Multicarrier Modulation with Blind Detection Capability Using Cosine Modulated Filter Banks Behrouz Farhang-Boroujeny Department of Electrical & Computer Engineering University of Utah email:[email protected]

Date: July 17, 2003 ECE Department, Univ of Alberta

1

Outline Introduction o ISI cancellation using multicarrier modulation (MCM)

Discrete Multitone Modulation (DMT/OFDM) o Time and frequency domain equalization

Filter Bank Based Multicarrier Modulation o Structure o Blind Equalization o Bandwidth Efficiency o Computer Simulations

Conclusions

2

Introduction Time spreading (Intersymbol Interference – ISI)

s (n)

{h(n)}

x ( n) = ∑i h(i ) s ( n − i )

Solution: Channel equalization s (n)

H (z )

z −∆ ≈ H (z )

s(n − ∆)

Problem: noise enhancement

3

Cancellation (reduction) of ISI using MCM By dividing the channel into a large number of sub-channels, each sub-channel will have almost flat gain, thus is free of ISI. H(f)

frequency

4

Structure of MCM System TRANSMITTER Serial input

S/P

Encoder

Wave shaping & mod.

P/S

Channel

RECEIVER Serial output

P/S

Decoder + FEQ

Filtering & Demod.

S/P

S/P: Serial-to-Parallel P/S: Parallel-to-Serial

5

Discrete Multitone (DMT/OFDM): an elegant

technique for efficient realization of MCM systems TRANSMITTER Serial input

S/P

IFFT + CP

Encoder

P/S

Channel

RECEIVER Serial output

P/S

Decoder + FEQ

S/P: Serial-to-Parallel P/S: Parallel-to-Serial

Remove CP +FFT

S/P + TEQ

CP: Cyclic Prefix TEQ: Time Domain Equalizer FEQ: Frequency Domain Equalizer

6

What are TEQ and FEQ? • Time domain equalizer is used to shorten the duration of the channel response. • Frequency domain equalizer is to compensate for gain distortion due to channel response.

7

MCM with Critically Sampled Filter Banks (also called discrete wavelet multitone –DWMT) TRANSMITTER

Data in

S/P

Synthesis Filter Bank + P/S

Channel

TEQ

RECEIVER

Data out

P/S

PostProcessing Equalizer

S/P +

Analysis Filter Bank

Synthesis and analysis are based on cosine modulated filter banks (CMFB). 8

Advantages of CMFB over DMT Higher efficiency no cyclic prefix and/or suffix more bandwidth efficient More immune to narrow-band interference More immune to intercarrier interference (some times)

No frame synchronization Simple blind equalization possible

9

Disadvantages of CMFB compared to DMT More Complex? Not compliant with the present standards

10

Cosine Modulated Filter Bank (CMFB) d0

⊗

G0 ( − z 2 M )

d1

z −1W −1 / 2

G1 ( − z 2 M )

(a) −1

z W

2M-point DFT

−1 / 2

⊗

Q1a ( z )

d 2 M −1

z −1W −1 / 2

⊗

G 2 M −1 ( − z 2 M )

Q2aM −1

Q0a ( z )

Q0a

Q1a

Q2a

Q2aM −1

Q2aM −1 ( z )

Q0a

(b)

π /M

ω 11

a a In the conventional CMFB the pairs of Qk (z ) and Q2 M −1−k ( z ) are combined together to make an analysis filter

H k ( z ) = Qka ( z ) + Q2aM −1−k ( z )

Q2aM −1−k

(k + 1)π − M

kπ − M

| H k ( e jω ) |

kπ M

Qka

(k + 1)π M

ω

12

Synthesis filters are matched to the analysis filters:

Q2aM* −1−k

(k + 1)π − M

kπ − M

| Fk (e jω ) |

kπ M

Qka*

(k + 1)π M

ω

13

Vestigial Side-Band Property of CMFB Modulation and Demodulation in CMFB

ω Modulation

− ωc

ω

ωc Demodulation

ω

14

a Q Output of k (z ) after demodulation:

π

ω

M

15

Distribution of the real and imaginary parts of xk(n):

16

Effect of channel and Equalization ASSUMPTION: Over each sunchannel, channel is flat. Hence, it can be modelled as a complex gain, and thus, equalization can be achieved using a complex gain.

