# Study and Analysis of Interference Signals of the LTE System of the GNSS Receiver
## 4 Simulation Studies
### Reception of Interference Signals  
In recent years, much attention has been paid to the design of antenna systems with radiators located on non-planar surfaces. Cylindrical antennas that provide communication within the full angular range using only one antenna are interesting from the perspective of application in modern cellular systems. Conformal antennas can also be successfully used in communication systems with airplanes and small spacecraft due to the fact that they can be easily mounted, for example, in the wings of aircraft or on the outer surface of the fuselage. Therefore, an important issue is the development of integrated multi-beam antenna systems, the radiating elements of which are distributed on arbitrarily selected surfaces. A conformal array of antennas is an arrangement \(n\) of radiation sources distributed along a certain curve. An example of such an antenna system, in which point radiating sources are evenly distributed along the hatch, is shown in the drawing above (Figure 4). The geometry of such an antenna array can be described by the radius of the arc \(R\) and the angle \(\xi\) between the rays \(R\) passing through two adjacent radiating elements, which can be represented in the form (24). \[ \begin{array}{l}F(\Theta)=a_{1}e^{i\phi 1}+a_{2}e^{i(2R\sin{(\xi)}\cos{(\frac{ \pi}{2}+(n-2)\xi-\Theta)}+\phi 2)}+a_{3}e^{i(2R\sin{(2\xi)}\cos{(\frac{\pi}{2}+(n-3)\xi-\Theta)}+\phi 3)}+\\ +\cdots+a_{n-1}e^{i(2R\sin{((n-2)\xi)}\cos{(\frac{\pi}{2}+\xi-\Theta)}+\phi n-1 )}+a_{n}e^{i(2R\sin{((n-1)\xi)}\cos{(\frac{\pi}{2}-\Theta)}+\phi n)}\end{array}  \tag{24}\]  
where \(R\)--radius of curvature; \(\xi\)--angle between rays \(R\) passing through two adjacent radiating sources. An antenna array configuration consisting of four elements was adopted in the research. Although the phase delays can be determined even with the use of two antennas, however, in order to reduce the phase ambiguity, it was decided to extend the system with two additional elements. There are known examples of implementations of four-element antenna arrays for counteracting jamming in systems. The greater the number of elements, the greater the efficiency of interference signal detection and spatial filtering. On the other hand, more signals require more computing power to process them. Moreover, with the limited physical dimensions of the array, placing the elements close to each other increases the coupling between them, which can affect the quality of the received signals. Apart from the number of antenna elements, their arrangement is also of great importance. Often, homogeneous arrays are used in which the distances between adjacent elements are the same. It should be added that both linear and planar systems as well as circular systems are popular. In the case of estimating the direction of signal arrival in two planes, it may be advantageous to use arrays with a three-dimensional configuration. The arrangement of antenna elements, adopted in this article, is presented in Figure 5.  
Figure 4: Antenna array—receiving signals in the GNSS receiver. The elements are located at the vertices of a square with a side equal to 0.45 of the carrier wavelength of 1575.42 MHz, which corresponds to a distance of approximately 86 mm. Distances greater than half the wavelength would result in ambiguity in the measurement of phase delays, meaning that the same phase delays could occur for signals with different arrival directions. In addition, a margin of 0.05 wavelength was adopted here to limit the possibility of phase ambiguity due to an estimation error caused, among others, by the presence of noise in the channel. Placing all antenna elements in one plane results in the same phase delay values of signals arriving from symmetrical directions with respect to this plane. The presented characteristics (Figure 6) show that in the case of radiating an electromagnetic wave by such an antenna, the plane of the solid phase would not form a sphere whose center would uniquely define the antenna phase center.