Grating lobe suppression and angle estimation method for OFDM system

Abstract

The invention relates to a grating lobe suppression and angle estimation method for an OFDM (Orthogonal Frequency Division Multiplexing) system, and belongs to the technical field of wireless communication. The method comprises the following steps: constructing a receiving model based on an OFDM signal, receiving the signal through a uniform linear array, and converting the signal into a baseband signal; the method comprises the following steps of: constructing an equivalent frequency array by using OFDM (Orthogonal Frequency Division Multiplexing) subcarriers, selecting any subcarrier as a reference for frequency normalization, and mapping a frequency difference between the subcarriers to an element interval of a uniform linear array; reconstructing a receiving signal model based on the equivalent frequency array; constructing a differential frequency array based on the equivalent frequency array; calculating a covariance matrix of the reconstructed received signal model, and obtaining an equivalent received signal of the differential frequency array based on the covariance matrix; a covariance matrix error is considered, an equivalent received signal is converted into a general received signal form, and angle estimation is performed by using a parameter estimation algorithm. According to the invention, the precision and robustness of angle measurement in scenes such as indoor environment place personnel positioning and the like can be improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and relates to a grating lobe suppression and angle estimation method for an OFDM system. BACKGROUND

[0002] In recent years, with the proposal and rapid development of integrated sensing and communication (ISAC) technology, researchers have paid more and more attention to the construction of sensing systems based on communication devices such as WiFi. By multiplexing existing communication infrastructure, such systems have been widely used in indoor positioning, human tracking and behavior recognition scenarios. Most of the systems are based on channel state information (CSI) construction, which uses multi-dimensional parameters extracted from CSI, such as angle of arrival (AoA), time of flight (ToF) and Doppler frequency shift (DFS), combines with predefined positioning or sensing models, and is supplemented by intelligent optimization algorithms, so as to achieve high-precision sensing. Therefore, accurate estimation of these parameters is a key prerequisite for the effective operation of the system.

[0003] However, existing methods usually assume that the system works under ideal conditions, such as half-wavelength antenna array spacing. But in actual communication devices (such as most WiFi and 5G terminals), the antenna array spacing often exceeds half-wavelength for communication performance optimization. Such large-interval sparse arrays are prone to spatial aliasing effects when performing direction estimation, causing beams from non-target directions to coherently superimpose at certain visible angles, forming grating lobes, and thus causing direction estimation errors. Therefore, to realize the ISAC sensing capability based on existing communication devices, it is urgent to solve the problem of angle estimation distortion caused by excessive antenna spacing. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a grating lobe suppression and angle estimation method for an orthogonal frequency division multiplexing (OFDM) system, which solves the problem of grating lobe interference caused by antenna array spacing greater than half-wavelength in existing direction estimation systems based on communication devices. The present application can improve the accuracy of angle estimation in large-interval arrays without changing the antenna hardware structure, and is suitable for target positioning and sensing tasks in ISAC systems.

[0005] To achieve the above purpose, the present application provides the following technical solutions:

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

[0007] A receiving model based on OFDM signal is constructed, the OFDM signal is received by a uniform linear array and converted into a baseband signal;

[0008] An equivalent frequency array is constructed by using OFDM subcarriers, an arbitrary subcarrier is selected as a reference for frequency normalization, and the frequency difference between the subcarriers is mapped to the element interval of the uniform linear array;

[0009] The receiving signal model is reconstructed based on the equivalent frequency array; and a differential frequency array is constructed based on the equivalent frequency array;

[0010] The covariance matrix of the reconstructed receiving signal model is calculated, and the equivalent receiving signal of the differential frequency array is obtained based on the covariance matrix;

[0011] The equivalent receiving signal is transformed into a general receiving signal form by considering the covariance matrix error, and a parameter estimation algorithm is used for angle estimation.

