On Discrete-Time Modeling of Time-Varying WSSUS Fading Channels

In this paper, we consider the serial concatenation of linear time-varying (LTV) systems and its impact on the discrete-time modeling of wide-sense stationary uncorrelated scattering (WSSUS) fading channels. By deriving an expression for the composite impulse response of the overall concatenated system, we find that unlike the time-invariant case, the concatenation of LTV systems is not commutative, i.e., the order of arrangement affects the overall impulse response. This has significant impact when a digital transmission over a time-varying fading channel, which is an LTV channel, is represented by an equivalent discrete-time model that incorporates both transmitter and receiver filters. We further show that if the maximum Doppler frequency is much smaller than the system bandwidth, the concatenation of LTV systems is approximately commutative, then a convenient and efficient representation in the discrete-time domain for WSSUS fading channels is obtainable.