Equalizer output:

yk (n) = ℜ{wk* xk (n)} = wk , R xR (n) + wk , I xI (n)

17

Blind Equalization We propose an algorithm that works based on the same principal as Godard’s algorithm.

Criterion: minimize

ξ = E [(| yk (n) | p − R) 2 ], R is a constant and p is an integer This is called dispersion function.

18

Update equation: We use the algorithm

wk (n + 1) = wk (n) − µ∇Cwk ξˆ where

∇

C wk

∂ ∂ = +j and ξˆ = (| y k (n) | p − R ) 2 ∂wk , R ∂wk , I

We obtain

wk (n + 1) = wk (n) − 2µxk (n)(sign ( yk (n))) p ( yk (n)) p −1 (| yk (n) | p − R)

19

The case of interest here is p = 1 :

wk (n + 1) = wk (n) − 2µxk (n)sign ( yk (n))(| yk (n) | − R) The optimum value of R is

[

]

E | s (n) |2 R= E [| s (n) |] For L-ary PAM:

2( L2 − 1) R= 3L

20

Blind equalizer is blind to a phase ambiguity of 180o.

Solution => differential encoding There is no loss of 3 dB.

21

Bandwidth Efficiency of CMFB-MCM • Each subchannel occupies a bandwidth of π / M and carries one PAM symbol. • In QAM signaling, we need a bandwidth of 2π (M1 + α ) to carry QAM symbols at the same rate as PAM symbols. • Each QAM symbol may be thought as 2 PAM symbols. • We thus find that compared to single carrier modulation, 1 1+α

CMFB requires times less bandwidth. α is the excess bandwidth. • Compared to OFMD, CMFB is more bandwidth efficient because of the absence of cyclic extensions. 22

Computer Simulations Learning Curves • Simulations are done for binary and 4-ary signaling. • Each result is based on 500 independent runs, • Learning curves are based on the error functions

[

]

For binary data:

J = E (| y k ( n) | −1) 2 ]

For 4-ary data:

J = E min{(| yk (n) | −1) 2 , (| y k ( n) | −3) 2 ]

[

]

23

An example of learning curves for binary symbols: 0 Subchannel 6 Subchannel 14 Subchannel 27

−2 −4

−8

2

J/σs (dB)

−6

−10 −12 −14 −16 −18

0

100

200 300 NO. OF ITERATIONS

400

500

1

An example of learning curves for 4-ary symbols: −6 Subchannel 6 Subchannel 14 Subchannel 27

−8

J/σs (dB)

−10

2

−12 −14 −16 −18 −20

0

100

200 300 NO. OF ITERATIONS

400

500

2

A comparison of CMFB-MCM (2 taps per subcarrier) and DWMT (33 taps per subcarrier) : 0 CMFB−MCM DWMT −5

MSE/σ2s (dB)

−10

−15

−20

−25

−30

0

20

40

60 80 SUBCHANNEL NO.

100

120

3

Bit-Error-Rate (BER) Comparison with OFDM Channel has a multipath Rayleigh fading model

h(t ) = ∑ a (t ,τ i )δ (t − τ i ) i

with power-delay profile 2τ i / T

σ (τ i ) = Kλ 2 a

where λ is a positive constant smaller than one.

24

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 64 OFDM block length = 32 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

4

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 128 OFDM block length = 64 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

5

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 256 OFDM block length = 128 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

6

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 512 OFDM block length = 256 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

7

VDSL Applications There are currently two candidates for VDSL, discrete multitone (DMT), and filtered multitone (FMT). • DMT is a DFT based solution and is very similar to OFDM. • FMT is a filterbank-based solution (similar to CMFB-MCM). The difference is that FMT uses filters which are nonoverlapping, thus suffer from bandwidth loss. Moreover, FMT solution requires very complex equalizers (36 taps for each subcarrier). • The fact that FMT has been received by the industry, is a good indication that filterbank solutions have recognized as good alternative solutions to the widely used DFT-based MCM techniques. 25

A thorough comparison of DMT, FMT and CMT (CMFB-based solutions) shows that: • DMT has the lowest computational complexity. • FMT and CMT are significantly superior to DMT in terms of latency and resistant to narrowband noise (HAM radio interference). • CMT offers the highest transmission rate. • While FMT and CMT may be the preferred choices to DMT in the application of VDSL because of much higher resistance to narrowband noise, we believe CMT is a better choice due to its much lower complexity. It is three times less complex.

