Research On The Digital Generation Method For Random Test Signals Based On Discrete Chaotic Map

Presently,several sectors,such as transportation,healthcare,medical,and electronic warfare,heavily rely on a significant quantity of high-performance electrical equipment.This equipment’s dependable and uniform operation is crucial for safeguarding national security,promoting economic development,and enhancing human well-being.The arbitrary waveform generator is extensively utilized as a signal source across the whole life cycle of electronic equipment,encompassing research and development,production,and maintenance.It enables the rapid generation of various test signals.However,using waveform-generating techniques can result in testing signals with limited randomization,making it challenging to imitate all possible signals and disruptions encountered in realworld channels.Consequently,enhancing the test fault coverage of electronic equipment and ensuring long-term operational stability poses challenges.Enhancing the volatility of test signals is essential.This dissertation explores the digital generation method of random test signals utilizing discrete chaotic maps(DCM)to meet the high demand for randomness in various situations.The primary research work consists of three main components: firstly,establishing the correlation between random test signals and pseudo-random number generator(PRNG); secondly,developing a novel model of DCM with varying dimensions using discrete memristors and bounded nonlinear functions; thirdly,focusing on the real-time digital generation method of test signals,including random periodic signals,high throughput rate noises,and arbitrarily distributed noises,by utilizing pseudo-random numbers(PRNs)generated by the DCM as seeds.(1)Aiming at the problem of random test signal generation based on DCM,this dissertation establishes a map model for random test signals and PRNG.The generalized discrete memristor model(GDMM)and its corresponding approach for shifting operating frequency were introduced.The DCM modeling method was also provided based on GDMM and modal operation.The operational frequency shifting technique covers the hysteresis loop characteristics’ inadequacies of commercially available devices.Achieving hysteresis loops operating at 10 GHz using a 500 KHz excitation signal on a hardware platform with a 20 MHz bandwidth entails a 20,000-fold increase in the equivalent operating frequency.The GDMM is compatible with existing memristor models and increases the operating frequencies.DCMs based on the GDMM exhibit complex and varied dynamics.DCMs that utilize modal operations demonstrate stable and continuous dynamics and controlled Lyapunov exponents(LEs).These characteristics offer a theoretical foundation for subsequent investigations.(2)Aiming at the problem of high-precision and high-efficiency generation of randomperiodic test signals,a method for digital generation of random-periodic test signals based on a three-dimensional parallel memristor logistic map(3D-PMLM)is proposed.A new3D-PMLM model was developed,and a random periodic test signal synthesis approach employing 3D-PMLM as a seed was presented in conjunction with the DDS-based waveform creation principle.Compared to previous maps,3D-PMLM has higher Shannon entropy(9.923),permutation entropy(3.903),and Kaplan-York dimensionality(3.000),and the PRNs can pass all NIST and Test U01 tests.An FPGA can generate test signals in real time with random variations in parameters such as amplitude,frequency,start phase,end phase,and number of cycles.The range of variation can be controlled,and the test signal can be created repeatedly.The signal duration has an average relative inaccuracy that is no greater than 0.73%.(3)Aiming at the problem of real-time controllable high throughput rate noise generation,a high throughput rate noise generation method based on a four-dimensional trigonometric-based memristor hyperchaotic map(4D-TBMHM)is proposed.This dissertation presented the establishment of a novel 4D-TBMHM model.The PRN throughput rate real-time improvement and homogenization methods were provided,taking advantage of FPGA parallel processing.Real-time controllable high throughput Gaussian noise and uniform noise digital generation methods were proposed.When compared to the current maps,4D-TBMHM exhibits higher values for sample entropy(1.758),permutation entropy(4.952),correlation dimensionality(1.998),and Kaplan-York dimensionality(4.000).Furthermore,the PRNs generated by 4D-TBMHM can be evaluated using NIST and Test U01.Compared to current PRNGs,the implementation is straightforward and practical,necessitating solely an FPGA to produce a noise signal at a rate of 195.2 Gbps,at least 6.35 times more.The noise signal’s distribution properties,crest factor,output power,and other parameters can be adjusted digitally,enabling the design of an additive noise generator using digital methods.(4)Aiming at the problem of real-time controllable arbitrary distributed noise generation,an arbitrary distributed noise digital generation method based on 9)-dimensional discrete hyperchaotic map(9)-D-DHM)is proposed.This thesis presented the generalized9)D-DHM model,optimized the hybrid Gaussian model,introduced an approach for generating specified distribution noise numerically,and proposed a method for generating random distribution noise based on inverse functions.Compared with current models,9)D-DHM contains controllable LEs and PRNs with controllable magnitudes that follow a uniform distribution.The two 6D-HDMs exhibit greater values for Shannon entropy(9.993),sample entropy(2.189),alignment entropy(6.576),correlation dimensionality(2.011),and Kaplan-York dimensionality(6.000).Additionally,PRNs can successfully satisfy all the test items from NIST and Test U01.The real-time generation method for specified and random distribution noise was validated on an FPGA.Compared to the look-up table-based approach,this method achieves non-repeating noise signal output,enhancing its randomness.Theoretical derivation,numerical simulation,and hardware validation have all attested to the proposed method for generating random test signals’ high randomness,efficiency,accuracy,and seamless integration.The advancement of random test signal implementation and utilization is facilitated by these qualities.