A frequency control array robust beamforming method based on P4 polyphase code

Abstract

This invention discloses a robust beamforming method for frequency-controlled arrays based on P4 polyphase codes. The method first selects the first element of the frequency-controlled array as the reference element and, utilizing the excellent correlation characteristics of P4 polyphase codes, sequentially sets the frequency offset of each element of the frequency-controlled array. Then, based on the target receiver location information, a beamforming matrix for the frequency-controlled array is generated. Finally, the radiated radio frequency signals from the frequency-controlled array are coherently superimposed at the receiver location, generating an ideal point-like radiation pattern, achieving precise radiation of the frequency-controlled array's radio frequency signals. By modulating the frequency offset of each element of the frequency-controlled array and generating the beamforming matrix, this invention effectively suppresses the range-azimuth coupling of the frequency-controlled array, ensuring that the radiated signals are coherently superimposed at the desired receiver location, generating an ideal point-like radiation pattern, achieving precise delivery of radio frequency signals, and ensuring the security of radio frequency transmission.

Description

Technical Field

[0001] This invention belongs to the field of antenna array signal processing technology, and particularly relates to a robust beamforming method for frequency-controlled arrays based on P4 polyphase codes. Background Technology

[0002] Phased arrays can generate multiple highly directional beams, effectively covering multiple targets in different airspaces, and are therefore widely used in radar detection / imaging, wireless communication, and other fields. However, while phased arrays can provide significant directional gain in the beam pointing direction and suppress interference from other directions, they cannot effectively address interference or detection threats from different distances in the same direction as the target.

[0003] To address the potential security issues associated with phased array radars, the U.S. Air Force Research Laboratory proposed a special phased array technology—frequency-controlled array—at the IEEE Radar Conference in 2006. By introducing minute frequency deviations at the radiation frequencies of each array element, the array's radiated beam is made dependent not only on the azimuth angle but also on the transmission distance, thus generating a radiation pattern with both range and azimuth correlations. Because frequency-controlled arrays can generate radiation patterns with range-dependent characteristics, this technology has attracted widespread attention from scholars both domestically and internationally since its inception and has become a research hotspot. In 2014, the U.S. Air Force Research Laboratory developed a prototype frequency-controlled array radar and conducted field tests, initially verifying the beam propagation characteristics of the frequency-controlled array. In 2016, it publicly released a general-purpose physical layer security test platform based on frequency-controlled arrays. Although the initial purpose of frequency-controlled arrays was to solve the problem of traditional phased array radars' inability to effectively control the range and direction of the transmitted beam, its precise electromagnetic signal radiation characteristics also make frequency-controlled array technology a promising area for wireless communication security.

[0004] The fundamental difference between frequency-controlled arrays and traditional phased arrays lies in whether the radiation frequencies of each element in the antenna array are consistent. For frequency-controlled arrays, the frequency offset of each element directly affects the shape of the radiation pattern, and thus the secure transmission performance of the frequency-controlled array radio frequency system. Initially, the U.S. Air Force Research Laboratory proposed the FDA element frequency offset linear uniform increment scheme (ULA-FDA), that is, making Δf n = (n-1)Δf, where the frequency offset factor Δf is a factor much smaller than the carrier frequency f. c The value of f is the carrier frequency f of the nth element of the frequency control array. n for:

[0005] f n =f c +Δf n =f c +(n+1)Δf,n=1,2,…,N

[0006] Where Δf n(Δf n < <f c ) represents the radiation frequency deviation between the nth array element and the reference array element (assuming the first array element is the reference array element), and the reference array element frequency offset Δf1 = 0.

[0007] While the radiation pattern generated by the ULA-FDA scheme exhibits range-azimuth correlation characteristics, the presence of a periodic component in the ULA-FDA steering vector results in an "S"-shaped radiation pattern. This periodic "S"-shaped pattern poses a high risk of signal leakage in ULA-FDA. Figure 1 As shown. In order to suppress the periodicity and range-azimuth coupling problem of FDA radiation pattern and generate a more accurate point radiation pattern, various nonlinear FDA array element frequency offset setting methods have been proposed. Among them, typical design schemes include the logarithmic frequency offset decoupling method (log-FDA), the exponential growth frequency offset decoupling scheme (exp-FDA), and the Taylor window-based frequency offset setting method (Taylor-FDA).

[0008] However, the aforementioned frequency control array nonlinear frequency offset setting schemes are generally based on Δf < <f c The assumption is that the small variables in the FDA array steering vector are ignored, so that an ideal point radiation pattern can be generated in theoretical analysis. However, this approximation is difficult to implement in actual engineering applications, and therefore it is difficult to generate an ideal point radiation pattern in practical applications. Summary of the Invention

[0009] The purpose of this invention is to address the technical deficiency of existing frequency control arrays, which suffer from range-azimuth coupling and make it difficult to generate ideal point radiation patterns. This invention provides a robust beamforming method for frequency control arrays based on P4 polyphase codes. This invention suppresses range-azimuth coupling, generates ideal point radiation patterns, and ensures the radiation efficiency and radio frequency transmission security of the frequency control array.