[0012] Further, for an OFDM signal containing I subcarriers, the subcarrier frequency is f i , and the signal is received by a uniform linear array composed of N elements, the element interval of the uniform linear array is d; the received signal of the subcarrier with frequency f i 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, n i (t) represents additive white Gaussian noise, a i (θ k ) represents a steering vector, θ k is the direction angle of the far-field target k;

[0015] The received signal vector is converted into a baseband signal, and after low-pass filtering, the following is obtained:

[0016]

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

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

[0019] The frequency of other subcarriers is normalized to obtain equivalent frequencies, the frequency difference between adjacent subcarriers is calculated according to the equivalent frequencies, and the interval Δd between adjacent subcarriers is obtained based on the frequency difference, that is, Δd = 2(f i ′-f′ i-1 )d0d / c, f′, f′ i-1 The equivalent frequencies are obtained by normalizing the frequencies of other subcarriers with respect to the frequency of any one subcarrier as a reference; the frequency difference between adjacent subcarriers is calculated according to the equivalent frequencies; and the interval Δd between adjacent subcarriers is obtained based on the frequency difference, that is, Δd = 2(f i ′-f′ i-1 )d0d / c; d0 is a half wavelength in the sense of normalized frequency, representing the interval between subarrays; and the N subarrays are combined to obtain an equivalent frequency array.

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

[0021]

[0022]

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

[0024] In the formula, s k (t) is a narrowband signal; n(t) is an unknown noise vector; a(θ k ) is a transposed vector; is the phase of the pth element, r p is the pth element of the equivalent frequency array.

[0025] The difference frequency array is constructed based on the equivalent frequency array, including: first, forward difference operation is performed on all adjacent subarrays in the equivalent frequency array; for two adjacent subarrays, forward difference operation is performed on each element in the latter subarray and each element in the former subarray to obtain I 2 element intervals, after eliminating the repeated element interval values, 2I element intervals corresponding to elements are obtained to form the forward subarray in the difference frequency array; similarly, negative difference operation is performed on all adjacent subarrays in the equivalent frequency array to obtain the negative subarray in the difference frequency array; then, difference operation is performed on the subarray 1 in the equivalent frequency array and itself to obtain the subarray 0 in the difference frequency array; the difference frequency array is composed of the forward subarray, the negative subarray and the subarray 0.

[0026] Further, according to the reconstructed received signal model and the differential frequency array, an equivalent received signal of the differential frequency array is constructed, comprising:

[0027] A covariance matrix of the reconstructed received signal model is calculated:

[0028]

[0029] wherein E{·} represents an expectation operator, I P represents a P×P unit matrix, represents a power of the kth signal, represents a noise variance, R s represents a covariance matrix of the received signal;

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

[0031]

[0032] wherein and respectively represent a Khatri-Rao product and a Kronecker product, A * is a conjugate of a transposed matrix A, a * (θ k ) is a conjugate of a transposed vector a(θ k ); o p represents a zero vector with the pth element being 1 and the rest being 0, and ρ is a signal power.

[0033] Further, considering the covariance matrix error and transforming the equivalent received signal into a general received signal form, comprising: first, estimating the covariance matrix T represents a number of snapshots; then calculating the covariance matrix error through R x and , and after vectorizing the covariance matrix error, the equivalent received signal considering the error term is Transforming the equivalent received signal into a general signal model:

[0034]

[0035] wherein ε represents the vectorized covariance matrix error,

[0036] The present application has the advantages of:

[0037] (1) For the spatial aliasing effect caused by the large antenna spacing of the existing communication equipment greater than half the wavelength, the application constructs two-level virtual array models of equivalent frequency array (EFA) and differential frequency array (DFA), and uses the OFDM multi-subcarrier characteristics to reconstruct the signal. Through frequency normalization and subcarrier difference operation, the physical large spacing array is converted into a high-density virtual array, which expands the array aperture and eliminates the coherent conditions caused by the grating lobe. Among them, the DFA model further realizes the expansion of the array aperture by positive / negative difference operation, thereby suppressing the grating lobe coherent superposition at the signal level, solving the distortion problem of direction estimation, and improving the accuracy and robustness of angle measurement in indoor environment personnel positioning and other scenes.

[0038] (2) The application is realized based on signal processing algorithm, without modifying the hardware structure of the existing communication equipment. The application converts the frequency domain information into virtual spatial dimension by multiplexing the inherent multi-subcarrier resources of the OFDM system, fully utilizes the physical characteristics of the communication signal itself, greatly reduces the deployment threshold of the ISAC system, and enables the existing commercial equipment (such as ordinary routers or terminals) to be directly converted into sensing nodes, promoting the large-scale application of integrated sensing technology.

