Frequency Selective Fading Channels

In the last lecture, two terms Average Delay and RMS Delay Spread were defined as below () () ∫ ∫ ∞ ∞ Φ Φ = 0 0 τ τ τ τ τ µ τ d d (1) () () () ∫ ∫ ∞ ∞ Φ Φ − = 0 0 2 τ τ τ τ µ τ σ τ τ d d c c (2) If the power density is discrete like Figure 1, the Average Delay and RMS Delay Spread for the multipath profile could be written in the following way: () () ∑ ∑ = k k k k k p p τ τ τ τ (3) () 2 2 τ τ σ τ − = (4) Delay Figure1: Discrete multipath profile Where, () () ∑ ∑ = k k k k k p p τ τ τ τ 2 2 (5) Coherence Bandwidth (c B) Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered " flat " (e.g. a channel that passes all spectral components with approximately equal gain and phase). Equivalently speaking, coherence bandwidth is the range of frequencies over which two frequency components have a strong potential for amplitude correlation. It is known that the coherence bandwidth is inversely proportional to the RMS delay spread: (τ σ 1 ∝ c B). It is important to note that an exact relationship between coherence bandwidth and RMS delay spread does not exit. In general, spectral analysis techniques and simulation are required to determine the exact impact that time varying multipath has on a particular transmitted signal. Doppler Spread (d B), Coherence Time (c T) RMS delay spread τ σ and coherence bandwidth c B are parameters which describe the time dispersive nature of the channel in a local area and they do not offer any information about the time varying nature of the channel due to the relative motion between the mobile station and base station. Doppler Spread d B is a measure of the spectral broadening caused by the time rate of change of the mobile radio channel and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. In other words, if the baseband signal bandwidth is much greater than d B , the effects of Doppler spread are negligible at the receiver. This is also called slow fading. Coherence …