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 }

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]

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

Uyen Ly Dang: Comparison of Receivers for SC-FDMA

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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

Uyen Ly Dang: Comparison of Receivers for SC-FDMA

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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

Uyen Ly Dang: Comparison of Receivers for SC-FDMA

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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

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 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

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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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

11

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

7

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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