Adaptive Channel Estimation in Wireless Communications - Adaptive Signal Processing in Wireless Communications - page 62

after iterations. The DML approach provides comparable error performance with TM
training, but at a higher data transmission rate. The valuable bandwidth resources can
thus be saved.
2.5.2 Example 2
Here we consider adaptive channel estimation at block-, subblock-, and symbol-adaptive lev-
els using time-multiplexed training. Four estimation and tracking schemes are compared:
1. The block-adaptive channel estimation in [36] (see section 2.4.1 ). We consider two
models corresponding to T = 200 and 400, respectively, so that Q = 5 and 9 by
(2.17). In the figures, this scheme is denoted by BA.
2. The channel tracking scheme in [35] using the first-order AR model, where the
time-varying channel is assumed to follow (2.12). Channel tracking is performed
at training sessions only. For data sessions, the receiver updates the channel via
h ( n ; l ) = α c h ( n - 1; l ). We assume that only the upper bound of the Doppler spread
is known. Then by (2.13) and (2.14) and Jakes' model, α c = J 0 (2π f d T s ) = 0.999 for
f d T s = 0.01, where J 0 (·) denotes the zero-th Bessel function of the first kind. This
scheme is denoted by AR (1)-KF in the figures.
3. We also compare the approach of joint channel estimation and data detection via
extended Kalman filtering in [34]. For fairness, the Turbo equalization procedure
in [34] is omitted. The AR parameter of the channel also follows (2.13) and (2.14),
as suggested by [34]. This scheme is denoted by Joint-KF.
4. Our proposed subblock-wise tracking using CE-BEM, which is denoted by
SUBBLOCK. We also take T = 200 and 400 for two different settings of CE-BEM,
and Q = 5 and 9 correspondingly.
The BERs for the schemes of BA, AR (1)-KF, and SUBBLOCK are evaluated by employ-
ing the Kalman detector described in section 2.4.2.2 with delay d = 5, using the channel
estimates obtained by each scheme. In each run, a symbol sequence of length 5,000 is
generated and fed into a random doubly selective channel. The first two hundred symbols
are discarded in evaluations. All the simulation results are based on five hundred runs.
In Figures 2.10 and 2.11 , the performances of the four schemes over different Dop-
pler spreads f d are compared. We set SNR = 20 dB, l t = 2 L + 1 = 5, and l d = 15 symbols,
so that 25% of the transmitted symbols are dedicated to training. For the BA scheme,
we use the oversampled CE-BEM with T B = T /2 and K = 2 in order to suppress spectral
leakage. For our SUBBLOCK scheme, we take α = 0.99 for T = 200, and α = 0.995 for T =
400. Since more unknown parameters (BEM coefficients) are involved in SUBBLOCK,
and therefore result in higher estimation variance, SUBBLOCK is slightly inferior to
AR (1)-KF for slow-fading channels. As f d increases, SUBBLOCK gradually outperforms
the other three schemes, since the time variations of the channel have been well cap-
tured in CE-BEM. For the BA scheme, more basis functions do not necessarily translate
into better performance since estimation variance also increases, whereas this strategy
can well improve the performance of SUBBLOCK since all past data are implicitly uti-
lized in Kalman filtering-based subblock tracking. Figures 2.12 and 2.13 compare the