Xiaohua(Edward) Li State Univ. of New York at Binghamton xli@binghamton
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Channel Independent Viterbi Algorithm (CIVA) for Blind Sequence Detection with Near MLSE Performance
Xiaohua(Edward) Li State Univ. of New York at Binghamton
xli@binghamton.edu
Contents
• Introduction• Basic idea of Probes and CIVA• Practical Algorithms
– Probes design– CIVA
• Simulations• Conclusion
Analogy From DNA Array
• Probes: all possible DNA segments• Probes are put on an array (chip)• DNA sample binds to a unique probe
Basic Idea of CIVA: Testing Vector
• Communication System Model
• Testing vectors
LnnTnL
H sshh sh ,0
nvnH
nx sh
0ggS
)()()( nss
ssnn
LMnLn
Mnn
)(ng
Basic Idea of CIVA: Noiseless Symbol Detection
• Find a testing vector for each possible symbol matrix
• Testing vector set: • Determine testing vector sequence
• Detect symbols from
iSig
1,,1 sLgi, KNiG g
0)()( 2
)(min
nnH
nGngx
g
)(ng
)(ng )(ns
Construct Probe as Testing Vector Group
• Requirement on testing vectors not always satisfied• Probe of : three cases
– right null subspace different from
– right null subspace in that of
– and have the same right null subspace,
iS jS iiijii gGgS0gS Probe:0,
iS
iS jS
jiijjji
ijii ggGgS0gSgS0gS
,0,0,
iS jSji GG
Blind Sequence Detection by Probes
• If are different in the right null subspace, then the corresponding probes are different
• Blind symbol detections:
• Do the probes sharing cases matter?
ji SS and
nHH snnnn
ii
)()()()( SGShxGG
Sequence Identifiability
• Assumption 1: sequences begin or terminate with the same symbol matrix.
• Assumption 2: • Proposition 1: Sequences can be
determined uniquely from each other.• Proposition 2: In noiseless case, symbols can be
determined uniquely from data sequence and probes.• If SNR is sufficiently high, then symbols can be
determined uniquely with probability approaching one.• Assumptions 1 and 2 can be relaxed in practice.
.0 then ,0 If jiH
ji gShgS ii GS and
Trellis Search With Probes
• Metric calculation
• Trellis optimization
)),((max)),(( 1 li nfnfil
gxGxGg
0 if),)(/(
0 if,)()),((
222
2
1
livlH
v
lilH
ln
nnf
gSgx
gSgxgx
))(),((min arg
(n)nnf
nGx
G
Trellis Search with Probes
• Metric updating along trellis
• An example:
)),(()1(min)( lii
j nfnn Gx
42
sLK
Channel length Over-estimation in Noise
• For known channel length, Probe & trellis dim parameters:
• Use over-estimated channel length and for probe and trellis design• Consider data matrix
• Choose proper
1length Constraint length. channel: known.: MLLLM s
oL 1 MLL os
)()(
1~
nss
ss
xx
xxn
sLnLNn
Mnn
MNnNn
Mnn
VX
H
11~ thatso
MLMNLLN os
How to Determine Optimal N?
• In noiseless case,
• A large magnitude change in
• Optimal value can be determined.
0)(min Otherwise
.0)(min then , if
i
io
n
nLLN
gX
gX
bigoptsmalli NNNn when ,)(min gX
Practical Algorithm I
• Probe Design Algorithm• Many symbol matrices have more than one dim
right null subspace: optimize testing vectors• Select/combine testing vectors based on the trellis
diagram: simplify probes design• Further simplification: each probe contains at most
three testing vectors.
• It is off-line! Probes are independent of channels.
Practical Algorithm II
• CIVA Algorithm• Probes design with over-estimated channel length• Form data matrix, determine the optimal • Trellis updating• Symbol determination
• Properties• No channel and correlation estimation• Fast, finite sample, global convergence
– Symbol detection within samples– Tolerate faster time-variation index
N
sL5
sL
Computational Complexity
• High computation complexity: trellis states
• May be practical for some wireless system• Complexity reduction: desirable and possible
– Parallel hardware implementation– Apply the complexity reduction techniques of VA– Integrated with channel decoder: promising complexity
reduction, may even lower than MLSE.– Fast algorithms combining the repeated/redundant
computations
MLSEin with compared CIVA,in 1 oos LMLL KKK
Simulations: Experiment 1
• Channel• Symbol matrix, probe
• Testing vectors
DBPSK. .4 0.8]. [1, sL
S1 g1S2 g2, g4, g1s3 g3,g6, g4s4 g4, g5, g3
101
,11
0,
101
,011
,11
0,
101
5 10 1510
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
Scheme 1Scheme 2Scheme 3
Simulations: Experiment 2
• Random Channel
• Index Ratio
• Determine N independent of channel
Microsoft Equation 3.0
84
2,1,0
s
o
LLL
iN
in
iN
inN n
nr
gX
gX
)(min
)(min)(
)1(
6 8 10 12 14 160
1
2
3
4
5
6
7
8Index for Determine N
Rat
io r
SNR (dB)
r(N=Nopt)r(N>Nopt)r(N<Nopt)
-2 -1 0 1 20
1
2
3
4
5
Order Mismatch
Rat
io r
Optimal N
N(opt)-1
Simulations: Experiment 2
• Comparison– CIVA– MLSE– VA w/ training– MMSE training– Blind:VA+blind
channel. est.• 500 samples• CIVA: 3 dB
from MLSE6 8 10 12 14 16
10-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
MLSE
VA CIVA
MMSE
Blind+VA
Simulations: Experiment 3
• GSM like packets• 3-tap random ch.• 150 DQPSK
samples/running• CIVA: blind• VA & MMSE: 30
training samples• CIVA practically
outperforms training methods. 5 6 7 8 9 10 11 12 13 14 15
10-3
10-2
10-1
100
SNR (dB)
BE
R
CIVAVAMMSE
Conclusions
• CIVA blind sequence detector using probes
• Properties• Near ML optimal performance• May practically outperform even training methods• Fast global convergence
• Near future: complexity reductions• Combining channel decoders• Fast algorithm utilizing repeated structures
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