# A Weighted Linearization Method for Highly RF-PA Nonlinear Behavior Based on the Compression Region Identification

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## Abstract

**:**

## 1. Introduction

## 2. Dynamic Modeling Stage

#### 2.1. Memory Polynomial Model (MPM)

#### 2.2. Weighted MPM as Dynamical Modeling and Linearization Stages

## 3. Experimental System-Level Setup

#### Measurement Procedure

## 4. Modeling and Linearization Stage Setup

#### Indirect Learning Approach for the Proposal Modeling Stage

- (i)
- An algorithm is performed for the offline training of the model (PA) and the predistorter (PD) block using the MPM and W-MPM approaches (running on MATLAB-PC with DSP blockset system environment) as defined in the overall block diagram in Figure 2.
- (ii)
- At every iteration, the model searches for a weighting subset of parameters to contribute in the minimization the LSE and NMSE.
- (iii)
- The developed chain through DSP Builder tool allows us to transfer the input signal compared with the amplification process by the DAC of the FPGA development board Cyclone V.
- (iv)
- Both signals are sampled using 10-bit resolution related to the address bus capability; the magnitude signals are sampled for the maximum resolution of the HSMC card with 14 bits.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental measurement testbed setup based on ARRIA V Board for a radio frequency power amplifier (RF-PA).

**Figure 2.**Indirect learning approach (ILA) algorithm block diagram: (

**a**) DSP-FPGA physical link for data conditioning, (

**b**) adaptive weighted memory polynomial model (W-MPM) modeling stage, and (

**c**) proposed ILA system control-based scheme.

**Figure 3.**Linearization based on ILA based on MPM for the device NXP 10 W at 2.34 GHz. (

**a**) AM/AM modeling and linearization stage and (

**b**) AM/PM modeling and linearization stage.

**Figure 4.**Linearization based on ILA based on W-MPM for the device NXP 10 W at 2.34 GHz. (

**a**) AM/AM modeling and linearization stage and (

**b**) AM/PM modeling and linearization stage.

**Figure 5.**Linearization based on ILA based on MPM for the device ZHL-42W+ at 2000 MHz 32.24 dBm RF-PA. (

**a**) AM/AM modeling and linearization stage and (

**b**) AM/PM modeling and linearization stage.

**Figure 6.**Linearization based on ILA based on W-MPM for the device ZHL-42W+ at 2000 MHz 32.24 dBm RF-PA. (

**a**) AM/AM modeling and linearization stage and (

**b**) AM/PM modeling and linearization stage.

PA NXP 10 W @ 2.34 GHz | |
---|---|

Parameter | Values |

Gain | 12.26 dB @ 2.34 GHz |

PA input Power | 23.84 dBm |

PA output Power | 36.10 dBm |

Device biasing | ${\mathrm{V}}_{\mathrm{DS}}$ = 50 V, ${\mathrm{I}}_{\mathrm{DS}}$ = 54 mA |

PA ZHL-42W+ @ 2.00 GHz | |
---|---|

Parameter | Values |

Gain | 34 dB @ 2.00 GHz |

Maximum power | 1.25 W |

DC Supply | 15 V, 1 A |

Bandwidth | 10–4200 MHz |

**Table 3.**Hardware resources occupation in Cyclone V 5CEFAF31I7 FPGA device with comparison for the W-MPM and MPM models.