26

Bit rate comparison of DMT, FMT and CMT (cosine modulated multitone): 40 z−DMT CMT FMT

35

Bit Rate (Mbps)

30 25 20 15 10 5 0

0

200

400

600 800 1000 Length of TP1 (m)

1200

1400

8

Comparison of DMT, FMT and CMT when channel is corrupted by an RF interference: 45 z−DMT w/o RFC z−DMT with RFC CMT FMT

40 35

SNR(dB)

30 25 20 15 10 5 0

0

0.5

1

1.5 2 Frequency(MHz)

2.5

3

3.5

9

Comparison of DMT, FMT and CMT when channel is corrupted by an RF interference: 45 z−DMT w/o RFC z−DMT with RFC CMT FMT

40 35

SNR(dB)

30 25 20 15 10 5 0

0

0.5

1

1.5 2 Frequency(MHz)

2.5

3

3.5

10

Conclusions • We proposed CMFB as an alternative MCM to OFDM for wireless applications. • CMFB-MCM was shown to be more bandwidth efficient than OFDM. • CMFB may be thought as a tool for VSB modulation of a number of PAM channels that are packed together in a minimum bandwidth. • Simple blind equalizer was proposed for CMFBMCM.

27

Some related research topics • Convergence study of the blind equalizer. • Tracking behavior of the CMFB-MCM in wireless channels. • Diversity combining techniques. • Space-time systems (MIMO). • Peak-to-average ratio controlling methods. • Carrier and timing recovery. • MC-CDMA and MCSS. 28

Date: July 17, 2003 ECE Department, Univ of Alberta

1

Outline Introduction o ISI cancellation using multicarrier modulation (MCM)

Discrete Multitone Modulation (DMT/OFDM) o Time and frequency domain equalization

Filter Bank Based Multicarrier Modulation o Structure o Blind Equalization o Bandwidth Efficiency o Computer Simulations

Conclusions

2

Introduction Time spreading (Intersymbol Interference – ISI)

s (n)

{h(n)}

x ( n) = ∑i h(i ) s ( n − i )

Solution: Channel equalization s (n)

H (z )

z −∆ ≈ H (z )

s(n − ∆)

Problem: noise enhancement

3

Cancellation (reduction) of ISI using MCM By dividing the channel into a large number of sub-channels, each sub-channel will have almost flat gain, thus is free of ISI. H(f)

frequency

4

Structure of MCM System TRANSMITTER Serial input

S/P

Encoder

Wave shaping & mod.

P/S

Channel

RECEIVER Serial output

P/S

Decoder + FEQ

Filtering & Demod.

S/P

S/P: Serial-to-Parallel P/S: Parallel-to-Serial

5

Discrete Multitone (DMT/OFDM): an elegant

technique for efficient realization of MCM systems TRANSMITTER Serial input

S/P

IFFT + CP

Encoder

P/S

Channel

RECEIVER Serial output

P/S

Decoder + FEQ

S/P: Serial-to-Parallel P/S: Parallel-to-Serial

Remove CP +FFT

S/P + TEQ

CP: Cyclic Prefix TEQ: Time Domain Equalizer FEQ: Frequency Domain Equalizer

6

What are TEQ and FEQ? • Time domain equalizer is used to shorten the duration of the channel response. • Frequency domain equalizer is to compensate for gain distortion due to channel response.

