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

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B.2 2 × 2 BPSK, Rate 1/2, I2S2O4p1. . . . . . . . . . . . . . . . . . . . . . . 138 B.3 2 × 2 BPSK, Rate 1/2, I2S2O4P 1. . . . . . . . . . . . . . . . . . . . . . . 138 B.4 2 × 2 BPSK, Rate 2/2, 2 × 2 × 2. . . . . . . . . . . . . . . . . . . . . . . . 138 B.5 2 × 2 BPSK, Rate 2/2, 2 × 4 × 1. . . . . . . . . . . . . . . . . . . . . . . . 138 B.6 2 × 2 QPSK, Rate 1/2, 8 × 2 × 1. . . . . . . . . . . . . . . . . . . . . . . . 138 B.7 2 × 2 QPSK, Rate 2/2, 4 × 2 × 2. . . . . . . . . . . . . . . . . . . . . . . . 139 B.8 2 × 2 QPSK, Rate 2/2, 4 × 4 × 1. . . . . . . . . . . . . . . . . . . . . . . . 139 B.9 2 × 2 QPSK, Rate 3/2, 2 × 2 × 4. . . . . . . . . . . . . . . . . . . . . . . . 139 B.10 2 × 2 QPSK, Rate 3/2, 2 × 4 × 2. . . . . . . . . . . . . . . . . . . . . . . . 140 B.11 2 × 2 QPSK, Rate 3/2, 2 × 8 × 1. . . . . . . . . . . . . . . . . . . . . . . . 140 B.12 2 × 2 QPSK, Rate 4/2, |S 5 | = 32, 2 × 2 × 8. . . . . . . . . . . . . . . . . . 140 B.13 2 × 2 QPSK, Rate 4/2, |S 5 | = 32, 2 × 4 × 4. . . . . . . . . . . . . . . . . . 140 B.14 2 × 2 QPSK, Rate 4/2, |S 5 | = 32, 2 × 8 × 2. . . . . . . . . . . . . . . . . . 141 B.15 2 × 2 QPSK, Rate 4/2, |S 5 | = 32, 2 × 16 × 1. . . . . . . . . . . . . . . . . 141 B.16 2 × 2 QPSK, Rate 4/2, |S 6 | = 64, 4 × 2 × 8. . . . . . . . . . . . . . . . . . 142 B.17 2 × 2 QPSK, Rate 4/2, |S 6 | = 64, 4 × 4 × 4. . . . . . . . . . . . . . . . . . 142 B.18 2 × 2 QPSK, Rate 4/2, |S 6 | = 64, 4 × 8 × 2. . . . . . . . . . . . . . . . . . 143 B.19 2 × 2 QPSK, Rate 4/2, |S 6 | = 64, 2 × 16 × 1. . . . . . . . . . . . . . . . . 144 ix
Abstract Space-time codes are effective means by which to combat fading by exploiting diversity in both spatial and temporal dimensions. In this work, code performance and design are considered in the context of Direct-Sequence Code-Division Multiple-Access (DS- CDMA) systems. The performance criteria, diversity gain and coding gain, are redefined as functions of the spreading code correlation. Uplink and downlink scenarios are both analyzed in multipath fading channels. Optimal codes are searched for both spread and non-spread systems. To reduce the decoding complexity, suboptimal linear decoders are classified and analyzed. The asymptotic achievable diversity level is derived when the number of receive antennae is large. Motivated by the structures found in computer optimized codes, via distance preserving isometries, Space-Time Block Codes (STBCs) are constructed bottom-up by optimizing the coding gain layer-by-layer and reusing the optimized structure. STBCs constructed in this way are dubbed Nonlinear Hierarchical Codes (NHCs). NHCs are essentially a generalization of Slepian’s group codes for the Gaussian channel to the multiple-input multiple-output quasi-static fading channel. NHCs consistently offer comparable or significantly better performance than constrained designs (orthogonal or unitary). Systematic Regular MTCM (RMTCM) design procedures are proposed to exploit the layered structure of NHCs which leads to optimized designs for various rates/block sizes/constellation sizes. The match between the distance spectrum of NHCs to the regular trellis structure optimizes coding gain directly, and full diversity is naturally maintained given the full rank of the constituent NHCs. Several factors which affect performance in both quasi-static and fast block fading channels are analyzed and exploited to improve the overall performance. Set expansion is used to improve high rate RMTCM designs. RMTCM offers the best tradeoff between performance and complexity among STTC and (interleaved) serial concatenated system. x
Page 1 and 2: COMMUNICATION SCIENCES INSTITUTE
Page 3 and 4: Dedication This dissertation is ded
Page 5 and 6: Contents Dedication Acknowledgement
Page 7 and 8: List Of Tables 2.1 The distance spe
Page 9: 3.4 The BLUE and LS estimators have
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
Page 111 and 112:
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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