[0010] The objective of this invention is achieved through the following technical solution:

[0011] This invention focuses on a uniform linear array comprising N isotropic array elements, wherein the distance between adjacent array elements is d, and the array radiation reference frequency is f. c In this invention, the first array element is selected as the reference array element. Based on the fundamental principles of frequency-controlled arrays, the carrier frequency of the nth array element is:

[0012] f n =f c +Δf n ,

[0013] Where Δf n (Δf n< <f c ) represents the radiation frequency deviation between the nth array element and the reference array element, where the reference array element frequency offset Δf1 = 0.

[0014] This invention utilizes the excellent aperiodic correlation characteristics of P4 polyphase codes to propose a robust beamforming scheme for frequency-controlled arrays based on P4 polyphase codes. This scheme uses P4 polyphase codes to adjust the frequency offset of array elements, eliminating the periodicity of the radiation pattern of the frequency-controlled array and suppressing the range-azimuth coupling of the radiation pattern, i.e., making...

[0015]

[0016] Let θ represent the physical direction of the array's radiated signal, and r represent the Euclidean distance from the array reference element to the far-field position. The distance from each element of the frequency-controlled array to the far-field position (θ, r) is r. n =r-(n-1)d sinθ, n=1, 2,...,N.

[0017] At this time, the phase factor of each element of the frequency control array to the far-field target position (θ, r) is... It can be represented as:

[0018]

[0019] Where c represents the speed of light. Correspondingly, the phase deviation of the transmitted signal between each element of the frequency-controlled array and the reference element... It can be represented as:

[0020]

[0021] The steering factor a of each element of the frequency control array to the far-field target position (θ, r) n (θ, r) is represented as:

[0022]

[0023] j is a complex number. The steering vector a(θ, r) from the frequency control array to the far-field position (θ, r) can be decomposed into an azimuth-dependent steering vector a. θ (θ, r) and distance-related steering vector a r (θ, r), that is, a = a θ (θ,r)⊙a r (θ, r), where the symbol “⊙” denotes the Hadamard product operation of vectors.

[0024]

[0025]

[0026] a θ (θ, r) and ar (θ, r) can be regarded as the frequency control array steering vector when r = 0 and θ = 0°, respectively, i.e., a θ (θ, r) = a(θ, r = 0), a r (θ, r) = a(θ = 0°, r).

[0027] Similarly, the beamforming vector w of the frequency-controlled array can also be decomposed into an azimuth-dependent beamforming vector w θ (θ, r) and range-dependent beamforming vector w r (θ, r) is:

[0028] w = w θ (θ,r)⊙w r (θ, r)

[0029] in:

[0030]

[0031]

[0032] At this moment, the projection B(θ, r) of the frequency-controlled array radiation pattern in the range dimension is... r The projection B of (θ, r) and azimuth dimension θ (θ, r) can be represented as:

[0033]

[0034]

[0035] Analysis of the above formula shows that, in the ULA-FDA scheme, the projection B of the frequency control array radiation pattern in the distance dimension... r (θ, r) exhibits obvious periodicity, with its minimum period being This results in a significant periodicity in the ULA-FDA radiation pattern, affecting the safety of frequency control array radio frequency transmission.

[0036] The robust beamforming scheme for frequency-controlled arrays based on P4 polyphase codes proposed in this invention has a projection of the range dimension as follows:

[0037]

[0038] In the above formula, n = 1, 2, ..., N is the expression for the P4 polyphase code. As shown in the above equation, the frequency-controlled array beamforming scheme based on the P4 polyphase code can effectively eliminate B... r The periodicity of (θ, r) is observed. Meanwhile, the P4 polyphase code exhibits good autocorrelation characteristics, which effectively suppresses sidelobe beam intensity.

[0039] The aforementioned main solution of the present invention and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed by the present invention. Those skilled in the art, after understanding the solution of the present invention, will realize that there are many combinations based on existing technology and common knowledge, all of which are technical solutions to be protected by the present invention, and will not be exhaustively listed here.

[0040] The beneficial effects of this invention are:

[0041] The method of this invention first selects the first element of the frequency-controlled array as the reference element, and utilizes the excellent correlation characteristics of the P4 polyphase code to sequentially set the frequency offset of each element of the frequency-controlled array. Then, based on the target receiver location information, a beamforming matrix of the frequency-controlled array is generated. Finally, the radiated radio frequency signals of the frequency-controlled array will be coherently superimposed at the receiver location to generate an ideal point-like radiation pattern, achieving the purpose of precise radiation of the radio frequency signals of the frequency-controlled array.

