Читать книгу Advanced Antenna Array Engineering for 6G and Beyond Wireless Communications - Richard W. Ziolkowski - Страница 22

One traditional method of producing multiple beams is to utilize Butler matrices [14]. These multiple beams can be steered together in principle, but not independently. Therefore, Butler matrices are almost exclusively used for fixed beams. A Butler matrix is an RF circuit consisting of couplers, delay lines, crossovers, and transition parts. An n‐way Butler matrix has n inputs and n outputs. A signal applied to a given input will lead to outputs of equal amplitude but with a uniform phase gradient, thus leading to a single steered beam. The phase increment between adjacent outputs is a multiple of depending on which input is fed. The phase increment across the outputs, that occurs if input i is fed, is , where i can take on integer values from 0 to n − 1. If the n outputs of the Butler matrix are connected to a linear array of n equally spaced radiating elements, a set of n beams equally spaced in angle will be generated if all of the inputs are fed. Figure 1.7 shows the configuration of a 4 × 4 Butler matrix and the 4 beams it produces with 4 radiating elements.

Figure 1.7 Typical implementation of a 4 × 4 Butler matrix (BM) connected to 4 radiating elements and the 4 beams it produces.

Unfortunately, multiple beamforming employing a Butler matrix has a number of disadvantages. First, the beams are fixed. Consequently, it is only a switched beam solution for tracking mobile users. Second, owing to the losses in the Butler matrix’s circuits, a major challenge for large antenna arrays is keeping the overall losses small, especially at millimeter‐wave frequencies. Third, a 2D Butler matrix would be required for two‐dimensional (2D) beamforming. However, the conventional structure is generally too bulky and too lossy owing to the complicated requisite crossovers. Fourth, a complete system engineering approach is required to achieve wideband operation with a Bulter matrix. These issues are only some of the challenges facing the antenna research community. They and some recently developed solutions will be addressed in several later chapters.