ON SIGNAL ENVELOPE CORRELATION AS FUNCTIONS OF TIME DIFFERENCE AND FREQUENCY DIFFERENCE IN RAYLEIGH FADING CHANNELS

Abstract

Wireless radio propagation channel models for narrowband and wideband signal have been proposed. The effects of arrival angle distribution, the antenna gain pattern and power delay profile on the signal envelope correlation coefficient have been discussed. Coherence time and coherence bandwidth associated with each model have also been presented in this thesis. For narrowband signal, by reviewing Gans[1] and Jakes[2]' model, we obtain a general expression of the signal envelope correlation coefficient as a function of both time difference and frequency difference. On the assumption that the distribution function of the arrival angle and the power delay profile are independent, the signal envelope correlation coefficient can be expressed as the product of a function of time difference only and a function of frequency difference only. This explicit product relation is only shown for the first time in this thesis. If arrival angle and delay spread are independent, the coherence time is only decided by the antenna gain pattern and the arrival angle distribution while the coherence bandwidth is determined only by the delay spread and the shape of power delay profile only. The envelope correlation coefficients with time difference based on a triangular distribution of arrival angle is compared with that of the uniform distribution of arrival angle. It can be seen that the coherence time for non-uniformly distributed arrival angles are always larger than the corresponding case with uniformly distributed arrival angle. The coherence time for the signal received by a directive antenna should also be lengthened. We also present envelope correlation coefficients with frequency difference of different power delay profiles. A new model of joint probability density function of arrival angle and delay spread for estimating the coherence time and bandwidth of a time variant mobile radio channel is proposed. We model the delay as dependent on the arrival angle being less in the direction of the base station, in which the delays are longer for a larger arrival angle. We compare the results with the new model to that obtained from Gans and Jakes' model. The coherence time resulting from the use of our model is identical with the one obtained using Jakes and Gans model. However, the coherence bandwidth resulting from the use of our model shows that they depend on the antenna gain pattern while the Gans and Jakes' model show that the traditional coherence bandwidth only depends on the shape of the delay profile. For wideband signal, we revise the propagation delay of the model proposed by Fekri [21] and analyze the envelope correlation of a wide band signal modulated on two subcarriers of one resolvable path in a Rayleigh fading channel. The results indicate that the frequency correlation of resolvable paths not only depends on the rms delay spread but also on the chip duration of the signal or signal bandwidth. By realizing that the output of the resolvable path is exactly the branch of the RAKE receiver, the results can be used in appropriately choosing the subcarriers of communication systems employing frequency diversity for wide band signals especially for RAKE receiver. With the growing use of wide band CDMA cellular mobile radio systems, propagation model for wideband signal is needed. Since wideband wireless communication are in great demand, research on wideband radio propagation channel modeling must be enhanced. This is suggested for further work in future.