National Taiwan University of Science and Technology A

Outline • Abstract • Predistorter concept • Crosstalk • Digital predistorter ▫ Crossover digital

Abstract • This paper proposes a low complexity crossover digital predistorter (CO-DPD) to compensate

Predistorter concept • A predistorter has inverse of nonlinear PA. the predistorter usually add

Crosstalk • Two or more signal sources will induce crosstalk effects which can be

Crosstalk Equation (5) used to represent the output signal after the PA under the

Crosstalk 串音干擾定義如下: Communication Research Laboratory 10 2021/3/12

Digital predistorter Fig. 4 IDL predistorter structure Communication Research Laboratory 12 2021/3/12

Digital predistorter Following above defined, we want Because we also want , and G=1。Training

Crossover digital predistorter Fig. 5 Crossover digital predistorter structure Communication Research Laboratory 15 2021/3/12

Crossover digital predistorter Similarly, training crossover digital predistorter as follow: Because we also want

Low complexity CO-DPD Fig. 6 low complexity Crossover digital predistorter structure Communication Research Laboratory

Low complexity CO-DPD Similarly, using SISO predistorter to compensation. We want Then uses another

Compare complexity We know that the matrix A multiplied by B has and (complex)

Compare complexity Crossover digital predistorter: Low complexity crossover digital predistorter: where and is Communication

Compare complexity Let , we calculate computational complexityof crossover digital predistorter: That has (complex)

Compare complexity That has (complex) multiplications and Communication Research Laboratory 24 (complex) additions. 2021/3/12

Compare complexity We compare CO-DPD with low complexity CO-DPD: Multiplication CO-DPD 18231120 NEW CO-DPD

Simulation Fig. 7 System structure Communication Research Laboratory 27 2021/3/12

Simulation Fig. 8 BER in 2× 2 SFBC OFDM : Crosstalk=-20 d. B, OBO=6.

Simulation Fig. 9 BER in 2× 2 SFBC OFDM : Crosstalk=-40 d. B, OBO=6.

Simulation Fig. 10 TD in 2× 2 SFBC OFDM : Crosstalk=-20 d. B Communication

Simulation Fig. 11 TD in 2× 2 SFBC OFDM : Crosstalk=-40 d. B Communication

Simulation Fig. 12 PSD in 2× 2 SFBC OFDM : 64 QAM, Crosstalk=-20 d.

Conclusion • The low complexity CO-DPD can reduce more than one half of the

Thanks for Your Attention. Communication Research Laboratory 35 2021/3/12

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National Taiwan University of Science and Technology A Study of Low Complexity Crossover Digital Predistorter for 2× 2 SFBC OFDM Systems Reporter: Lee, Chang Lung Data : 2012/11/1 2021/3/12 1

Outline • Abstract • Predistorter concept • Crosstalk • Digital predistorter ▫ Crossover digital predistorter ▫ Low complexity crossover digital predistorter ▫ Compare complexity • Simulation • Conclusion Communication Research Laboratory 2 2021/3/12

Abstract • This paper proposes a low complexity crossover digital predistorter (CO-DPD) to compensate the nonlinear effects due to the power amplifier (PA) and crosstalk interference in a 2× 2 space frequency block code (SFBC) orthogonal frequency division multiplexing (OFDM) systems. The computational complexity of both conventional CO-DPD and our low complexity CO-DPD is computed and compared. Communication Research Laboratory 4 2021/3/12

Predistorter concept • A predistorter has inverse of nonlinear PA. the predistorter usually add before PA. Fig. 1 Predistorter concept Where is PA gain. Fig. 2 Predistorter chart. Communication Research Laboratory 6 2021/3/12

Crosstalk • Two or more signal sources will induce crosstalk effects which can be seen in MIMO systems. In Fig. 3, the crosstalk effects can be found before the nonlinear PA, which come from the local oscillator or IC. Fig. 3 DPD and PA with nonlinear crosstalk in systems. Communication Research Laboratory 8 2021/3/12

