Transcript Document
Turbo-NFSK: Iterative Estimation,
Noncoherent Demodulation,
and Decoding for Fast Fading
Channels
Shi Cheng and Matthew C. Valenti
West Virginia University
Don Torrieri
U.S. Army Research Laboratory
This work sponsored by the Xenotran Corporation, Glen Burnie, MD
10/19/2005
1
Outline
Iterative M-ary NFSK demodulation and decoding
ML estimator using EM algorithm
Performance of iterative estimation, NFSK
demodulation and decoding
Methods to reduce the complexity of the estimator
Conclusions
10/19/2005
2
BICM-ID: Bit Interleaved Coded
Modulation with Iterative Decoding
uk
uˆk
Binary
Encoder
Soft-In
Binary
Decoder
bk'
zk'
vk'
Soft-Output Estimates
of Coded Bits
Bitwise
Interleaver
Bitwise
Deinterleaver
Bitwise
Interleaver
bk
zk
vk
Binary
to M-ary
mapping
sm
M-arymodulator
Complex flat-fading
c(t )
AWGN
n(t )
LLR
Bit Metric
Calculation
y
Receiver
front
end
s (t )
y(t )
Noncoherent M-FSK
Using A Priori Probabilities
Bit LLRs are calculated based on the channel
observation and the extrinsic information feedback
from the decoder
p( y | s ) p(s
i
zk ln
i
| bk 1)
i
| bk 0)
iS k(1)
p( y | s ) p(s
i
iS k( 0 )
m
m
2
a
E
y
2
a
E
y
S
i
S
i
i
i
ln I
max*ln I
max*
b
v
b
v
0
j
j
0
j
j
j 1
j 1
iS k( 0 )
iS k(1)
N
N
0
0
j k
j k
Where
max*( x, y) max(x, y) ln1 exp{ | x y |}
10/19/2005
4
BICM ID and CM Capacity
11
10
Minimum Eb/No (in dB)
9
M=2
M=4
M=16
M=64
BICM ID Performance using
CDMA2000 length 6138 codeword
20 iterations, BER = 10-4
Reference:
M.C.Valenti and S. Cheng, “Iterative
demodulation and decoding of turbo
coded M-ary noncoherent
orthogonal modulation”
8
7
IEEE Journal on Selected Areas in
Communications, Sept. 2005.
BICM
6
BICM ID
5
4
3
2
1
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Code
Code Rate
Rate RR
0.45
0.5
0.55
0.6
Block Fading Channel
Fading coefficient is fixed within one block.
Independent fading from block to block
1
2
0
4
3
192
...
8
767
N=4
1
0
2
96
...
8
767
N=8
CDMA 2000 turbo codeword rate ½ length 1530 with 16-NFSK
10/19/2005
6
Estimation of One Block
Channel state information is needed to calculate bit
LLRs
2a ES yi
ln I 0
N
0
Perform estimation of A and B independently block
by block, where A N0 , B 2a ES
uˆk
y
Soft-In
Binary
Decoder
'
k
z
vk'
10/19/2005
Bitwise
Deinterleaver
Bitwise
Interleaver
zk
vk
LLR
Bit Metric
Calculation
Ai ,Bi
Channel
Estimator
7
Channel Estimator with Known
Transmitted Sequence
Form the log-likelihood function based on the known
sequence d =[d0,d1,…,dN-1] of S [sd , sd ,...,sd ]
0
N 1
1
L ln f (Y | A, B, d )
Solving A and B to maximize L
N 1
4MNBˆ yd i
2
i
Bˆ ydii F
4C NBˆ 2
N i 0
ˆ2
1
N
B
C
Aˆ
MN
4
N 1 M 1
Where C yki
i 0 k 0
10/19/2005
2
I1 ( x)
F ( x)
I 0 ( x)
8
ML Estimator with A Priori
Information of the Sequence
The sequence d is never known.
Form log-likelihood function based on the a
priori information of d
M 1
L ln f ( yi | A, B, di k ) p(di k
i 0
k 0
N 1
Too complex to find the solution to maximize
this function. We resort to EM algorithm.
