In this paper, a new METHOD for calculating the numerical APPROXIMATION of the nonlinear Urysohn integral equations is proposed based on Haar wavelets. Also, the convergence analysis and numerical stability of these METHOD are discussed. Conducting numerical experiments confirm the theoretical results of the applied METHOD and endorse the accuracy of the METHOD.

This paper presents a modification of SUCCESSIVE APPROXIMATION METHOD by using projection operator to solve nonlinear Volterra-Hammerstein integral equations of the second kind. In this paper, it is proved that under some conditions the sequence of iterated solutions converges to the exact solution. Applicability of this modification has been shown with some numerical examples. Comparisons with some other METHODs are also addressed which highlight superiority of the METHOD.

A reliable and effective hybrid beamforming design for dual functioning multi-input multi-output (MIMO) radar is a challenging research problem because of the concerns related to limited user capacity, interference, and lack of performance trade-off. Due to the shortage of available spectrum, radar frequency spectrum sharing has become vital in emerging 5G communication systems. This will reduce spectrum congestion, therefore receiving significant attention. The existing hybrid beamforming METHODs reduce the radio frequency (RF)  chains but improving user capacity is still a major concern. Future dual radar-communication designs are having challenges in enhancing the user capacity with minimum RF chains, interference mitigation, and hardware cost reduction. This work proposes a novel approach to a hybrid beamforming mechanism for dual-functioning MIMO radar. This mechanism uses the dimension-reduced baseband piecewise SUCCESSIVE APPROXIMATION integrated with a digital precoder. At the analog precoder, the piecewise SUCCESSIVE iterative APPROXIMATION approach is applied to perform the analog beamforming. The novel hybrid beamforming with lens antenna array integration improves the user capacity and reduces power requirement, interference, and expenses. The simulation results showed improved performances compared to existing state-of-the-art METHODs in terms of bit error rate, spectral efficiency, energy efficiency, and response time.

In this paper, we consider a fractional Sturm-Liouville equation of the form, 􀀀, cD,0+ ,D,0+y(t) + q(t)y(t) = , y(t),0 < ,< 1,t 2 [0,1],with Dirichlet boundary conditions I1􀀀, ,0+ y(t)jt=0 = 0,and I1􀀀, ,0+ y(t)jt=1 = 0,where, the sign ,is composition of two operators and q 2 L2(0,1), is a real-valued potential function. We use a recursive METHOD based on Picard's SUCCESSIVE METHOD to , nd the solution of this problem. We prove the METHOD is convergent and show that the eigenvalues are obtained from the zeros of the Mittag-Le, er function and its derivatives.

This paper studies the problem of Simultaneous Sparse APPROXIMATION (SSA). This problem arises in many applications that work with multiple signals maintaining some degree of dependency, e. g., radar and sensor networks. We introduce a new METHOD towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion of the convergence of our METHOD, called Simultaneous Iterative METHOD (SIM). In this study, we compared our METHOD with other group-sparse reconstruction techniques, namely Simultaneous Orthogonal Matching Pursuit (SOMP) and Block Iterative METHOD with Adaptive Thresholding (BIMAT), through numerical experiments. The simulation results demonstrated that SIM outperformed these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIM is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.