[0039] Other advantages, objects, and features of the present application will be in part apparent and in part pointed out hereinafter in the specification, and will be learned from a reading of the following specification and by practicing the present application. The objects and other advantages of the present application will be realized and attained by the structure particularly pointed out in the specification. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred detailed description of the present application will be combined with the drawings to describe the present application, in which:

[0041] Figure 1 The grating lobe suppression and angle estimation method flowchart for the OFDM system provided by the embodiment of the present application;

[0042] Figure 2 The schematic diagram of the uniform linear array structure;

[0043] Figure 3 The principle diagram for constructing the EFA array;

[0044] Figure 4 The principle diagram for constructing the DFA array;

[0045] Figure 5 The grating lobe suppression result diagram of the present application;

[0046] Figure 6 The angle estimation result diagram of the present application. DETAILED DESCRIPTION

[0047] Following specific embodiments of the present application are illustrated by specific examples, and other advantages and effects of the present application can be easily understood by those skilled in the art from the disclosure of this specification. The present application can also be implemented or applied by other different specific embodiments, and various modifications or changes can be made to the details in this specification based on different views and applications without departing from the spirit of the present application. It should be noted that the drawings provided in the following examples only illustrate the basic concept of the present application in a schematic manner, and the following examples and features in the examples can be combined with each other without conflict.

[0048] In the drawings, only for exemplary illustration, only schematic views are shown, not actual views, and should not be understood as a limitation of the present application; in order to better illustrate the embodiments of the present application, some components in the drawings can be omitted, enlarged or reduced, and do not represent the actual size of the product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings can be omitted.

[0049] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that if the terms "upper", "lower", "left", "right", "front", "back" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only used for exemplary illustration, and should not be understood as a limitation of the present application, for those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0050] As shown in Figure 1 , a grating lobe suppression and angle estimation method for OFDM system provided by an embodiment of the present application is as follows:

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

[0052] 1. Consider an OFDM signal with a bandwidth of M MHz, whose subcarrier frequency is f i , and a total of I subcarriers. The signal is received by a linear array composed of N elements (as shown in Figure 2 ), and the element spacing is d.

[0053] For the subcarrier with frequency f i , where i = 1, 2,..., I, the multi-path signal from K far-field targets, which are located at the direction of arrival θ kwhere k e {1, 2,..., K}, can be expressed as:

[0054]

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

[0056] 2. Assuming that it is white noise in space and time; the steering vector a i (θ k ) corresponds to the direction of arrival θ k , is expressed as:

[0057]

[0058] where, λ i = c / f i represents the wavelength corresponding to f i , and c is the speed of wave propagation.

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

[0060]

[0061] where, A i = [a i (θ1),..., a i (θ K )], is the signal strength of the ith subcarrier and the kth path.

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

[0063] Introduce L i = 2d / λ, and the set of frequency-normalized array positions can be expressed as:

[0064]

[0065] where d0 is the half wavelength in the sense of normalized frequency (i.e. not referring to a specific frequency), represents the spacing between the subarrays in the constructed virtual array, and Δd = 2(fi -f i-1 )d0d / c represents the spacing between elements in a sub-array. Since this array is obtained by frequency transformation, it is called equivalent frequency array (EFA). As shown in Figure 3 , the EFA consists of N sub-arrays, corresponding to the number of physical sensors in the original array. Each sub-array contains I elements, equal to the number of subcarriers. The I elements of the sub-array 0 overlap, so there are P = I x (N - 1) + 1 elements in the constructed EFA in total.

[0066] III. Reconstructing the received signal model based on the EFA, which can be written as:

[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 )], The narrowband signal s k (t) = ρ (k) exp(j2πft), λ is the wavelength of the signal source, r p represents the pth element of x(t). n(t) = [n1(t), n2(t),..., n P (t)] T is an unknown noise vector. d p represents the spacing of the pth element, a(θ k ) represents the transposed vector, ρ (k) represents the amplitude of the multipath signal, represents the phase of the pth element.

[0070] For each k ∈ {1, 2,..., K}, the multipath signals s k (t) are mutually independent and subject to complex Gaussian distribution with mean zero and common variance Each element of the noise vector n(t) is also mutually independent and subject to complex Gaussian distribution with mean zero and variance

[0071] Four, construct DFA received signal model with covariance error term.

