Rayleigh and Ricean distribution:

• When all of the multipath signals have random uniformly distributed phase, then the amplitude of the resulting signal has a Rayleigh distribution.

Whereas,

When a signal in one path has a higher amplitude than the others then the amplitude of the signal has a Rician distribution.

• Rayleigh distribution occurs when there is no single dominant signal path.

Whereas,

Ricean distribution occurs when there is a dominant signal path.

• In Rayleigh multipath component follows a Gaussian distribution on the receiver side.

Whereas,

In Ricean random multipath components arriving at different angles are superimposed on a stationary dominant signal.

• Rayleigh distribution has a probability density function (pdf) given by

where p(r) is the rms value of the received voltage signal before envelope detection.

Whereas,

The Ricean distribution is given by The parameter A denotes the peak amplitude of the dominant signal and Io is the modified Bessel function of the first kind and zero-order