Crosstalk Equation (5) used to represent the output signal after the PA under the crosstalk interference: Where and are the functions representing the nonlinear PA response at each branch. SISO predistorter: Communication Research Laboratory 9 2021/3/12

Crosstalk 串音干擾定義如下: Communication Research Laboratory 10 2021/3/12

Digital predistorter Fig. 4 IDL predistorter structure Communication Research Laboratory 12 2021/3/12

Digital predistorter Following above defined, we want Because we also want , and G=1。Training predistorter is as follow: , we use LS to calculate DPD coefficient: where is pseudo-inverse. We know that LS only training once, then Communication Research Laboratory 13 : 2021/3/12

Crossover digital predistorter Fig. 5 Crossover digital predistorter structure Communication Research Laboratory 15 2021/3/12

Crossover digital predistorter Similarly, training crossover digital predistorter as follow: Because we also want where and Communication Research Laboratory and , we use LS to calculate DPD coefficient: . 16 2021/3/12

Low complexity CO-DPD Fig. 6 low complexity Crossover digital predistorter structure Communication Research Laboratory 18 2021/3/12

Low complexity CO-DPD Similarly, using SISO predistorter to compensation. We want Then uses another path to compensation. We want Communication Research Laboratory 19 and . . 2021/3/12

Compare complexity We know that the matrix A multiplied by B has and (complex) additions. (complex) multiplications The computational complexity of the inverse matrix of Gaussian elimination has multiplications and additions when the size of a matrix is. Communication Research Laboratory 21 2021/3/12

Compare complexity Crossover digital predistorter: Low complexity crossover digital predistorter: where and is Communication Research Laboratory matrix, 22 and is a vector. 2021/3/12

Compare complexity Let , we calculate computational complexityof crossover digital predistorter: That has (complex) multiplications and Communication Research Laboratory 23 (complex) additions. 2021/3/12

Compare complexity That has (complex) multiplications and Communication Research Laboratory 24 (complex) additions. 2021/3/12

Compare complexity We compare CO-DPD with low complexity CO-DPD: Multiplication CO-DPD 18231120 NEW CO-DPD 8935380 Addition CO-DPD 18114480 NEW CO-DPD 8830890 Communication Research Laboratory 25 2021/3/12

Simulation Fig. 7 System structure Communication Research Laboratory 27 2021/3/12

Simulation Fig. 8 BER in 2× 2 SFBC OFDM : Crosstalk=-20 d. B, OBO=6. 1 d. B, 8. 5 d. B and 8. 5 d. B Communication Research Laboratory 28 2021/3/12

Simulation Fig. 9 BER in 2× 2 SFBC OFDM : Crosstalk=-40 d. B, OBO=6. 1 d. B, 8. 5 d. B and 8. 5 d. B Communication Research Laboratory 29 2021/3/12

Simulation Fig. 10 TD in 2× 2 SFBC OFDM : Crosstalk=-20 d. B Communication Research Laboratory 30 2021/3/12

Simulation Fig. 11 TD in 2× 2 SFBC OFDM : Crosstalk=-40 d. B Communication Research Laboratory 31 2021/3/12

Simulation Fig. 12 PSD in 2× 2 SFBC OFDM : 64 QAM, Crosstalk=-20 d. B, OBO=8. 5 d. B Fig. 13 PSD in 2× 2 SFBC OFDM : 64 QAM, Crosstalk=-40 d. B, OBO=8. 5 d. B ACPR(Crosstalk=-20 d. B) ACPR(Crosstalk=-40 d. B) PA -25. 4774 d. B -26. 7509 d. B CO-DPD -29. 7316 d. B -34. 1253 d. B Low complexity CO-DPD -29. 9013 d. B -34. 199 d. B Communication Research Laboratory 32 2021/3/12

Conclusion • The low complexity CO-DPD can reduce more than one half of the number of calculations. • The low complexity CO-DPD can perform almost as well as CO-DPD when crosstalk is -40 d. B. • Low complexity CO-DPD has a adaptive if we set error function in compensation self. Communication Research Laboratory 34 2021/3/12

Thanks for Your Attention. Communication Research Laboratory 35 2021/3/12