Optimized Fast Convolution Based Filtered-OFDM Processing for 5G

European Conference on Networks and Communications (EuCNC’2017)

Physical Layer and Fundamentals (PHY)

Optimized Fast Convolution Based Filtered-OFDM Processing for 5G Juha YLI-KAAKINEN, Toni LEVANEN, Markku RENFORS, and Mikko VALKAMA Laboratory of Electronics and Communications Engineering, Tampere University of Technology, FINLAND

June 15, 2017

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Introduction Fast-convolution (FC) filtering schemes provide flexible and effective waveform generation and processing in the fifth generation (5G) systems

OFDM OFDM MODULATOR MODULATOR

Tx 20

FC FC PROCESSING PROCESSING Synthesis Synthesis filter filterbank bank

OFDM OFDM MODULATOR MODULATOR

Rx FC FC PROCESSING PROCESSING Analysis Analysis filter filterbank bank

OFDM OFDM DEMODULATOR DEMODULATOR OFDM OFDM DEMODULATOR DEMODULATOR

Analysis bank MSE on active subcarriers

1x12 SCs with 30 kHz SCS

0

Power in dB

OFDM OFDM MODULATOR MODULATOR

6x12 SCs with 60 kHz SCS

−20

24x12 SCs with 15 kHz SCS

−40 −60 −80 −500

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−300

−200

−100

0

Subcarrier n

OFDM OFDM DEMODULATOR DEMODULATOR .

J. Yli-Kaakinen, T. Levanen, M. Renfors, and M. Valkama

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Optimized Fast Convolution Based Filtered-OFDM Processing for 5G

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Fast Convolution ▶

Fast convolution processing is an efficient implementation of high-order time-domain filters in frequency domain ▶ ▶

▶

Replace time-domain convolution with frequency-domain multiplication Overlap-and-save (OSA) processing is used with long sequences

Implementation complexity can be fine tuned by relaxing the correspondence between the time-domain and frequency-domain models ▶

Exact representation possible, but not optimal from computational complexity – performance trade-off perspective

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Fast Convolution – Overlap-and-Save Processing Input signal OVERLAP OF 20 %

Input block 1 OVERLAP OF 20 %

OVERLAP OF 20 %

Input block 2 OVERLAP OF 20 %

Processing

OVERLAP OF 20 %

Input block 3

OVERLAP OF 20 %

Processing THROW AWAY

Output block 1 THROW AWAY

THROW AWAY

Processing

Output Block 2 THROW AWAY

THROW AWAY

Output Block 3

Output signal

THROW AWAY

■ Input signal is divided into overlapping blocks (e.g. with 40% overlap) ■ Blocks are transformed to frequency-domain for processing (filter) ■ Processed blocks are transformed back to time-domain for concatenation .

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Fast Convolution – Overlap-and-Add Processing Input signal INSERT ZEROS

Input block 1 INSERT ZEROS

INSERT ZEROS

Input block 2 INSERT ZEROS

Processing

INSERT ZEROS

Input block 3

INSERT ZEROS

Processing OVERLAP & ADD

Output block 1 OVERLAP & ADD

OVERLAP & ADD

Processing

Output Block 2 OVERLAP & ADD

OVERLAP & ADD

Output Block 3

Output signal

OVERLAP & ADD

■ We use the overlap-and-save because of its better properties in finite wordlength implementation ■ This is due to the possible transients at the beginning and end of each overlap-add processing block

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J. Yli-Kaakinen, T. Levanen, M. Renfors, and M. Valkama

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Fast Convolution – Synthesis Filterbank Tx Processing Input signal x0

Input signal x1

Input signal xM –1

Serial to parallel with LO,0 overlap

Serial to parallel with LO,1 overlap

Serial to parallel with LO,M –1 overlap 0 0

L0-point FFT

L1-point FFT

LM –1-point FFT

d0

d1

dM –1

N-point IFFT

Parallel to serial with NO = N – NS sample discard

■ Low-rate narrowband subchannels are combined into a high-rate wideband channel ■ The bandwidth and the shape of the subchannels can be adjusted by modifying the weight masks dm ’s ■ Subband signals are detectable with basic OFDM receiver

Output signal y .

