# Design and Analysis of Multiple-Input Multiple-Output Radar System Based on RF Single-Link Technology

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## Abstract

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## 1. Introduction

_{0}-norm algorithm for fast sparse DOA estimation has been proposed for multiple measurement vectors in MIMO radar systems [18]. The results indicated that it can eliminate the white or colored Gaussian noises and achieve better DOA estimation performance. The nuclear norm minimization algorithm [19] was proposed to extend the virtual array aperture, which provides better performance compared with the conventional sparse recovery-based algorithms and can handle the case of underdetermined DOA estimation in MIMO radar systems. The single-link MIMO system was originally developed on the basis of virtual array elements. Different methods to realize the physical structure of the single radio frequency (RF) link radar receivers are discussed in [20]. The single RF link MIMO transmission system was investigated more systematically in [21]. The antenna feed terminal entity element in the MIMO system was replaced by a virtual antenna element, and the transmitter array was more efficient by using the binary phase shift keying (BPSK) modulation. This technique not only solves the size problem of MIMO antennas, but reduces the mutual coupling between antennas, which greatly improves the efficiency of MIMO systems. The single RF link MIMO-OFDM system was proposed [22,23,24] to realize the purpose of multicarrier signal transmission. Several signals were superimposed in the time domain and the OFDM waveform was finally formed. This solves the problem of replication interference caused by the beam switching in the receiver of MIMO antennas compared to the previous systems. A beam-switched antenna was realized by using eight parasitic antenna elements and PIN diodes, which effectively met the demand of generating more waveforms at the transmitter. A compact frequency tunable single RF link MIMO transmission scheme was proposed in [25]. This approach simplifies the DC bias circuit and various loads in the BPSK modulation, so the external reconfigurable matching circuits can be omitted for simplification.

(·)^{H}: Conjugate transpose | G(·): Gamma distribution |

U(x): unit step function | K_{v}(·): v order Bessel function |

J_{0} (·): zero order Bessel function | E[·]: expected operation |

## 2. MIMO Radar Principle

_{eff}denotes the number of the symbol period division for different patterns. The received vector at the end of the period can be described as:

_{v}(·) is the v order Bessel function of the second kind. v and a denote the shape coefficient and scaling factor, respectively. For a variable θ that is uniformly distributed between 0 and 2π, the characteristic function C

_{Y}(u;v) can be defined as:

_{0}(·) and E[·] represent the zero-order Bessel function expected operation. When the second Bessel function approaches infinity, the characteristic function C

_{Y}(u;v) has a limited value:

_{i}= 2, …, n + 2} is non-negative, which means the variables of Rayleigh distribution can be considered as a mixture of several two-dimensional χ

^{2}distribution variables. Defining a sequence of weights {p

_{1}(i); i = 0, 1, 2, …}, where p

_{1}(i) = α

_{i}when i = 2, 3, 4, …, n + 2 and p

_{1}(i) = 0 when i takes other values, then we can express (11) as:

_{m}(i); i = 0, 1, 2, …} is obtained after M times convolution of itself, which means p

_{m}(i) = p

_{m−1}(i)* p

_{1}(i) and the coefficient sequence can be obtained by the fast Fourier transformation (FFT) algorithm.

## 3. MIMO Radar Simulation Platform

#### 3.1. Signal Generation Module

#### 3.2. Noise and Data Receiver Module

_{d}is the Doppler shift of the radar target. The clutter and noise of the Rayleigh distribution are generated by Gaussian signal generator. The difference is that the bandwidth is different from the amplitude. After the superposition, the target delay is added by a delay element and the distance of the target can be calculated. The resulting signal is a reflected signal with clutter, noise, and target information.

#### 3.3. Signal Receiving and Processing Module

_{d}and f

_{PRF}are the target Doppler shift and pulse repetition rate of the pulse radar, respectively. N and n are the sampling number and the serial number of the FFT process, respectively.

## 4. System Performance Discussion

#### 4.1. Performance Comparison Results

#### 4.2. Parameter Discussion on System Performance

#### 4.2.1. Switch Time

_{on}and T

_{off}, can be used to indicate the starting point and ending point, respectively. For SPDT switches, the switching time is 0 under ideal conditions, and two-way signals can be seamlessly switched at any time. In the nonideal case, the signal is changing during the switching time, which will lead to the control signal error result during the sampling process. In order to eliminate the error of the control signal, T

_{on}and T

_{off}should be smaller than the sampling interval to ensure the correctness of the control signal. With a stable symbol rate, this goal is achieved by selecting switch components with appropriate switching time.

_{1}(t) as input signal and v

_{2}(t) as the control signal, v

_{3}(t) and v

_{4}(t) as two outputs, and the threshold value of control signal as 0.5, if v

_{2}(t) is larger than 0.5, the main input signal outputs from the v

_{3}(t) path. If the switch is switched at t = T instant, the two outputs are:

_{2}(t) is smaller than 0.5, the main input signal outputs from the v

_{4}(t) path. If the switch is switched at t = T instant, the two outputs are:

_{on}or T

_{off}should be less than the sampling time interval. In the case of fixed symbol rate, we want to achieve this goal by selecting components that have a suitable switching time.

#### 4.2.2. Isolation

#### 4.2.3. Signal-to-Noise Ratio

#### 4.2.4. Insertion Loss

#### 4.2.5. Dynamic Range

_{max}and P

_{min}are the upper limit and lower limit of the receiving signal amplitude, respectively. In order to make sure the system is working under the linear area of the receiver, the transmitter has to consume more energy, which reduces the efficiency of the single RF link MIMO radar system. Meanwhile, the introduction of insertion loss will theoretically increase and lead to the decrease of dynamic range. Therefore, for the single RF link MIMO radar, the insertion loss introduced by the newly added SPDT switch will greatly affect the performance of the radar. In order to work properly, it is very important to adopt an SPDT switch with small loss.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the multiple-input multiple-output (MIMO) radar model. There are M elements in the transmitting array and N elements in the receiving array. The transmitted signal is reflected by the radar target and received by the receiving antenna.

