Research On The Sampling Technology Of Large Dynamic Range Signals Based On Compressive Sensing

With the extensive application of wireless communication technologies and systems, theradio signals distributed in the spatial domain, time domain and frequency domain areincreasingly crowded. Reasonable and effective allocation and management of the band, powerand communication resources are the basis of protecting all wireless communication systemuptime and the safety of band resources, and are also very important for the national security andsocial stability.Electromagnetic spectrum monitoring is an important technical means to achieve efficientand rational allocation and management of communication resources. The large number andvarious types of communication systems, especially the current short-distance wirelesscommunication systems, have been widely used, which put forward higher requirements to thegranularity of the electromagnetic spectrum monitoring. A prominent problem is how tomonitoring the very weak signals such as short-range wireless signals under strong backgroundsignals. The major challenge to solve this problem is how to avoid irreversible loss of the weaksignal information result from the too low quantization signal-to-noise ratio in broadband signalacquisition process.Compressive sensing has exhibited excellent characteristics for its efficient acquisition andprecise reconstruction of the signals in the compressed domain, which has attracted more andmore attention. Making full use of compressed sensing characteristics and applying it to solvethe problem of sampling of large dynamic range signals have important theoretical significanceand application value.This paper applies Compressive Sensing to solve the problem of monitoring of small signalsblended with large signals. The compression and reconstruction of non-uniform block sparsesignals, quantization noise of compressive sampling, the methods of sampling for large dynamicrange signals and electromagnetic spectrum monitoring program realized in frequency domaincompletely have been mainly researched. The main work and innovations in the article are asfollows:1. In practice, the signals in the target frequency band often characterized asnon-uniform block sparse. The decay property of restricted isometry constant is analyzedin theoretically, and the important conclusion is obtained that the reconstruction algorithmcan get higher signal reconstruction probability when the block sparse characteristic isintroduced into reconstruction algorithm. A blind signal reconstruction algorithm withoutknowing the sparse order and block distribution based on echelon variable block lengthsegmentation is proposed, which can estimate positions of blocks accurately and thenimprove the success rate of signal reconstruction. The Classical analysis of CompressiveSensing for block sparse signals assumes that the signals obey uniform block sparse model.However, in practice, for the reason of the differences of bandwidth and frequency, the signals inthe monitoring band are typically subject to a non-uniform block sparse model. Themeasurement process of non-uniform block sparse signals is studied firstly; and then the decay property of Restricted Isometry Constant is proved, which further describes that introducingblock sparse model to the reconstruction algorithm can bring a higher probability of signalreconstruction. A blind reconstruction algorithm based on echelon variable block lengthsegmentation is proposed and the success rate of signal reconstruction of this algorithm isapproved, just because this algorithm achieved accurate estimation of non-uniform position ofthe block through splitting the sparse signal several times with echelon decreasing block length.Simulation results show that the proposed algorithm has higher success rate of reconstructionthan the method which directly use usual reconstruction algorithm to non-uniform block sparsesignal.2. The key factor that restricts the recovery of small signal information is that thein-band quantization SNR of small signal is too low. Firstly, the quantization noisespectrum and in-band quantization noise for sinusoidal and Gauss random signal inputhave been analyzed and the relevant conclusions are given. The quantization noise ofCompressive Sensing is analyzed thoroughly, the important conclusion that thequantization noise spectrum of Compressive Sensing is always white and unrelated withthe input. The upper and lower bounds of reconstruction error in the presence ofquantization noise are set. From the aspects of decreasing of sampling rate and the fairnessof measurements, the advantages of Compressive Sensing for sampling of large dynamicsignals are analyzed comprehensively. Most of the analysis of quantization noise spectrum forinput sinusoidal signal usually assume that the input sine signal is deterministic signal, weassume the input sinusoidal signal as a random process, and derive quantization noise spectrum,which also concluded that the quantization noise spectrum is discrete. The quantization noisewithin signal band for sinusoidal input is studied and we obtained that the in-band quantizationnoise power was decline in the form of polyline as the increase of sampling rate. Thequantization noise spectrum for Gaussian random