Rate Adaptation in Time Varying Channels using Acknowledgement ...

Throughput
5
4.8
4.6
4.4
4.2
4
3.8
3.6
Realized throughput
using particle filter
benchmark:
throughput capacity
achieved with no CSI
3.4
0 100 200 300 400 500 600 700 800 900 1000
Packet index k
100 particles, ρ =0.99
100 particles, ρ =0.98
100 particles, ρ =0.90
Fig. 3. Throughput achieved using successive rate adaptation over time;
¯γ =20dB.
Throughput
8
7
6
5
4
3
2
1
successive optimization,
100 particles, ρ =0.99
successive optimization,
100 particles, ρ =0.98
maximum possible:
throughput capacity
achieved with full CSI
0
0 5 10 15 20 25 30
Fig. 4.
SNR (dB)
benchmark:
throughput capacity
achieved with no CSI
Comparison of the successive optimization for different SNR.
aged over 100 runs, is plotted in Fig. 4 for different SNR. For
the ρ values shown here, it is worthwhile using successive
optimization. For example, to achieve a throughput of 4
bits/symbol when ρ =0.98 requires about 2.5dB less SNR
as compared to the benchmark. However, some problem for
improvement may still be possible. In Fig. 4, the maximum
achievable throughput capacity with full CSI (as computed in
[8]) is still significantly higher. We envision that rate adaptation
using more advanced coding schemes with incremental
redundancy, rather than independent packet by packet coding
used here, would close that gap further.
VII. CONCLUSION
For packet switched systems with time varying channels, the
global optimal rate adaptation scheme is practically difficult to
find or implement. We propose a sub-optimal rate adaptation
solution which uses successive optimization, implemented
with a particle filter for estimating the required channel a posteriori
probability. In a finite state Markov channel with slow
time variation, the technique recovers a substantial amount of
throughput compared to the case when a fixed optimized rate is
selected for each SNR. Observations on realizations of the rate
adaptation scheme also bring forth a sensible general strategy.
When a NACK is received, decrease rate rapidly; when an
ACK is received, increase rate cautiously if the rate is already
high or decrease the rate aggressively if the rate is low.
APPENDIX
Using (2), (3) and (6), the throughput (9) can be computed
as
T K
ave(¯γ,r all )=
1
K∑ ∑
∫
R k × p(A k =1|R k ,h k )p(h k , a k−1 )dh k (14)
K
k=1 a k
h k
for discrete a k and continuous h k . With (12), the throughput
can be calculated if the initial probability p(h 1 ), the transition
probability p(h k |h k−1 ) and the outage probability p(A k =
1|h k ) is specified.
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