Research On Adaptive Beamforming Techniques Under Constant Mode Constraints

Beamforming techniques,which are at the core of array signal processing techniques,are widely used in various fields^[1]-[3],such as radar,navigation,wireless communication,astronomy,seismology,medical imaging and wireless sensor networks.With the development of signal processing technology,the design of beamformers with only phase variation,i.e.constant mode constraint on the Spatial filter weights,has attracted widespread attention in order to reduce power loss and computing time of signal processing equipment.In this thesis,the adaptive beamforming algorithm with constant-mode constraint will be studied to investigate how to improve the performance of the algorithm and reduce the computational complexity,with the following main innovative work:（1）In this thesis,a conjugate gradient algorithm based on Riemann manifolds is proposed to solve the phase-only beamforming problem.Beamformers usually only change the phase of the filter weight vector in order to reduce the loss of signal,i.e.a constant-mode constraint（CMC）is placed on the weight vector.Due to the CMC the problem is non-convex and usually requires the introduction of a relaxation condition to solve it,however,the relaxation process introduces an approximation error that affects performance.To avoid the relaxation error,we first project the problem onto a complex circular manifold to ensure that the constant-mode constraint is not relaxed,then introduce a conjugate gradient algorithm on the complex circular manifold,calculate the intermediate solution by iteratively computing the descent direction and descent step,and finally project the intermediate solution back to the constant-mode space to obtain the optimal solution,which improves the performance of the beamformer and has low computational complexity.（2）In this thesis,we propose an adaptive beamforming algorithm based on accelerated coordinate descent applicable to both the continuous phase and discrete phase cases.We exploit the decomposability of the constraints and propose a coordinate descent algorithm that first decomposes the optimisation problem into multiple one-dimensional problems,solves the optimal solution of the one-dimensional problem first,and then obtains the optimal solution of the overall problem by iterative computation.This method reduces the computational complexity compared to the direct calculation of the phase in a high-dimensional space.The coordinate descent algorithm is then accelerated with a square iteration technique,reducing the computational time.Considering the discrete nature of digital systems and the complex environment in practical applications,discrete and non-isotropic scenarios are considered in this thesis,and the algorithm achieves good beampattern performance with fast convergence in all scenarios.（3）In this thesis,a MIMO radar adaptive beamforming algorithm based on demand-free inverse model adaptive deep learning network is proposed.Since the adaptive beamforming of MIMO radar is often coupled to the waveform design problem at the transmitter,a joint design is required.Due to the limitation of constraints,the joint optimization problem is non-convex and difficult to solve.Therefore,we first propose a composite manifold space,map the original problem to the composite manifold space,which guarantees that the constraint is not relaxed,and then use the gradient descent method as the network layer for optimization,where the step size is adaptive calculation through network learning,and finally the solution obtained is mapped back to the original space to find the optimal solution.Since the step size is adaptive and does not require relaxation to find inverses,the proposed method has low computational complexity and improved performance.