Direction Finding and Performance Analysis With 1 bit Time Modulated Array

Abstract

A novel single-channel direction finding (DF) method with spatial spectrum estimation is proposed based on 1 bit time-modulated array (TMA). Its performance is analyzed from theoretical derivation to numerical simulations and compared with other existing DF methods. The proposed DF method is implemented as follows. First, the received sideband signals from the 1 bit modulated single-channel signal are deduced, followed by the detailed analysis of the received noise distribution. Second, the harmonic recovery (HR) method with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2} $ </tex-math></inline-formula> -norm approximation is utilized to recover the original array signals. Finally, conventional spatial spectrum estimation methods are easily applied for high-accuracy DF. Meanwhile, The DF accuracy of the proposed 1 bit method is analyzed under the Gaussian noise model, and its Cramér–Rao lower bounds (CRLBs) are deduced for the first time and compared with conventional arrays and other DF TMA systems. Numerical simulations are provided to show that the proposed 1 bit TMA system and HR method can achieve better accuracy performance over the existing TMA systems when the circuit noise is predominant in the received noises. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -band 1 bit TMA system is fabricated and implemented to experimentally verify the feasibility of the proposed method under circumstances of a single incident source and two coherent sources.