Equalization for OFDM over Doubly-Selective Channels

ICC 20-24 June 2004 - Paris

Equalization for OFDM over Doubly-Selective Channels

Imad Barhumi, Geert Leus, and Marc Moonen K.U.Leuven-ESAT/SCD-SISTA

T.U.Delft-Faculty of Electrical Engineering

Outline

Introduction Motivation

Wireless Communication Channels System Model

Equalization for OFDM over DS:

Time-Domain approach

Frequency-Domain (Per-Tone) approach

Simulation Results

Introduction

Introduction

OFDM possesses the following key advantages

Introduction

OFDM possesses the following key advantages High data rates

Robust against multipath fading channels

Simple equalization techniques

Introduction

OFDM possesses the following key advantages High data rates

Robust against multipath fading channels Simple equalization techniques

Pending on:

Introduction

OFDM possesses the following key advantages High data rates

Robust against multipath fading channels Simple equalization techniques

Pending on:

CP length is greater than channel order

Frequency selective channels (or slowly time varying)

Introduction

OFDM possesses the following key advantages High data rates

Robust against multipath fading channels Simple equalization techniques

Pending on:

CP length is greater than channel order

Frequency selective channels (or slowly time varying)

Result:

Introduction

OFDM possesses the following key advantages High data rates

Robust against multipath fading channels Simple equalization techniques

Pending on:

CP length is greater than channel order

Frequency selective channels (or slowly time varying) Result:

Orthogonality is preserved NO ICI is present

1-tap FEQ

Motivation

OFDM over Doubly-Selective Channels (rapidly-time varying) The CP is possibly less than the channel order

Orthogonality between subcarriers is destroyed ICI/IBI is present

The simple 1-tap FEQ is not sufficient Complex equalization is required

To restore orthogonality

reduce or completely eliminate ICI

Types of fading depend on:

Symbol period vs. delay spread BW vs. Doppler spread

Carrier frequency

BEM is an alternative model with fewer parameters.

The time variety of each tap is captured by Q TV complex exponentials.

h(n; ν) =

L

X

l=0

δ _v−l

Q/2

X

q=−Q/2

h _q,l e ^jω

^n/K

K is the BEM resolution, (multiple of the block size) Q = 2⌈f _d KT _s ⌉

−20

−10 0 10

τ)| (dB)

0.3 0.4 0.5 0.6 0.7

MSE

S/P

CP

P/S D/A

TV Channel

A/D EQUALIZER

Xk

N-PointIFFT

Xˆk

h(t; τ )

WGN

Single-Input Multiple-Output (SIMO) Doubly-Selective Channel

Max. Doppler frequency f _max Max. Delay spread τ _max

Jakes’ Model Channel, parameterized using the BEM The channel BEM coeff. are known or can be estimated Equalization:

Time-Domain Equalizer

Frequency-Domain Equalizer

Equalization for OFDM over Doubly-Selective Channels (TEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

Equalization for OFDM over Doubly-Selective Channels (TEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

∆ g^N_Q′^r/2,1 g^N_Q′^r/2,2

g^N_Q′^r/2,0

g_−Q^(Nr′⁾/2,2

g_−Q^(Nr)′/2,0 g_−Q^(Nr)′/2,1 g_−Q^(Nr)′/2,L^′

∆

g^N_Q′^r/2,L^′

∆

∆

∆ ∆

e^{−j2πQ′/2 n/K}

e^{j2πQ′/2 n/K}

Equalization for OFDM over Doubly-Selective Channels (TEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

∆ b(ν)

Equalization for OFDM over Doubly-Selective Channels (TEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

∆ b(ν)

Equalization for OFDM over DS Channels (TEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

∆ b(ν)

TEQ: to convert the doubly-selective channel into purely frequency-selective

and/or to the shorten the channel to fit within the CP

Constraints are applied to avoid the trivial solution

1-tap FEQ is still required

Equalization for OFDM over DS Channels (FEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

∆ b(ν)

Equalization for OFDM over DS Channels (FEQ)

FEQ CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

g(n; ν)

CP

S/P

N-PointFFT

Xˆk

Equalization for OFDM over DS Channels (FEQ)

↓ N + ν

∆

↓ N + ν

↓ N + ν

↓ N + ν

∆

↓ N + ν

∆

↓ N + ν

↓ N + ν

↓ N + ν

∆

e^j2πQ

′/2n/K

CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

N+ L^′

0

0

w˜^(r,0)q′,0 w˜^(r,0)q′,L′

−1 w˜^(r,0)q′,L′

˜ w(r,N−1)

q′,L′−1w˜(r,N−1) q′,L′ 0

w˜q^(r,k)′,L′ w˜^(r,k)q′,L′

−1

˜ w(r,N−1)

q′,0

N w˜^(r,k)q′,0

c

a a + b.c

b Multiply-Add cell

N+ L^′

0

0

˜

w^(r,0)q′,0 w˜^(r,0)q′,L′−1w˜^(r,0)q′,L′

w˜^(r,N−1)q′,L′−1

˜w^(r,N−1)q′,L′ 0

˜ w^(r,k)q′,L′

˜ w^(r,k)q′,L′−1

w˜^(r,N−1)q′,0

N

∆

˜ w^(r,k)q′,0

y^(r)[n]

y^(r)[n]

