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