fractionally spaced equalization and frequency diversity...
TRANSCRIPT
Fractionally Spaced Equalization and Frequency Diversity Methods
for Block Transmission with Cyclic Prefix
Yuki Yoshida, Kazunori Hayashi, Hideaki SakaiDepartment of System Science,
Graduate School of Informatics, Kyoto University
Outline
Background & Motivation
The System Configuration of the Proposed Fractionally Spaced Equalizer (FSE)
Derivation of the Equalizer Weights
Frequency Diversity Method using the FSE
Simulation Results
Summary
Background & Motivation
・Block Transmission with Cyclic Prefix (CP)OFDM (Orthogonal Frequency Division Multiplexing)
DTV, DAB, Wireless LAN
SC-CP (Single Carrier block transmission with CP)
DMT (Discrete Multitone) ADSL
・FDE (Frequency Domain Equalization)Simple Implementation using FFTRobustness to Frequency Selective Fading Channels
Existing FDEers work at symbol rate (SSE : Symbol Spaced Equalizer )
Background & Motivation (cont’d)
Fractionally Spaced Equalizer (FSE)based on oversampling the received signal
ex) 4 times oversampling → T/4 - FSE
Zero- Forcing (ZF) based T/2-FSE has been proposed by Vaidyanathan and Vrcelj, 2002
How can we adopt the FSE to FDE systems?
Extension of Vaidyanathan’s method to general oversampling factor cases (T/K-FSE) Derivation of ZF and minimum mean-square-error (MMSE) weights of the T/K-FSEA simple frequency diversity method using the T/K-FSE
Fractionally Spaced EqualizationSSE
FSE (Oversampling Factor K)
Channel SSENoise
Equalizer Output
Transmitted Signal
FSE
(Uniformly Sampled Version of Continuous quantity )
DecimatorExpander
(If m is multiple of K)(else)
SC-CP SchemeSystem Configuration of SC-CP Scheme (Single Carrier with CP)
S/P P/S
Txfilter
Rx filter S
/P
P/S
DFT
IDFTFD
E
Add CP
Remove CP
Fading
Additive Noise&
Frequency Domain Equalization
DFT IDFTChannel Matrix Equalizer Weights
Noise Block
Received Signal Block
Block Diagram of SC-CP Scheme
n-th Input Signal Block
(Circulant) Matrix Matrix Matrix
n-th Equalizer Output Block
SC-CP SchemeS
/P P/S
Txfilter
Rx filter S
/P
P/S
DFT
IDFTFD
E
Add CP
Remove CP
Frequency Domain Equalization
System Configuration of SC-CP Scheme (Single Carrier with CP)
DFT IDFTChannel Matrix Equalizer Weights
Noise Block
Received Signal Block
Block Diagram of SC-CP Scheme
Fading
Additive Noise&
(Circulant) Matrix Matrix Matrix
n-th Equalizer Output Blockn-th Input Signal Block
CP Length: (Channel Order)
M×M Circulant Matrix
:Channel Impulse Response, ( :Symbol Spacing )
SC-CP SchemeSystem Configuration of SC-CP Scheme (Single Carrier with CP)
S/P P/S
Txfilter
Rx filter S
/P
P/S
DFT
IDFTFD
E
Add CP Frequency Domain Equalization
Remove CP
DFT IDFTChannel Matrix Equalizer Weights
Noise Block
Received Signal Block
Block Diagram of SC-CP Scheme
Fading
Additive Noise&
n-th Input Signal Block
(Circulant) Matrix Matrix Matrix
n-th Equalizer Output Block
M×M DFT Matrix
(Unitary)
SC-CP SchemeSystem Configuration of SC-CP Scheme (Single Carrier with CP)
S/P P/S
Txfilter
Rx filter S
/P
P/S
DFT
IDFTFD
E
Add CP
Remove CP
Frequency Domain Equalization
DFT IDFTChannel Matrix Equalizer Weights
Noise Block
Received Signal Block
Block Diagram of SC-CP Scheme
Fading
Additive Noise&
n-th Input Signal Block
(Circulant) Matrix Matrix Matrix
n-th Equalizer Output Block
Diagonalized by DFT
DFT IDFTDiagonal
Efficiently Equalized
OFDM SchemeSystem Configuration of OFDM Scheme
(Orthogonal Frequency Division Multiplexing)
S/P P/S
Txfilter
Rx filter S
/P
P/S
DFT
FDE
Add CP
Remove CPID
FT
Fading
Additive Noise&
Frequency Domain Equalization
Block Diagram of OFDM Scheme
n-th Input Signal Block
Channel Matrix(Circulant)
Noise BlockReceived Signal Block
