One-bit radar, performing signal sampling and quantization by a one-bit ADC, is a promising technology for many civilian applications due to its low-cost and low-power consumptions. In this paper, problems encountered by one-bit LFMCW radar are studied and a two-stage target detection method termed as the dimension-reduced generalized approximate message passing (DR-GAMP) approach is proposed. Firstly, the spectrum of one-bit quantized signals in a scenario with multiple targets is analyzed. It is indicated that high-order harmonics may result in false alarms (FAs) and cannot be neglected. Secondly, based on the spectrum analysis, the DR-GAMP approach is proposed to carry out target detection. Specifically, linear preprocessing methods and target predetection are firstly adopted to perform the dimension reduction, and then, the GAMP algorithm is utilized to suppress high-order harmonics and recover true targets. Finally, numerical simulations are conducted to evaluate the performance of one-bit LFMCW radar under typical parameters. It is shown that compared to the conventional radar applying linear processing methods, one-bit LFMCW radar has about $1.3$ dB performance gain when the input signal-to-noise ratios (SNRs) of targets are low. In the presence of a strong target, it has about $1.0$ dB performance loss.
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