Q^′+ 1 sliding FFTs

∆ e^{−j2πQ′/2n/K}

SlidingN-PointFFTSlidingN-PointFFT

Equalization for OFDM over DS Channels (FEQ)

↓ N + ν

∆

↓ N + ν

↓ N + ν

↓ N + ν

∆

↓ N + ν

↓ N + ν

↓ N + ν

Sliding N-Point FFT

CP

P/S

N-PointIFFT

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

c

a a + b.c

b Multiply-Add cell

P sliding FFTs

N+ L^′

∆

∆

0

0

w^(r,k)p,0,L′

0

w^(r,k)p,1,0 w^(r,k)_p,1,L′

w^(r,k)_p,−1,0 w^(r,k)_p,−1,L′−1w^(r,k)_p,−1,L′

w^(r,k)p,0,0 w^(r,k)p,0,L′−1

w^(r,k)_p,1,L′−1 tone k

tone k + 1 tone k − 1

y^(r)[(i + 1)(N + ν) − d − 1]

N+ L^′

∆

0

0

w^(r,k)_p,0,L′

0

w^(r,k)p,1,0 w^(r,k)p,1,L′

w_p,−1,0^(r,k) w^(r,k) p,−1,L^′−1w^(r,k)

p,−1,L^′

w^(r,k)p,0,0 w^(r,k)_p,0,L′−1

w^(r,k)p,1,L′−1 tone k

tone k + 1 tone k − 1

SlidingN-PointFFTSlidingN-PointFFT

Equalization for OFDM over DS Channels (FEQ)

0

0

0 0

0

0

∆

∆

↓ N + ν ↓ N + ν ↓ N + ν

↓ N + ν

↓ N + ν

↓ N + ν

∆

∆

↓ N + ν ↓ N + ν ↓ N + ν

↓ N + ν

↓ N + ν

CP

P/S

↓ N + ν

c

a a + b.c

b Multiply-Add cell

N

+

∆

−

tone k − 1

tone k

tone k + 1

∆

∆

 v^(r,k)p



|Qp|+L′

 v^(r,k)p



(x−1)

 v^(r,k)p



x

 v^(r,k)p



(x+1)

y^(r)[n]

P FFTs with diff. terms

+

∆

−

tone k − 1

tone k

tone k + 1

∆

∆

 v(r,k)

p



|Qp|+L′

 v(r,k)

p



(x−1)

 v(r,k)

p



x

 v(r,k)

p



(x+1)

y^(r)[n]

ej2π(P −1)n/K

S/P D/A

TV Channel

Xk h(t; τ ) A/D

WGN

N-PointIFFT N-PointFFT N-PointFFT

Complexity

Implementation complexity comparison:

MA/tone/rx FFT/rx TEQ (Q ^′ + 1)(L ^′ + 1) 1 PTEQ 1 (Q ^′ + 1)(L ^′ + 1) Q ^′ + 1 PTEQ 2 (Q ^′ + 1)(L ^′ + 1) P PTEQ 3 P (L ^′ + 1) + Q ^′ + 1 P

Design complexity of the PTEQ is higher than the design

complexity of the TEQ

System parameters

Number of subcarriers N = 128;

Symbol period T = 25µs;

Max. Doppler-spread f _max = 100Hz Max. Delay-spread τ _max = 150µs BEM resolution K = P N , P = 1, 2

Number of basis functions Q = 2⌈f max KT ⌉ = 2, 4;

Channel order L = ⌈τ _max /T ⌉ = 6.

Jakes’ Model Channel taps correlated in time (r _hh = J ₀ (2πf _max τ ))

QPSK signaling

Performance is measured in terms BER vs. SNR

Evaluate TEQ and PTEQ

PTEQ, Q ^′ = 10 TEQ, Q ^′ = 14, L ^′ = 14 ν = L = 6

10⁻³ 10⁻² 10⁻¹ 10⁰

BER

TEQ, UEC TEQ, UNC PTEQ, L’=0, P=1 PTEQ, L’=0, P=2 PTEQ, L’=6, P=1 PTEQ, L’=6, P=2 Block MMSE, P=1 Block MMSE, P=2 FEQ, TI

PTEQ and TEQ: Q ^′ = 8, L ^′ = 8 ν = 3

0 5 10 15 20 25 30

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

SNR (dB)

BER

TEQ, UEC, P=1 TEQ, UEC, P=2 TEQ, UNC, P=1 TEQ, UNC, P=2 PTEQ, P=1 PTEQ, P=2 Block MMSE, P=1 Block MMSE, P=2 FEQ, TI

PTEQ with true channel

10⁻² 10⁻¹ 10⁰

BER

N_r=1 N_r=2 P=1 P=2

Conclusions

We propose Time-Domain and Frequency-Domain Per-Tone equalization techniques for OFDM over DS channels

PTEQ significantly outperforms the TEQ

Frequency-domain oversampling factor P > 1

Combine adjacent subcarrier to cancel ICI on a specific subcarreir

For the case L = ν approaches(outperforms) the MMSE equalizer of the TI channel

The proposed PTEQ unifies and extends many existing frequency-domain equalization techniques

Questions ©