Study of Correlation Coefficients of Complex Envelope and Phase in a Domain with Time and Frequency Axes in Narrowband Multipath Channel

As a basic multipath property required to allocate the pilot signal in orthogonal frequency division multiplexing (OFDM) and compose antennas in the multiple-input multiple-output (MIMO) technique, correlation coefficients of the complex envelope in the received signal level and phase in multipath channels were studied theoretically and by computer simulation in a domain with time, frequency, and space axes. First, correlation coefficient rho_e(Deltax) of the envelope was derived in the domain with a variable Deltax= f_mT_s + Deltafsigma, where f_mT_s is on the time axis (f_mT_s: normalized maximum fading frequency) and Deltafsigma is on the frequency and space axes (Af. frequency separation, sigma: delay spread). Bird´s-eye views of rho_e(Deltax) and rho_p(Deltax) of the phase in multipath channels are shown in the domains to give a good overall grasp of them. The theoretical values of rho_e(Deltax) and rho_p(Deltax) agree with the simulated ones. Furthermore, it is shown that the cumulative distributions influenced on bit error rate performance depended strongly on Deltax and spread as Deltax increased.