. .
Summer Summer
. . . . . .
hI(t) hQ(t)
The phases n are chosen to reasonably approximate an aggregate phase with uniform distribution,
whose value is 1/2. The Jakes model assumes N equal strength rays with uniformly distributed
arrival angles.
The Jakes model can also be written as (in nonnormalized form)
(3.90) Hk(t) saM
n1
[cos(bn) jsin(bn)] # cos(2pfn # cos(ant) unk) 22cos(2pfmt u0k)
With and . Now to generate multiple waveforms we make use of the following
phase offset for each of the kth multipath waveform.
(3.91)
The simulated channel should produce a reasonable approximation to the Rayleigh distribution. If M
is very large then we can make use of the central limit theorem (CLT) to state that H(t) is a complex
Gaussian random process and so |H(t)| is Rayleigh.
As discussed earlier in this chapter the autocorrelation of the generated multipath fading signal
should closely approximate, Jo(wmt). It has been shown by many authors that this accuracy improves
with increasing the number of sinusoids. Avery good approximation can be had for M greater than
32 frequency sinusoids.
As the need for wideband channel modeling increases, it is important to be able to generate multipath
faded signals that are uncorrelated.
Pages:
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263