feedback reliability calculation for an iterative block decision feedback equalizer (ib-dfe) gillian...
TRANSCRIPT
Feedback Reliability Calculation for
an Iterative Block Decision
Feedback Equalizer (IB-DFE)
Gillian Huang, Andrew Nix and Simon Armour
Centre for Communications Research
Outline
• Introduction to linear equalizer (LE), hybrid decision
feedback equalizer (H-DFE) and iterative block
decision feedback equalizer (IB-DFE)
• Feedback Reliability (FBR) Calculation Techniques
• Performance comparison of IB-DFE with the
proposed feedback reliability calculation and the
training sequence (TS) method
• Conclusions
SC-FDE with Linear Equalizer (LE)
• Single-carrier (SC) systems have low PAPR at the TX.
• MMSE-FDE is equivalent to LE. The LE filtered noise results in a large performance gap to the matched filter bound (MFB).
• DFE can be used to reduce the filtered noise by cancelling the ISI in the FB process.
Encoder+MOD
InsertCP
DEMOD,Decoder
RemoveCP
Channel
TX
M-pointFFT
N-pointIFFT
MMSEFDE
RX
Informationbits
Decodedbits
Note: frequency-selective channel does not introduce ISI to OFDM systems since the baseband symbols are directly mapped onto the subcarriers in the FD.
Hybrid Decision Feedback Equalizer (H-DFE)
S/P
DFT
DEMAP
IDFT
P/S
TD-FBfilter
nr mx̂
0LE,G
1,LE MG
0,FFG
1,FF MG
…...
……
……
……
……
…...
…...
…...
mx~
kY
IDFT
P/S
…... C P
FD-FFfilter
MMSE-LEMMSE-LE is used to
obtain initial FB symbols
TD-FB:symbol-by-symbol process
FD-FF: block process
• While the TD-FB filter aims to cancel all the postcursor-ISI, FD-FF filter minimizes the sum of the precursor-ISI and FF filtered noise. Since the FF filtered noise is smaller than the LE filtered noise, better performance can be achieved with H-DFE.
• However, the H-DFE is liable to error propagation, especially in the coded systems. This is because the hard-limited equalized symbols can be very unreliable before decoding.
Iterative Block Decision Feedback Equalizer (IB-DFE)
• All the detected symbols from the previous iteration are used as the FB symbols. Hence both precursor and postcursor ISI can be cancelled.
• The operation of IB-DFE is optimized at each iteration according to the reliability of the FB symbols. Hence IB-DFE is robust against error propagation.
• Both FF and FB filters are implemented in the FD efficiently.
S/P
DFT
nr ……
……
……
……
0R0r
1Pr 1PR
)(0lC
)(1lPC
……
……
IDFT
P/S
)(0lu)(
0lU
)(1lPU
DFT
S/P
)(
1l
Iterationdelay
)(~ lnx
nΟ(First iteration)
……
……
……
……
……
……
)1(0ˆ lX
)1(0ˆ
lx
)1(1ˆlPx
)(1
lPu
)1(1
ˆ lPX
)(0lB
)(1lPB
)(0lY
)(1lPY
……
……
……
……
……
……
)1(ˆ lnx
FD-FF Filter
FD-FB Filter
FD-ISIcancellation
Iterative Block DFE (cont.)
22)1(2
*)(
1 pl
s
plp
HpE
HC
)()()1()( lp
lp
llp HCpB
• At the first iteration, p=0. The FF filter coincides with MMSE-LE. The FB filter is turned off.
• When p=1, the FF filter coincides with the matched filter. The FB filter aims to cancel all the ISI.
• As the FBR increases, the FB filter tends to cancel more and more ISI.
• How do we calculate the FBR?
s
nlnl
E
xxEp
*)1()1( ˆ
FF filter:
FB filter:
FB reliability is defined as:
Feedback Reliability (FBR) Calculation
• One solution is the training sequence (TS) method. However, this lowers the bandwidth efficiency. Since the TS must have the same modulation and coding scheme as the data sequence, it cannot be shared with the existing reference signals.
