Study On Array Pattern Synthesis Based On Convex Optimization

The antenna arrays have been widely used in the field of wireless communication-s,such as weather forecast,radar?airborne early warning radar,air surveillance radar?,radio astronomy,remote sensing satellite,and so on,due to their advantages of easy to obtain patterns with ultralow sidelobe level?high gain?narrow mainlobe as well as easy to control for and shaped beam and scanning beam.Convex optimization is a special type of mathematical optimized theory,which contains mathematical program-ming and least-squares optimization.Once an optimization problem is dealt with as a convex optimization problem,the global optimality of the solution can be guaranteed and it can be solved efficiently and accurately with a cvx solver,which is achievable in practice.Owing to the introduction of the convex optimization,an iterative tech-nique to solve efficiently non convex array synthesis problems is presented.A better radiation performance of beam pattern?e.g.,narrower half-power beamwidth,lower-maximum sidelobe levels?,a smaller number of array elements and a much narrower spatial aperture can be obtained compared with the case of uniformly spaced arrays.The innovations of this work are summarized as follows:1.We present an effective approach to the optimal mask-constrained power pat-tern synthesis of uniformly spaced array antennas able to dynamically reconfigure their radiation pattern by modifying only the amplitudes or excitation phases.The approach makes use of the property that for linear?or planar?array with uniform element spac-ing,an inverse fourier transform relationship exists between the array factor and the element excitations.Because of this relationship,a direct fourier transform performed on array factor will obtained the excitation weights of the radiated elements.The pro-posed approach relies on the repetitive use of both types of fourier transforms?fast fourier transform and invert fast fourier transform?.During each generation,the newly obtained array factor is matched to the prescribed pattern,which then is used to cal-culate an updated set of excitation weights.In addition,this step enforce a variety of phase?or amplitude?constraint on the resulting excitation weights.Only those excita-tion weights associated with the aperture are retained to calculate a new array factor.The whole process is repeated until the allowed number of iterations is reached,or the prescribed requirements for array factor are satisfied.2.The high-resolution requirement determines that the two-dimensional aperture should be large enough for a three-dimensional detection.However,such a solution is impractical and infeasible in practice due to the electromagnetic interferences,weight and the complexity of the Beam Forming Network.The proposed design technique allows to maximize the radiation performance?e.g.,narrower half-power beamwidth?of beampattern over assigned directions subject to completely arbitrary masks for side-lobe bounds.Dynamic control and Multi-convex formulation is used so that the upper and non-convex lower bound constraints on the beampattern can be convex.This ap-proach selects a proper array performance online depending on the real-time system state.More precisely,by using the proposed approach,the synthesis process is recur-sively feasible and the optimal results can be tracked.In this work,the definition of the starting point generating the patterns within the desired power constraints is given by means of an iterative projection method based on the iterative fourier technique.The proposed synthesis method based on the multi-convex programming can be used to deal with the complex-valued array patterns.3.An iterative constrained optimization method for the synthesis of sparse arrays radiating focused beampattern is presented.The sparseness of the array arrangement is achieved by properly exploiting the principles of compressive sensing.This design corresponds to the proposed method where only the array coefficients are optimized and the positions of the elements are fixed at predefined values.From a practical s-tandpoint,arrays with pre-defined element positions are preferred,mainly because of their simplicity of implementation.It should be noted that in previous procedures,the symmetric weight constraint limits its result in real-valued patterns and thus lacks the degree of freedom than that containing complex terms,and therefore,only sym-metric power patterns are realizable,which preclude asymmetric sidelobe distribution.In practice,many applications require complex-valued array responses like scanned beams or shaped beam patterns.In this work,satisfactory solutions can be obtained thanks to the possibility of synthesizing asymmetric arrays?with more degree of free-dom?and to the simultaneous optimizations of the distribution of array elements ex-citations and positions.This is an approach that has numerous advantages in terms of saving the space and reducing the hardware complexity.4.In this paper,a new array synthesis approach is developed for the design of re-configurable sparse arrays radiating sum and difference patterns.An iterative scheme is used where the prescribed pattern response in the mainlobe is cast as a multi-convex problem at each step that the nonconvex lower bound constraint is relaxed while in-cluding a reweighted l₁-norm minimization based on the magnitudes of the elements.Thus,a better performance of beam pattern?e.g.,narrower half-power beamwidth,lower maximum sidelobe levels?and a smaller number of elements can be obtained compared with the case of uniformly spaced array.The proposed approach provides a signifcant reduction in the complexity of the Beam Forming Network,which is fulfilled by reducing the number of antenna elements in the array and sharing some excitation weights for the sum and difference channels.Consequently,a large part of the whole architecture is common to both modes with a non negligible saving of costs.5.In this paper,an approach for the synthesis of sum and difference patterns in monopulse antennas is described.A signifcant reduction in the complexity of the Beam Forming Network is proposed.Instead of the available model that the element weighting affords the sum beam and subarray weighting produces the difference beam,the provided solutions is obtained by reducing the number of array elements and keep-ing the elements at the edges of the array with common excitations for both sum and difference modes.The algorithm consists in solving a sequence of weighted l₁convex optimization problems.In the optimization procedure,the objective is the minimiza-tion of the number of radiating elements and the number of subarrays.Thus,a smaller number of elements can be achieved compared with the case of uniformly spaced ar-rays.Design of two-dimensional reconfigurable monopulse arrays with subarrays and common aperture tail is an effective way to reduce system costs and hardware imple-mentation complexity.6.To compensate for mutual coupling or array imperfections in practice,robust beampattern constraints are derived in the optimization stage by using worst-case per-formance optimization technique.To ensure robustness of the array,we also constrain the white noise gain to be above a prescribed level.In addition,the performance of the optimized designs obtained by the proposed convex optimization algorithm is also verified by electromagnetic simulations.