The Multigrid Beta Function Approach for Modeling of Background Error Covariance in the Real-Time Mesoscale Analysis (RTMA)

We describe a method for the efficient generation of the covariance operators of a variational data assimilation scheme which is suited to implementation on a massively parallel computer. The elementary components of this scheme are what we call ‘beta filters’, since they are based on the same spatial profiles possessed by the symmetric beta distributions of probability theory. These approximately Gaussian (bell-shaped) polynomials blend smoothly to zero at the ends of finite intervals, which makes them better suited to parallelization than the present quasi-Gaussian ‘recursive filters’ used in operations at NCEP. These basic elements are further combined at a hierarchy of different spatial scales into an overall multigrid structure formulated to preserve the necessary self-adjoint attribute possessed by any valid covariance operator. This paper describes the underlying idea of the beta filter and discusses how generalized Helmholtz operators can be enlisted to weight the elementary contributions additively in such a way that the covariance operators may exhibit realistic negative sidelobes, which are not easily obtained through the recursive filter paradigm. The main focus of the paper is on the basic logistics of the multigrid structure by which more general covariance forms are synthesized from the basic quasi-Gaussian elements. We describe several ideas on how best to organize computation, which led us to a generalization of this structure which made it practical so that it can efficiently perform with any rectangular arrangement of processing elements. Some simple idealized examples of the applications of these ideas are given.

The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator

In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map (L), and the 1D skew-tent map (S), are weakly coupled by a predefined coupling matrix M. The mixing technique combined with the weak coupling technique of the three chaotic maps allows preserving the system against side-channel attacks (SCAs). The proposed system was implemented on a Xilinx XC7Z020 PYNQ-Z2 FPGA platform. Logic resources, throughput, and cryptanalytic and statistical tests showed a good tradeoff between efficiency and security. Thus, the proposed SCbSC can be used as a secure stream cipher.

Coefficient quantization effects on new filters based on Chebyshev fourth-kind polynomials

The aim of this paper is to construct non-recursive filters, extensively used type of digital filters in digital signal processing applications, based on Chebyshev orthogonal polynomials. The paper proposes the use of the fourth-kind Chebyshev polynomials as functions in generating new filters. In this kind, low-pass filters with linear phase responses are obtained. Comprenhansive study of the frequency response characteristics of the generated filter functions is presented. The effects of coefficient quantization as one type of quantization that influences a filter characteristic are investigated here also. The quantized-coefficient errors are considered based on the number of bits and the implementation algorithms.

Efficiency of adaptive filter with envelope tracking algorithm when receiving signals with multi-position PSK against the background of non-fluctuation interferences

The energy and spectral advantages of signals with phase-shift keying predetermined their widespread use in modern digital navigation, communications and television systems. The use of this type of signal in a multi-position format with an increased number of possible phase states allows increasing the information capacity of the channel signal, and consequently the throughput rate of radio channels. The presence of non-fluctuation interference in such radio channels greatly reduces the noise immunity of information reception. A well-known way to deal with such interference is to use adaptive non-recursive filters in the receiver. The article evaluates the effectiveness of using such a filter with an algorithm for setting weight coefficients that controls the constant envelope of a useful signal when receiving signals with multi-position phase shift keying against the background of noise and non-fluctuation interference. Two types of such interference are considered – harmonic and relayed. Using computer simulation, the optimal filter parameters (adaptation coefficient and its length) are determined; the effect of the filter on the noise immunity of the quadrature signal receiver with multi-position phase shift keying for various combinations of interference and their intensity is estimated. It is shown that such an adaptive filter can successfully cope with the most dangerous sighting harmonic interference.