# A Modified Dolph-Chebyshev Approach for the Synthesis of Low Sidelobe Beampattern with Adjustable Beamwidth

01 Jan 2003-Vol. 51, Iss: 10

TL;DR: In this paper, a new method for the synthesis of low sidelobe beampatterns is presented, which enables beamwidth and sidelobe level to be adjusted with relative independence.

Abstract: A new method for the synthesis of low sidelobe beampatterns is presented, which enables beamwidth and sidelobe level to be adjusted with relative independence. Unlike existing methods for the synthesis of arbitrary beampatterns, the proposed method is based on a modification of the Dolph-Chebyshev design and requires only a few parameters to be optimized, regardless of the array size. Due to its much lower complexity, the method is implementable in wireless communications applications requiring fast and cheap, adaptive algorithms for low sidelobe arrays. The method is applicable, for instance, to the design of adaptive sector-like antennas with uniform circular arrays (UCAs), and to the design of quasi-steering-invariant beampatterns with uniform linear arrays (ULAs).

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TL;DR: In this paper, a series-fed microstrip patch array with Dolph-Chebyshev current distribution is proposed to achieve a very compact array with $0.3 ε-λ -0.

Abstract: Compact series-fed microstrip patch arrays are presented that are excited with Dolph–Chebyshev distributions realized with periodic stub-loaded slow wave transmission line (SW-TL) feed networks. The methodology to design these SW-TL feed networks is described in detail. The developed equivalent circuit representation reveals that their characteristic impedance can be modulated while maintaining their propagation constant (guided-wavelength) simply by modifying the widths of their stubs. These stub-loaded SW-TL feed networks are seamlessly integrated with uniformly spaced microstrip patch arrays. The desired Dolph–Chebyshev excitations are realized simply by modulating the widths of their stubs. Moreover, the slow wave property of the SW-TLs facilitates an advantageous closely spaced Dolph–Chebyshev current distribution, i.e., a very compact array with $0.3\lambda _{0}$ spacing between the array elements is attained. The Dolph–Chebyshev SW-TL feed networks are employed to excite microstrip patch arrays that radiate a broadside main beam with −30 dB sidelobe levels and a grating-lobe-free 50° tilted main beam. A measured prototype of the broadside-radiating array confirms its simulated performance characteristics. In comparison with conventional Dolph–Chebyshev arrays implemented with standard microstrip transmission line (MTL) feed networks, the optimized designs are grating-lobe-free and have enhanced bandwidths.

23 citations

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TL;DR: In this paper, the design of passive coherent location radar, which exploits broadcasting transmitters of opportunity in the very high frequency (VHF) radio bandwidth, is presented, where the authors primarily focus on the system set-up and on the digital pre-processing steps.

Abstract: The design of passive coherent location radar, which exploits broadcasting transmitters of opportunity in the very high frequency (VHF) radio bandwidth, is presented. Here, the authors primarily focus on the system set-up and on the digital pre-processing steps. Emphasis is given to the antenna section analysis. The eight-element circular array, which is used for the signal acquisition, is analysed by means of simulations and measurements. Compensation for the mutual coupling effect between the different channels is achieved by applying a technique in the digital domain. An innovative digital beamforming algorithm is introduced to reduce the sidelobe level of the circular array pattern. Direct path interference suppression, range/Doppler data processing, greatest-of constant false alarm rate algorithm and range/Doppler-time plots extraction provide the final output of the processing chain. Experimental validation of the processing architecture is presented and the final detection results are compared with an automatic dependent surveillance broadcast data set. © 2012 The Institution of Engineering and Technology.

19 citations

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TL;DR: The idea to FDA multi-beam pattern synthesis based on the convex optimization problem with joint sparse constraint between angle dimension weight matrix and range dimension weight Matrix is expanded to include frequency diverse array (FDA) range-angle-dependent beampattern synthesis.

Abstract: For frequency diverse array (FDA) range-angle-dependent beampattern synthesis, the objective is to obtain the desired beampattern performance using fewer antenna elements or smaller aperture. This paper proposes a FDA single-beam pattern synthesis by joint $\ell _{1}$ -norm minimization and convex optimization in the beginning. A virtual uniform FDA array with small element spacing and corresponding frequency increment is created first. Then, we formulate the array pattern synthesis (APS) problem as finding a joint sparse weight vector, which can be obtained by solving a convex optimization problem with the joint sparse constraint between angle dimension weight vector and range dimension weight vector, where some small entries of the vector can be regarded as zeros without significantly changing the array pattern performance. The antenna elements corresponding to the mapping positions of nonzero values of the joint sparse weight vector are placed to form a non-uniform FDA. Finally, convex optimization is further conducted to obtain the optimal weight vector of the non-uniform FDA. Besides, we expand the idea to FDA multi-beam pattern synthesis based on the convex optimization problem with joint sparse constraint between angle dimension weight matrix and range dimension weight matrix. Numerical examples are provided to verify the efficiency of achieving the desired radiation pattern with the fewer antenna elements, and better APS performance for given array elements.

14 citations

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TL;DR: To increase the output signal-to-interference-plus-noise ratio of a radar system, this paper presents an approach to design the low SLL with matrix tapering method to broaden the nulls and enhance the robustness for the possible errors.

