Applications Of Optimization Algorithms In Array Signal Processing

Array signal processing plays an important role in many modern signal processing applications.From antenna array which process electromagnetic wave signals to sonar and microphone array which process acoustic wave signals,designing appropriate array signal processing algorithms is a necessary priority to meet different signal processing tasks.With the development of electronic digital technology,large-scale and distributed array signal processing technology have been widely used in more and more signal processing tasks due to its increased gain and spatial diversity.The accompanying array signal processing algorithms hence face new difficulties such as high computational complexity and strong nonlinearity of the mathematical model.On the other hand,the development of optimization theory provides a foundation for solving those difficulties.This dissertation focuses on designing and analyzing optimization algorithms for solving the difficulties arising in the three key applications in the field of modern array processing.The main research contents of this dissertation include: robust beamforming technology for large-scale array,multisensor registration technology and sub-array partitioning technology for phased array.In the filed of the robust beamforming technology,the performance of existing robust beamforming technology is usually limited by the application scenario.On the other hand,solving the robust beamforming model often requires a specified optimization algorithm with computationally expensive cost,which cannot be effectively used in large-scale array.Therefore,based on the physical factors which degrade the beamforming performance,a new robust beamformer is proposed.Specifically,the proposed beamformer model introduces robustness against the direction of arrival error and signal sample error by enforcing inequality constraints in multiple directions around the target and the interfering signals,balances the impact of array steering vector error and the limited degrees of freedom by penalizing the inequality constraints and the norm of the beamformer.According to the mathematical form of the proposed beamfomer model,the beamfomer is named as the penalized inequality-constrainted minimum variance beamformer.In order to efficiently solve the beamformer,especially for large-scale array applications,this dissertation develops a low computational complexity optimization algorithm based on the alternating direction method of multiplier.In addition,the proposed beamformer contains a series of model parameters,which are used for adjusting the beamformer model for facing different application requirements.The simulation experiments verified the robustness and flexibility of the proposed beamformer in the applications of robust adaptive interference suppression,microphone array for speech enhancement,and special pattern synthesis for large-scale antenna array.Multi-sensor registration process is a necessary prerequisite for the success of multi-sensor data fusion.Most existing research works for sensor registration in the past few decades are based on the synchronization assumption,which cannot be applied to the multi-sensor system that actually works asynchronously.Based on the sensor measurement model,a new nonlinear least squares model is proposed to estimate all sensor range and azimuth biases from the asynchronous measurements.In order to avoid the model mismatch error caused by the first-order approximation of the nonlinear coordinate transformation between sensors(this is the issue faced by the most of the existing research works),this dissertation introduces the semi-definite relaxation method for solving the subproblem for estimating azimuth biases(non-convex problem).In addition,a theoretical analysis is provided,which guarantees that the semi-definite relaxation method can globally solve the azimuth bias estimation subproblem even it is non-convex.Based on the theoretical analysis,an alternative optimization algorithm is developed to solve the proposed nonlinear least squares model,with one step for estimating range bias and the other step for estimating azimuth bias.Compare with five existing approaches,the proposed model and algorithm not only have higher estimation accuracy in noisy scenarios,but also theoretically guarantee exact recovery of sensor biases in noiseless scenario.To study the subarray partition for phased array,this dissertation first analyzes the basic array signal model of phased array with subarray configuration.Based on the analyzed signal model,two kinds of subarray partition optimization criteria,the beam pattern matching criterion and the adaptive interference suppression criterion,are proposed.The proposed two criteria are used for synthesizing desired beam patterns and adaptively suppressing interference at subarray level.The corresponding optimization models of the two proposed criteria have the same mathematical form,which jointly optimizes subarray configuration(corresponds to 0-1 variables)and subarray weight coefficients(corresponds to complex variables),both are mixed 0-1 programming problems.Therefore,based on coordinate descent algorithm,this dissertation develops a unified optimization algorithm with low computational complexity for solving the two optimization models.The simulation experiments demonstrate that,for the beam pattern matching criterion,the developed algorithm can simultaneously form stable sum and difference beams with low sidelobe at subarray level.For the adaptive interference suppression criterion,the developed algorithm effectively optimize the subarray configuration for suppressing more interferences.