n-th Equalizer Output Block
DFTMatrix
Equalizer WeightsMatrixIDFT
Matrix
Fractionally Spaced EqualizationSSE
Equalizer Output
Transmitted Signal
SSEChannel Noise
FSE (Oversampling Factor K)FSE
DecimatorExpander
(If m is multiple of K)(else)
Configuration of the SC-CP Scheme with Proposed T/K-FSE
S/P P/S Tx
filterTransmitter:
Frequency Selective Fading
Additive Noise&
Add CP
Rx filter
S/P
S/P
KM
-poi
nt D
FT
Remove CP
One-tap FDE using KM-point DFT
Decimator
K times Oversampling
KM
-poi
nt ID
FT
Receiver:
Signal Modeling
Received Signal:
Equalizer Output:
DFT IDFTExpander DecimatorEqualizer Weights
Channel(Circulant)
(Diagonal)
Noise Received SignalEqualizer OutputInput Signal
Signal Modeling
Received Signal:
Equalizer Output:
DFT IDFTExpander DecimatorEqualizer Weights
Channel(Circulant)
(Diagonal)
Noise Received SignalEqualizer OutputInput Signal
KM×M Expander Matrix
denotes the M x KM Decimator Matrix
Signal Modeling
Received Signal:
Equalizer Output:
DFT IDFTExpander DecimatorEqualizer Weights
Channel(Circulant)
(Diagonal)
Noise Received SignalEqualizer OutputInput Signal
KM×KM Channel Matrix (Circulant)
: Channel Response including Tx and Rx filter:Symbol Period :Channel Order
Signal Modeling
Received Signal:
Equalizer Output:
DFT IDFTExpander DecimatorEqualizer Weights
Channel(Circulant)
(Diagonal)
Noise Received SignalEqualizer OutputInput Signal
Simplification of T/K-FSE
Equalizer Output:
Same as the (m, n) element of M-point DFT matrix
: M x M Identity Matrix)(
Simplification of T/K-FSE (cont’d)
Equalizer Output:
is M×M diagonal submatrix of (k=1, 2, ・・・, K)
Simplification of T/K-FSE (cont’d)Received Signal Equalizer Output
Block Diagram of the proposed T/K-FSE
M-point IDFT
KM-point DFT
DFT IDFT DecimatorEqualizer Weights
Input and Output relation
is M×M submatrix of (k=1, 2, ・・・, K)
ZF Weights of Proposed T/K-FSE
ZF Condition: s.t.
SSE (K=1) Uniquely determined
Channel nulls result in Noise enhancement
T/K-FSE (K>1)
Certain Degree of Freedom in the choice of Equalizer Weights
ZF Weights of Proposed T/K-FSE (cont’d)
Minimization of the noise power at the equalizer output
Noise component at the equalizer output:
Minimization Problem
min
s.t.
ZF Weights of Proposed T/K-FSE (cont’d)
Minimization Problem
min
s.t.
ZF Weights of Proposed T/K-FSE:
MMSE Weights of Proposed T/K-FSE Cost function ( Mean-Square-Error ):
MMSE Weights of Proposed T/K-FSE:
Optimum Linear MMSE T/K-FSE
Optimum Linear MMSE T/K-FSE:
Expander ChannelEqualizer(M X KM)
Optimum Linear MMSE Equalizer can’t be realized by the one-tap FDE because of the colored noise
Simulation Settings
Mod/Demod. Scheme QPSK / Coherent DetectionBlock Size M = 256
Length of CP 32Channel Model 10-path rayleigh fading channels with
an exponentially decaying power profile
Tx & Rx Filter square-root raised-cosine filter (roll-off factor α = 0.5)
Channel Estimation IdealChannel Noise AWGN
# of Iteration 10,000
Oversampling Rate K = 1, 2, 4 (i.e. SSE, T/2-FSE, T/4-FSE)
BER Performance of Proposed T/K-FSE
OFDM Scheme SC-CP Scheme
Performance of T/K-FSEPassband width and Performance Improvement via FSE
No energy on this band
Exploiting Band
Not exploited in SSE case
We can’t expect any performance Improvement in K >2
Frequency Diversity Method using Proposed T/K-FSE
S/P P/S Tx
filter
CP InsertionOriginal Spectrum
(P-1) CopiesP times Symbol Rate
Transmit Signal Spectrum
Band Width:
Rx filter S
/P
S/P
IDFT
CP RemovalM
M
KM
-poi
nt D
FT
M-pointK times Oversampling
Equalization and diversity combining are achieved simultaneously
BER Performance of the SC-CP via Proposed FDE/DC
0 5 10 15 20 25
10
10
10
10
10
-1
-2
-3
-4
-5
1
[dB]
BER
K=P=1
