# Understanding Digital Radio Frequency Memory Performance in Countermeasure Design

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## Abstract

**:**

## 1. Introduction

## 2. DRFM Systems

#### 2.1. Digital Radio Frequency Memory

#### 2.2. Sources of Distortion

## 3. DRFM System Model

#### 3.1. Radar Transmitter

#### 3.2. Jammer Receiver

#### 3.3. DRFM Model

#### 3.4. Signal Correlator

## 4. DRFM Performance Results

#### 4.1. Effects of DRFM Coherence and Radar Waveforms

#### 4.2. Effects of DRFM Receiver Signal-to-Noise Ratio

#### 4.3. Effects of DRFM ADC Resolution

#### 4.4. Effects of Waveform Time-Bandwidth Product

## 5. Multiple Scatterer DRFM

#### 5.1. Multiple Scatterer Targets

#### 5.2. Multiple Scatterer DRFM Implementation

#### 5.3. Multiple Scatterer DRFM Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The Simulink model for the radar transmitter, using manual switches to change waveforms for testing.

**Figure 3.**Example waveforms generated by the testbed for the Phase Shift Keying (PSK) and Linear Frequency Modulated (LFM) signals; in this case, 10 MHz LFM signal at top and a 13-bit Barker code at the bottom.

**Figure 4.**The Simulink model for the jammer receiver and encoding system. Note that the scopes in the upper right were used as part of the test bed to examine the instantaneous amplitude, phase, and frequency while conducting hardware-in-the-loop testing.

**Figure 5.**The Field Programmable Gate Array (FPGA) implementation of the ES receiver threshold detector, using a low-pass-filter and Hilbert transform to measure the signal envelope and find the rising and falling edges. Fixed thresholds are used to determine the edge detections; however, the values are stored in registers allowing for further development into a constant-false-alarm rate receiver.

**Figure 6.**The top level sub-system model of the DRFM in Simulink, including both the amplitude and I-Q DRFM on the left and right, respectively.

**Figure 8.**The top level sub-system model of the radar receiver in Simulink, showing the correlators implemented for the three signals of interest: the original waveform, the amplitude DRFM, and the I-Q DRFM.

**Figure 9.**Correlation results for a linear frequency modulated wave with a pulse width of 10 μs and a bandwidth of 5 MHz.

**Figure 10.**Correlation results for a waveform with a 13-bit Barker code, with a pulse width of 10 μs.

**Figure 11.**Correlation results for a linear frequency modulated wave with a pulse width of 10 μs and a bandwidth of 5 MHz using a variety of SNR values in the DRFM receiver.

**Figure 12.**Correlation results for a waveform with a 13-bit Barker code, with a pulse width of 10 μs using a variety of SNR values in the DRFM receiver.

**Figure 13.**Correlation results for a linear frequency modulated wave with a pulse width of 10 μs and a bandwidth of 5 MHz using a variety of ADC resolutions.

**Figure 14.**Correlation results for a waveform with a 13-bit Barker code, with a pulse width of 10 μs using a variety of ADC resolutions.

**Figure 15.**Correlation results for a linear frequency modulated wave with a pulse width of 10 μs and a variety of bandwidths from an envelope DRFM.

**Figure 16.**Correlation results for a linear frequency modulated wave with a pulse width of 10 μs and a variety of bandwidths from an IQ DRFM.

**Figure 18.**The radar cross section of 10 randomly distributed cylinders with a 0.5 m radius and height of 1 m.

**Figure 20.**Example of a multi-scatterer DRFM signal generated as the sum of four scatterers compared to the received radar signal.

**Figure 21.**The component signals that, when superimposed, create the signal from the DRFM shown in Figure 20.

${\mathit{G}}_{\mathit{p}}$ | $\mathbf{\Delta}\mathit{t}$ | SLL | |
---|---|---|---|

LFM Complex | ≈0 dB | ≈0 $\mathsf{\mu}$s | 5.0 dB |

LFM Envelope | $-8.0$ dB | $8.5\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$s | 1.0 dB |

PSK Complex | ≈0 dB | ≈0 $\mathsf{\mu}$s | 11 dB |

PSK Envelope | $-4.0$ | $6.2\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$s | 1.0 dB |

SNR (dB) | ${\mathit{G}}_{\mathit{p}}$ (dB) | $\mathbf{\Delta}\mathit{t}$ | SLL (dB) | Noise Floor (dB) | |
---|---|---|---|---|---|

LFM | 20 | ≈0 | ≈0 | 5 | 3 |

10 | ≈0 | ≈0 | 5 | 7 | |

0 | ≈0 | ≈0 | 5 | 11 | |

−10 | ≈0 | ≈0 | 5 | 14 | |

PSK | 20 | ≈0 | ≈0 | 11 | 14 |

10 | ≈0 | ≈0 | 11 | 12 | |

0 | ≈0 | ≈0 | 11 | 10 | |

−10 | ≈0 | ≈0 | 9 | 7 |

ADC Bits | 1 | 2 | 4 | 6 |
---|---|---|---|---|

SLL—LFM | $-9$ dB | $-12$ dB | $-18$ dB | $-22$ dB |

SLL—PSK | $-3$ dB | $-6$ dB | $-12$ dB | $-12$ dB |

Envelope | Complex | ||||
---|---|---|---|---|---|

Bandwidth | $\mathbf{\Delta}\mathit{t}$($\mathsf{\mu}$s) | ${\mathit{G}}_{\mathit{p}}$(dB) | $\mathbf{\Delta}\mathit{t}$($\mathsf{\mu}$s) | ${\mathit{G}}_{\mathit{p}}$(dB) | SLL (dB) |

1 MHz | 7.5 | $-4$ | ≈0 | ≈0 | $-6$ |

2 MHz | 8.5 | $-5$ | ≈0 | ≈0 | $-9$ |

5 MHz | 9.5 | $-8$ | ≈0 | ≈0 | $-12$ |

10 MHz | 10.0 | $-9$ | ≈0 | ≈0 | $-15$ |

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**MDPI and ACS Style**

Davidson, K.; Bray, J.
Understanding Digital Radio Frequency Memory Performance in Countermeasure Design. *Appl. Sci.* **2020**, *10*, 4123.
https://doi.org/10.3390/app10124123

**AMA Style**

Davidson K, Bray J.
Understanding Digital Radio Frequency Memory Performance in Countermeasure Design. *Applied Sciences*. 2020; 10(12):4123.
https://doi.org/10.3390/app10124123

**Chicago/Turabian Style**

Davidson, Kyle, and Joey Bray.
2020. "Understanding Digital Radio Frequency Memory Performance in Countermeasure Design" *Applied Sciences* 10, no. 12: 4123.
https://doi.org/10.3390/app10124123