Digital Signal Processing Reference
In-Depth Information
2.5
Simulation Examples
In this section we present two simulation examples to illustrate some of the approaches
to channel estimation. In both examples a random time- and frequency-selective Ray-
leigh fading channel is considered. We take
L
= 2 (three taps) in (2.63), and
h
(
n
;
l
) are
zero-mean complex Gaussian with variance σ
h
2
/( ). For different
l
's,
h
(
n
;
l
)'s are
mutually independent and satisfy Jakes' model [22]. To this end, we simulated each sin-
gle tap following [62] (with a correction in the appendix of [61]).
We consider a communication system with carrier frequency of 2 GHz, data rate of
40 kBd (kilo-Bauds), therefore
T
s
= 25 μs, and a varying Doppler spread
f
d
in the range
of 0 to 400 HZ, or the normalized Doppler spread
f
d
T
s
from 0 to 0.01 (corresponding
to a maximum mobile velocity from 0 to 216 km/h). The additive noise was zero-mean
complex white Gaussian. The (receiver) SNR refers to the average energy per symbol
over one-sided noise spectral density. The time-multiplexed training scheme of [36]
described in section 2.4.1 is adopted, where during data sessions the information
sequence is modulated by binary phase-shift keying (BPSK) with unit power. The train-
ing session is described by (2.72) with γ= 21
=+
11
L
L
so that the average symbol power of
training sessions is equal to that of data sessions.
We evaluate the performance of various approaches by considering the normal-
ized channel mean square error (NCMSE) and the bit error rate (BER). The NCMSE is
defined as
∑∑∑
i
M
T
−
1
L
2
r
ˆ
()
(
−
()
()
i
()
i
h
nl
h
n
;
l
NCMSE:=
=
1
n
=
0
l
=
0
,
∑∑∑
1
M
T
−
1
L
2
r
h
()
i
nl
i
=
n
=
0
l
=
0
where
h
(
i
)
(
n
;
l
) is the true channel and
ĥ
(
i
)
(
n
;
l
) is the estimated channel at the
i
t h
run,
among total
M
r
runs.
2.5.1 Example 1
Here we consider block-adaptive channel estimation and restrict our attention to a
single block. We compare superimposed training-based approaches with time-multi-
plexed training-based approaches. The superimposed training sequence was picked as
a periodic repetition of a length 7
m
-sequence (maximal length pseudo-random binary
sequence) {1,-1,-1,1,1,1,-1}. In the simulations, the average transmitted power σ
c
2
in
c
(
n
)
was 0.3 of the power in
b
(
n
), leading to a training-to-information power ratio TIR :=
σ
c
2
/ σ
b
2
= β/(1 - β) = 0.3. We consider both critically sampled CE-BEM and DPS-BEM for
channel modeling. For comparison, we consider a CE- or DPS-BEM-based periodically
placed time-multiplexed training with zero padding, following the design of [36]. We
took a training subblock of size 2
L
+ 1 = 5 symbols with the recommended structure
{
}
,,
( )
+, ,
2
2
00
21
L
σσ ,
00
b
c
Search WWH ::
Custom Search