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As a robust online learning approach, adaptive filtering based on correntropy has attracted more attentions. Recently, researchers have made efforts to develop complex correntropy to deal with adaptive filtering issues in complex domain. However, most of the literature on complex correntropy lack details regarding the processing of noncircular signals. Up to now, the maximum improper complex correntropy criterion (MICCC) algorithm for noncircular and widely-linear (WL) adaptive filtering utilizes the gradient descent method to find the maximum of the objective function. However, the MICCC algorithm fails to guarantee both low steady-state weight error power and fast convergence. To overcome this defect, this paper proposes a class of adaptive filtering algorithms which are based on fixed-point instead of gradient descent. It is worth noting that we manage to avoid the massive calculation of matrix inversion in traditional fixed-point based methods by utilizing the lemma of matrix inversion properly and further provide two alternative recursive algorithms. Finally, the local convergence analysis of mean and mean square is performed, and the simulated results offer strong evidences for the superior performance of the proposed algorithms over widely-linear complex least mean square (WL-CLMS), widely-linear recursive least square (WL-RLS) and MICCC. [ABSTRACT FROM AUTHOR]

This paper presents a COordinate Rotation Digital Computer (CORDIC)-based architecture for the computation of Nth root and proves its feasibility by hardware implementation. The proposed architecture performs the task of Nth root simply by shift-add operations and enables easy tradeoff between the speed (or precision) and the area. Technically, we divide the Nth root computation into three different subtasks, and map them onto three different classes of the CORDIC accordingly. To overcome the drawback of narrow convergence range of the CORDIC algorithm, we adopt several innovative methods to yield a much improved convergence range. Subsequently, in terms of convergence range and precision, a flexible architecture is developed. The architecture is validated using MATLAB with extensive vector matching. Finally, using a pipelined structure with fixed-point input data, we implement the example circuits of the proposed architecture with radicand ranging from zero to one million, and achieve an average mean of approximately 10−7 for the relative error. The design is modeled using Verilog HDL and synthesized under the TSMC 40-nm CMOS technology. The report shows a maximum frequency of 2.083 GHz with $197421.00~{\mu }\text{m}^{2}$ area. The area decreases to $169689.98~{\mu }\text{m}^{2}$ when the frequency lowers to 1.00 GHz. [ABSTRACT FROM AUTHOR]

This paper introduces a new concept called impulsive control inclusion condition, i.e., the impulsive condition is presented, in the first time, as inclusion related to multivalued maps and controls. The notion of approximate controllability of a class of semilinear Hilfer fractional differential control inclusions in Banach spaces is established. For the main results, we use fractional calculus, fixed point technique, semigroup theory and multivalued analysis. An appropriate set of sufficient conditions for the considered system to be approximately controllable is studied. Finally, we give an illustrated example to provide the obtained theory. [ABSTRACT FROM AUTHOR]

This paper analyzes the fixed-point and floating-point roundoff errors in different Filter Bank MultiCarrier (FBMC) receiver implementations. Two different structures are considered: the polyphase network based and frequency spreading based. Theoretical closed-form formulas for the total Quantization Noise Power (QNP) are derived and verified through simulation. The results show the effects of each parameter and signal processing block on the overall QNP. Also, the results show that the total QNP for an arbitrary set of parameters can be determined using the derived results without performing exhaustive simulations. The effects of the chosen bit-resolution on the bit-error rate performance are also analyzed. Furthermore – based on the theoretical results – FBMC receivers can be designed with an optimal number of bits used in the arithmetic units without significantly affecting the receiver performance. • Different FBMC receiver architectures are compared in terms of quantization noise. • Analytical formulas for the roundoff errors at the output of FBMC receivers are derived. • The effect of the quantization noise on the BER of the FBMC receivers is analyzed over AWGN and multipath channels. • A bound on the BER is determined for a given number of quantization bits. [ABSTRACT FROM AUTHOR]

This paper investigates Filter Bank MultiCarrier (FBMC) modulation implemented with frequency spreading and polyphase network-based in terms of the introduced quantization noise. As FBMC is considered one of the future candidates for 5G/6G communication systems due to its advantageous spectral properties, the introduced quantization noise in the implementation is an essential design criterion. Analytical expressions for fixed- and floating-point Quantization Noise Power (QNP) in FBMC transmitter schemes are given. Based on the results, it can be stated that the total QNP depends on the number of carriers, overlapping symbols, and the resolution of the quantizer. The results are verified through simulations. Estimating the quantization noise in FBMC systems in the function of the selected bit resolution and keeping it at an acceptable level is an essential design step. The results can be directly employed in the preliminary hardware design of FBMC transmitters, where the choice of the arithmetical units and the bit resolution is a key factor. • Different FBMC transmitter architectures are compared in terms of quantization noise. • Analytical formulas for the QNP at the output of FBMC transmitters are derived. • The effect of the Quantization noise on the PSD of the FBMC signal is analyzed. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation, via measure of noncompactness. Our results improve and extend some previous results obtained in other studies. We will also include some examples which show that our results are applicable where the previous ones are not. [Copyright &y& Elsevier]

We present a channel signal-to-noise ratio (SNR) estimator for M-ary phase shift keying (M.PSK) and differential M-PSK. The estimator is non data aided and is shown to have the following advantages: 1) It does not require prior carrier synchronization; 2) the estimator has a compact fixed-point hardware implementation suitable for field-programmable gate arrays and application-specific integrated circuits; 3) it requires only 1 sample/symbol; 4) accurate estimates can be generated in real time; and 5) the estimator is resistant to imperfections in the automatic gain control circuit. We investigate the proposed estimator theoretically and through simulations. In particular, we investigate the required quantization necessary to achieve a good estimator performance. General formulas are developed for SNR estimation in the presence of frequency-flat slow fading, and specific results are presented for Nakagami-m fading. The proposed estimator is then compared with other SNR estimators, and it is shown that the proposed method requires less hardware resources while, at the same time, providing comparable or superior performance. [ABSTRACT FROM AUTHOR]

We perform in this report a comparative analysis between differential fractional operators applied to the non-linear Kaup–Kupershmidt equation. Such operators include the Atangana–Beleanu derivative and the Caputo–Fabrizio derivative which respectively follow the Mittag-Leffler law and the exponential law. We exploit the fixed points of the dynamics and the stability analysis to demonstrate that the exact solution exists and is unique for both types of models. Methods of performing numerical approximations of the solutions are presented and illustrated by graphical representations exhibiting a clear comparison between the dynamics under the influence of Mittag-Leffler law and those under the exponential law. Different cases are presented with respect to values of the derivative order 0 < α ≤ 1. We note a slight difference between both dynamics in terms of individual points, but their global pictures remain similar and close to the traditional and popular traveling wave solution of the standard Kaup–Kupershmidt model (α = 1). [ABSTRACT FROM AUTHOR]