LTE Emulator

TUCN – Data Transmission Laboratory
22
2
p = ; 0 r ;
2
σ
(4)
( r)
2
⎧ r ⎛ r ⎞
⎪ ⋅ exp 2
2
σ ⎜
⎜−
⎪ 2 σ ⎟
⎝ ⋅ ⎠
⎪
⎨ ≤ ≤ ∞
⎪0
; r < 0
⎪
⎪
⎩
To calculate the global instantaneous signal to noise ration at a given moment the following
procedure is us:
o the amplitude of the first propagation path (the main path) is considered to equal 1 and
(ai, τi) are the attenuations (expressed as ratios) and the relative delays of the other
multiple propagation paths;
o the amplitudes of the secondary propagation paths will be ai, and the phases of these
paths, relative to the one of the first path are given by:
i
i
r
2
=
φ = 2 π ⋅ f ⋅τ
(5)
where f is the signal frequency; (5) considers only one spectral component, the channel
model being applied separately to each spectral component;
Note: for a single carrier narrow-band transmission, a flat fading in the signal
frequency band should be considered since the amplitude variation of the carrier is
quasi-identical to the variations of the other spectral components of the modulated
signal. For a multi-carrier transmission (OFDM), the global fading which affects
the signal with multipath propagation and implicitly the instantaneous value of the
SNR, have to be computed for each sub-carrier or for each chunk, if the sub-carriers
are grouped.
o The global fading which affects the signal with multipath propagation, i.e. the amplitude
variation of this signal is computed with the following algorithm:
r
g _ cos
r
g _ sin
r
g
=
= f
=
r
N
a
∑
i=
1
2
g _ cos
2
( 1 2)
+ ∑ f a ( ai
2)
⋅ ai
⋅ cos(
φi
)
f
a
i=
1
2 ( a 2)
⋅ a ⋅sin(
φ )
i
+ r
N
2
g _ sin
where rg is the amplitude of the signal affected by the multipath propagation and fast
fading, and fa(p) is the value of the Rayleigh fading corresponding to a signal with power
level p;
o The total instantaneous SNR of the main user, SNRp, and those of the secondary users,
SNRs_i, are given by the following relations:
SNR
SNR
p
s _ i
= SNR
p _ 0
= SNR
p _ 0
+ 20⋅
log
i
10
+ 20⋅
log
i
( rg
0 )
( r ⋅ a )
where rg0 is the signal level of the main user, SNRp_0 is the signal to noise ratio of the
first propagation paths of the main user, rgs_i is the signal level of the secondary user i,
as_i is the attenuation associated to secondary user i (see chapter 5.), SNRp is the
instantaneous total signal to noise ratio of the main user, and SNRs_i is the instantaneous
total signal to noise ratio of the secondary user i; the total SNR considers all the multiple
propagation paths;
10
gs _ i
s _ i
(6)
(7)