Bit-wise Decomposition of M-ary Symbol Metric

179 Pages·2004·2.33 MB·English

Bit-wise Decomposition of M-ary Symbol Metric
Prepared by Chia-Wei Chang
Advisory by Prof. Po-Ning Chen
In Partial Fulfillment of the Requirements
For the Degree of
Master of Science
Department of Communications Engineering
National Chiao Tung University
Hsinchu, Taiwan 300, R.O.C.
E-mail: [email protected]
June, 2004
Acknowledgements
I am deeply grateful to my advisor, Prof. Po-Ning Chen, for his encouragement, support and
brilliant guidance throughout this research. This work would not been possible without his
advice and commitment.
I would like to thank Prof. Yunghsiang S. Han and Prof. T.Y. Hsu, for their enthusiastic
discussion,valuable suggestions and innovative ideas.
I would like to give special thanks to my dear friends, Chia-Long, Liang-wei, Ya-ting,
Ming-Chun and Dan for their great care and assistance throughout my time in Network
Technology Laboratory.
I would like to thank Nation Chiao-Tung University for providing such a wonderful en-
vironment and such many resources for me in my graduate life.
This thesis is dedicated to my family and to Yu-Fang, for their love, support, and en-
couragement.
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Contents
Abstract i
List of Tables vi
List of Figures xiii
1 Introduction and Background 1
1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objective of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Systematic Bit-wise Decomposition of M-ary Symbol Metric 8
2.1 Analysis of Bit-wise Metric for Soft-decision Decoding of Coded High QAM . 8
2.2 Bit-wise Decompositions of 16QAM, 64QAM and 256QAM Symbol Metrics . 10
2.3 Alternative Structures for Receiver with Soft-decision Decoding . . . . . . . 17
2.3.1 Soft-demapping for Bit-interleaved Coded Modulation . . . . . . . . . 17
2.3.2 Bit Metrics Recursively Generated from Other First-bit Metric . . . . 18
3 Performance Evaluation over the AWGN Channel and the Rayleigh Flat
ii
Fading Channel 21
3.1 Simulation Results for the AWGN Channel . . . . . . . . . . . . . . . . . . . 21
3.2 Simulation Results for Rayleigh Flat Fading Channel . . . . . . . . . . . . . 22
4 Robustness Against Imperfect System Parameters 31
4.1 Effect of Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Effect of Imperfect Automatic Gain Control . . . . . . . . . . . . . . . . . . 38
4.3 Effect of Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 Performance Evaluation Over the Punctured Codes 59
5.1 Description of the Puncture Procedure . . . . . . . . . . . . . . . . . . . . . 59
5.2 Performance of Punctured Codes . . . . . . . . . . . . . . . . . . . . . . . . 60
6 Realization of the Systematic Bit-wise Decomposition Metric 71
6.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Architecture of Branch Metric Unit . . . . . . . . . . . . . . . . . . . . . . . 71
7 Concluding Remarks 75
Appendix 76
A DetailedDerivationofBit-wiseMetricforSoft-decisionDecodingof64QAM,
256QAM, 1024QAM Modulations 76
A.1 Derivation of Bit-wise Metric of 64QAM Modulation . . . . . . . . . . . . . 77
A.2 Derivation of Bit-wise Metric of 256QAM Modulation . . . . . . . . . . . . . 86
iii
A.3 Derivation of Bit-wise Metric of 1024QAM Modulation . . . . . . . . . . . . 118
B An Intuitive Soft-demapping Decoding for 16QAM and 64QAM Modula-
tions 137
B.1 Soft-demapping Metric of 16QAM Modulation . . . . . . . . . . . . . . . . . 137
B.2 Soft-demapping Metric of 64QAM Modulation . . . . . . . . . . . . . . . . . 138
C TheoreticalPerformancesandSimulationsofQAMModulationoverAWGN
and Rayleigh Flat Fading Channels 143
C.1 Theoretical Performances of QAM Modulation over AWGN Channel . . . . . 143
C.1.1 Bit Error Probabilities from Symbol Error Probabilities under AWGN
Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
C.2 Theoretical Performances of QAM Modulation over Rayleigh Flat Fading
Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
