The nexus between military expenditure and economic growth has been analyzed using different methods and techniques in the economic growth literature, but most previous findings are indecisive, i.e., non-significant, positive, or negative. The primary purpose of this article was to explain the military expenditure-economic growth nexus in Pakistan by capturing the asymmetrical effects of military expenditures on economic growth using the non-linear autoregressive distribution lag-NARDL technique. Data were analyzed from 1972-2018. The results indicated that a decrease in military spending (adverse shocks) enhanced economic growth in the long term. An increase in military spending (positive shocks) had an insignificant effect on economic growth in Pakistan, suggesting that a focus on cost reduction in military expenditure may benefit economic growth. More so, the Wald test validated the asymmetries both in the long- and short term. Capital formation and labor force, as a control variable, positively affected economic growth in the long run. Based on these findings, the paper offers some critical suggestions for policymakers.

The inverse beamforming (IBF) is a mature method to improve azimuth resolution. However, for weak targets it is not applicable as IBF enhances side lobes. In this paper, an improved IBF algorithm is proposed to raise the azimuth resolution under the premise of ensuring the detection ability for weak targets. Firstly, from the point of phase compensation, we analyze the cause of side lobes when IBF is applied. Then the improved IBF algorithm recorded as GIBF (the improved inverse beamforming) is proposed by changing the Toeplitz average into the phase construction. The theoretical derivation and simulation data processing show the proposed method can improve the resolution of the N sensors to the standard of 2N − 1 sensors under different signal-to-noise ratios. Compared with IBF, GIBF has great advantages in detecting weak targets. Passive sonar data are used to further verify the advantages of GIBF; the trajectories on azimuth history diagrams become clear, the azimuth resolution is improved, and the detection ability for weak targets is still robust. In addition, GIBF is combined with the common DOA (direction of arrival) estimation algorithms, such as conventional beamforming and minimum variance distortionless signal response, which proves the applicability of the algorithm.

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In shallow-water waveguide, the normal mode information of acoustic signals plays an important role in localization research. In this paper, an extraction algorithm of modal intensity distribution based on horizontal circular array is proposed. By using the horizontal wavenumber of each mode, the modal domain beamforming is used to estimate the modal intensity distribution of the acoustic signal. The theoretical derivation, data simulation and experimental data are used to verify the feasibility of the algorithm based on circular array and the superiority compared with the line array extraction algorithm. At the last part of the paper, an application based on modal intensity distribution is proposed: water surface interference suppression, and the effectiveness of the interference suppression algorithm is verified from theoretical derivation and simulation experiments.