7

MCM with Critically Sampled Filter Banks (also called discrete wavelet multitone –DWMT) TRANSMITTER

Data in

S/P

Synthesis Filter Bank + P/S

Channel

TEQ

RECEIVER

Data out

P/S

PostProcessing Equalizer

S/P +

Analysis Filter Bank

Synthesis and analysis are based on cosine modulated filter banks (CMFB). 8

Advantages of CMFB over DMT Higher efficiency no cyclic prefix and/or suffix more bandwidth efficient More immune to narrow-band interference More immune to intercarrier interference (some times)

No frame synchronization Simple blind equalization possible

9

Disadvantages of CMFB compared to DMT More Complex? Not compliant with the present standards

10

Cosine Modulated Filter Bank (CMFB) d0

⊗

G0 ( − z 2 M )

d1

z −1W −1 / 2

G1 ( − z 2 M )

(a) −1

z W

2M-point DFT

−1 / 2

⊗

Q1a ( z )

d 2 M −1

z −1W −1 / 2

⊗

G 2 M −1 ( − z 2 M )

Q2aM −1

Q0a ( z )

Q0a

Q1a

Q2a

Q2aM −1

Q2aM −1 ( z )

Q0a

(b)

π /M

ω 11

a a In the conventional CMFB the pairs of Qk (z ) and Q2 M −1−k ( z ) are combined together to make an analysis filter

H k ( z ) = Qka ( z ) + Q2aM −1−k ( z )

Q2aM −1−k

(k + 1)π − M

kπ − M

| H k ( e jω ) |

kπ M

Qka

(k + 1)π M

ω

12

Synthesis filters are matched to the analysis filters:

Q2aM* −1−k

(k + 1)π − M

kπ − M

| Fk (e jω ) |

kπ M

Qka*

(k + 1)π M

ω

13

Vestigial Side-Band Property of CMFB Modulation and Demodulation in CMFB

ω Modulation

− ωc

ω

ωc Demodulation

ω

14

a Q Output of k (z ) after demodulation:

π

ω

M

15

Distribution of the real and imaginary parts of xk(n):

16

Effect of channel and Equalization ASSUMPTION: Over each sunchannel, channel is flat. Hence, it can be modelled as a complex gain, and thus, equalization can be achieved using a complex gain.

Equalizer output:

yk (n) = ℜ{wk* xk (n)} = wk , R xR (n) + wk , I xI (n)

17

Blind Equalization We propose an algorithm that works based on the same principal as Godard’s algorithm.

Criterion: minimize

ξ = E [(| yk (n) | p − R) 2 ], R is a constant and p is an integer This is called dispersion function.

18

Update equation: We use the algorithm

wk (n + 1) = wk (n) − µ∇Cwk ξˆ where

∇

C wk

∂ ∂ = +j and ξˆ = (| y k (n) | p − R ) 2 ∂wk , R ∂wk , I

We obtain

wk (n + 1) = wk (n) − 2µxk (n)(sign ( yk (n))) p ( yk (n)) p −1 (| yk (n) | p − R)

19

The case of interest here is p = 1 :

wk (n + 1) = wk (n) − 2µxk (n)sign ( yk (n))(| yk (n) | − R) The optimum value of R is

[

]

E | s (n) |2 R= E [| s (n) |] For L-ary PAM:

2( L2 − 1) R= 3L

20

Blind equalizer is blind to a phase ambiguity of 180o.

Solution => differential encoding There is no loss of 3 dB.

21

Bandwidth Efficiency of CMFB-MCM • Each subchannel occupies a bandwidth of π / M and carries one PAM symbol. • In QAM signaling, we need a bandwidth of 2π (M1 + α ) to carry QAM symbols at the same rate as PAM symbols. • Each QAM symbol may be thought as 2 PAM symbols. • We thus find that compared to single carrier modulation, 1 1+α

CMFB requires times less bandwidth. α is the excess bandwidth. • Compared to OFMD, CMFB is more bandwidth efficient because of the absence of cyclic extensions. 22

Computer Simulations Learning Curves • Simulations are done for binary and 4-ary signaling. • Each result is based on 500 independent runs, • Learning curves are based on the error functions

[

]

For binary data:

J = E (| y k ( n) | −1) 2 ]

For 4-ary data:

J = E min{(| yk (n) | −1) 2 , (| y k ( n) | −3) 2 ]

[

]

23

An example of learning curves for binary symbols: 0 Subchannel 6 Subchannel 14 Subchannel 27

−2 −4

−8

2

J/σs (dB)

