Space-Time Block Codes for Wireless Systems - The ...

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3 On Suboptimal Linear Decoders for Space-Time Block Codes 56 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.2 Uplink Signal Model for Spread Systems . . . . . . . . . . . . . . . . . . . 57 3.3 Linear Equalizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.4 The Mapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.5 The Effect of Large Number of Receive Antennae . . . . . . . . . . . . . . 65 3.6 Fisher’s Information Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.7 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.7.1 The BLUE and LS Decoders . . . . . . . . . . . . . . . . . . . . . 70 3.7.2 The LM Decoders . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.7.3 The LMMSE Decoders . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.7.4 The Effect of Number of Receive Antennae L r . . . . . . . . . . . 71 3.7.5 The Effect of Number of Active Users K . . . . . . . . . . . . . . . 72 3.7.6 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4 Nonlinear Hierarchical Codes 76 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2 Signal Model and Isometries . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3 Building Nonlinear Hierarchical Codes . . . . . . . . . . . . . . . . . . . . 82 4.4 The Hierarchical Structure of Optimal 2 × 2 QPSK Codes . . . . . . . . . 91 4.5 Code Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5 Regular Multiple Trellis Coded Modulation 98 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.3 RMTCM Design Parameters and Procedures . . . . . . . . . . . . . . . . 100 5.4 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.5 RMTCM Designs Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.5.1 2 × 2 BPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.5.2 2 × 2 QPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.5.3 2 × 2 8PSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.5.4 3 × 3 BPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.5.5 3 × 3 QPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.5.6 3 × 3 8PSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6 Conclusions 125 Reference List 126 Appendix A Code Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Appendix B RMTCM Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 v
List Of Tables 2.1 The distance spectra for rate 1 BPSK 2 × 2 Class 1 OMM code. . . . . . 26 2.2 OMM codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 Detailed Structure of rate 1 OMM 2×2 8PSK and 16PSK Codes. ( u n = e i 2π n ) 39 2.4 Rate 1 OMM 3 × 3 BPSK Codes. . . . . . . . . . . . . . . . . . . . . . . . 40 2.5 Three space-time code structures and their performance comparison. . . . 54 3.1 CPU time in seconds for 200 runs. . . . . . . . . . . . . . . . . . . . . . . 72 4.1 Code list of the 2 × 2 QPSK NHC. . . . . . . . . . . . . . . . . . . . . . . 92 4.2 List of Hierarchical Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.1 The length M of single error event for given b and g. . . . . . . . . . . . . 108 5.2 Rate 1/2 MTCM designs for 2 × 2 BPSK. . . . . . . . . . . . . . . . . . . 112 5.3 Regular MTCM design for 2 × 2 BPSK |S 3 | = 8 codewords. . . . . . . . . 113 5.4 MTCM design for 2 × 2 QPSK |S 4 | = 16 codewords. . . . . . . . . . . . . 114 5.5 Hierarchical structure in Hamming distance. . . . . . . . . . . . . . . . . . 118 A.1 2 × 2 BPSK codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 A.2 2 × 2 QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 A.3 2 × 2 8PSK code list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 A.4 2 × 2 8PSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.5 3 × 3 BPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.6 3 × 3 QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.7 3 × 3 QPSK code list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.8 3 × 3 8PSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.9 3 × 3 8PSK code list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.10 4 × 3 BPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.11 4 × 3 QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.12 4 × 3 QPSK code list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 vi
Page 1 and 2: COMMUNICATION SCIENCES INSTITUTE
Page 3 and 4: Dedication This dissertation is ded
Page 5: Contents Dedication Acknowledgement
Page 9 and 10: 3.4 The BLUE and LS estimators have
Page 11 and 12: Abstract Space-time codes are effec
Page 13 and 14: spreading. The focus of [HMP01] is
Page 15 and 16: 5, respectively: first, for an arbi
Page 17 and 18: Chapter 2 Space-Time Block Codes in
Page 19 and 20: easily achieve maximum diversity (t
Page 21 and 22: For example, a BPSK 2 × 2 block co
Page 23 and 24: multipaths corresponding to each tr
Page 25 and 26: where G(t) = [G (1) (t), . . . . .
