Understanding Time, Bandwidth, and Angle Characteristics and Impacts
Coherence Time (Tc) indicates the duration over which the channel is considered statistically stable and is approximated by the relationship between maximum Doppler frequency (fd) and Tc ≈ k/fd. The constant 'k' depends on how "coherence time" is defined, specifically based on the level of the channel's autocorrelation function. For example, k ≈ 0.423 for the time it takes autocorrelation to drop to 0.5 (a common standard based on Clarke's fading model), and k ≈ 0.35 for a drop to 0.9. A simple approximation of k = 1 is also used.
Higher moving speeds or higher carrier frequencies increase channel fluctuation due to the Doppler effect, resulting in higher fd and shorter Tc.
Input: v = km/h ( m/s), f = GHz, k =
fd = ( × ) / c ≈ Hz
Tc ≈ / ≈ ms
Coherence Bandwidth (Bc) indicates the frequency range where the channel is consistent (considered flat) in a multipath propagation environment. A larger RMS (Root Mean Square) Delay Spread increases frequency selectivity due to multipath components, resulting in a smaller coherence bandwidth. This is particularly notable in reflection-rich environments like urban areas.
Input: τrms = ns ( s)
Bc ≈ 1 / (2π × ) ≈ MHz
Coherence Angle indicates the angular range where spatial channel correlation is maintained. A larger number of antenna elements (N) creates narrower beams, and shorter wavelengths (λ) in high-frequency bands improve angular resolution. It also depends on the Angle of Incidence (θ) relative to the receiving antenna.
(1) f = GHz → λ = c/f ≈ m
(2) N = , d ≈ m ()
(3) θHPBW ≈ / ( × × sin(°)) ≈ °