Coded Modulation in
Fading Channels
Ryan Aures
Matthew Holland
ECE 492 Mobile Communications
Motivation

Benefits/Drawbacks of coding
•
•
•
•
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+Increased capacity
+Lower BER
-Higher power
-Lower throughput
Benefits/Drawbacks of adaptive
modulation
•
•
•
•
+Increased capacity
+Energy efficient
-Complexity of demodulation
-Need accurate channel estimation
Coded 16-QAM


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Increased capacity over current cellular
standard 40 – 85%
Same QoS as currently used QPSK
systems
Use CSI at receiver to decode message
• Weighting function
Trellis Coding (coset codes) with
adaptive modulation

Superimpose coding techniques for AWGN
channels onto fading channels with adaptive
modulation

Variable rate variable power MQAM

Higher order trellis codes approach capacity limit


Achieve same coding gains as seen for AWGN
channels
Up to 20dB power savings
Coding with 16-QAM
Brief description of the system

Motivation: Current use of π/4-QPSK in
new cellular systems lack capacity

Solution: Coded 16-QAM

Fast flat fading channel

Viterbi coding with weighting and channel
information aided by pilot tones
Block diagram of the system
Describe channel estimation with
pilot tones
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Every frame a pilot tone is sent over the
channel
This pilot tone is an arbitrary symbol sent
that is known at the transmitter and
receiver
For a frame of N symbols the pilot to data
ratio is 1:(N-1)
• For large N the estimation of the channel will
not be as accurate
• For small N there is a decrease in throughput
The Viterbi algorithm
A trellis encoder is used on the bit
stream
 The encoded data then undergoes
block interleaving

• Block interleaving is to avoid burst
errors
• It destroys the memory of the channel
Describe the weighting function


The signal is reconstructed using the
Viterbi algorithm to find the most likely
path the message could take.
By applying a weighting function the
estimates of the message can be
improved by removing the weight of
symbols that occurred during deep fades
Block diagram of the system
BER Performance
Capacity Performance

There is a significant capacity increase in the
coded system
General Results – 16-QAM

16-QAM in flat fading channel
• Gain over un-coded system 7-10 dB
• Capacity over QPSK systems 40-85%
gain
Adaptive Coded Modulation
Overview

Motivation: Improve energy efficiency and
increase data rate over a fading channel

Coding and modulation designed
separately
• Trellis, lattice codes normally used for AWGN
channels can be used
• Variable Modulation (MQAM, others)
• Same result (gain) as AWGN channel

Results approach Shannon Capacity Limit

Power Savings up to 20dB
System Model


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√g(t) = ergodic channel gain, mean(g) = 1
Assume perfect channel estimate (ŷ(t) = y(t))
Assume zero delay in feedback path(Tf = 0)
Basic Premise
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Coding gain is a function of dmin, the minimum
distance between signal point sequences.
dmin= min{ds, dc}
• ds = minimum distance between coset
sequences
• dc = minimum distance between coset points
Goal of adaptive modulation is to maintain
constant dmin across different SNR values
For each SNR level γ, find values of:
• M(γ) - constellation size
• S(γ) – transmit power
• T(γ) – duration of transmission
Block Diagram
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Channel coding and modulation separable
Channel coding same as non-adaptive coded modulation
Trellis coded Adaptive MQAM
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Specific implementation of general
scenario with coding + adaptive
modulation
Trellis codes
• Four state and Eight state codes
M-ary QAM
• Only square constellations
Coding and Modulation are separable
Choose Parameters for MQAM
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Symbol period T(γ) remains constant,
difficult to change in practice
Choose M(γ) based on SNR, then choose
power level S within each M
Parameters chosen to maintain desired
minimum distance
• Based on required SNR
Gives power as a continuous function of
SNR
Results for Raleigh fading – MQAM
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Perfect CSI at Tx and Rx is known
Raleigh fading and lognormal shadowing
simulated, results only for Raleigh fading but
similar results found for lognormal shadowing
MQAM restricted to constellation sizes of
0,4,16,64, and 256
Results obtained both from simulation and
analytically
Coding Gain
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
Moderate gain at BER requirement = 10-3, must
increase BER requirement to 10-6 to see 3dB
improvement
Caused by codewords being off by more than one
neighbor at lower values of SNR
Constellation size

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At higher BER, good spectral efficiency
Lowering BER requirement -> higher
coding gain
Higher state trellis codes
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For higher number of states: better coding gain, better
spectral efficiency, closer to capacity
Exponential increase in complexity of decoding, limited to
eight or fewer states in practice
Results – Coded MQAM
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Coding gain of 3dB for four state code,
3.6dB gain for eight state code
• This gain in addition to gain from adaptive
MQAM

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Adaptive modulation gives power savings
of 5dB min, 20dB max for low state codes
with low required BER’s
Possible improvements: constellation
shaping and turbo codes, get even close
to capacity limit
References
[1] “Adaptive coded modulation for
fading channels”, A. Goldsmith and
S. Chua
[2] “A coded 16 QAM scheme for fast
fading mobile radio channels”,
D. Subasinghe-Dias and K. Feher