Performance Analysis of One-Bit Digital Beamforming

One-bit quantization brings considerable convenience if applied in digital array radar systems, from a hardware viewpoint. In the topic of one-bit beamforming, our previous work has characterized one-bit array signal and revealed that the resulting angle dispersion effect would lead to spatial filter mismatch when forming beams on receive. But the analysis was limited to a high-SNR or noiseless case. Considering a low-SNR input, this article begins with developing a one-bit array signal model incorporating channel-independent noise, finding the harmonic amplitude noise-associated with the output. We proceed to formulate the one-bit correlation matrix as a sum of infinite harmonic signal plus noise correlation matrices, indicating that signal and noise are separable in spatial correlation, whereas inseparable in the waveform. Accordingly, we describe the one-bit effect of harmonic angle dispersion and power attenuation. More importantly, we quantitatively evaluate one-bit beamforming performance in high (low)-SNR cases by measuring the signal-to-harmonics (noise) ratio at the output. Eventually, the conclusion is achieved that quantifying the array signal at one bit does not necessarily lead to beamforming performance degradation. Particularly, given a low-SNR input, the ratio improves after one-bit beamforming. Numerical results are also provided by simulation to confirm our theoretical findings.