Comparison of Receivers for SC-FDMA Transmission over Frequency Selective MIMO Channels Uyen Ly Dang, Michael Ruder, Wolfgang Gerstacker Chair of Mobile Communications University of Erlangen-Nürnberg
WICAT Workshop Polytechnic University NY, 13.03.2009
Outline
1
System Model
2
Linear Equalization
3
Trellis-based Equalization
4
Successive Interference Cancelation
5
Results and Resumee
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Overview
1
System Model
2
Linear Equalization
3
Trellis-based Equalization
4
Successive Interference Cancelation
5
Results and Resumee
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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SC-FDMA Modulator / Demodulator Modulator DFTM
al [k]
Al [µ]
Subcarrier Mapping
IDFTN
Sl [ν]
ˆ sl [k]
- M-point discrete fourier transformation (DFTM ) into frequency domain - Assignment of M samples Al [µ] to N subcarriers - N-point inverse DFTN in time domain with N > M
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SC-FDMA Modulator / Demodulator Modulator DFTM Subcarrier al [k]
Al [µ]
Subcarrier Mapping
IDFTN
Sl [ν]
ˆ sl [k]
- M-point discrete fourier transformation (DFTM ) into frequency domain - Assignment of M samples Al [µ] to N subcarriers - N-point inverse DFTN in time domain with N > M Demodulator: reverse SC-FDMA modulation
ˆ ri [k]
DFTN
Ri [ν]
Subcarrier Demapping
IDFTM
Yi [µ]
yi [k]
- Subcarrier Demapping: extract from block of N subcarriers the M relevant subcarriers Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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System Model ˆ n1 k] a1 [k]
SC-FDMA Modulator
CP
CP
ˆ ˆ Insertion s1,cp [k] s1 [k]
SC-FDMA
ˆ Removal r1 [k] ˆ Demodulator y1 [k] r1,cp [k] ˆ n2 [k]
a2 [k]
SC-FDMA Modulator
ˆ s2 [k]
CP Insertion
CP
ˆ s2,cp [k]
SC-FDMA
ˆ Removal r2 [k] ˆ Demodulator y2 [k] r2,cp [k]
Notations: al [k] : transmit symbols with al [k] ∈ A and power σa2 ni [k] :
2 additive white noise in receiver i with power σn
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System Model ˆ n1 k] a1 [k]
SC-FDMA Modulator
CP
SC-FDMA
CP
ˆ ˆ Insertion s1,cp [k] s1 [k]
ˆ Removal r1 [k] ˆ Demodulator y1 [k] r1,cp [k] ˆ n2 [k]
a2 [k]
SC-FDMA Modulator
ˆ s2 [k]
CP Insertion
SC-FDMA
CP
ˆ s2,cp [k]
MIMO-transmission model rcp,1 H11 = rcp,2 H21
ˆ Removal r2 [k] ˆ Demodulator y2 [k] r2,cp [k]
H12 H22
scp,1 scp,2
+
n1 n2
Notations: al [k] : transmit symbols with al [k] ∈ A and power σa2 ni [k] : additive white noise in receiver i with power σn2 rcp,i = [ri [0] . . . ri [N − 1]]T Hil : linear convolution matrix of channel hil from antenna l to antenna i Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Overview
1
System Model
2
Linear Equalization
3
Trellis-based Equalization
4
Successive Interference Cancelation
5
Results and Resumee
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Joint Linear Equalization ˆ r[k]
R[ν]
Subcarrier Demapping
DFTN
Y[µ]
FD-MMSE
D[µ]
Equalization
d[k] IDFTM
Signal after subcarrier demapping in frequency domain
Y1 [µ] Y2 [µ]
A1 [µ] N1 [µ] H11 [µ] H12 [µ] + = A2 [µ] H21 [µ] H22 [µ] N2 [µ] {z } |
H[µ]
Hil [µ]: to A1 [µ] and A2 [µ] corresponding coefficients of DFTN {hil }
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Joint Linear Equalization ˆ r[k]
R[ν]
Subcarrier Demapping
DFTN
Y[µ]
FD-MMSE
D[µ]
d[k] IDFTM
Equalization
Signal after subcarrier demapping in frequency domain
Y1 [µ] Y2 [µ]
A1 [µ] N1 [µ] H11 [µ] H12 [µ] + = A2 [µ] H21 [µ] H22 [µ] N2 [µ] {z } |
H[µ]
Linear equalization by D[µ] = F[µ]Y[µ] according to the MMSE-criterion
F[µ] = HH [µ]H[µ] + ξI2
−1
HH [µ]
and ξ =
σn2 σa2
Hil [µ]: to A1 [µ] and A2 [µ] corresponding coefficients of DFTN {hil } Ix : Identity matrix of size (x × x) Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Overview
1
System Model
2
Linear Equalization
3
Trellis-based Equalization
4
Successive Interference Cancelation
5
Results and Resumee
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Joint Trellis-Based Equalization
Time domain equalization using soft-output reduced-state sequence estimation (RSSE): - Near optimal symbol estimation using the BCJR algorithm - Demands minimum phase equivalent overall impulse response - Demands signal impaired by white noise
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Joint Trellis-Based Equalization r[k]
MMSE Filtering
x[k]
Noise Whitening
u[k]
Time Domain BCJR
d[k]
Time domain equalization using soft-output reduced-state sequence estimation (RSSE): - Near optimal symbol estimation using the BCJR algorithm - Demands minimum phase equivalent overall impulse response - Demands signal impaired by white noise
Prefiltering: conditioning of equivalent impulse response - Linear MMSE equalization in frequency domain - Noise whitening
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Prefiltering (1) Power spectral density of error e in signal x = a + e after MMSE filtering