J. Yli-Kaakinen, T. Levanen, M. Renfors, and M. Valkama

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Fast Convolution – Analysis Filterbank Rx Processing Input signal x Serial to parallel with NO = N – NS sample overlap

N-point FFT d0

d1

dM –1 0

0

L0-point IFFT

L1-point IFFT

LM –1-point IFFT

Parallel to serial with LO,0 discard

Parallel to serial with LO,1 discard

Parallel to serial with LO,M –1 discard

Output signal y0

Output signal y1

Output signal yM –1

■ High-rate wideband channel is divided into low-rate narrowband subchannels ■ N in synthesis and analysis filterbanks don’t have to be equal ■ The subcarrier-wise channel equalizer coefficients can be combined with the weight masks dm ’s .

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Matrix Model for FC Processing – Synthesis Filterbank m Fm,r = SN W−1 N Mm,r Dm PLm

(L /2)

dL m−1, m

SN

Parallel-to-serial

FFT shift

d1, m

–1

Overlap-save processing (N O sample discard)

Dm

 

WN

N-point IFFT

 

PL(Lmm/2)

d0, m

L m-point FFT

Serial to parallel with L O,m overlap

W Lm

Common TX FC processing for all subbands

Mm,r

Mapping L m frequency-domain points to N points

Single subband of FC based TX processing

WLm

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Matrix Model for FC Processing – Analysis Filterbank Similarly for analysis filterbank Gm,r = S¯Lm W¯−1 P Lm N

(N/2)

⊺

Dm Mm,r WN

In our approach FC design is done in frequency-domain by optimizing the weight coefficients embedded in Dm ▶ Two symmetric transition bands with non-trivial weights (very low memory requirement) ▶ All passband weights are 1 ▶ All stopband weights are 0 .

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Optimized Fast Convolution Based Filtered-OFDM Processing for 5G

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FC-F-OFDM

▶

FC filtered CP-OFDM/DFTs-OFDM (FC-F-OFDM) is a scheme where the FC processing is used to implement highly adjustable and computationally efficient subband filtering for CP-OFDM or DFTs-OFDM signals

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J. Yli-Kaakinen, T. Levanen, M. Renfors, and M. Valkama

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FC-F-OFDM (processing structure for one filtered group of PRBs) Single subchannel of FC based TX processing

OFDM TX processing

Common FC TX processing for combining all subchannels

x OFDM,m

f t

FD windowing d0,m

Overlap-save(OSA) (OSA)processing processing Overlap-save withNN L L  + N + N T T  = λN = λN overlap overlap with

0

d1,m

N-pointIFFT IFFT N-point

-pointFFT FFT LL m m-point

S/Pwith withLLL,m overlap L,m + L  + LT,m T,moverlap S/P

X 0,m xx X 1,m xx xx X Lact−1,m xx 0

Parallelto toserial serial(P/S) (P/S) Parallel

xx xx xx xx

InsertLLCP,m -pointCP CP CP,m-point Insert

0 -pointIFFT IFFT OFDM,m-point LLOFDM,m

Input OFDM symbols X m

0

dL m−1,m

x CP-OFDM,m Lact,0

− Interpolation factor: N/Lm = NS/LS,m

FD window

Lact,1 FD window

Lact,2 FD window

Discrete frequency axis with N frequency-domain points. The number of active subcarrier Lact,m can be different for each subband. .

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FC-F-OFDM – PSDs of Fullband Filtered OFDM

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Power in dB

Power in dB

Optimization based on minimizing the inband MSE (or EVM) given the attenuation target at the end of transition band

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−306 −100

−300 −294 0 100 200

Subcarrier n

(a)

(c)

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Figure: 40-dB attenuation target 20

Analysis bank EVM on active subcarriers

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0

B

−400

−60 −312 −300 −200

Subcarrier n

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CP−OFDM signal Synthesis bank Transmitted signal

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Figure: 20-dB attenuation target 20

0 −20 −40

CP−OFDM signal Synthesis bank Transmitted signal

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Analysis bank EVM on active subcarriers

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FC-F-OFDM – PSDs of Filtered Groups of PRBs

CP−OFDM signal Synthesis bank Transmitted signal

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Supports flexible spectrum allocations and adjustable subcarrier spacings Subcarrier n −80 −500

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−200

−100

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200

300

400

500

Analysis bank MSE on active subcarriers

1x12 SCs with 30 kHz SCS

Power in dB

0 6x12 SCs with 60 kHz SCS

24x12 SCs with 15 kHz SCS

−20 −40 −60 −80 −500

−400

−300

−200

−100

0

100

200

300

400

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Subcarrier n

Figure: Three RBGs of Nact = {12, 72, 288} active subcarriers with subcarrier spacing of {30, 60, 15} kHz, respectively. .