Page 27 and 28: where D α and D β are two codewor
Page 29 and 30: For the quasi-static fading channel
Page 31 and 32: and the non-zero segment of any lin
Page 33 and 34: Let us consider the issue of achiev
Page 35 and 36: as A and B respectively, and observ
Page 37 and 38: L c = 1 0 7 9 14 0 0.00 30.56 16.00
Page 39 and 40: where D (k) (t) is defined in Equat
Page 41 and 42: For this special case of fixed spre
Page 43 and 44: where ˜R = ŘT 1 Ř−1 2 Ř 1 . (
Page 45 and 46: 2.5 Optimal Minimum Metric Codes In
Page 47 and 48: index ρ c rate size constl OMM 1 1
Page 49 and 50: 16 0 9 32-16ρ 2 32-16ρ 2 16 16 16
Page 51 and 52: Class ρ ∆ p (ζ v ) N p code ind
Page 53 and 54: 2. In a spread system (ρ = 0.3), t
Page 55 and 56: 10 0 SNR OMM spread orthogonal 10
Page 57 and 58:
ρ c =0.3 10 0 SNR Rate 1 4X2 2 Rat
Page 59 and 60:
Code Comparison, Joint ML Decoder,
Page 61 and 62:
2.6 Practical Considerations In thi
Page 63 and 64:
2.6.2 Sensitivity to Correlation Us
Page 65 and 66:
structure ] 1 structure ] 2 structu
Page 67 and 68:
Chapter 3 On Suboptimal Linear Deco
Page 69 and 70:
where σ t is signal-to-noise ratio
Page 71 and 72:
decorrelator. Denote ‖x‖ 2 R x
Page 73 and 74:
3.4 The Mapper Recall that the outp
Page 75 and 76:
Now we evaluate the overall decoder
Page 77 and 78:
and lim L HH R 3 H = r→∞ L r [1
Page 79 and 80:
the FIM for random d is [ ∂ ln P
Page 81 and 82:
Apparently R d is singular, which i
Page 83 and 84:
L t =2, L r =1, K=1, ρ=0.3, ignori
Page 85 and 86:
L t =2, L r =2, K=1, ρ=0.3, two re
Page 87 and 88:
Chapter 4 Nonlinear Hierarchical Co
Page 89 and 90:
signal corresponding to N c symbol
Page 91 and 92:
1. full diversity ∆ H (D i − D
Page 93 and 94:
epresent both for convenience. All
Page 95 and 96:
We may construct the whole set from
Page 97 and 98:
2. Most right isometries P are redu
Page 99 and 100:
★ ✥ S k ✧ a U j , P j ✲ b
Page 101 and 102:
3. Given Isometries U k U j and P j
Page 103 and 104:
[ 2 ] [ 168 ] [ 42 ] [ 128 ] 1 1
Page 105 and 106:
which are very likely to be optimal
Page 107 and 108:
4X3 BPSK(8 Codewords) and QPSK(64 C
Page 109 and 110:
Chapter 5 Regular Multiple Trellis
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The high rate performance is poor,
Page 113 and 114:
ehavior of a regular trellis are: t
Page 115 and 116:
All the NHCs found in this work sat
Page 117 and 118:
Whenever there exist parallel trans
Page 119 and 120:
M m g=1 g=2 g=4 g=8 next jump b=2 2
Page 121 and 122:
provides a lower bound on the numbe
Page 123 and 124:
Label S k S Comment Figure 1/2 I2S2
Page 125 and 126:
Label S k O(= gbp) S(= gb) Figure 1
Page 127 and 128:
2X2 QPSK, |S 5 |=32 codewords 10 0
Page 129 and 130:
S k d S k S k ′ d H S 1 (1, 1, 1,
Page 131 and 132:
Rate 6/2 2X2 8PSK, |S 7 |=128 vs |S
Page 133 and 134:
1 172 251 330 1 1 1 304 413 486 87
Page 135 and 136:
Rate 5/3, 3X3 QPSK, |S 7 |=128 Code
Page 137 and 138:
parameters: the number of trellis g
Page 139 and 140:
[DS87] D. Divsalar and M. K. Simon.
Page 141 and 142:
[SHHS01] [Sle68] A. Shokrollahi, B.
Page 143 and 144:
ù"ú"ú"û ù"ü"ù ù"ý0øJþ ÿ
Page 145 and 146:
©¤¥¢©©©©¤©¤©©¤©¤©
Page 147 and 148:
J;KL4MNL=L;L0K=O;P=Q;ORO=Q;O=Q;Q;MN
Page 149 and 150:
0 1 14 1 7 8 Figure B.2: 2 × 2 BPS
Page 151 and 152:
0 2 168 42 128 93 247 117 223 1 30
Page 153 and 154:
0 2 168 42 128 93 247 117 223 30 18
Page 155:
0 2 168 42 128 93 247 117 223 30 18
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