Develop an approach for generating sampled values of a set of correlated Gaussian processes each having a different PSD (see Example).

Example

In this example we simulate the BER performance of a QPSK system operating over a fixed 3-ray multipath channel with AWGN, and compare the BER performance with an identical system operating over an ideal AWGN channel (no multipath). In order to simplify the simulation model we will make the following assumptions:

1. The channel has three paths consisting of an unfaded LOS path and two Rayleigh components. The received power levels associated with each path, and the differential delays between the three paths, are simulation parameters.

2. The Rayleigh fading in the channel affects only the amplitude of the transmitted signal. The instantaneous phase is not affected.

3. The magnitude of the attenuation of each multipath component is constant over a symbol interval and has independent values over adjacent intervals (no doppler spectral shaping required).

4. No transmitter filtering is used, and the receiver model is an ideal integrateand-dump receiver. The received signal for this example can be written as