Research And Implementation Of Signal Recovery System In Modulated Widband Converter Based On Compressed Sensing

With the development of modern communication technology and digital signal processing technology,Analog-to-Digital Converters(ADC)are required to directly process ultra-wideband signals,which poses great challenges to the design and implementation of traditional Nyquist sampling ADCs.Restricted by the current development level of ADCs,single-chip ADCs cannot simultaneously meet high sampling rates and high resolutions.However,for some specific applications,such as radar,image processing,cognitive radio,etc.,although the ultra-wideband signal is to be processed,this ultra-wideband signal is sparse in a certain transform domain,that is,the signal can be The sparse representation of the transformation matrix,then we can use Compressed Sensing(CS)theory to project the high-dimensional original signal onto the low-dimensional domain through an observation matrix that is not related to the sparse transform basis,to achieve sub-Nyquist compression sampling of the original signal.This structure is called an Analog-to-Information Converter(AIC).AIC can replace the traditional ADC,targeted and real-time sampling of broadband analog signals at a lower rate,to obtain the information of interest,to discard a lot of redundancy,and the use of reconstruction algorithms can be the original signal from the low-dimensional projection value Recovered.This sampling mechanism effectively avoids the bottleneck of traditional Nyquist sampling and is considered to be an efficient broadband sampling mechanism.However,this kind of structure requires a large number of observation points to recover when reconstructing the signal.The recovery matrix has a large scale and complex calculations,and is not suitable for real-time hardware implementation.Modulated Wideband Converter(MWC)is a variant structure of AIC.It uses periodic pseudo-random sequences to greatly simplify the signal recovery matrix,and can reduce the complexity of the front-end hardware by introducing expansion coefficients.However,the current related research is almost based on the ideal model of MWC,which requires a large number of ideal low-pass filters,and the ideal lowpass filter cannot be realized in practical applications.The use of non-ideal filters will reduce the signal reconstruction accuracy of the system and severely limit the practical capabilities of the MWC system.In this paper,in view of the impact of non-ideal analog low-pass filters on signal reconstruction performance in MWC systems,the two most representative analog filters are studied,and a method for compensating the non-ideality of analog filters in the frequency domain is proposed.The method effectively improves the reconstructed signal-to-noise ratio.In order to reduce the amount of calculation and hardware complexity,and further improve the MWC system signal recovery algorithm with expansion coefficients,the structure based on Fast Fourier Transform(FFT)is used to subdivide the sampled signal in the frequency domain.It avoids the introduction of digital filter convolution operations and related errors,reduces nearly 90% of the computational complexity in the recovery process,and improves the signal reconstruction power and reconstructed Signal-to-Noise Ratio(SNR).This paper further optimizes the proposed MWC back-end signal reconstruction algorithm for hardware,and proposes a square-root-free Multi-measurement vector complex Orthogonal Matching Pursuit(M-OMP)algorithm,which calculates two sparse coefficients per iteration,and The structure of the dual-port storage unit and the dualvector multiply-add unit is used to improve the operation speed of the algorithm.The circuit is designed,synthesized and automatically placed and routed using Vivado software.It is verified on Xilinx Virtex-7 series FPGA chips,and the static timing,area and power analysis are completed.The implemented circuit uses a 22-bit fixedpoint data structure and can run at a clock frequency of 200 MHz.The experimental results show that the signal reconstruction circuit designed in this paper can successfully reconstruct the Nyquist frequency of 1 GHz with sparsity of 12 using the ADC sampling rate of 66.67 MHz and the measurement matrix size of the 4-channel MWC system with 256 sampling points per channel,which is equal to an ADC with sampling rate of 1 GHz.The compression ratio is 26.7%,reconstruction time is only51.25 us,and reconstruction signal-to-noise ratio is 50.23 d B.The reconstruction speed does not reduce the reconstruction signal compared to software implementation and it has increased by more than 20 times.