Low Correlation Interference OFDM-NLFM Waveform Design for MIMO Radar Based on Alternating Optimization

The OFDM chirp signal is suitable for MIMO radar applications due to its large time-bandwidth product, constant time-domain, and almost constant frequency-domain modulus. Particularly, by introducing the time-frequency structure of the non-linear frequency modulation (NLFM) signal into the design of an OFDM chirp waveform, a new OFDM-NLFM waveform with low peak auto-correlation sidelobe ratio (PASR) and peak cross-correlation ratio (PCCR) is obtained. IN-OFDM is the OFDM-NLFM waveform set currently with the lowest PASR and PCCR. Here we construct the optimization model of the OFDM-NLFM waveform set with the objective function being the maximum of the PASR and PCCR. Further, this paper proposes an OFDM-NLFM waveform set design algorithm inspired by alternating optimization. We implement the proposed algorithm by the alternate execution of two sub-algorithms. First, we keep both the sub-chirp sequence code matrix and sub-chirp rate plus and minus (PM) code matrix unchanged and use the particle swarm optimization (PSO) algorithm to obtain the optimal parameters of the NLFM signal’s time-frequency structure (NLFM parameters). Next, we keep current optimal NLFM parameters unchanged, and optimize the sub-chirp sequence code matrix and sub-chirp rate PM code matrix using the block coordinate descent (BCD) algorithm. The above two sub-algorithms are alternately executed until the objective function converges to the optimal solution. The results show that the PASR and PCCR of the obtained OFDM-NLFM waveform set are about 5 dB lower than that of the IN-OFDM.

Grade Prediction in Blended Learning Using Multisource Data

Today, blended learning is widely carried out in many colleges. Different online learning platforms have accumulated a large number of fine granularity records of students’ learning behavior, which provides us with an excellent opportunity to analyze students’ learning behavior. In this paper, based on the behavior log data in four consecutive years of blended learning in a college’s programming course, we propose a novel multiclassification frame to predict students’ learning outcomes. First, the data obtained from diverse platforms, i.e., MOOC, Cnblogs, Programming Teaching Assistant (PTA) system, and Rain Classroom, are integrated and preprocessed. Second, a novel error-correcting output codes (ECOC) multiclassification framework, based on genetic algorithm (GA) and ternary bitwise calculator, is designed to effectively predict the grade levels of students by optimizing the code-matrix, feature subset, and binary classifiers of ECOC. Experimental results show that the proposed algorithm in this paper significantly outperforms other alternatives in predicting students’ grades. In addition, the performance of the algorithm can be further improved by adding the grades of prerequisite courses.

The generalized relations among the code elements for a new complex Fibonacci matrix

In this paper, we introduce a new complex Fibonacci matrix [Formula: see text] whose elements are complex Fibonacci numbers and we developed a new coding and decoding method followed from this complex Fibonacci matrix [Formula: see text]. We establish the relations among the code matrix elements, error detection and correction for this coding theory.

Revised fast convolution

It is assumed that linear time-invariant (LTI) system input signal samples are updated by a sensor in real time. It is urgent for every new input sample or for small part of new samples to update a convolution as well. The idea is that fast Fourier transform (FFT) algorithm, used to calculate output frequency samples (f.s.), should not be recalculated with every new input sample. It is needed just to modify the convolution algorithm, when the new input sample replaces the old one. An example of computation of the convolution with ordinary and modified 8-point Fourier code matrix is presented.

Coding theory on Lucas p numbers

In [K. Kuhapatanakul, The Lucas [Formula: see text]-matrix, Internat. J. Math. Ed. Sci. Tech. (2015), http://dx.doi.org/10.1080/0020739X.2015.1026612], Kuhapatanakul introduced Lucas [Formula: see text] matrix, [Formula: see text] whose elements are Lucas [Formula: see text] numbers. In this paper, we developed a new coding and decoding method followed from Lucas [Formula: see text] matrix, [Formula: see text]. We established the relations among the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is [Formula: see text]% for [Formula: see text] and for [Formula: see text], the correction ability is [Formula: see text]%. In general, correction ability of this method increases as [Formula: see text] increases.

Coding theory on h(x) extension of m sequences for Fibonacci numbers

In this paper, we introduced h(x) extension of m sequences of Fibonacci numbers polynomials of order m and a new Sn matrix of order m where h(x)(> 0) is a polynomial with real coefficients. Thereby, we discuss various properties of Sn matrix and the Fibonacci coding theory followed from this matrix. We established the relations among the code matrix elements, error deduction and correction for this coding theory. In general, correct ability potential of this method increases and it is independent of h(x). But h(x) being a polynomial, improves the cryptography protection.