−6

−10 −12 −14 −16 −18

0

100

200 300 NO. OF ITERATIONS

400

500

1

An example of learning curves for 4-ary symbols: −6 Subchannel 6 Subchannel 14 Subchannel 27

−8

J/σs (dB)

−10

2

−12 −14 −16 −18 −20

0

100

200 300 NO. OF ITERATIONS

400

500

2

A comparison of CMFB-MCM (2 taps per subcarrier) and DWMT (33 taps per subcarrier) : 0 CMFB−MCM DWMT −5

MSE/σ2s (dB)

−10

−15

−20

−25

−30

0

20

40

60 80 SUBCHANNEL NO.

100

120

3

Bit-Error-Rate (BER) Comparison with OFDM Channel has a multipath Rayleigh fading model

h(t ) = ∑ a (t ,τ i )δ (t − τ i ) i

with power-delay profile 2τ i / T

σ (τ i ) = Kλ 2 a

where λ is a positive constant smaller than one.

24

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 64 OFDM block length = 32 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

4

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 128 OFDM block length = 64 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

5

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 256 OFDM block length = 128 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

6

BER comparison of CMFB-MCM and OFDM CMFB-MCM block length = 512 OFDM block length = 256 0

10

−1

10

−2

BER

10

−3

10

−4

10

CMFB−MCM, λ=0.5 CMFB−MCM, λ=0.7 CMFB−MCM, λ=0.9 OFDM, λ=0.5 OFDM, λ=0.7 OFDM, λ=0.9

−5

10

−6

10

0

5

10

15

20 25 SNR (dB)

30

35

40

45

7

VDSL Applications There are currently two candidates for VDSL, discrete multitone (DMT), and filtered multitone (FMT). • DMT is a DFT based solution and is very similar to OFDM. • FMT is a filterbank-based solution (similar to CMFB-MCM). The difference is that FMT uses filters which are nonoverlapping, thus suffer from bandwidth loss. Moreover, FMT solution requires very complex equalizers (36 taps for each subcarrier). • The fact that FMT has been received by the industry, is a good indication that filterbank solutions have recognized as good alternative solutions to the widely used DFT-based MCM techniques. 25

A thorough comparison of DMT, FMT and CMT (CMFB-based solutions) shows that: • DMT has the lowest computational complexity. • FMT and CMT are significantly superior to DMT in terms of latency and resistant to narrowband noise (HAM radio interference). • CMT offers the highest transmission rate. • While FMT and CMT may be the preferred choices to DMT in the application of VDSL because of much higher resistance to narrowband noise, we believe CMT is a better choice due to its much lower complexity. It is three times less complex.

26

Bit rate comparison of DMT, FMT and CMT (cosine modulated multitone): 40 z−DMT CMT FMT

35

Bit Rate (Mbps)

30 25 20 15 10 5 0

0

200

400

600 800 1000 Length of TP1 (m)

1200

1400

8

Comparison of DMT, FMT and CMT when channel is corrupted by an RF interference: 45 z−DMT w/o RFC z−DMT with RFC CMT FMT

40 35

SNR(dB)

30 25 20 15 10 5 0

0

0.5

1

1.5 2 Frequency(MHz)

2.5

3

3.5

9

Comparison of DMT, FMT and CMT when channel is corrupted by an RF interference: 45 z−DMT w/o RFC z−DMT with RFC CMT FMT

40 35

SNR(dB)

30 25 20 15 10 5 0

0

0.5

1

1.5 2 Frequency(MHz)

2.5

3

3.5

10

Conclusions • We proposed CMFB as an alternative MCM to OFDM for wireless applications. • CMFB-MCM was shown to be more bandwidth efficient than OFDM. • CMFB may be thought as a tool for VSB modulation of a number of PAM channels that are packed together in a minimum bandwidth. • Simple blind equalizer was proposed for CMFBMCM.

27

Some related research topics • Convergence study of the blind equalizer. • Tracking behavior of the CMFB-MCM in wireless channels. • Diversity combining techniques. • Space-time systems (MIMO). • Peak-to-average ratio controlling methods. • Carrier and timing recovery. • MC-CDMA and MCSS. 28