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This paper proposes an adaptive array beamforming method by embedding antennas’ active pattern in the worst-case performance optimization algorithm. This method can significantly reduce the beamformer’s performance degradation caused by inconsistency between hypothesized ideal array models and practical ones. Simulation and measured results consistently demonstrate the robustness and effectiveness of the proposed method in dealing with array manifold mismatches.

The assumption of ideal array elements in conventional adaptive beamforming technologies can cause severe performance degradation in real implementations due to ignored array imperfections (e.g., gain and phase mismatches and mutual coupling between elements), particularly for increasingly widely used small-profile arrays. Robust beamforming algorithms have been proposed to deal with these imperfections by treating an array’s response inconsistencies as nonspecific manifold mismatches. There are some classic algorithms, such as the diagonal loading (DL) method (also called loaded sample matrix inversion (LSMI) beamformer) [

The problem of array modelling mismatches is typically studied by antenna researchers. An earlier work exploiting the gain and frequency properties of practical antennas was reported in [

In this paper, by creatively integrating antenna mismatch modelling into beamforming design, we propose a robust worst-case performance optimization beamformer with an embedded array’s AP. We call it as active pattern worst-case (APWC) method which can significantly improve the beamformer robustness under various mismatches. The APWC method essentially introduces the AP method [

We consider an

Assume omnidirectional antenna elements. Let

The well-known sample matrix inversion (SMI) beamformer solves a constrained minimization problem

There are always mismatches, that is, the fluctuation of array parameters during design, processing, measuring, and assembling, between the ideal steering vector

In this paper, we use an improved array steering vector

This new steering vector

Define the approximation error for the radiation pattern expressions with and without considering mismatches as

Assume that the norm of

It can be rewritten as

The APWC method belongs to the class of DL method. Similar to the WCRB method [

We refer to a practical 4-element uniform circular microstrip array shown in Figure

A miniature circular microstrip array. The center frequency of each right-hand circular polarized element is

We simulate array mismatches using HFSS and then abstract and store the corresponding AP for each mismatch. Three types of common mismatches are studied, including (a) the element’s position mismatches, (b) size errors of the metal working platform, and (c) dielectric parameter errors of elements’ substrate, including relative dielectric permittivity (RDP) and loss tangent (LT). The sample covariance matrix

Steering vector mismatches (norm of the difference) under different situations: a: element 1’s position mismatch (+2 mm along axis

We assume that the desired signal and interference have a plane wavefront with

Figure

Output SINR versus antenna elements’ position. Element 1 is moved along the

Output SINR versus the size of the working platform. The length of the elliptical platform’s major axis varies from 132 mm to 136 mm.

In Figures

Output SINR versus the substrate’s RDP. Element 1’s RDP varies from 19.6 to 20.4.

Output SINR versus substrates’ LT. Each element’s LT varies from 0.0005 to 0.005.

The array mentioned in Section

The active gain of designed array (

Element’s number | _{d} (dB) |
_{f} (dB) | ||
---|---|---|---|---|

1 | −4.91 | −0.40 | −3.03 | −0.48 |

2 | −2.84 | −0.50 | −2.53 | −0.54 |

3 | −3.62 | −0.24 | −3.38 | −0.53 |

4 | −3.56 | −0.50 | −0.81 | −0.12 |

Figure

Output SINR versus training data size for SNR = 25 dB.

Output SINR versus SNR for training data size of

In this paper, we propose an improved adaptive beamforming algorithm APWC, which embeds the array’s electromagnetic characteristics in a robust beamformer. Mathematical analysis, computer simulation, and measured results illustrate the effectiveness and robustness of the proposed algorithm to array manifold mismatches. APWC is particularly suitable for systems with small and compact arrays, where serious mutual coupling and environment scattering could significantly influence antennas’ radiation and the performance of conventional beamforming algorithms.

The authors declare that they have no conflicts of interest.