Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 36

For a uniform linear array, the first sidelobe is approximately 13.5 dB lower than the main lobe when the same excitation is used for each array element. For many practical applications, lower sidelobe levels are often required. In 1946, C.L. Dolphy proposed a method for obtaining lower sidelobe patterns in a classic paper. This method considers the properties of the Chebyshev polynomial and establishes the relationship from polynomial to array sidelobe level.

The Chebyshev polynomial T_2N(u) has the characteristics of an undamped oscillation function when –1 ≤ u ≤ 1, and the monotonic increase is characteristic of the absolute value outside this oscillation interval. The undamped oscillation characteristics correspond to equal sidelobe levels, while the monotonic characteristics correspond to the main lobe. The Chebyshev polynomial whose order is 2N and number of elements is 2N + 1 can be expressed as

The relationship between the Chebyshev polynomial and the array antenna parameters is

where θ denotes the angle between the spatial orientation and the array.

The sidelobe level of the array antenna is expressed as 201gη in dB, where η = T_2N(u₀).

The above polynomial can also be expressed in the product form of the polynomial root.

where c is a constant and the root is given by

When the excitation current is symmetrically distributed, the root of the polynomial is a pair of complex conjugates. And through a series of mathematical derivations, the pattern can be expressed as

This is the Chebyshev pattern with 2N + 1 array elements.

The above Chebyshev pattern gives an array antenna pattern synthesis method which can control the sidelobe level to minimize the maximum sidelobe level. However, the method has the following problems as well. The excitation current between the antenna intermediate unit and the external unit varies greatly, which is difficult to implement. The far-sidelobe level is too high. These problems make the Chebyshev pattern encounter some difficulties in practical applications, which means that its physical achievability is poor.