[0042] By modulating the frequency offset of each element of the frequency control array using this invention, a beamforming matrix is ​​generated. This effectively eliminates periodic components in the steering vector of the frequency control array and suppresses range-azimuth coupling, allowing the radiated signals from the frequency control array to coherently superimpose at the desired receiving position, producing an ideal point-like radiation pattern and achieving precise radiation of the frequency control array's radio frequency signals. Furthermore, the robust beamforming scheme proposed in this invention can generate a precisely oriented point-like radiation pattern, effectively improving the energy efficiency of the radio frequency signal, reducing the probability of malicious interception and eavesdropping, and enhancing message transmission security. Attached Figure Description

[0043] Figure 1 The system block diagram of the P4-FDA beamforming scheme proposed in this invention.

[0044] Figure 2a This is the P4-FDA radiation pattern proposed in this invention;

[0045] Figure 2b This is the Log-FDA radiation pattern;

[0046] Figure 2c This is a Taylor-FDA radiation pattern. 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 also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0048] It should be noted that, in order to make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0049] Example 1

[0050] Consider a uniform linear array containing 20 isotropic elements, with an array radiation frequency of f. c =10GHz, the distance between adjacent array elements is The basic element frequency offset factor Δf = 30kHz. Taking the first element of the array as the reference element, the carrier frequencies of all elements in the array are:

[0051]

[0052] If the receiving node is located in the direction of the transmitting array (30°, 100km), then the beamforming vector w of the frequency control array can be expressed as:

[0053] Among them, a θ (θ, r) and a r (θ, r) are the steering components in the azimuth and distance dimensions, respectively.

[0054]

[0055]

[0056] In this way, the frequency control array can effectively suppress the range-azimuth coupling of the frequency control array, so that the radiated signals of the frequency control array are coherently superimposed at the desired receiving position, generating an ideal point radiation pattern, realizing the accurate delivery of radio frequency signals, and ensuring the security of radio frequency transmission.

[0057] See Figure 2a , Figure 2b and Figure 2c This invention provides a performance comparison between a frequency-controlled array robust beamforming method based on P4 codes and log-FDA and Taylor-FDA methods. Log-FDA uses a logarithmic form to set the element frequency offset, while Taylor-FDA uses a Taylor window function. Simulations were performed at multiple far-field target locations: (100km, 30°), (100km, -30°), (200km, 45°), and (200km, -45°). Compared to frequency-controlled array beamforming schemes, the proposed P4-FDA scheme can generate an ideal point-like radiation pattern in the far field and effectively suppress sidelobe beam intensity.

[0058] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robust beamforming method for frequency-controlled arrays based on P4 polyphase codes, characterized in that, The frequency-controlled array robust beamforming method includes: For a frequency-controlled array antenna array containing N linearly uniformly distributed elements, the first element of the frequency-controlled array is selected as the reference element. The frequency offset of the array elements is set using P4 polyphase code. The carrier frequency offset of each antenna element in the frequency-controlled array is: wherein Δf represents the frequency offset factor of the frequency-controlled array, Δf n represents the radiation frequency deviation between the nth array element and the reference array element, n = 1, 2, …, N; Then, for the uniform linear frequency control array containing N array elements, the carrier frequency of each antenna array element is f n : wherein f c is the array radiation reference frequency, f c >>Δf; At this time, the carrier frequencies of the N elements of the frequency control array are:

2. The frequency-controlled array robust beamforming method as described in claim 1, characterized in that, For a uniform linear frequency-controlled array containing N elements, the beamforming matrix is ​​configured as follows to guide the point beam to the far-field target position (θ,r): w = w θ (θ, r) Θ w r (θ, r) Where the symbol "⊙" represents the Hadamard product operation of vectors, w θ (θ,r) azimuth-dependent beamforming vector, w r (θ,r) is the range-dependent beamforming vector.

3. The frequency-controlled array robust beamforming method as described in claim 2, characterized in that, The azimuth-dependent beamforming vector and the range-dependent beamforming vector are respectively expressed as: Where θ is the angle between the line connecting the target point and the reference element and the normal direction of the frequency-controlled array antenna, and r is the Euclidean distance between the target point and the reference element; a θ (θ,r) and a r (θ,r) are the steering components in the azimuth and distance dimensions, respectively.

4. The frequency-controlled array robust beamforming method as described in claim 3, characterized in that, Where j is the complex number identifier.

5. The frequency-controlled array robust beamforming method as described in claim 4, characterized in that, Where d represents the distance between adjacent array elements within the array.

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