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FC-F-OFDM Performance with optimized transition band weights Average EVM

Worst−case EVM

−10

−10 λ = 1/4 λ = 1/2

As = 40 dB As = 30 dB

−14

As = 20 dB

QPSK

As = 10 dB −18

16−QAM

−22

EVM in dB

EVM in dB

−18

−14

64−QAM

−26

−22

−26

−30

−30

−34 256−QAM

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1

3

5

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1

3

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Transition band bins

Transition band bins

(c)

(d)

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Figure: Isolated group of 4 PRBs with both Tx and Rx filtering .

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FC-F-OFDM Complexity Table: Rx MSE versus complexity No. active subcarriers

Overlap factor λ

4 PRBs

1/2 1/4

50 PRBs 12×4 PRBs

Rx complexity (muls/MC-symbol)

Rx complexity (muls/symbol)

Rx complexity relative to OFDM

17 302 11 758

360.46 244.96

×2.41 ×1.64

1/2 1/4

38 468 28 131

64.11 46.89

×5.36 ×3.92

1/2 1/4

35 430 25 774

61.51 44.75

×4.94 ×3.59

Table: Corresponding FIR realization complexity for the 50 PRB case FIR filter length

Rx complexity (muls/MC-symbol)

Rx complexity relative to OFDM

50

51 200

×7.14

100

102 400

×14.28

150

153 600

×21.42

■ The FC filtering complexity is defined by the number of FC processing blocks, subband bandwidth, and number of filtered subbands. ■ To minimize complexity ▶

reducing overlap reduces the number of FC processing blocks

▶

minimizing small transform size with respect to the subband size reduces related complexity .

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Performance Comparison Case 1a, 55 PRBs in 10 MHz channel, spectral localization example 25

25

20

20

15

15 10

PSD [dBm/30 kHz]

PSD [dBm/30 kHz]

10 5 0 −5 −10

LTE OOBEM 30 kHz FC-F-OFDM, 3 bin TBW, As = 30 dB FC-F-OFDM, 2 bin TBW, As = 30 dB

−20

FC-F-OFDM, 2 bin TBW, As = 10 dB −25 −5.06

−5.04

−5.02

−5

−4.98

−4.96

−4.94

0 −5 −10 −15

FC-F-OFDM, 4 bin TBW, As = 40 dB

−15

5

−4.92

Frequency offset from 4 GHz center frequency [MHz]

−20

LTE OOBEM 30 kHz FC-F-OFDM, 2 bin TBW, As = 10 dB, meas BW 30 kHz f-OFDM, TO = 0, meas BW 30 kHz WOLA, Nws = 72, meas BW 30 kHz

−25 −30 −5.06

−5.04

−5.02

−5

−4.98

−4.96

−4.94

−4.92

Frequency offset from 4 GHz center frequency [MHz]

EVM: FC-F-OFDM 0.8 %, f-OFDM 1.1 %, and WOLA 0.7 % .

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Performance Comparison Case 2, mixed numerology DL, victim 15 kHz SCS, aggressor 30 kHz SCS GB = 30 kHz 10 0

BLER

BLER

10 0

10 -1

10 -2 10

10 -1

CP-OFDM reference FC-F-OFDM, 2 bin TBW, As=10 dB

CP-OFDM reference FCFB, 2 bin TBW, As=10 dB

CP-UF-OFDM, NFIR =73

CP-UF-OFDM, NFIR =37

f-OFDM, TO=0 WOLA, Nws=72

f-OFDM, TO=0 WOLA, Nws=72

CP-OFDM without interference 15

20

25

10 -2 30

35

40

10

CP-OFDM without interference 15

20

25

SNR [dB]

TDL-C 300 ns, 256-QAM, R = 3/4

35

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TDL-C 1000 ns, 64-QAM, R = 3/4 .

