Coded Modulation in Coded Modulation in Fading ChannelsFading Channels

Ryan AuresRyan Aures

Matthew HollandMatthew Holland

ECE 492 Mobile CommunicationsECE 492 Mobile Communications

MotivationMotivation

Benefits/Drawbacks of codingBenefits/Drawbacks of coding• +Increased capacity+Increased capacity• +Lower BER+Lower BER• -Higher power-Higher power• -Lower throughput-Lower throughput

Benefits/Drawbacks of adaptive Benefits/Drawbacks of adaptive modulationmodulation• +Increased capacity+Increased capacity• +Energy efficient+Energy efficient• -Complexity of demodulation-Complexity of demodulation• -Need accurate channel estimation-Need accurate channel estimation

Coded 16-QAMCoded 16-QAM

Increased capacity over current cellular Increased capacity over current cellular standard 40 – 85%standard 40 – 85%

Same QoS as currently used QPSK systemsSame QoS as currently used QPSK systems

Use CSI at receiver to decode messageUse CSI at receiver to decode message• Weighting functionWeighting function

Trellis Coding (coset codes) with Trellis Coding (coset codes) with adaptive modulationadaptive modulation

Superimpose coding techniques for AWGN Superimpose coding techniques for AWGN channels onto fading channels with adaptive channels onto fading channels with adaptive modulationmodulation

Variable rate variable power MQAMVariable rate variable power MQAM

Higher order trellis codes approach capacity limitHigher order trellis codes approach capacity limit

Achieve same coding gains as seen for AWGN Achieve same coding gains as seen for AWGN channelschannels

Up to 20dB power savingsUp to 20dB power savings

Coding with 16-QAMCoding with 16-QAM

Brief description of the systemBrief description of the system

Motivation: Current use of Motivation: Current use of ππ/4-QPSK in /4-QPSK in new cellular systems lack capacitynew cellular systems lack capacity

Solution: Coded 16-QAMSolution: Coded 16-QAM

Fast flat fading channelFast flat fading channel

Viterbi coding with weighting and channel Viterbi coding with weighting and channel information aided by pilot tonesinformation aided by pilot tones

Block diagram of the systemBlock diagram of the system

Describe channel estimation with Describe channel estimation with pilot tonespilot tones

Every frame a pilot tone is sent over the Every frame a pilot tone is sent over the channelchannel

This pilot tone is an arbitrary symbol sent This pilot tone is an arbitrary symbol sent that is known at the transmitter and that is known at the transmitter and receiver receiver

For a frame of N symbols the pilot to data For a frame of N symbols the pilot to data ratio is 1:(N-1)ratio is 1:(N-1)• For large N the estimation of the channel will For large N the estimation of the channel will

not be as accuratenot be as accurate• For small N there is a decrease in throughput For small N there is a decrease in throughput

The Viterbi algorithmThe Viterbi algorithm

A trellis encoder is used on the bit A trellis encoder is used on the bit streamstream

The encoded data then undergoes The encoded data then undergoes block interleavingblock interleaving• Block interleaving is to avoid burst Block interleaving is to avoid burst

errorserrors• It destroys the memory of the channelIt destroys the memory of the channel

Describe the weighting functionDescribe the weighting function

The signal is reconstructed using the The signal is reconstructed using the Viterbi algorithm to find the most likely Viterbi algorithm to find the most likely path the message could take.path the message could take.

By applying a weighting function the By applying a weighting function the estimates of the message can be estimates of the message can be improved by removing the weight of improved by removing the weight of symbols that occurred during deep fadessymbols that occurred during deep fades

Block diagram of the systemBlock diagram of the system

BER PerformanceBER Performance

Capacity PerformanceCapacity Performance There is a significant capacity increase in the There is a significant capacity increase in the

coded systemcoded system

General Results – 16-QAMGeneral Results – 16-QAM

16-QAM in flat fading channel16-QAM in flat fading channel• Gain over un-coded system 7-10 dBGain over un-coded system 7-10 dB• Capacity over QPSK systems 40-85% Capacity over QPSK systems 40-85%

gaingain

Adaptive Coded Modulation Adaptive Coded Modulation

OverviewOverview Motivation: Improve energy efficiency and Motivation: Improve energy efficiency and

increase data rate over a fading channelincrease data rate over a fading channel

Coding and modulation designed Coding and modulation designed separatelyseparately• Trellis, lattice codes normally used for AWGN Trellis, lattice codes normally used for AWGN

channels can be usedchannels can be used• Variable Modulation (MQAM, others)Variable Modulation (MQAM, others)• Same result (gain) as AWGN channelSame result (gain) as AWGN channel

