Phase distribution characteristics in mobile radio channels - phase difference between symbol intervals and adjacent channels

We evaluate the phase difference distribution with and without diversity in multipath propagation by computer simulation, and find some parts theoretically. The distribution is discussed from two points of view in the time and frequency domains. In the time domain, (a) probability and cumulative density functions are derived, (b) the distribution depends on the product of fading frequency, f_m, and symbol interval, T_s, (c) the cumulative value of beyond plus and minus π/4 in phase difference, p(|x|>π/4), is calculated. In the frequency domain, (a) the distribution depends on the product of subchannel bandwidth, f₀, and excess delay time, τ_i, (b) the phase difference at a cumulative value of 50% is <2πf₀τ_i>, and is zero off, (c) the cumulative value of p(|x|>π/4) is also calculated. Furthermore, the distribution with thermal noise is simulated. As an example of the application of the distribution, we estimate the BER of DQPSK by using the distribution, and this agrees well with the theoretical value.