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Short Video Paper | Low-Precision Quantization MIMO Radar Constant Modulus Waveform Design Method Based on ADPM
To achieve excellent beamforming performance, MIMO radar systems typically configure a large number of active antenna units. However, using high-precision (over 10 bits) digital-to-analog converter (DAC) components significantly increases the complexity, energy consumption, and cost of the system. In contrast, low-precision DAC components can significantly reduce system power consumption and cost and have been widely applied in various scenarios, such as low-power ultra-wideband communication systems and large or ultra-large scale MIMO systems. Existing MIMO radar waveform design methods mainly target systems using high-precision DAC components, while methods for designing waveforms for low-precision DAC components are relatively scarce. Directly quantizing the transmit signals based on existing algorithms designed for infinite precision DACs to adapt to low-precision DAC components will severely degrade system performance.
Figure 1: System structure diagram of the MIMO radar transmitter with low-precision DAC components
Using low-precision DAC components can effectively overcome the above issues; however, existing MIMO radar waveforms designed under the condition of infinite precision DACs are often difficult to directly apply to low-precision DAC systems. The core difficulty of low-precision quantization waveform design lies in solving the non-convex constraints of discrete phases or discrete amplitudes. The most straightforward method is to use exhaustive search, but as the signal dimension and the number of snapshots increase, the computational complexity and time increase exponentially.
In recent years, Associate Professor Liao Bin’s team at Shenzhen University has conducted in-depth research on low-precision quantization waveform design for radar.
Figure 2: Associate Professor Liao Bin’s team at Shenzhen University
They proposed a method for designing MIMO radar transmit waveforms based on low-precision quantization. By designing a constant modulus transmit waveform sequence that is low-precision quantized, the transmit waveform can better adapt to low-precision quantization DAC components, achieving the best match for transmitting waveforms of arbitrary precision. To solve the non-convex optimization problem of the modeled constant modulus discrete phase constraints, the quadratic fraction is first transformed into a subtraction form using the Dinkelbach algorithm, and then the Alternating Direction Penalty Method (ADPM) framework is employed to transform the discrete phase constraints into parallel trigonometric function problems, gradually approaching the optimal solution through alternating iterations.
Figure 3: Feasible regions of low-precision 1-bit and 2-bit quantized waveform elements
This work has been published in the 4th issue of the “Radar Journal” 2022 paper titled Low-Precision Quantization MIMO Radar Constant Modulus Waveform Design Method Based on ADPM (Wan Huan, Yu Xianxiang, Quan Zhi, Liao Bin).
This paper uses the ISMR criterion to design constant modulus transmit signals. The optimization problem model is described as:
The objective function of this optimization problem is a quadratic fraction, and the constraints include non-convex discrete phase constraints. This problem is NP-hard and difficult to solve. For this non-convex problem, this paper first transforms the quadratic fractional form of the objective function into a subtraction form using the Dinkelbach algorithm, and then based on the ADPM framework, auxiliary variables are introduced to transform the discrete phase constraints into separate parallel trigonometric function problems, gradually approaching the optimal solution through iterations. The algorithm steps are as follows:
Figure 4: Algorithm steps of the low-precision quantization MIMO radar constant modulus waveform design based on Dinkelbach alternating direction penalty method
Finally, numerical simulations were conducted to analyze the performance of the proposed method for extremely low precision 1-bit and low precision 2-5 bit quantized waveform direction patterns and integral sidelobe ratios (ISMR), verifying the effectiveness of the method.
Figure 5: Direction pattern of the waveform quantized at extremely low precision 1 bit and the relationship between ISMR and iteration count
Figure 6: Direction pattern of the low precision 2-5 bit quantized waveform and the relationship between ISMR and iteration count
The low-precision constant modulus transmit model design method proposed by Associate Professor Liao Bin’s team at Shenzhen University can be applied to the design of transmit waveforms of any quantization precision. Compared to other low-precision design methods, it achieves better integral sidelobe ratio (ISMR) performance, providing theoretical basis and reference value for the selection of waveform performance requirements and DAC quantization precision in practical engineering applications.
Wan Huan (1992-), female, from Nanchang, Jiangxi, PhD. In 2022, she obtained her PhD degree from the School of Electronics and Information Engineering at Shenzhen University and is currently a lecturer at the School of Artificial Intelligence at Shenzhen Polytechnic. Her main research directions include array signal processing, radar waveform design, and optimization theory algorithms.
Yu Xianxiang (1991-), male, from Sichuan, PhD. In 2020, he obtained his PhD degree from the University of Electronic Science and Technology and is currently a postdoctoral researcher at the University of Electronic Science and Technology. His main research directions include radar waveform design and processing, optimization theory algorithms, and array signal processing. He has published more than 10 papers in IEEE Transactions journals.
Quan Zhi (1978-), male, from Liuzhou, Guangxi, distinguished professor at Shenzhen University, doctoral supervisor, and recipient of the National Excellent Youth Science Fund. His main research directions include long-range wideband wireless communication systems, RF system calibration and testing, and data-driven signal processing. He serves on the editorial board of journals such as IEEE Transactions on Signal Processing.
Liao Bin (1983-), male, from Pingxiang, Jiangxi, distinguished researcher at Shenzhen University, doctoral supervisor, and deputy director of the Guangdong Key Laboratory of Intelligent Information Processing. His main research directions include array signal processing, adaptive signal processing, and radar signal processing. He serves on the editorial board of journals such as IEEE Transactions on Aerospace and Electronic Systems.
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