A State-Space Model for Flat Fading Channels with a Novel Method of Rational Function Filter Design

Clarke's model [1] and Jakes' spectrum [2] have been traditionally accepted in wireless channel modeling. In comparison with measured spectra, Jakes' spectrum has limitations - it is unbounded and does not incorporate the effect of temporal phase fluctuations. Previous work [5] extended Clarke's model to yield a theoretical power spectrum that is consistent with measured data. The modified spectrum, which includes the effects of phase fluctuations explicitly, is more appropriate as a theoretical basis for channel spectrum analysis and simulations. We develop here a state-space model that represents a wireless channel with these modified spectral characteristics. This is achieved by developing the relationship between a continuous-time state-space model and the theory of the rational transfer function. A novel method for the design of a rational transfer function of a linear system is proposed. The system input is a Gaussian white noise process, which generates a wireless channel with a desired arbitrary power spectrum. We represent the rational transfer function via the Observable Canonical Form (OCF) to obtain the continuous-time state-space model. A discrete-time version of the state-space model is then provided to represent and simulate a discrete-time flat fading wireless channel.