Results approach Shannon Capacity LimitResults approach Shannon Capacity Limit

Power Savings up to 20dBPower Savings up to 20dB

System ModelSystem Model

√√g(t) = ergodic channel gain, g(t) = ergodic channel gain, mean(mean(g) = 1g) = 1 Assume perfect channel estimate (ŷ(t) = y(t))Assume perfect channel estimate (ŷ(t) = y(t)) Assume zero delay in feedback path(TAssume zero delay in feedback path(Tff = 0) = 0)

Basic PremiseBasic Premise Coding gain is a function of dCoding gain is a function of dminmin, the minimum , the minimum

distance between signal point sequences.distance between signal point sequences.

ddminmin= min{d= min{dss, d, dcc}}• ddss = minimum distance between coset = minimum distance between coset

sequencessequences• ddcc = minimum distance between coset points = minimum distance between coset points

Goal of adaptive modulation is to maintain Goal of adaptive modulation is to maintain constant dconstant dminmin across different SNR values across different SNR values

For each SNR level For each SNR level γγ, find values of: , find values of: • M(M(γγ) - constellation size) - constellation size• S(S(γγ) – transmit power) – transmit power• T(T(γγ) – duration of transmission) – duration of transmission

Block DiagramBlock Diagram

Channel coding and modulation separableChannel coding and modulation separable Channel coding same as non-adaptive coded modulationChannel coding same as non-adaptive coded modulation

Trellis coded Adaptive MQAMTrellis coded Adaptive MQAM

Specific implementation of general Specific implementation of general scenario with coding + adaptive scenario with coding + adaptive modulationmodulation

Trellis codesTrellis codes• Four state and Eight state codesFour state and Eight state codes

M-ary QAMM-ary QAM• Only square constellationsOnly square constellations

Coding and Modulation are separableCoding and Modulation are separable

Choose Parameters for MQAMChoose Parameters for MQAM

Symbol period T(Symbol period T(γγ) remains constant, ) remains constant, difficult to change in practicedifficult to change in practice

Choose M(Choose M(γγ) based on SNR, then choose ) based on SNR, then choose power level S within each M power level S within each M

Parameters chosen to maintain desired Parameters chosen to maintain desired minimum distanceminimum distance• Based on required SNRBased on required SNR

Gives power as a continuous function of SNRGives power as a continuous function of SNR

Results for Raleigh fading – MQAMResults for Raleigh fading – MQAM

Perfect CSI at Tx and Rx is knownPerfect CSI at Tx and Rx is known

Raleigh fading and lognormal shadowing Raleigh fading and lognormal shadowing simulated, results only for Raleigh fading but simulated, results only for Raleigh fading but similar results found for lognormal shadowingsimilar results found for lognormal shadowing

MQAM restricted to constellation sizes of MQAM restricted to constellation sizes of 0,4,16,64, and 2560,4,16,64, and 256

Results obtained both from simulation and Results obtained both from simulation and analyticallyanalytically

Coding Gain Coding Gain Moderate gain at BER requirement = 10Moderate gain at BER requirement = 10-3-3, must increase , must increase

BER requirement to 10BER requirement to 10-6-6 to see 3dB improvement to see 3dB improvement Caused by codewords being off by more than one Caused by codewords being off by more than one

neighbor at lower values of SNRneighbor at lower values of SNR

Constellation sizeConstellation size At higher BER, good spectral efficiencyAt higher BER, good spectral efficiency Lowering BER requirement -> higher Lowering BER requirement -> higher

coding gaincoding gain

Higher state trellis codesHigher state trellis codes For higher number of states: better coding gain, better For higher number of states: better coding gain, better

spectral efficiency, closer to capacityspectral efficiency, closer to capacity Exponential increase in complexity of decoding, limited to Exponential increase in complexity of decoding, limited to

eight or fewer states in practiceeight or fewer states in practice

Results – Coded MQAMResults – Coded MQAM

Coding gain of 3dB for four state code, Coding gain of 3dB for four state code, 3.6dB gain for eight state code3.6dB gain for eight state code• This gain in addition to gain from adaptive This gain in addition to gain from adaptive

MQAMMQAM

Adaptive modulation gives power savings Adaptive modulation gives power savings of 5dB min, 20dB max for low state codes of 5dB min, 20dB max for low state codes with low required BER’swith low required BER’s

Possible improvements: constellation Possible improvements: constellation shaping and turbo codes, get even close to shaping and turbo codes, get even close to capacity limitcapacity limit

ReferencesReferences

[1] “Adaptive coded modulation for [1] “Adaptive coded modulation for fading channels”, A. Goldsmith and fading channels”, A. Goldsmith and S. ChuaS. Chua

[2] “A coded 16 QAM scheme for fast [2] “A coded 16 QAM scheme for fast fading mobile radio channels”,fading mobile radio channels”,D. Subasinghe-Dias and K. FeherD. Subasinghe-Dias and K. Feher