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

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Based on the design criteria, which is related to spreading code correlation, this work further attempts to optimize codes based on coding gain. The found codes, deemed Optimal Minimum Metric (OMM) code, provide solid gains over known codes which have more structure, like orthogonal codes [TJC99, Ala98] and unitary group codes [SHHS01], in flat/multipath fading channels and single-user/multiuser systems. The structure of optimized codes leads to the construction of Nonlinear Hierarchical Codes (NHC) [GM03b], which is the focus of Chapter 4. The effect of the multipath fading channel on code performance is evaluated. Stronger statement than those in [TNSC99] are made regarding diversity gain and coding gain. Chapter 2 only considers the optimal Maximum Likelihood (ML) decoder. When the numbers of active users and space-time block codes (STBC) are large, the ML decoder is impractical due to large decoding complexity. In Chapter 3, we consider several different suboptimal linear decoders for STBC. The suboptimal decoders considered are structurally similar to those of [NSTC98], which employ a two stage decoding algorithm. In the first stage, a linear equalizers suppresses MAI and spatial inter-symbol interference. Subsequently, a mapper is implemented to map the linear filter soft outputs to a valid STBC(see Figure 3.2). The asymptotic achievable diversity level is evaluated for each linear decoders when the number of receive antennae grows. The Fisher Information Matrix for random code vector is also considered to reveal the favorable code structure for Linear Minimum Mean Squared Error (LMMSE) estimator. The performance criteria for a space-time system, diversity gain and coding gain, demand a significantly different code design strategy than that for Gaussian channels, because the code space defined by the coding gain is a non-linear, non-metric space. The space (transmit antenna) dimension also introduces more degrees of freedom in the code space than using the time dimension only. In Chapter 2, exhaustive computer searches are used to seek the optimal STBC code set for certain STBCs with small size and low rate, but the search is NP-hard and quickly becomes infeasible when the block code size grows large and code rate is high. The computer optimized codes exhibit very nice layered structure which motivates the construction of NHC in Chapter 4. The construction of NHC is fundamentally different from that of constrained designs (unitary, orthogonal) by manipulating the relationship between codewords rather than properties of the individual codewords. Two questions are to be addressed in Chapters 4 and 3
5, respectively: first, for an arbitrary size STBC from an nPSK constellation, how do we find the optimal (or near optimal) code set of various rates resulting in a distance spectrum with good structure? Secondly, for such found codes, how do we introduce memory among blocks to systematically utilize the structure of the distance spectrum? Distance spectrum is the enumeration of the distance measure of interest between all possible codeword pairs. The methodology of NHC construction via isometries for MIMO quasi-static fading channels is an extension of Slepian’s group codes [Sle68], where group structure (and hence distance uniformity), is conserved in most cases. A sufficient condition for NHCs to achieve geometric uniformity [GDF91] is established. The NHC construction starts from some initial codeword matrices with no constraint on the size and structure, and by means of isometries, systematically builds higher rate codes from lower rate codes, while preserving the good structure of the lower rate code. It is the relationship between codewords, rather than the structure of each individual codeword, that is exploited to optimize coding gain. The found NHCs match those found via exhaustive computer search, and exhibit not only optimized coding gain at each layer, but also great symmetry and structure to be exploited in Chapter 5 of this work. STBCs are usually insufficient to provide the needed protection from the effects of a fading channel, therefore memory is needed. Space-time trellis codes (STTC) [TSC98, BBH02, YB02, Gri99] usually rely on a convolutional encoder to introduce memory among symbols, but there are no good design rules to optimize coding gain rather than exhaustive computer search. Multiple Trellis Coded Modulation (MTCM) [BDMS91, DS87, SF02, JS02] serves as an ideal bridge to combine the advantages of both block codes and trellis codes, and offers simple and intuitive design rules to optimize coding gain systematically. The MTCM designs in [SF02, ATP98] use STBCs as an inner code of a convolutional encoder. However, such serial concatenation usually cannot take full advantage of the structure in STBCs, and therefore introduces memory among blocks “blindly”. Chapter 5 of this work proposes systematic MTCM designs where memory is introduced between block codes directly, instead of through an outer convolutional encoder. Because of the symmetric structure in the trellis and constituent NHCs, such designs are dubbed RMTCM designs. 4
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 and 10: 3.4 The BLUE and LS estimators have
Page 11 and 12: Abstract Space-time codes are effec
Page 13: spreading. The focus of [HMP01] is
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
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Now we evaluate the overall decoder
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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
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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
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signal corresponding to N c symbol
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1. full diversity ∆ H (D i − D
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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
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★ ✥ S k ✧ a U j , P j ✲ b
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3. Given Isometries U k U j and P j
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[ 2 ] [ 168 ] [ 42 ] [ 128 ] 1 1
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which are very likely to be optimal
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4X3 BPSK(8 Codewords) and QPSK(64 C
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Chapter 5 Regular Multiple Trellis
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The high rate performance is poor,
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ehavior of a regular trellis are: t
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All the NHCs found in this work sat
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Whenever there exist parallel trans
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M m g=1 g=2 g=4 g=8 next jump b=2 2
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provides a lower bound on the numbe
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Label S k S Comment Figure 1/2 I2S2
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Label S k O(= gbp) S(= gb) Figure 1
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2X2 QPSK, |S 5 |=32 codewords 10 0
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S k d S k S k ′ d H S 1 (1, 1, 1,
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Rate 6/2 2X2 8PSK, |S 7 |=128 vs |S
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1 172 251 330 1 1 1 304 413 486 87
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Rate 5/3, 3X3 QPSK, |S 7 |=128 Code
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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
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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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