} denotes the expectation operator, I P Denotes the identity matrix of P×P. This represents the power of the k-th signal.

[0077] Construct the equivalent received signal of the DFA, and R x Vectorization:

[0078]

[0079] in, and Let A represent the Khatri-Rao product and the Kronecker product, respectively. * Let a be the conjugate of the transpose matrix A. * (θ k ) is the transpose vector a(θ) k ) conjugate. o p Let p represent the zero vector, where all elements except the p-th element are 0, and ρ is the signal power.

[0080] V. Consider the covariance matrix error and transform the equivalent received signal of the DFA into a general model.

[0081] 1. For simplicity, define Therefore, the equivalent received signal of the DFA can be expressed as

[0082]

[0083] 2. Covariance matrix It is usually estimated from a limited number of snapshots, that is:

[0084]

[0085] This will lead to approximation errors. Consider that the approximation error of the vectorized covariance matrix follows an asymptotically complex Gaussian distribution, as follows:

[0086]

[0087] Therefore, considering the error term, the equivalent received signal of the DFA can be expressed as:

[0088]

[0089] 3. Transform the DFA equivalent received signal into a general signal model:

[0090]

[0091] Based on the above, this invention constructs a DFA model using the multicarrier of OFDM signals, suppresses grating lobes, and transforms the obtained DFA-based signal model into a general signal model, which can then be solved using classic parameter estimation methods, such as multi-signal classification and orthogonal matching pursuit algorithms.

[0092] This embodiment verifies the DFA's ability to suppress grating lobes through simulation and simulates the angle estimation error under different signal-to-noise ratios. The simulation conditions are: OFDM signal, 2.8 GHz center frequency, 100 MHz bandwidth, 64 subcarriers, and antenna spacing of one wavelength. Simulation results are shown below. Figure 5 and Figure 6 .

[0093] like Figure 5 As shown, the DFA model proposed in this invention utilizes the frequency difference of OFDM subcarriers to effectively suppress the grating lobe and reduce the main lobe width by 3dB, thereby providing angle estimation accuracy.

[0094] like Figure 6 The results show the angle estimation, which were performed using orthogonal matching pursuit and multiple signal classification algorithms, and compared with the lower bound of the error. Figure 6 It can be seen that the DFA model proposed in this invention can effectively suppress grating lobes and estimate angles using traditional parameter estimation algorithms.

[0095] In summary, this invention overcomes the grating lobe problem caused by antenna spacing being greater than half a wavelength, enabling angle measurement even when the antenna spacing is greater than half a wavelength, and achieving higher measurement accuracy than in scenarios where the antenna spacing is half a wavelength.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for grating lobe suppression and angle estimation in OFDM systems, characterized in that, The method includes: A receiver model based on OFDM signals is constructed, which receives OFDM signals through a uniform linear array and converts them into baseband signals; for signals containing I There are 1 subcarrier, and the subcarrier frequency is 1 OFDM signal, through a... The receiver is a uniform linear array of n elements, where the spacing between the elements in the uniform linear array is 1. d ; frequency is The received signal of the subcarrier is represented as: ， In the formula, Indicates the amplitude of the multipath signal. K Indicates the number of far-field targets. This represents additive white Gaussian noise. Indicates the guide vector. For far-field targets k Direction angle; The received signal vector is converted into a baseband signal, and then low-pass filtered to obtain: In the formula, , ; An equivalent frequency array is constructed using OFDM subcarriers. An arbitrary subcarrier is selected as the reference for frequency normalization, mapping the frequency difference between subcarriers to the element spacing of a uniform linear array. Another arbitrary subcarrier is selected as the reference for frequency normalization, and the frequencies of other subcarriers are normalized to obtain the equivalent frequency. The frequency difference between adjacent subcarriers is calculated based on the equivalent frequency, and the spacing between adjacent subcarriers is determined based on this frequency difference. , , The equivalent frequency is obtained by constructing a system based on each antenna of the uniform linear array and the subcarrier signal received by each antenna. N There are several subarrays, where subarray 0 contains 1 element, and subarrays 1 through 1... N The number of elements in -1 is all I And subarray 1 to subarray N In -1, the interval between elements is ; The half-wavelength in the normalized frequency sense represents the spacing between each subarray; N The subarrays are combined to obtain an equivalent frequency array; The received signal model is reconstructed based on the equivalent frequency array; at the same time, a differential frequency array is constructed based on the equivalent frequency array. Reconstructing the received signal model based on the equivalent frequency array includes adjusting the number of elements in the equivalent frequency array. P The reconstructed received signal model is as follows: ， ， ， ， In the formula, It is a narrowband signal; The noise vector is unknown. It is the transpose vector; For the first The phase of each element, For the first p Spacing between elements The first of the equivalent frequency array One element; Constructing a differential frequency array based on an equivalent frequency array includes: first, performing a forward difference operation on all adjacent subarrays in the equivalent frequency array; for two adjacent subarrays, performing a forward difference operation between each element of the latter subarray and each element of the former subarray to obtain... After removing duplicate element spacing values ​​from the element spacing values, we get... The elements corresponding to the element spacing form the positive subarray in the differential frequency array; similarly, the negative subarray is obtained by performing a negative differential operation on all adjacent subarrays in the equivalent frequency array; then, the subarray 1 in the equivalent frequency array is differentially operated with itself to obtain the subarray 0 in the differential frequency array; the differential frequency array is formed by the positive subarray, the negative subarray, and subarray 0. Calculate the covariance matrix of the reconstructed received signal model, and obtain the equivalent received signal of the differential frequency array based on the covariance matrix; Considering the covariance matrix error and transforming the equivalent received signal into a general received signal form, angle estimation is performed using a parameter estimation algorithm.

2. The method according to claim 1, characterized in that, Based on the reconstructed received signal model and the differential frequency array, the equivalent received signal of the differential frequency array is constructed, including: Calculate the covariance matrix of the reconstructed received signal model: In the formula, Represents the expectation operator. express The identity matrix, Indicates the first The power of each signal, Indicates the noise variance. The covariance matrix represents the received signal; The equivalent received signal of the differential frequency array is obtained by vectorizing the covariance matrix: In the formula, , , and These represent the Khatri-Rao product and the Kronecker product, respectively. Transpose matrix conjugate, Transpose vector The conjugate; , , Indicates except the first A zero vector with 1 element and all other elements being 0. This represents the signal power.

3. The method according to claim 2, characterized in that, Considering the covariance matrix error and transforming the equivalent received signal into a general received signal form, this includes first estimating the covariance matrix based on a finite number of snapshots. , T Indicates the number of snapshots; then through and After calculating and vectorizing the covariance matrix error, the equivalent received signal considering the error term is obtained as follows: ; Equivalent received signal Transform into a general signal model: In the formula, The error represents the vectorized covariance matrix. .

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