signal input is analyzed, the conditions ofwhiteness of quantization noise spectrum is obtained. These conditions are more conducive tothe engineering practice than traditional quantitative theory. The quantization noise spectrum ofCompressive Sensing is analyzed, and we conclude that the quantization noise is always whiteand independent of the input signal, based on which the upper and lower bounds of signalreconstruction error in the presence of quantization noise are established. From the aspects ofdecreasing of sampling rate and the fairness of measurements, a comprehensive analysis of itsadvantage of Compressive Sensing for sampling of large dynamic signals is conducted.3. The sampling of large dynamic range signals is transformed to selective samplingproblem. And then the selective AIC structure which makes the measure process haveselective function is proposed. The key issue of S-AIC is the construction of selective factors.Two kinds of selective factors based on orthogonal projection and oblique projectionseparately are given. And then the sampling method for large dynamic range signals baseon selective AIC is proposed, which improves the performance of sampling for small signals.For the traditional sampling technology, the input signal to the ADC often is assumed as a singlesignal. In this paper, we assume the input signals as blended signals, and then transform the sampling of large dynamic range signals to selective sampling problem, and propose theselective AIC structure, named S-AIC. The key issue of S-AIC is the construction of selectivefactors. Two kinds of selective factors based on orthogonal projection and oblique projectionseparately are given. The oblique projection selective factor is able to eliminate the interferencesignal embodied in measurements and at the same time can keep that the structure of the targetsignal, and thus it has a better performance than the selective factor based on orthogonalprojection. Simulation results further confirmed this conclusion. A large dynamic signalsacquisition framework based on S-AIC is proposed at last and the theoretical analysis andsimulation results also verify the effectiveness of the method.4. Appling Compressive Sensing thought of compressing some scale of signal intransform domain to the acquisition of large dynamic range signals, a sampling method oflarge dynamic range signals based on conducting nonlinear compression in the separabledomain of blended signals is proposed, the separable transformation and nonlinearcompression which are the two core issues of this method are discussed in detailed. Theselection principles of nonlinear compression function are given. Three methods ofsampling for large dynamic range signals based on analog Fourier transform andself-convolution conducted in analog domain are proposed, which can improvequantization precision of small signals. Constitutionally, Compressive Sensing is a kind ofcompression of some scale of signal conducted in transform domain. With this idea, we proposeda method that compresses the dynamic range of signal in separable domain. Firstly, the dynamicrange of signal is compressed by separable and nonlinear transform in analog domain, so that thesignal can obtain higher quantization precision, and then the recovery of signal is completed indigital domain. The premise of this method is that the blended signals are separable in somedomain. So the separable transform of mixed signals is defined. The principles of choosing thenon-linear compression function are given. According to the concept of achieving the separabletransformation and nonlinear compression in two steps, two kinds of large dynamic mixed-signalsampling methods based on Analog Fourier Transform are proposed, mainly by gating anddynamic gain control in two ways to sort or amplify the weak signal, so as to ensure the higherquantization SNR for weak signals. According to the concept of achieving the separabletransformation and nonlinear compression in single step, a method based on self-convolutionconducted in analog domain is proposed. the simulation results verify the feasibility of thesemethods.5. According to the requirements of National Significant Science and TechnologyProject, named "Research on the Key Technologies of Electromagnetic SpectrumMonitoring Sensor Network", a complete frequency domain electromagnetic spectrummonitoring program based on Compressive Sensing, AIC and S-AIC is designed.Traditional electromagnetic spectrum monitoring programs often use sweep way to makecomplete coverage of the broad frequency range, it has a higher probability of undetectedinstantaneous burst signal. The application of Compressed Sensing can effectively improve theinstantaneous processing bandwidth and frequency sweeping speed, and then decrease the probability of undetected instantaneous burst signal. In addition, the program uses the parallelstructure of dual-channel (AIC and S-AIC), so that the system is capable of monitoring largedynamic range signals. Complete frequency domain processing thoughts not only can simplifyimplementation of the program, but also can save storage and hardware resources. Meanwhile itensures the algorithm can be loaded flexibility and is conducive to miniaturization, networkmonitoring system of the electromagnetic spectrum.