Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

18 Fundamentalswhere p =|a p | 2 (1.6)is the power of path p. The RMS delay spread is defined asτ RMS =√N p −1∑p=0N p −1∑p=0τ 2 p p p− τ 2 . (1.7)Similarly, the Doppler power density spectrum S(f D ) characterizes the time variance ofthe mobile radio channel and gives the average power of the channel output as a functionof the Doppler frequency f D . The frequency dispersive properties of multi-path channelsare most commonly quantified by the maximum occurring Doppler frequency f Dmax andthe Doppler spread f Dspread . The Doppler spread is the bandwidth of the Doppler powerdensity spectrum and can take on values up to two times |f Dmax |,i.e.f Dspread ≤ 2|f D max |. (1.8)1.1.3 Channel Fade StatisticsThe statistics of the fading process characterize the channel and are of importance forchannel model parameter specifications. A simple and often used approach is obtainedfrom the assumption that there is a large number of scatterers in the channel that contributeto the signal at the receiver side. The application of the central limit theorem leads toa complex-valued Gaussian process for the channel impulse response. In the absence ofline of sight (LOS) or a dominant component, the process is zero-mean. The magnitudeof the corresponding channel transfer functiona = a(f,t) =|H(f,t)| (1.9)is a random variable, for brevity denoted by a, with a Rayleigh distribution given byp(a) = 2a e−a2 / , (1.10)where = E{a 2 } (1.11)is the average power. The phase is uniformly distributed in the interval [0, 2π].In the case where the multi-path channel contains a LOS or dominant component inaddition to the randomly moving scatterers, the channel impulse response can no longerbe modeled as zero-mean. Under the assumption of a complex-valued Gaussian process