Calculation Angular Spread and Coherence Distance is very easy let’s see.

So far, we have focused on how the channel response varies over time and how to quantify its delay and correlation properties. However, channels also vary over space. We do not attempt to rigorously treat all aspects of spatial/temporal channels but will summarize a few important points.

The RMS angular spread of a channel can be denoted as and refers to the statistical distribution of the angle of the arriving energy. A large implies that channel energy is coming in from many

directions a small implies that the received channel energy is more focused. A large angular spread generally occurs when there is a lot of local scattering, which results in more statistical diversity in the channel more focused energy results in less statistical diversity.

The dual of angular spread is coherence distance. As the angular spread increases, the coherence distance decreases, and vice versa. A coherence distance means that any physical positions separated by have an essentially uncorrelated received signal amplitude and phase. An approximate rule of thumb is

**Dc = 2 λ/ ΘRMS**

The case of Rayleigh fading, assumes a uniform angular spread; the well-known relation is

**Dc = 9λ/ 16π**

An important trend to note from the preceding relations is that the coherence distance increases

with the carrier wavelength. Thus, higher-frequency systems have shorter coherence distances.

Angular spread and coherence distance are particularly important in multiple-antenna systems. The coherence distance gives a rule of thumb for how far apart antennas should be spaced in order to be statistically independent. If the coherence distance is very small, antenna arrays can be effectively used to provide rich diversity.

On the other hand, if the coherence distance is large, space constraints may make it impossible to take advantage of spatial diversity. In this case, it would be preferable to have the antenna array cooperate and use beamforming. The trade-offs between beamforming and linear array processing is discussed in other part.