Digital Signal Processing Reference
In-Depth Information
2.4.2
Adaptive Channel Estimation via Subblock Tracking
Suppose that we collect the received signal over a time interval of
T
symbols. We wish to
estimate the time-variant channel using a channel model and time-multiplexed training
(such as that discussed in section 2.4.1 and [36]), and subsequently using the estimated
channel, estimate the information symbols. For CE-BEM, if we choose
T
as the block
size, then in general the
Q
value will be very high, requiring estimation of a large num-
ber of parameters, thereby degrading the channel estimation performance. If we divide
T
into blocks of size
T
B
, and then fit CE-BEM block by block, we need smaller
Q
; how-
ever, estimation of
h
q
(
l
is is now based on a shorter observation size of
T
B
symbols, which
might also degrade channel estimation performance. Thus, one has to strike a balance
between estimation variance and block size. Such considerations do not apply to the AR
channel model fitting. In the sequel, we propose a novel subblock tracking approach to
CE-BEM channel estimation where we update estimates of
h
q
(
l
)'s every subblock based
on all of the past training symbols.
By exploiting the invariance of the coefficients of CE-BEM over each block, hence each
of the
P
subblocks per block of length
T
B
symbols, we seek subblock-wise tracking of the
BEM coefficients of the doubly selective channel. Consider two overlapping blocks that
differ by just one subblock: blocks with
n
=
m
,
m
+ 1,
…
,
m
+
T
B
- 1, where
m
=
m
0
for the
past block and
m
=
m
0
+
l
b
for the current block. If the two blocks overlap so significantly,
one would expect the BEM coefficients to vary only a little from the past block to the
current overlapping block. Therefore, rather than estimate
h
q
(
l
)'s anew with every non-
overlapping block, as in section 2.4.1 and [36], we propose to track the BEM coefficients
subblock by subblock using a first-order AR model for their variations.
Stack the channel coefficients in (2.15) into vectors
T
:=
() ()
()
,
h
l
hl
hl
hl
(2 .74)
1
2
Q
T
:=
T
T
T
hh
h
1
h
(2.75)
0
L
of size
Q
and
M
:=
Q
(
L
+ 1), respectively. The coefficient vector in (2.75) for the
p
th
sub-
block (
p
= 0, 1,
…
) will be denoted by
h
(
p
). We assume that the BEM coefficients over
each subblock are Markovian: a simplified model is given by the first-order AR process,
i.e.,
()
=
( )
+
()
h
p
α 1
h
p
w
p
,
(2.76)
where α is the AR coefficient, and the driving noise vector
w
(
p
) is zero-mean com-
plex Gaussian with variance σ
wM
2
I
. If the channel is stationary and coefficients
h
q
(
l
) are independent (as assumed in [36]), then by (2.76), σσ α
2
2 2
=(||)/
Q
with
w
h
2
:=
∗
σ
h
Ehnlhnl
{(
;
)( )}. Since the coefficients evolve slowly, we have α ≈ 1 (but α < 1 for
;
tracking).
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