A Study of Narrow Band Multi-path Channel Phase Difference Characteristics on Domain with Time and Frequency Axes

Multi-path phase difference distribution in a narrow mobile radio channel, which is required for allocating a pilot signal and predicting bit error rate (BER) degradation, was studied on a domain with time f_mT_s and frequency f₀sigma axes using theoretical and simulated results. Assuming that multi-path amplitude decreases exponentially, and multi-path phase thetas(t, f_c), symbol period of digital signal T_s, sub-channel bandwidth f₀, the total phase difference zeta;zeta = thetas(t+T_s, f_c+f₀) - thetas(t, f_c) was discussed in great detail by using the cumulative distribution. First, we verified that the theoretical cumulative distribution obtained by (4) and (6) showed good agreement with the simulated distribution with a wide range of 0.001 to 99.999 %. Next, a phase difference cumulative value locus was determined by using coordinates (f_mT_s, f₀sigma) on a domain with time and frequency axes for a certain cumulative value. Last, for the phase difference applications, we showed that using the cumulative value enabled the M-array differential quadrature phase shift keying BER to be estimated and using the locus enabled a pilot signal on the domain to be allocated flexibly.