10/19/2005
9
ML Estimator using EM Algorithm
ˆ (0) , Bˆ (0)
0. Select A
Normalization factor
(l )
(l )
~
1. pki p d i k | yi , Aˆ , Bˆ
Bˆ (l ) yki
i I0
Aˆ (l )
pd i k
Outer
Iteration
2. Bˆ (l 1)
4MNBˆ (l 1) yki
2 N 1 M 1 ~
pki yki F
2
4C N Bˆ (l 1)
N i 0 k 0
Inner
Iteration
1
N ˆ (l 1) 2
( l 1)
ˆ
3. A MN C 4 B
10/19/2005
10
BER of 16-ary NFSK in Rayleigh Fading
Channel with Different Block Size
0
10
N=32
N=16
N=8
N=4
N=1
CDMA2000 Turbo Code,
Rate ½, Length 1530
-1
10
Independent Block Fading
Iteration #20
-2
BER
10
-3
10
Estimator
-4
10
Perfect CSI
5
5.5
6
6.5
7
7.5
8
Eb/No (dB)
8.5
9
9.5
10
BER of NFSK in Rayleigh Fading
Channel with Different Alphabet Size
0
10
CDMA2000 Turbo Code, Rate ½,
Length 1530 Data Rate = 24bits/ block
Iteration #20
-1
10
M=2
M=4
M=16
M=64
Estimator
-2
BER
10
Perfect CSI
-3
10
-4
10
4
5
6
7
8
9
Eb/No (dB)
10
11
12
BER of 16-ary NFSK in Rician Fading
Channel (K=10dB)
0
10
N=16
N=8
N=4
N=1
-1
10
Estimator
-2
BER
10
Perfect CSI
-3
10
CDMA2000 Turbo Code,
Rate ½, Length 1530
-4
10
Independent Block Fading
Iteration #20
3
3.2
3.4
3.6
3.8
Eb/No (dB)
4
4.2
4.4
4.6
Methods to Reduce the
Complexity of the Estimator
ˆ (0) , Bˆ (0)
0. Select A
ˆ (l ) y
B
ki
~
1. pki i I 0 ˆ (l )
A
Outer
Iteration
Making hard decision
pd i k
Normalization factor
2. Bˆ (l 1)
4MNBˆ (l 1) yki
2 N 1 M 1 ~
pki yki F
2
4C N Bˆ (l 1)
N i 0 k 0
1
N ˆ (l 1) 2
( l 1)
ˆ
3. A MN C 4 B
10/19/2005
Inner
Iteration
Linear approximation of F
14
Methods to Reduce the
Complexity of the Estimator
ˆ (0) , Bˆ (0)
0. Select A
Making hard decision
(l )
ˆ
B
yki
1 k arg maxln I 0
Aˆ (l )
k
1. ~pki
otherwise
0
log2 M 1k
b j v j
j 0
Outer
Iteration
2. Bˆ (l 1)
4MNBˆ (l 1) yki
2 N 1 M 1 ~
pki yki F
2
4C N Bˆ (l 1)
N i 0 k 0
1
N ˆ (l 1) 2
( l 1)
ˆ
3. A MN C 4 B
10/19/2005
Linear approximation of F
15
Linear Approximation of F
1.5
Linear
Approximation
F(x)
1
0.5
0
0
1
2
3
4
5
x
6
7
8
9
10
Complexity of Different Estimators
CPU Cycles/BICMID iteration
3
x 10
7
EM estimator
2.5
2
16-ary NFSK, CDMA2000
turbo codeword with rate
½ and length 1530.
Decoder
N=4 symbols per block
independent Rayleigh
fading
1.5
Hard Linear EM
Demodulator
1
Linear EM
0.5
0
5.6
5.8
6
6.2
Eb/No (dB)
6.4
6.6
6.8
7
BER Performance of Low
Complexity Estimators
0
10
Perfect
EM
linear EM
hard linear EM
16-ary NFSK, CDMA2000 turbo codeword with
rate ½ and length 1530. N=4 symbols per block,
independent Rayleigh fading, iteration #20
-1
10
-2
BER
10
-3
10
-4
10
5
5.2
5.4
5.6
5.8
6
6.2
Eb/No (dB)
6.4
6.6
6.8
7
Conclusions
Robust noncoherent channel estimator, dealing with severe channel
conditions.
The estimator works without needing to know the fading statistics
model. The only requirement is the coherence time of the fading
amplitude is larger than 4 symbols.
Although the estimator using the exact EM algorithm is complex, linear
approximation of F(x) = I1(x)/I0(x) and hard decision of ~pki can be used
to reduce the comlexity.
For 16-NFSK, when fading block size is larger than 4 symbols per block,
the system has acceptable BER performance.
When there are 4 symbols per block, the BER of the iterative estimation,
demodulation and decoding is about 0.6~0.8dB away from the one with
perfect CSI.
10/19/2005
19