**Figure 2.**Cell-averaging constant false alarm rate (CA-CFAR) algorithm flowchart. There are n unit signals at each side of the protection unit. The CFAR processor will process the input signal and transmit the clutter estimation to the multiplier for target detection.

**Figure 3.**MIMO radar simulation platform schematic. The system noise, channel noise, and clutter are added to the radar target reflected signal, then the sum signal is processed for data analysis.

**Figure 4.**Linear frequency modulation (LFM) signal. The blue line and the red line represent the real part and imaginary part of the signal, respectively. LFM signals with large time width will not only improve the radar speed, accuracy, and resolution, but also the radar’s detection range.

**Figure 5.**Schematic diagram of target and noise. Gaussian signal generator will generate the clutter and noise of the Rayleigh distribution and the interference will be added to the input data after the Doppler shift.

**Figure 6.**Schematic diagram of a MIMO radar data-receiving module. In the data-receiving module, the received signal first passes the bandpass filter to filter out the clutter from the outside, then go through the digital receiver and the matched bandpass filters.

**Figure 7.**Schematic diagram of the frequency conversion module. The frequency conversion module is composed of oscillator, bandpass filter, amplifier, and mixer.

**Figure 8.**The target was not detected after the pulse detection (PD) process. If the target was not detected, no significant peaks are found in the received waveform.

**Figure 9.**The target was detected after the PD process. If the target was detected, there will be significant peaks in the received waveform, as is shown in the figure.

**Figure 10.**Schematic diagram of the pulse compression process. The two broad pulses are compressed into two narrower pulses through a pulse compression process, with one path representing the reference signal and the other path representing the received signal.

**Figure 11.**Single-link radiofrequency (RF) MIMO radar system proposed in this paper. The system consists of signal generator module, control signal, signal processing module, up-conversion module, clutter module, single-link MIMO module, and receiver module.

**Figure 12.**Receiver operating characteristic (ROC) curves of two radar systems. The points on the curve reflect the sensitivity of the two different radar systems. The areas under curve (AUC) of the single link MIMO radar is larger than the traditional MIMO radar and has the better detection ability.

Target Type | Fluctuation Type | Probability Density Function |
---|---|---|

Swerling I | Slow | $P(\sigma )=\frac{1}{\overline{\sigma}}\mathrm{exp}(-\frac{\sigma}{\overline{\sigma}})$ |

Swerling II | Fast | $P(\sigma )=\frac{1}{\overline{\sigma}}\mathrm{exp}(-\frac{\sigma}{\overline{\sigma}})$ |

Swerling III | Slow | $P(\sigma )=\frac{4\sigma}{{\overline{\sigma}}^{2}}\mathrm{exp}(-\frac{2\sigma}{\overline{\sigma}})$ |

Swerling IV | Fast | $P(\sigma )=\frac{4\sigma}{{\overline{\sigma}}^{2}}\mathrm{exp}(-\frac{2\sigma}{\overline{\sigma}})$ |

Parameter | Sampling Rate | Baseband Frequency | Intermediate Frequency | Operation Frequency | Pulse Repetition | Pulse Width |
---|---|---|---|---|---|---|

Value | 20 MHz | 60 MHz | 2.9 GHz | 10 GHz | 20 kHz | 500 ns |

Radar Type | Target Distance | Range Error Rate | Target Speed | Speed Error Rate |
---|---|---|---|---|

Single Link MIMO Radar | 9082.5 m | 0.9% | 262.5 m/s | 2.8% |

Traditional MIMO Radar | 9052.5 m | 0.6% | 271.875 m/s | 0.7% |

Parameter | Switch Time | Insertion Loss | Isolation | Clutter | Noise | Clutter Bandwidth | Noise Bandwidth |
---|---|---|---|---|---|---|---|

Value | 8 ns | 0.5 dB | 30 dB | 5 V | 1 V | 10 KHz | 6 MHz |

Clutter Amplitude | 8 V | 9 V | 10 V | 11 V | 12 V | 13 V | 14 V |
---|---|---|---|---|---|---|---|

Detection Probability | 0.996 | 0.993 | 0.993 | 0.991 | 0.987 | 0.981 | 0.978 |

Insertion Loss | 0 dB | 0.5 dB | 1 dB | 1.5 dB | 2 dB | 2.5 dB | 3dB |
---|---|---|---|---|---|---|---|

Detection Probability | 0.997 | 0.997 | 0.995 | 0.987 | 0.986 | 0.982 | 0.968 |

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## Share and Cite

**MDPI and ACS Style**

Yu, H.; Yang, G.; Li, Y.; Meng, F.
Design and Analysis of Multiple-Input Multiple-Output Radar System Based on RF Single-Link Technology. *Symmetry* **2018**, *10*, 130.
https://doi.org/10.3390/sym10050130

**AMA Style**

Yu H, Yang G, Li Y, Meng F.
Design and Analysis of Multiple-Input Multiple-Output Radar System Based on RF Single-Link Technology. *Symmetry*. 2018; 10(5):130.
https://doi.org/10.3390/sym10050130

**Chicago/Turabian Style**

Yu, He, Guohui Yang, Yingsong Li, and Fanyi Meng.
2018. "Design and Analysis of Multiple-Input Multiple-Output Radar System Based on RF Single-Link Technology" *Symmetry* 10, no. 5: 130.
https://doi.org/10.3390/sym10050130