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SNR [dB]

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Performance Comparison Case 3, asynchronous UL 10 0

BLER

BLER

10 0

10 -1

10 -2 10

10 -1

CP-OFDM reference FC-F-OFDM, 2 bin TBW, As =10 dB

CP-OFDM reference FC-F-OFDM, 2 bin TBW, As =10 dB

CP-UF-OFDM, Nf =73

CP-UF-OFDM, NFIR=37

f-OFDM, TO=0 WOLA, Nws =72

f-OFDM, TO=0 WOLA, Nws =72

CP-OFDM without interference CP-OFDM synchronous UL reference, GB = 45 kHz 15

20

CP-OFDM without interference CP-OFDM synchronous UL reference, GB = 15 kHz

10 -2 25

30

35

40

5

10

15

SNR [dB]

TDL-C 300 ns, 64-QAM, R = 3/4, GB = 45 kHz

25

30

TDL-C 1000 ns, 64-QAM, R = 1/2, GB = 15 kHz .

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SNR [dB]

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Performance Comparison Case 4, mixed numerology UL, victim 15 kHz SCS, aggressor 30 kHz SCS 10 0

BLER

BLER

10 0

10 -1

10 -2 10

10 -1

CP-OFDM reference FC-F-OFDM, 2 bin TBW, As =10 dB

CP-OFDM reference FC-F-OFDM, 2 bin TBW, As =10 dB

CP-UF-OFDM, N FIR=73

CP-UF-OFDM, N FIR=37

f-OFDM, TO=0 WOLA, N ws =72

f-OFDM, TO=0 WOLA, N ws =72 10 -2

CP-OFDM without interference 15

20

25

30

35

40

CP-OFDM without interference 5

10

15

SNR [dB]

TDL-C 300 ns, 64-QAM, R = 3/4, GB = 45 kHz

25

30

TDL-C 1000 ns, 64-QAM, R = 1/2, GB = 15 kHz .

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SNR [dB]

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Conclusions ▶

▶

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FC processing provides a computationally efficient, flexible, and highly selective subband filtering engine Can be used with CP-OFDM, DFTs-OFDM, ZT-DFTs-OFDM, and single carrier waveforms Given the number of transition-band bins, the performance can be optimized for adjusting the trade-off between the in-band MSE and the spectral containment For more complete description and performance analysis, see J. Yli-Kaakinen et al. “Efficient fast-convolution based waveform processing for 5G physical layer,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 6, pp. 1309–1326, 2017. .

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References 1

J. Yli-Kaakinen, T. Levanen, S.Valkonen, M. Renfors, and M. Valkama, “Efficient fast-convolution based waveform processing for 5G physical layer,” IEEE Journal on Selected Areas in Communications (Special Issue on Deployment Issues and Performance Challenges for 5G), vol. 35, no. 6, pp. 1309–1326, 2017.

2

M. Renfors, J. Yli-Kaakinen, T. Levanen, M. Valkama, T. Ihalainen, and J. Vihriälä, “Efficient fast-convolution implementation of filtered CP-OFDM waveform processing for 5G,” in Proc. IEEE Globecom Workshops, San Diego,CA, USA, Dec. 2015.

3

M. Renfors, J. Yli-Kaakinen, T. Levanen, and M. Valkama, “Fast-convolution filtered OFDM waveforms with adjustable CP length,” in Proc. Global Conference on Signal and Information Processing (GlobalSIP), Greater Washington, D.C., USA, pp. 635–639.

4

J. Yli-Kaakinen and M. Renfors, “Optimized reconfigurable fast convolution based transmultiplexers for flexible radio access,” IEEE Trans. Circuits Syst II, 2017, to be published.

5

M. Renfors, J. Yli-Kaakinen, and F. Harris, “Analysis and design of efficient and flexible fast-convolution based multirate filter banks,” IEEE Trans. Signal Processing, vol. 62, no. 15, pp. 3768–3783, Aug. 2014.

6

K. Shao, J. Alhava, J. Yli-Kaakinen, and M. Renfors, “Fast-convolution implementation of filter bank multicarrier waveform processing,” in IEEE Int. Symp. on Circuits and Systems (ISCAS), Lisbon, Portugal, May 24–27 2015, pp. 978–981.

7

M. Renfors and J. Yli-Kaakinen, “Flexible fast-convolution implementation of single-carrier waveform processing,” in IEEE Int. Conf on Communications Workshops (ICCW), London, UK, Jun. 8–12 2015, pp. 1243–1248.

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J. Yli-Kaakinen and M. Renfors, “Optimization of flexible filter banks based on fast convolution,” Journal of Signal Processing Systems, vol. 85, no. 1, pp. 101–111, Aug. 2016. .

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