 Multipath propagation

Multipath propagation occurs when a signal reaches a receiver along several routes, for example a direct acoustic wave and a wave reflection from a wall. In a linear, stationary model the received field can be represented aswhere each path has delay ${\tau }_j$ and an appropriate amplitude factor $a_j$. More general paths can filter the signal as well as delay it.

A short pulse can produce distinct echoes when the delays are separated enough to resolve. For a narrowband tone, the copies instead overlap with different wave phases and can reinforce or cancel. Moving the receiver changes the path differences and can cause large changes in measured wave intensity even if source power stays constant. Comparing an early direct arrival with later echoes separates propagation time from reflection geometry. This is useful in sonar, room acoustics and radio communication, where delayed copies can obscure the intended signal.