Research On 1-bit Compressive Sensing Algorithms

Compressive Sensing(CS)theory is a burgeoning theory of collecting and processing signals.The basic principle can be summarized as follows:the signal is compressible or sparse in certain transform domain,the sparsed signal can be projected into a low-dimension measurement by certain sparse basis matrix which is namely as observation matrix.At present,the CS theory is widely utilized in image processing,military radar,signal transmission and other fields.With the development of CS,many relevant branches have been developed and 1-bit compressed sensing(1-bit CS)is an important branch among them for its simple structure and easy implementation.The main difference between 1-bit CS and the conventional CS theories is that 1-bit CS only reserves the amplitude information of the measurement.This paper mainly studies the reconstruction algorithms of 1-bit CS.The main contributions are as follows:(1)1-bit CS reconstruction algorithms based on hamming distance.Considering the particularity of the measurement in 1-bit CS,we can take advantage of hamming distance as the measure of the measurement and the measurement matrix in space domain.Hamming distance is usually used to measure the difference between the positions of two vectors.It can also be regarded as the number of binary bits that are not equal between the two measuring vectors.This paper extends hamming distance to the reconstruction of 1-bit CS signals and proposes hamming iterative hard thresholding for the one-signal situation.Further,we propose mean-hamming iterative hard thresholding for multi-signal situation.(2)The reconstruction algorithm of 1-bit CS with perturbation for massive MIMO system.Specifically,in the traditional transmission model,the measurement matrices between the transmitter and the receiver are generally the same,however,in reality,the transmitter and receiver do not match which may cause difference of the mearement matrices.This difference is modeled as additive perturbation.This paper proposes the perturbed binary iterative hard thresholding algorithm considering above perturbation in multi-user MIMO frequency division duplex system to improve the channel reconstruction performance in the actual transmission.All the reconstruction algorithms propose in this paper are given the corresponding simulation results,so that the proposed schemes can be compared with existing algorithms.