Simulation of SISO and MIMO Multipath Fading Channels

Accurate software simulation is an important step for testing mobile communication systems. It allows the evaluation of the system performance without the need for physical experiments. At an early testing stage, simulations are usually done considering transmissions over additive white Gaussian noise (AWGN) channels, which do not account for obstacles or motion between the transmitter (Tx) and the receiver (Rx). According to the AWGN channel model, only the thermal noise which comes from the receiver amplifiers and from many natural sources is considered and added to the transmitted signal. This means that the received signal is a copy of the transmitted signal embedded in Gaussian noise, whose intensity depends on the propagation scenario (including the amplifiers of the Tx and the Rx) and can be controlled in simulation by tuning the Gaussian process variance. It is easy to understand that AWGN channel models do not capture the conditions of a real radio channel where the presence of obstacles between the Tx and the Rx causes multipath propagation and may lead to frequency selective channels. In this situation, several replicas of the transmitted signal get to the Rx antenna with different propagation delays. If these delays are not negligible compared to the transmission interval Ts, the attenuation caused by the channel in the frequency-domain is not constant and a distortion is introduced1. Moreover, if there is motion between the Tx and the Rx, the received signal may be affected by a time-domain multiplicative distortion called fading. This happens because, being the Rx in motion relative to the Tx, the propagation channel characteristics vary with time and their effect can be modeled as a time-domain distortion affecting the transmitted signal. By combining both the effects of multipath propagation and fading on a wireless transmission, the received signal baseband equivalent r(t)may be expressed as