Φee [µ] = σn2 (HH [µ]H[µ] + ξI2 )−1
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Prefiltering (1) Power spectral density of error e in signal x = a + e after MMSE filtering
Φee [µ] = σn2 (HH [µ]H[µ] + ξI2 )−1
⇒ Noise whitening to eliminate the correlation in the error
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Prefiltering (1) Power spectral density of error e in signal x = a + e after MMSE filtering
Φee [µ] = σn2 (HH [µ]H[µ] + ξI2 )−1
⇒ Noise whitening to eliminate the correlation in the error Cyclic correlation matrix sequence of error after filtering
Aee [k] = Aee,il [k] =
Aee,11 [k] Aee,12 [k] Aee,21 [k] Aee,22 [k]
M −1 X
2π
Φee,il [µ]ej M µk
µ=0
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Prefiltering (2) Temporal Whitening
x[k]
+
up [k]
-
Spatial Whitening
u[k]
Noise Prediction
Cyclic temporal whitening filter
Pe [0] = I2 Pe [κ] = −P[κ] with κ = 1(1)qp
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Prefiltering (2) Temporal Whitening
x[k]
+
up [k]
-
u[k]
Spatial Whitening
Noise Prediction
Cyclic temporal whitening filter
Pe [0] = I2 Pe [κ] = −P[κ] with κ = 1(1)qp Coefficients P[κ] are obtained by Yule-Walker equations
Aee [0] Aee [−1]
··· ···
.. .
..
Aee [−(qp − 1)]
···
.
PH [1] Aee [qp − 1] Aee [−1] H Aee [qp − 2] P [2] Aee [−2] = .. .. .. . . . Aee [0]
PH [qp ]
Aee [−qp ]
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Prefiltering (3) Autocorrelation matrix of the error after temporal whitening
Ap = Aee [0] −
qp X
P[κ]Aee [−κ]
κ=1
Spatial whitening by u[k] = G−1 up [k]
G is obtained by Cholesky decomposition Ap /σn2 = GGH
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Prefiltering (3) Autocorrelation matrix of the error after temporal whitening
Ap = Aee [0] −
qp X
P[κ]Aee [−κ]
κ=1
Spatial whitening by u[k] = G−1 up [k]
G is obtained by Cholesky decomposition Ap /σn2 = GGH ⇒ Equivalent overall impulse response of length qheq is given by heq [k] = G−1 Pe [k] Correlation in noise is eliminated, but ISI is introduced that is taken into account in trellis-based equalization Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Time Domain Equalization via BCJR Algorithm Approach: optimal maximum-a-posteriori symbol-by-symbol estimation using trellis decoding Calculation of the probability of the transmitted symbols Pr(˜ a[k]| u) for each time step and every state BCJR algorithm: recursive computation while stepping through the trellis diagram
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Time Domain Equalization via BCJR Algorithm Approach: optimal maximum-a-posteriori symbol-by-symbol estimation using trellis decoding Calculation of the probability of the transmitted symbols Pr(˜ a[k]| u) for each time step and every state BCJR algorithm: recursive computation while stepping through the trellis diagram Adaption: Tailbiting-trellis diagram to consider cyclic convolution in SC-FDMA 00 01 10 11
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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State Reduction Problem: high computational complexity with increasing number of states mz in the trellis diagram
mz = |A|2qheq Remedy: reduced-state sequence estimation (RSSE)
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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State Reduction Problem: high computational complexity with increasing number of states mz in the trellis diagram
mz = |A|2qheq Remedy: reduced-state sequence estimation (RSSE) Set partitioning - Reducing the number of subsets Nsubsets in the symbol alphabet
A
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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State Reduction Problem: high computational complexity with increasing number of states mz in the trellis diagram
mz = |A|2qheq Remedy: reduced-state sequence estimation (RSSE) Set partitioning - Reducing the number of subsets Nsubsets in the symbol alphabet
A
Delayed decision-feedback - First qtr < qh channel taps are considered in the BCJR algorithm - Remaining channel taps are taken into account by state dependent feedback
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Overview
1
System Model
2
Linear Equalization
3
Trellis-based Equalization
4
Successive Interference Cancelation
5
Results and Resumee
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Successive Interference Cancelation ˜ [k] n
a1 [k] H1
y[k] a2 [k] H2
Split MIMO channel into two SIMO channels
˜ y = H1 a 1 + H 2 a 2 + n Notations: Hi : convolution matrix of overall channel including SC-FDMA modulation in transmitter and SC-FDMA demodulation in receiver
al : block of transmitted symbols of length M for transmitter l y : = [y1 [0], y2 [0], . . . , y1 [M − 1], y2 [M − 1]]T ˜ : noise after receiver-side SC-FDMA demodulation n Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Successive Interference Cancelation - Structure yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Signals of different transmit antennas are equalized subsequently in time