Description | W-MPM Resource Utilization | MPM Resource Utilization |
---|---|---|

Logic Utilization (ALMs) | 340/56,480 (<1%) | 378/56,480 (<1%) |

Total Registers | 771 | 751 |

Total Pins I/O | 40/480 (8%) | 40/480 (8%) |

Total block memory bits | 43,008/7,024,0640 (<1) | 43,008/7,024,0640 (<1) |

Total PLLs | 1/7 (14%) | 1/7 (14%) |

Complexity Metric | W-MPM | MPM |
---|---|---|

Number of distinct operators | 7 | 7 |

Number of distinct operands | 7 | 7 |

Total number of operators | 9 | 11 |

Total number of operands | 7 | 7 |

Program vocabulary | 14 | 14 |

Program length: | 16 | 18 |

Calculated estimated program length | 39.30 | 39.30 |

Volume | 60.92 | 68.53 |

Difficulty | 3.50 | 3.50 |

Effort | 213.21 | 239.86 |

Time required to program (s) | 11.85 | 13.33 |

Number of delivered bugs | 0.07 | 0.08 |

Model Stage | RF-PA Linearity | Technology | Nonlinearity and Memory Effects | Coefficients Number | Accuracy NMSE (dB) |
---|---|---|---|---|---|

Proposed work, Device: PA NXP 10 W @ 2.34 GHz | |||||

W-MPM model | Nonlinear | GaN HEMT | High order | 55 | −38.03 and −44.9028 |

MPM model | Nonlinear | GaN HEMT | High order | 67 | −32.72 and −44.349 |

Proposed work, Device: ZHL-42W+ @2000 MHz 32.24 dBm | |||||

W-MPM model | Nonlinear | CMOS+LVDS | High order | 55 | −27.8946 |

MPM model | Nonlinear | CMOS+LVDS | High order | 67 | −24.8707 |

Related works | |||||

Hammerstein ${}^{\u2020}$, [28] | Nonlinear | GaN | High order | N/A | −33.55 |

Hammerstein ${}^{\u2021}$, [28] | Nonlinear | GaN | High order | N/A | −35.72 |

MP, [29] | Nonlinear | GaN Doherty | High order | N/A | −32.2 |

EMP, [29] | Nonlinear | GaN Doherty | High order | N/A | −24.9 |

SVR, [30] | Nonlinear | LDMOS | High order | 256 | −36.5 |

DVR, [31] | Nonlinear | GaN Doherty | High order | 99 | −31 |

Device NXP 10 W @ 2.34 GHz | Estimated EVM | EVM with ILA |

MPM | $15.624\%$ | $2.547\%$ |

W-MPM | $16.54\%$ | $1.06\%$ |

Device ZHL-42W+ @ 2000 MHz 32.24 dBm | Estimated EVM | EVM with ILA |

MPM | $25.28\%$ | $1.18\%$ |

W-MPM | $25.18\%$ | $0.96\%$ |

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**MDPI and ACS Style**

Galaviz-Aguilar, J.A.; Vargas-Rosales, C.; Cárdenas-Valdez, J.R.; Martínez-Reyes, Y.; Inzunza-González, E.; Sandoval-Ibarra, Y.; Núñez-Pérez, J.C. A Weighted Linearization Method for Highly RF-PA Nonlinear Behavior Based on the Compression Region Identification. *Appl. Sci.* **2021**, *11*, 2942.
https://doi.org/10.3390/app11072942

**AMA Style**

Galaviz-Aguilar JA, Vargas-Rosales C, Cárdenas-Valdez JR, Martínez-Reyes Y, Inzunza-González E, Sandoval-Ibarra Y, Núñez-Pérez JC. A Weighted Linearization Method for Highly RF-PA Nonlinear Behavior Based on the Compression Region Identification. *Applied Sciences*. 2021; 11(7):2942.
https://doi.org/10.3390/app11072942

**Chicago/Turabian Style**

Galaviz-Aguilar, Jose Alejandro, Cesar Vargas-Rosales, José Ricardo Cárdenas-Valdez, Yasmany Martínez-Reyes, Everardo Inzunza-González, Yuma Sandoval-Ibarra, and José Cruz Núñez-Pérez. 2021. "A Weighted Linearization Method for Highly RF-PA Nonlinear Behavior Based on the Compression Region Identification" *Applied Sciences* 11, no. 7: 2942.
https://doi.org/10.3390/app11072942