[0072] 1, construct differential frequency array (DFA), further suppress grating lobe, specifically, can use Construct DFA.

[0073] As Figure 4 Illustrated, with the construction of DFA subarray 1 (denoted as ) for example. The nth subarray of EFA is denoted as Specifically, in order to get To be forward difference operation between EFA2 and EFA1, specifically, each element in EFA2 and each element in EFA1 are forward difference operation, get I 2 Element spacing, after eliminating the repeated element spacing value, get 2I element spacing corresponding element, element spacing value is d0±iΔd. The maximum spacing is d0+IΔd (obtained by difference operation between And The minimum spacing is d0-IΔd ( And ) (obtained by difference operation between Figure 4 It can be seen that compared with EFA1, the array width and the number of elements of Both expand by two times. Similarly, other subarrays of DFA can also be obtained by the same process, it should be noted that the subarray EFA1 is obtained by difference operation with itself to get a DFA subarray, which is DFA subarray 0, namely DFA0. In addition, negative difference operation between EFA subarrays will produce additional DFA - Subarray, finally DFA - Subarray, DFA + Subarray and DFA0 together constitute DFA array.

[0074] 2, in order to obtain the equivalent received signal of DFA, first calculate the covariance of the reconstructed received signal model, assuming there are stable source signal and noise, the covariance matrix of output vector x(t) can be written as:

[0075]

[0076] Where, E{·} represents the expectation operator, I P Denotes P×P identity matrix, Denotes the power of the kth signal.

[0077] The equivalent received signal of the DFA is constructed, and R x Vectorization is:

[0078]

[0079] Wherein, And Respectively represent Khatri-Rao product and Kronecker product, A * Is the conjugate of the transpose matrix A, a * (θ k ) is the conjugate of the transpose vector a(θ k ). o p Indicates that the zero vector is 1 except that the pth element is 0, and ρ is the signal power.

[0080] Five, consider the covariance matrix error and transform the equivalent received signal of DFA into a general model.

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

[0082]

[0083] 2, the covariance matrix Usually estimated from a limited number of snapshots, that is:

[0084]

[0085] This will result in approximation error. Consider the approximation error of the vectorized covariance matrix, which follows the asymptotic complex Gaussian distribution, as follows:

[0086]

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

[0088]

[0089] 3, transform the DFA equivalent received signal into a general signal model:

[0090]

[0091] According to the above, the DFA model is constructed by using the multi-carrier of OFDM signal, the grating lobe is suppressed, and the obtained DFA-based signal model is transformed into a general signal model, that is, the classical parameter estimation method can be used for solving, such as multiple signal classification, orthogonal matching pursuit and other algorithms.

[0092] The embodiment verifies the grating lobe suppression capability of the DFA by simulation, and simulates the angle estimation error under different signal-to-noise ratios. Figure 5 and Figure 6 .

[0093] As shown in Figure 5 , the DFA model provided by the application effectively suppresses the grating lobe by using the frequency difference of the OFDM subcarriers, reduces the 3dB width of the main lobe, and can provide angle estimation accuracy.

[0094] As shown in Figure 6 , the angle estimation results are obtained by using the orthogonal matching pursuit and multiple signal classification algorithms for angle estimation and compared with the error lower bound. Figure 6 It can be seen that the DFA model provided by the application can effectively suppress the grating lobe and estimate the angle by using the conventional parameter estimation algorithm.

[0095] In summary, the application overcomes the grating lobe problem caused by the antenna spacing greater than half the wavelength, can realize angle measurement when the antenna spacing is greater than half the wavelength, and has higher measurement accuracy than the scenario where the antenna spacing is half the wavelength.

[0096] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the application and not to limit the application, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the application can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, and all should be covered in the scope of the claims of the application.