C.2.1 BitErrorProbabilitiesfromSymbolErrorProbabilitiesunderRayleigh
Flat Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
References 163
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List of Tables
5.1 Rate-dependent parameters in the std. of IEEE 802.11a/g . . . . . . . . . . 64
C.1 Symbol error rates of theory and simulation are consistent, and the bit error
rate of simulation result also conforms to the distributions of the bit error
numbers in the error symbols. Formula P =(1*P1bit +2*P2bit )*P /2 . . . . 148
b error error s
C.2 Symbol error rates of theory and simulation are consistent, and the bit error
rateofsimulationresultalsoconformstothedistributionsofthebiterrornum-
bersintheerrorsymbols. FormulaP =(1*P1bit +2*P2bit +3*P3bit +4*P4bit )
b error error error error
*P /4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
s
C.3 Symbol error rates of theory and simulation are consistent, and the bit er-
ror rate of simulation result also conforms to the distributions of the bit er-
ror numbers in the error symbols. Formula P =(1*P1bit +2*P2bit +3*P3bit
b error error error
+4*P4bit +5*P5bit +6*P6bit )*P /6 . . . . . . . . . . . . . . . . . . . . . . . 150
error error error s
C.4 Symbol error rates of theory and simulation are consistent, and the bit error
rateofsimulationresultalsoconformstothedistributionsofthebiterrornum-
bers in the error symbols. Formula P =(1*P1bit +2*P2bit +3*P3bit +4*P4bit
b error error error error
+5*P5bit +6*P6bit +7*P7bit +8*P8bit )*P /8 . . . . . . . . . . . . . . . . . . 156
error error error error s
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C.5 Symbol error rates of theory and simulation are consistent, and the bit error
rateofsimulationresultalsoconformstothedistributionsofthebiterrornum-
bers in the error symbols. Formula P =(1*P1bit +2*P2bit +3*P3bit +4*P4bit
b error error error error
+5*P5bit +6*P6bit +7*P7bit +8*P8bit +9*P9bit +10*P10bit)*P /10 . . . . . 157
error error error error error error s
C.6 Symbol error rates of theory and simulation are consistent, and the bit error
rate of simulation result also conforms to the distributions of the bit error
numbers in the error symbols. Formula P =(1*P1bit +2*P2bit )*P /2 . . . . 158
b error error s
C.7 Symbol error rates of theory and simulation are consistent, and the bit error
rateofsimulationresultalsoconformstothedistributionsofthebiterrornum-
bersintheerrorsymbols. FormulaP =(1*P1bit +2*P2bit +3*P3bit +4*P4bit )
b error error error error
*P /4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
s
C.8 Symbol error rates of theory and simulation are consistent, and the bit er-
ror rate of simulation result also conforms to the distributions of the bit er-
ror numbers in the error symbols. Formula P =(1*P1bit +2*P2bit +3*P3bit
b error error error
+4*P4bit +5*P5bit +6*P6bit )*P /6 . . . . . . . . . . . . . . . . . . . . . . . 160
error error error s
C.9 Symbol error rates of theory and simulation are consistent, and the bit error
rateofsimulationresultalsoconformstothedistributionsofthebiterrornum-
bers in the error symbols. Formula P =(1*P1bit +2*P2bit +3*P3bit +4*P4bit
b error error error error
+5*P5bit +6*P6bit +7*P7bit +8*P8bit )*P /8 . . . . . . . . . . . . . . . . . . 161
error error error error s
C.10 Symbol error rates of theory and simulation are consistent, and the bit error
rateofsimulationresultalsoconformstothedistributionsofthebiterrornum-
bers in the error symbols. Formula P =(1*P1bit +2*P2bit +3*P3bit +4*P4bit
b error error error error
+5*P5bit +6*P6bit +7*P7bit +8*P8bit +9*P9bit +10*P10bit)*P /10 . . . . . 162
error error error error error error s
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List of Figures
1.1 An exemplified receiver design. . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Therelationbetweenthebitsfor16QAMmappingandthebitsforabranchin
the(2,1,6)convolutionalcodetrellisspecifiedinIEEE802.11a. (r ,r )and
I,1 Q,1
(r ,r )representthereceivedvectorsfortwo16QAMsymbols, respectively.
