Single-bit Compressed Sensing Radar Target Time Delay Estimation

In wideband and ultra-wideband radars,due to the limitation of analog-to-digital conversion(ADC)technologies,radar data acquisition based on nyquist sampling theorem is difficult to meet practical needs.Compressed sensing(CS),which acquires compressive measurements by randomly projecting high-dimensional sparse signals onto a low-dimensional subspace,brings us new ideas of radar data acquisition.Compressed sensing radar based on the theory of compressed sensing is favorable to resolve the problems of high sampling rate and large data volume on radar.In practice,compressive measurements of compressed sensing radar must be quantized for transmission and storage.One-bit compressed sensing(a.k.a.1-bit compressed sensing)radar is a radar that quantizes compressive measurements into one-bit form.Compared with general quantitative compressed sensing radar,one-bit compressed sensing radar uses a comparator to implement the quantization function,which greatly simplifies the structure of quantizer.More importantly,compared with high-bit quantization compressed sensing,it has better reconstruction performance and anti-noise performance under the same number of bits.In radar signal processing,time delay is a key parameter of target distance.Therefore,time delay estimation has always been a basic problem in the research of radar signal processing.In traditional compressed sensing radar,for on-grid target,we construct a dictionary matrix sparsely representing radar echoes,and then use sparse reconstruction theory to estimate time delay.For off-grid target,time delay is estimated based on parameterized bases or atomic norms.Since one-bit measurements are nonlinear measurements of echo signal,time delay estimation methods based on linear measurements in the conventional compressed sensing radar cannot be directly applied to one-bit compressed sensing radar.Therefore,this paper derives the Cramér-Rao bound(CRB)of time delay parameter and proposes methods of on-grid and off-grid target time delay estimation for one-bit compressed sensing radar.The main work of this paper is as follows:1.Derive CRB of the target time delay for one-bit compressed sensing radar.CRB is the best estimation accuracy of the unbiased estimation.Simultaneously,it provides a bound for the variance of any unbiased estimator.Hence,we derive CRB of time delay for one-bit compressed sensing radar in this paper.The relationship between CRB of time delay parameter and the input signal-to-noise ratio,compression ratio,target sparsity is given by simulation experiments.It is a theoretical performance benchmark for time delay estimation methods in the following chapters.2.Study method of on-grid target time delay estimation for one-bit compressed sensing radar.First,scene echo is sampled by nyquist sampling theory and measured by the measurement matrix,and one-bit quantization is performed to obtain one-bit measurement vector.Then the possible delay range is uniformly discretized to construct dictionary matrix.And echo can be sparsely represented by the dictionary matrix to establish a one-bit compressed sensing model.Finally,the parameter estimation problem is transformed into a one-bit sparse reconstruction problem.The binary iterative hard thresholding(BIHT)algorithm or convex optimization method is used to solve sparse representation coefficient and time delay estimation is completed.3.Propose method of off-grid target time delay estimation for one-bit compressed sensing radar.Since echo of off-grid targets mismatches when it is represented by dictionary matrix,the parameterized atom is used to accurately sparsely represent radar echo.And time delay of each target is divided into the nearest grid and deviation of time delay.Then,the Taylor or polar interpolation is used to approximate radar echo at the nearest grid of time delay,and the corresponding one-bit compressed sensing model is constructed.Finally,BIHT algorithm or convex optimization is used to solve one-bit sparse reconstruction problem for obtaining the nearest grid.The deviation is solved by the nonlinear least squares problem.Thus,time delay estimation of off-grid target is obtained.According to the different interpolation and sparse reconstruction methods,this paper proposes four concrete implementation forms,namely Taylor-BIHT,TaylorConvex,Polar-BIHT,Polar-Convex,and the performance differences of these methods are compared by simulation experiments.