Claims

1. A grating lobe suppression and angle estimation method for OFDM systems, characterized by, The method comprises: A receiving model based on an OFDM signal is constructed, the OFDM signal is received by a uniform linear array, and is converted into a baseband signal; An equivalent frequency array is constructed by using OFDM subcarriers, an arbitrary subcarrier is selected as a reference for frequency normalization, and frequency differences between the subcarriers are mapped onto element intervals of the uniform linear array; The receiving signal model is restructured based on the equivalent frequency array; and a differential frequency array is constructed based on the equivalent frequency array; A covariance matrix of the restructured receiving signal model is calculated, and equivalent receiving signals of the differential frequency array are obtained based on the covariance matrix; Angle estimation is performed by using a parameter estimation algorithm, in consideration of covariance matrix errors and conversion of the equivalent receiving signals into a general receiving signal form.

2. The method of claim 1, wherein, For an OFDM signal comprising I subcarriers, with subcarrier frequencies f i , received by an uniform linear array of N elements with element spacing d; the received signal of a subcarrier with frequency f i is represented as: where p (k) (t) denotes the amplitude of the multipath signal, K denotes the number of far-field targets, n i (t) denotes additive white Gaussian noise, a i (θ k ) denotes the steering vector, θ k is the direction angle of the far-field target k; The received signal vector is converted into a baseband signal, and after low-pass filtering, the following is obtained: In the formula, A i = [a i (θ1),...,a i (θ K )], 3. The method of claim 2, wherein, The frequency of other subcarriers is normalized to obtain equivalent frequencies, the frequency difference between adjacent subcarriers is calculated according to the equivalent frequencies, and the interval Δd = 2(f i ′-f′ i-1 )d0d / c, f′, f′ i-1 The equivalent frequency array is obtained by combining the N subarrays. The equivalent frequency array is obtained by combining the N subarrays. i ′-f′ i-1 )d0d / c; d0 is a half wavelength in the sense of normalized frequency, representing the interval between subarrays. The N subarrays are combined to obtain an equivalent frequency array.

4. The method of claim 3, wherein, The receiving signal model is restructured based on the equivalent frequency array, and according to the number P of elements in the equivalent frequency array, the receiving signal model is restructured as follows: n(t) = [n1(t), n2(t),..., n P (t)] T where s k (t) is a narrowband signal; n(t) is an unknown noise vector; a(θ k ) is a transpose vector; is the phase of the pth element, d p is the distance of the pth element, r p is the pth element of the equivalent frequency array.

5. The method of claim 4, wherein, The application discloses a method for constructing a differential frequency array based on an equivalent frequency array, and belongs to the technical field of array signal processing. 2 The method comprises the following steps: firstly, performing forward difference operation on all adjacent sub-arrays in the equivalent frequency array; for two adjacent sub-arrays, performing forward difference operation on each element in the latter sub-array and each element in the former sub-array, thereby obtaining I 2 element spacings; after removing repeated element spacing values, 2I elements corresponding to the element spacings are obtained, and the elements constitute forward sub-arrays in the differential frequency array; similarly, performing negative difference operation on all adjacent sub-arrays in the equivalent frequency array, thereby obtaining negative sub-arrays in the differential frequency array; then, performing difference operation on the sub-array 1 in the equivalent frequency array and the sub-array 1 itself, thereby obtaining the sub-array 0 in the differential frequency array; finally, the forward sub-arrays, the negative sub-arrays and the sub-array 0 constitute the differential frequency array.

6. The method of claim 5, wherein, According to the restructured receiving signal model and the differential frequency array, the equivalent receiving signals of the differential frequency array are constructed, including: The covariance matrix of the restructured receiving signal model is calculated: where E{•} denotes the expectation operator, I P denotes a P x P identity matrix, denotes the power of the kth signal, denotes the noise variance, R s denotes the covariance matrix of the received signals; The equivalent receiving signals of the differential frequency array are obtained by vectorizing the covariance matrix: where and denote Khatri-Rao product and Kronecker product, respectively, A * is the conjugate of the transpose matrix A, a * (θ k ) is the conjugate of the transpose vector a(θ k ); o p denotes a zero vector with 1 at the pth element and 0 elsewhere, and p is the signal power.

7. The method of claim 6, wherein, Considering the covariance matrix error and transforming the equivalent received signal into a general received signal form, including, first estimating the covariance matrix according to a limited number of snapshots T represents the number of snapshots; then calculating R x and The equivalent received signal considering the error term is obtained by calculating the covariance matrix error and vectorizing the covariance matrix error Transforming the equivalent received signal into a general signal model: where ε represents the vectorized covariance matrix error,

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