Abstract: Sum ( $\Sigma$ ) and difference ( $\Delta$ ) beampatterns are commonly utilized to estimate the bearings of targets in the radar system. However, the nulls of $\Delta $ -pattern are not always aligned with those of $\Sigma $ -pattern, and this phenomenon would become more severe in practical scenario since the array errors exist. Meanwhile, the sidelobe level (SLL) of the array would also increase due to the unavoidable errors. The above-described factors would dramatically decrease the performance of radar in the adaptive suppression of interference. To increase the output signal-to-interference-plus-noise ratio of a radar system, this paper presents an approach to design the low SLL $\Sigma \Delta $ -patterns where the nulls of the $\Delta $ -pattern, excluding the central null, are always aligned with those of the $\Sigma $ -pattern in the presence of errors. Two schemes are addressed to obtain the covariance matrix for null-alignment constraint, which is exploited to force nulling in desired angles accordingly. In the sequel, the matrix tapering method is adopted to broaden the nulls and enhance the robustness for the possible errors. With the proposed approach, the low SLL and nulls alignment can be achieved simultaneously. Numerical examples are provided and discussed to demonstrate the effectiveness of the proposed solution, including the results based on a linearly spaced microstrip array antenna.

12 citations

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TL;DR: A Zero Placement for Flat Top (ZPFT) beam pattern synthesis algorithm that identifies the zeros of the array factor directly and computes the weight without iteration and can achieve the same optimal performance as the iteration based global optimisation techniques like Semi-Definite Relaxation (SDR).

Abstract: Flat top beam pattern synthesis is increasingly important for beamformer in high mobility scenarios due to the rapid change of Direction of Arrival (DOA). A Zero Placement for Flat Top (ZPFT) beam pattern synthesis algorithm is presented in this article. It works in Z domain directly and breaks down the total response into two portions. The first portion satisfies the beamwidth requirement with low Sidelobe Level (SLL) which is realized through algorithms like Dolph-Chebyshev algorithm. The second portion is then used to create a broadening effect. The location of the broadening zeros are derived using principles result from the broadening effect analysis of two quadratic functions. Compared to conventional Finite Impulse Response (FIR) method or iterative methods, the proposed method identifies the zeros of the array factor directly and computes the weight without iteration. Since it works in the spatial angle domain directly, the steering of the mainlobe beam could be implemented through a simple angle shift. Numerical simulation confirms the effectiveness of the algorithm. ZPFT can achieve 22dB lower SLL while maintaining the same main beam performance as compared with FIR method for an Uniform Linear Array (ULA) with 7 elements. It can achieve the same optimal performance as the iteration based global optimisation techniques like Semi-Definite Relaxation (SDR) with about 380 times less computing time in an Intel Core i7 Windows platform. ZPFT can steer the main beam easily in real time. All these make it an ideal candidate for high mobility applications where the DOA changes rapidly.

11 citations

##### References

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01 Jan 1999TL;DR: It is shown that using multiple transmit antennas and space-time block coding provides remarkable performance at the expense of almost no extra processing.

Abstract: We document the performance of space-time block codes, which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and space-time block coding provides remarkable performance at the expense of almost no extra processing.

1,958 citations

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01 Jun 1946

TL;DR: In this article, a one-parameter family of current distributions for symmetric broadside arrays of equally spaced point sources energized in phase was derived, and design curves relating the value of the parameter to side-lobe level as well as the relative current values expressed as a function of side lobe level were given for the cases of 8-, 12-, 16-, 20-, and 24-element linear arrays.

Abstract: A one-parameter family of current distributions is derived for symmetric broadside arrays of equally spaced point sources energized in phase. For each value of the parameter, the corresponding current distribution gives rise to a pattern in which (1) all the side lobes are at the same level; and (2) the beam width to the first null is a minimum for all patterns arising from symmetric distributions of in-phase currents none of whose side lobes exceeds that level. Design curves relating the value of the parameter to side-lobe level as well as the relative current values expressed as a function of side-lobe level are given for the cases of 8-, 12-, 16-, 20-, and 24-element linear arrays.

1,096 citations

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01 Feb 1985TL;DR: In this article, a polynomial representation of the antenna pattern produced by an equispaced linear array is introduced, where certain roots are displaced from the unit circle radially, to fill a portion of the pattern, which before this displayed lobes interspersed by deep nulls.

Abstract: A technique is introduced which uses the conventional polynomial representation of the antenna pattern produced by an equispaced linear array. Certain roots are displaced from the unit circle radially, to fill a portion of the pattern, which before this displayed lobes interspersed by deep nulls. The angular and radial positions of all the roots are simultaneously adjusted so that the amplitude of each ripple in the shaped region and the height of each sidelobe in the nonshaped region are individually controlled. Applications to a cosec
2
θ × cos θ pattern and to a flat-topped beam are presented. Experimental validation is also offered.

247 citations

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TL;DR: In this paper, a new formulation for the design of Chebyshev arrays is presented which makes no direct use of Chebyhev polynomials and is expressed in terms of cosine/cosine-hyperbolic functions based on which all analysis and design steps are carried out.

Abstract: A new formulation for the design of Chebyshev arrays is presented which makes no direct use of Chebyshev polynomials. The array factor is expressed in terms of cosine/cosine-hyperbolic functions based on which all analysis and design steps are carried out. Zeros of the array factor are used to obtain a system of equations for excitation currents. Solving this system of equations, current magnitudes are determined in terms of the current of one element chosen as the independent variable. A general formulation for an even or odd but otherwise arbitrary number of elements is presented. The minimum number of elements required to achieve the desired beamwidth and side lobe level is obtained in a single step without resorting to an iterative process. The optimum spacing between elements for broadside and end fire arrays is also addressed. Numerical results for example cases are provided. >

96 citations