K=P=2K=P=4
ZFMMSE
Mod./ Demod. QPSK Block Size M = 256CP Length N=32
Channel:10-path rayleigh fading channels
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)
Channel Estimation: Ideal
(Energy per Bit over Noise Power Density)
BER Performance of the OFDM via Proposed FDE/DC
0 5 10 15 20 25
10
10
10
10
10
-1
-2
-3
-4
-5
1
[dB]
BER
Mod./ Demod. QPSK Block Size M = 256CP Length N=32
Channel:10-path rayleigh fading channels
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)
Channel Estimation: Ideal
ZF & MMSE
K=P=1
K=P=2
K=P=4
(Energy per Bit over Noise Power Density)
Applications of FDE/DC
Robust Communication with Poor Receiversex) Sensor Network, Traffic lights Network, Inter Vehicle Communication, etc
One Alternative Rate Reduction Technique for Adaptive Modulation Systems
ex) Wi-Fi
QPSK
Im
Re
Im
Re
BPSK
1 2 3 4 5 6 7 8
1 0 2 0 3 0 4 0 Expanded Version
Original Block
FDE/DC
Rate Reduction Technique via FDE/DCOFDM
DFTIDFTExpander DecimatorEqualizer Weights
Channel
DFTIDFT Equalizer Weights
Channel
Change the WeightsAdd Decimator
Reduce the RateAdd Expander
BER Performance of the SC-CP via FDE/DC for a given transmission rate
10
10
10
10
10
-1
-2
-3
-4
-5
1
BER
0 5 10 15 20 25[dB]
K=P=1 M=512 BPSK ZF
K=P=2 M=256 QPSK ZF
K=P=4 M=128 16QAM ZF
Mod./ Demod.BPSK, QPSK, 16QAM Block SizeM =128, 256, 512(FFT size = 512)CP Length N=32
Channel:10-path rayleigh fading channels
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)
Channel Estimation: Ideal
Pre- and Post- Equalization
DFT IDFTExpander DecimatorFDEChannel
Post-FDE/DC
Expander DecimatorChannel
(Frequency Domain Equalizer and Diversity Combiner)
FDEDFT IDFT
Pre-FDE/DC
Pre- and Post- Equalization
DFT IDFTExpander DecimatorFDEChannel
Post-FDE/DC
Expander DecimatorChannel
(Frequency Domain Equalizer and Diversity Combiner)
FDEDFT IDFT
Pre-FDE/DC
Configuration of the SC-CP Scheme with Proposed Pre-FDE/DC
S/P
P/S
CP Insertion
Transmitted Signal
DFT
IDFT
Transmitter:
Rx filter
P times Symbol RateBand Width:
Receiver:
S/P
CP Removal
P/S
Output
Rx filter
Sampling at Symbol Rate
Weights of Proposed Pre-FDE/DC
ZF based:
MMSE based:
BER Performance of the SC-CP via Proposed Pre-FDE/DC
0 5 10 15 20 25
10
10
10
10
10
-1
-2
-3
-4
-5
1
[dB]
BER
ZFMMSE
K=P=1
K=P=2K=P=4
Mod./ Demod. QPSK Block Size M = 256CP Length N=32
Channel:10-path rayleigh fading channels
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)
Channel Estimation: Ideal
AWGN
BER Performance of the OFDM via Proposed Pre-FDE/DC
0 5 10 15 20 25
10
10
10
10
10
-1
-2
-3
-4
-5
1
[dB]
BER
ZFMMSE
K=P=1
K=P=2K=P=4
Mod./ Demod. QPSK Block Size M = 256CP Length N=32
Channel:10-path rayleigh fading channels
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)
Channel Estimation: Ideal
AWGN
Summary
T/K-FSE methods for block transmission with cyclic prefix are proposed
ZF and MMSE weights of the proposed T/K-FSE are derived
Based on the idea of T/K-FSE, two simple frequency diversity method is also proposed
Computer simulations reveal the performance improvements by proposed methods
PAPR of the SC-CP via Proposed Pre-FDE/DC
CCDF=complementary cumulative distribution function
0 2 4 6
10
10
10
10
-1
-2
-3
-4
1
8 10 12 14 16
CC
DF
PAPR [dB]
OFDM(M=256)
ZFMMSE
SC-CP(M=256)
K=P=2 Mod./ Demod. QPSK Block Size M = 256CP Length N=32
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)
CCDF=complementary cumulative distribution function
PAPR of the OFDM via Proposed Pre-FDE/DC
0 2 4 6
10
10
10
10
-1
-2
-3
-4
1
8 10 12 14 16
CC
DF
PAPR [dB]
K=P=2
ZFMMSE
OFDM(M = 256)
Mod./ Demod. QPSK Block Size M = 256CP Length N=32
Order of Channel: L=30
Tx/Rx Filter:square-root raised-cosine filter ( α=0.5)