Innovative Systems Design and Engineering ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No.11, 2012
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impulse response of the channel. A modified Clarke-based channel model is used for the fading channel process [13]. 3.1 Rayleigh Fading Process The Rayleigh fading process
r for the l th path can be expressed as:
rl (t ) = Al ( t ) e jβ l ( t )
(5)
with
β l (t ) = ω m cosα l (t ) + φl (t )
(6)
and
αl =
Ns
∑
i =1
2π i + θ i Ns
(7)
where ω m (= 2πf m ) is the maximum angular Doppler frequency shift; Al (t ) is the fade amplitude (or th attenuation); α l (t ) and φl (t ) are the angle of arrival and phase of the l path, respectively, and are statistically independent and uniformly distributed over [-π, π); f m is the maximum Doppler frequency shift, which is given as:
fm = where
Ns
vf c c
(8)
f c is the carrier frequency, c is the speed of electromagnetic wave and v is the speed of the MT.
sinusoids are assumed to generate the fading process, (5) can be rewritten as:
rl ( t ) = Al ( t ) ∑ (cos β l ,i t + j sin β l ,i t ) Ns
(9)
i
Expressing (9) in inphase and quadrature form gives:
rl ( t ) = r I ( t ) + jr Q ( t )
(10)
rl (t ) is the normalized low-pass fading process whose pdf is Rayleigh. The fade envelope of rl (t ) is then obtained as:
{
rl (t ) = ℜ rI (t ) + rQ (t ) 2
2
}
(11)
and the phase is:
rQ (t ) rI (t )
φl (t ) = tan −1 where
(12)
ℜ{⋅} denotes the real part. (9) is a modified Clarke’s model which is a Wide-Sense Stationary Uncorrelated
Scattering (WSSUS) Rayleigh fading simulation model. The fading process is generated for all the paths and the
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