Rayleigh Archives - Page 2 of 2

BER for BPSK in Rayleigh channel

Long back in time we discussed the BER (bit error rate) for BPSK modulation in a simple AWGN channel (time stamps states August 2007). Almost an year back! It high time we discuss the BER for BPSK in a Rayleigh multipath channel.

In a brief discussion on Rayleigh channel, wherein we stated that a circularly symmetric complex Gaussian random variable is of the form,

$h = h_{re} + jh_{im}$ ,

where real and imaginary parts are zero mean independent and identically distributed (iid) Gaussian random variables with mean 0 and variance $\sigma^2$ .

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Deriving PDF of Rayleigh random variable

In the post on Rayleigh channel model, we stated that a circularly symmetric random variable is of the form $Z = X + jY$ , where real and imaginary parts are zero mean independent and identically distributed (iid) Gaussian random variables. The magnitude $|Z|$ which has the probability density,

$p(z) = \frac{z}{\sigma^2}e^{\frac{-z^2}{2 \sigma^2}},\ \ \ z\ge 0$

is called a Rayleigh random variable. Further, the phase $\theta$ is uniformly distributed from $[0,\ 2\pi]$ . In this post we will try to derive the expression for probability density function (PDF) for $|Z|$ and $\theta$ .

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Rayleigh multipath channel model

The article gives a quick overview of a simple statistical multipath channel model called Rayleigh fading channel model.

Multipath environment

In a multipath environment, it is reasonably intuitive to visualize that an impulse transmitted from transmitter will reach the receiver as a train of impulses.

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