March – Signal Propagation in a City

Mobile telephone signal propagation in a city is characterized essentially by obstacles which reflects the signal. In a city, the aggregate received signal follows approximately Rayleigh statistics if there is no line-of-sight path present between the transmitter and the receiver.

Here is just couple of nice figures I made to help myself to perceive what is going on. First figure demonstrates how a simple sine signal propagates between buildings, and second figure shows how aggregate signal power (interference) from many transmitters develops in time.

Figure: Helmholtz equation solved by finite element method. The white boxes represents buildings, and the little white circle is the transmitter. You can see how reflections will cause the signal strength either to increase or decrease depending on the location.
Image sin

Figure: Interference field developing in time. Transmitters in random locations are moving to random directions in time, and the aggregate signal strength is plotted. There is a line-of-sight component is present – that is we assume in fact Rician fading. Red occurrences will cause remarkable disturbance in communication as interference from other transmitters gets large. Time can't be considered to be in scale here.
Image rician

References:

1
François Baccelli, Bartlomiej Blaszczyszyn Stochastic Geometry and Wireless Networks, Volume I -Theory

2
Nicolae Cindea (2021). Movie to GIF Converter, MATLAB Central File Exchange. Retrieved June 14, 2021.