Demonstration of Time Varying Channel Gain in Mobile Radio

In mobile radio, signals usually get from transmitter to receiver by a number of paths, each produced by one or more reflections. Because the paths have various lengths and therefore various phase shifts, they might combine constructively or destructively at the receiver. In complex envelope terms, we can think of the overall effect as a complex gain applied to the signal. Constructive? Destructive? It all depends on where the antenna is located, since that determines phase shifts.

If the antenna moves - for example, in a vehicle or as one walks with a cellphone - then the complex gain varies. In fact, it varies so quickly that the signal strength can move from strong reinforcement to almost complete cancellation in a quarter of a wavelength. How long is that? At 1000 MHz, it's just 7.5 cm. Imagine the effect on transmission if the cellphone is in a car moving at 100 km/h!

This demo illustrates the time-varying nature of the complex gain with a pair of animations. The links take you to presentations in rectangular coordinates and in polar coordinates. It's set up in two separate files because the animations may take some time to download.