Praise for Fundamentals of WiMAX

3.4 The Broadband Wireless Channel: Fading 87τRMS=∫0∞2( ∆τ − µ ) A ( ∆τ) d(∆τ)τ∞∫ A τ( ∆ τ) d ( ∆ τ)0τ. (3.31)Intuitively, τ RMSgives a measure of the width, or spread, of the channel response in time. Alarge τ RMSimplies a highly dispersive channel in time and a long channel impulse response(large v), whereas a small τ RMSindicates that the channel is not very dispersive and hence mightrequire only a few taps to accurately characterize. A general rule of thumb is that τ .max≈ 5τRMSTable 3.2 shows some typical values for the RMS delay spread and the associated channelcoherence bandwidth for two candidate WiMAX frequency bands. This table demonstrates thatlonger-range channels have more frequency-selective fading.The channel coherence bandwidth B cis the frequency-domain dual of the channel delayspread. The coherence bandwidth gives a rough measure for the maximum separation between afrequency f 1and a frequency f 2where the channel frequency response is correlated. That is:| f − f | ≤ B ⇒ H( f ) ≈ H( f )1 2 c1 2| f − f |> B ⇒ H( f ) and H( f ) are uncorrelated1 2 c1 2(3.31)Just as τ maxis a ballpark value describing the channel duration, B cis a ballpark value describingthe range of frequencies over which the channel stays constant. Given the channel delay spread,it can be shown that11 .B c≈ ≈5τRMS τmax(3.32)Exact relations can be found between B cand τ RMSby arbitrarily defining notions of coherence,but the important and prevailing feature is that and τ are inversely related.B c3.4.2 Doppler Spread and Coherence TimeWhereas the power-delay profile gave the statistical power distribution of the channel over timefor a signal transmitted for only an instant, the Doppler power spectrum gives the statisticalpower distribution of the channel versus frequency for a signal transmitted at one exact frequency,generally normalized as f =0for convenience. Whereas the power-delay profile wascaused by multipath between the transmitter and the receiver, the Doppler power spectrum iscaused by motion between the transmitter and receiver. The Doppler power spectrum is the Fouriertransform of A ( ∆ t ) , that is:tf tρ t t∫∞−( ∆f)= A ( ∆t) e ∆ ⋅∆( d∆t). (3.33)−∞