• We propose to calculate the FBR from the SNR at the equalizer output. The SNR at the equalizer output can be estimated as
1
0
2)1()1(
)1(
ˆ~1SNR
P
n
ln
ln
sl
xxP
E
Feedback Reliability Calculation – 4QAM
k=2
k=1
k=3
j12
1 j 12
1
j 12
1 jx 12
1
s
nln
s
nlnl
E
xeE
E
xxEp
*)1(*)1()1( ˆ
1ˆ
)1(ˆ lne
• We can use the probability integration method to derive the expression of as a function of SNR.
• Hence the FBR for 4QAM can be calculated as
• The FBR:
(where is the hard-decision error)
*)1(ˆ nln xeE
sQp 21
Feedback Reliability Calculation – 16QAM
i
baerfp ii 2
1
2
1ˆ
0750.0ˆ a
• The linear regression method is used to obtain the best-fit reliability curve. For 16QAM, and .
• We propose to use a Gaussian CDF model to approximate the reliability curve for 16QAM, i.e.
• where is the SNR value in dB. The parameters a and b can adjust the Gaussian CDF curve.
4098.0ˆb
-30 -20 -10 0 10 20 30-2
-1
0
1
2
3
z
Simulation
Regression line
Regression range
-30 -20 -10 0 10 20 300
0.2
0.4
0.6
0.8
1
SNR (dB)
Re
liab
ility
Simulated reliability
Approximation
• The derivation of the FBR for 16QAM is very tedious.
Feedback Reliability Calculation – Channel Coding Case
• When operating the IB-DFE with channel coding, it is recommended to decode the equalized symbols and use the re-encoded symbols to form the FB symbols with higher reliability.
• There is no explicit method to derive the reliability of the re-encoded FB symbols.
• We propose to use a pre-define lookup table for FBR mapping in the channel coding case.
-30 -20 -10 0 100
0.2
0.4
0.6
0.8
1
SNR (dB)
Rel
iabi
lity
4QAM
16QAM
Simulation Parameters
• SC-FDE with 512 subcarriers is used.• The urban macro scenario of the Spatial Channel
Model Extended (SCME) is used.• The subframe structure in the LTE uplink is adopted to
calculate the bandwidth efficiency. Each subframe has six data blocks and one pilot blocks. The bandwidth efficiency for the proposed FBR calculation is 6/7.
• Assuming one data block is used as the TS in the TS method, the bandwidth efficiencies for the TS method is 5/7.
Simulation Results – 4QAM
• Large performance gap between LE and MFB.
• The proposed FBR gives similar BER performance as the TS method.
• The second iteration gives a large gain over the first iteration (since the filtered noise is significantly reduced).
• The second iteration gives similar performance as the H-DFE. However, IB-DFE (2) gives a lower complexity due to the efficient FD-FB filter.
Simulation Results – 16QAM
• Similar results as the 4QAM case.
• The FBR calculation method outperforms the TS method in the 16QAM. This is because 16QAM symbols do not have uniform reliability. The TS composed of random 16QAM symbols can result in more FBR mismatch, while the proposed Gaussian CDF model is based on the average FBR.
Simulation Results – 16QAM with Channel Coding
• The proposed FBR method has similar BLER performance as the TS method.
• The second iteration gives a 2.5dB gain over the first iteration (i.e. LE). The fourth iteration performs within 1dB to the MFB.
• The H-DFE gives worse performance than the LE due to error propagation.
• Higher throughput is achieved with the proposed FBR method due to better bandwidth efficiency.
Conclusions
• For broadband single-carrier systems, LE gives a large
performance gain to the MFB due to large LE filtered noise.
DFE can be used to improve the equalization performance.
• While the H-DFE is liable to error propagation (especially in
the channel coding case), the IB-DFE is robust against error
propagation. Moreover, the IB-DFE provides a low complexity
iteration solution due to the efficient FD-FB filters.
• The proposed FBR method shows a similar or better error rate
performance as the TS method without lowering the bandwidth
efficiency.
Centre for Communications Research
Thank You
Gillian Huang, Andrew Nix and Simon Armour