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Successive Interference Cancelation - Structure yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Signals of different transmit antennas are equalized subsequently in time SINR after filtering with fγ indicates what signal to be processed first (η, γ ∈ {1, 2})
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Successive Interference Cancelation - Structure yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Signals of different transmit antennas are equalized subsequently in time SINR after filtering with fγ indicates what signal to be processed first (η, γ ∈ {1, 2}) MISO filter design according to MMSE-criterion 2 2 H −1 2 fγ = (σa2γ Hγ HH γ + σn I2M + σaη Hη Hη ) σaγ hγ 2 −1 2 fη = (σa2η Hη HH η + σn I2M ) σaη hη
hi : First column of Hi Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Feedback Design yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Hard feedback: detection by hard decision
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Feedback Design yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Hard feedback: detection by hard decision Soft feedback: dγ [k]
Soft Demapper
a ˆγ [k] Soft Mapper
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Feedback Design yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Hard feedback: detection by hard decision Soft feedback: dγ [k]
Soft Demapper
a ˆγ [k] Soft Mapper
Decoded feedback: channel decoding after soft demapping (for multi user MIMO)
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Feedback Design yc [k]
y[k]
dη [k] fηH
a ˆγ [k]
dγ [k] fγH
Q
z[k]
Hγ
Hard feedback: detection by hard decision Soft feedback: dγ [k]
Soft Demapper
a ˆγ [k] Soft Mapper
Decoded feedback: channel decoding after soft demapping (for multi user MIMO)
ˆ γ = aγ Genius-aided feedback: no detection errors with a
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Overview
1
System Model
2
Linear Equalization
3
Trellis-based Equalization
4
Successive Interference Cancelation
5
Results and Resumee
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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Simulation Settings Settings for simulations are chosen following the standard for LTE a[k] DFTM
Subcarrier Mapping
IDFTN
CP Insertion
Channel Encoding: Turbocoding with code rate R = 2/3 Modulation mapping: QPSK Number of occupied subcarriers M = 300 Number of given subcarrier N = 512 Cyclic prefix length Lcp = 144 Single-User MIMO Blockfading
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Settings for Equalization
Trellis-based equalization Prediction length qp = 5 State reduction
Z = [Nsubsets,1 × Nsubsets,1 , . . . , Nsubsets,qtr × Nsubsets,qtr ] Successive interference cancelation Feedback type: genius-aided feedback (SIC-GE), soft feedback (SIC-SF) Filter length qf = 60
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Simulation Results - Pedestrian A 0
10
BLER
MMSE Z = [4x4,4x4] Z = [4x4,2x2] Z = [2x2,2x2] Z = [2x2] SIC−GE SIC−SF
−1
10
−2
10
1
2
3
4
5
6 7 8 10log10(Eb/N0) [dB]
9
10
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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12
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Simulation Results - Pedestrian B 0
10
BLER
MMSE Z = [4x4,4x4] Z = [4x4,2x2] Z = [2x2,2x2] Z = [2x2] SIC−GE SIC−SF
−1
10
−2
10
1
2
3
4 5 10log10(Eb/N0) [dB]
6
Uyen Ly Dang: Comparison of Receivers for SC-FDMA
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8
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Resumee Linear equalization: - Frequency domain equalization very simple - Effected by noise enhancement
Trellis-based time domain equaliztion: - Prefiltering by MMSE equalization and noise whitening - Symbol estimation with soft output RSSE and tailbiting trellis - High computational complexity
Succesive Interference Cancelation: - Transmit signals are reconstructed subsequently - Reliable feedback is essential for the performance
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Resumee Linear equalization: - Frequency domain equalization very simple - Effected by noise enhancement
Trellis-based time domain equaliztion: - Prefiltering by MMSE equalization and noise whitening - Symbol estimation with soft output RSSE and tailbiting trellis - High computational complexity
Succesive Interference Cancelation: - Transmit signals are reconstructed subsequently - Reliable feedback is essential for the performance
Time domain approaches show lower BLER than linear frequency domain filtering Trellis-based receiver can achieve same BLER as ideal SIC receiver
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