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
H

xn h s n + vn
h H  h0  hL , sTn  sn  sn L 
• Testing vectors g(n)
 s n  sn  M 
S(n)g(n)   
 g(n)  0
sn L  snM  L 
Basic Idea of CIVA: Noiseless Symbol Detection
• Find a testing vector gi for each possible
symbol matrix Si
L 1


G

g
i

1
,

,
N

K
• Testing vector set:
i,
g
• Determine testing vector sequence g(n) 
s
min
g ( n)G
 x H (n) g(n)
2
0
n
• Detect symbols s(n)  from g(n) 
Construct Probe as Testing Vector Group
• Requirement on testing vectors not always satisfied
• Probe of Si : three cases
– Si right null subspace different from S j
S i g i  0,
S j g i  0 : Probe G i   g i 
– Si right null subspace in that of S j
Si gi  0,
Si g j  0,
S j gi  0 
 G i  gi , g j
S jg j  0 


– Si and S j have the same right null
subspace, G i  G j
Blind Sequence Detection by Probes
• If Si and S j are different in the right null subspace,
then the corresponding probes are different
• Blind symbol detections:
x H (n)  h H S(n)  G(n)  S(n)  sn
Gi
Gi
• Do the probes sharing cases matter?
Sequence Identifiability
• Assumption 1: sequences begin or terminate with the
same symbol matrix.
• Assumption 2: If Si g j  0, then h H Si g j  0.
• Proposition 1: Sequences Si and G i  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.
Trellis Search With Probes
• Metric calculation
f (x(n), Gi )  max f1(x(n), gl )
gl Gi
2

H
x ( n )g l ,
if Si g l  0

f1 (x(n), g l )  
2
2
H
  v /( x (n)g l +  v2 ), if Si g l  0

• Trellis optimization
arg min  f (x(n), G(n))
G (n)  n
Trellis Search with Probes
• Metric updating along trellis
 j (n)  min  i (n  1) + f (x(n), G l ) 
i
• An example:
K 2
Ls  4
Channel length Over-estimation in Noise
• For known channel length, Probe & trellis dim parameters:
M : known. L : channel length. Constraint length Ls  L + M + 1
• Use over-estimated channel length Lo and Ls  Lo + M + 1
for probe and trellis design
• Consider data matrix
 xn
X(n)   
 xn N
 sn
xnM 
 sn  M 



   H 
  + V ( n)
s
 xn N M 
 sn L~ +1 
n

N

L
s



• Choose proper N so that
~ 
Ls  L + N + M + 1  Lo + M + 1
How to Determine Optimal N?
• In noiseless case,
if N + L  Lo , then min X(n)g i  0.
Otherwise min X(n)g i  0
• A large magnitude change in
min X(n)gi , when Nsmall  Nopt  Nbig
• Optimal value can be determined.
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 N
Trellis updating
Symbol determination
• Properties
• No channel and correlation estimation
• Fast, finite sample, global convergence
– Symbol detection within 5 Ls samples
– Tolerate faster time-variation index Ls
Computational Complexity
• High computation complexity: trellis states
K Ls 1  K Lo +M in CIVA, compared with K Lo in MLSE
• 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
Simulations: Experiment 1
 1
 0 ,
 
 1 
0
 1,
 
 1 
1
1,
 
0
1
0,
 
1
0
 1,
 
 1
 1
0
 
 1 
0
10
-1
10
BER
• Channel [1, 0.8]. Ls  4. DBPSK.
• Symbol matrix, probe
S1
g1
S2
g2, g4, g1
s3
g3,g6, g4
s4
g4, g5, g3
• Testing vectors
-2
10
Scheme 1
Scheme 2
Scheme 3
-3
10
-4
10
5
10
SNR (dB)
15
Simulations: Experiment 2
5
• Random Channel
Optimal N
Lo  4
3
Ratio r
L  0,1, 2
4
Ls  8
2
N(opt)-1
1
• Index Ratio
rN 
0
-2
-1
 n min i X( N +1) (n)g i
 n min i X
(N )
1
2
Index for Determine N
8
( n )g i
r(N=Nopt)
r(N>Nopt)
r(N<Nopt)
7
6
5
Ratio r
• Determine N
independent of
channel
0
Order Mismatch
4
3
2
1
0
6
8
10
12
SNR (dB)
14
16
Simulations: Experiment 2
• Comparison
CIVA
MLSE
VA w/ training
MMSE training
Blind:VA+blind
channel. est.
• 500 samples
• CIVA: 3 dB
from MLSE
Blind+VA
-1
10
BER
–
–
–
–
–
0
10
MMSE
-2
10
CIVA
VA
-3
10
MLSE
-4
10
6
8
10
12
SNR (dB)
14
16
Simulations: Experiment 3
-1
10
BER
• GSM like packets
• 3-tap random ch.
• 150 DQPSK
samples/running
• CIVA: blind
• VA & MMSE: 30
training samples
• CIVA practically
outperforms
training methods.
0
10
CIVA
VA
MMSE
-2
10
-3
10
5
6
7
8
9
10
11
SNR (dB)
12
13
14
15
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