This paper proposes a method to improve the spu-rious-free dynamic ranges(SFDRs)of 1-bit sampled signals greatly,which is very beneficial to multi-tone signals detection.Firstly,the relationship between the fundamenta...This paper proposes a method to improve the spu-rious-free dynamic ranges(SFDRs)of 1-bit sampled signals greatly,which is very beneficial to multi-tone signals detection.Firstly,the relationship between the fundamental component and the third harmonic component of 1-bit sampled signals is analyzed for determining four contiguous special frequency bands,which do not contain any third harmonics inside and co-ver 77.8%of the whole Nyquist sampling frequency band.Then,we present a special 4-channel monobit receiver model,where appropriate filter banks are used to obtain four desired pass bands before 1-bit quantization and each channel can sample and process sampled data independently to achieve a good in-stantaneous dynamic range without sacrificing the real-time per-formance or computing resources.The simulation results show that the proposed method effectively eliminates the effect of the most harmonics on SFDRs and the mean SFDR is increased to to 20 dB.Besides,the multi-signals simulation results indicate that the maximum amplitude separation(dynamic range)of two signals in each channel is 12 dB while the proposed monobit re-ceiver can deal with up to eight simultaneous arrival signals.In general,the designing method proposed in this paper has a po-tential engineering value.展开更多
Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or ...Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit.展开更多
文摘This paper proposes a method to improve the spu-rious-free dynamic ranges(SFDRs)of 1-bit sampled signals greatly,which is very beneficial to multi-tone signals detection.Firstly,the relationship between the fundamental component and the third harmonic component of 1-bit sampled signals is analyzed for determining four contiguous special frequency bands,which do not contain any third harmonics inside and co-ver 77.8%of the whole Nyquist sampling frequency band.Then,we present a special 4-channel monobit receiver model,where appropriate filter banks are used to obtain four desired pass bands before 1-bit quantization and each channel can sample and process sampled data independently to achieve a good in-stantaneous dynamic range without sacrificing the real-time per-formance or computing resources.The simulation results show that the proposed method effectively eliminates the effect of the most harmonics on SFDRs and the mean SFDR is increased to to 20 dB.Besides,the multi-signals simulation results indicate that the maximum amplitude separation(dynamic range)of two signals in each channel is 12 dB while the proposed monobit re-ceiver can deal with up to eight simultaneous arrival signals.In general,the designing method proposed in this paper has a po-tential engineering value.
基金supported by the Engineering and Physical Sciences Research Council of UK (Grant No. #EP/K00946X/1)
文摘Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit.