I,2 Q,2
The 4 bit-pairs that constitute convolutional code branches in a trellis are
[b (0),b (1)], [b (1),b (0)], [b (0),b (1)] and [b (1),b (0)]. . . . . . 3
I,1 I,2 I,1 I,2 Q,1 Q,2 Q,1 Q,2
1.3 The received 16QAM quadrature components are indicated by a solid-lined
upright rectangular; each column consists of 6 quadrature components. The
de-interleaver should then exchange (the weights of) the least significant bit
and the most significant bit of the quadrature components for those columns
indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 After de-interleaving, each 2-bit trellis branch for convolutional decoding is
indicated by the flat rectangular in sequences from left to right. . . . . . . . 7
2.1 The metric values of Soft-demap for 16QAM. . . . . . . . . . . . . . . . . . . 18
2.2 ThemetricvaluesofSoft-TB,simplifiedSoft-TB,andSoft-proposedfor16QAM. 20
2.3 ThemetricvaluesofSoft-TB,simplifiedSoft-TB,andSoft-proposedfor64QAM. 20
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3.1 SystemperformancesundertheAWGNchannelforBPSK,QPSK,and16QAM
modulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 System performances under the AWGN channel for 64QAM and 256QAM
modulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 System performances under the AWGN channel for 1024QAM modulation. . 27
3.4 Block diagram of a frequency-nonselective slowly fading channel with perfect
channel knowledge, which can be described as r = α·s+n, where s and r are
respectivelychannelinputandoutputsymbols, α isRaileighdistributedchan-
nel attenuation that can be perfectly estimated, and n denotes the additive
white Gaussian noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 SystemperformancesundertheRayleighflatfadingchannelforBPSK,QPSK,
and 16QAM modulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6 System performances under the Rayleigh flat fading channel for 64QAM and
256QAM modulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.7 System performances under the Rayleigh flat fading channel for 1024QAM
modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1 Performanceimpactofquantizationfor16QAMmodulationundertheAWGN
channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Performanceimpactofquantizationfor16QAMmodulationundertheRayleigh
flat fading channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Performanceimpactofquantizationfor64QAMmodulationundertheAWGN
channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
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4.4 Performanceimpactofquantizationfor64QAMmodulationundertheRayleigh
flat fading channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5 Performanceimpactofquantizationfor256QAMmodulationundertheAWGN
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.6 Performanceimpactofquantizationfor256QAMmodulationundertheRayleigh
flat fading channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.7 Performanceimpactofquantizationfor1024QAMmodulationundertheAWGN
channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.8 Performanceimpactofquantizationfor1024QAMmodulationundertheRayleigh
flat fading channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.9 Sensitivity to gain-mismatch for 16QAM under the AWGN channel. The
taken values of E /N for Soft-proposed & Soft-TB, Soft-demap and Hard are
b 0
respectively 6.8 dB, 7.5 dB and 9.7 dB. The non-drift step-size is 0.125 . . . 44
4.10 Sensitivity to gain-mismatch for 16QAM under the Rayleigh flat fading. The
taken values of E /N for Soft-proposed & Soft-TB, Soft-demap and Hard are
b 0
respectively 11.0 dB, 16.0 dB and 18.5 dB. The non-drift step-size is 0.125 . 45
4.11 Sensitivity to gain-mismatch for 64QAM. The taken values of E /N for Soft-
b 0
proposed & Soft-TB are respectively 9.8 dB and 14.2 dB under the AWGN
and the Rayleigh flat fading channels. The non-drift step-size is 0.0625 . . . 46
4.12 Sensitivity to gain-mismatch for 64QAM. The taken values of E /N for
b 0
Soft-demap are respectively 11.1 dB and 20.2 dB under the AWGN and the
Rayleigh flat fading channels. The non-drift step-size is 0.125 . . . . . . . . . 47
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