Investigation On Adaptive Beamforming Algorithm Based On Logarithmic Function

With the rapid development of signal processing theory and hardware technology,in the field of signal transmission,people have achieved a leap from single-channel to multi-channel,single-element transmission to array transmission.When performing data transmission in space,it is often necessary to enhance the target signal and suppress interference or noise.The beamforming algorithm was born to face these kinds of problems,and it has become the most popular spot in the study of signal processing.When the traditional beamforming algorithm is working,it is often necessary to make all the sensors work to achieve the desired effect.However,in the actual application environment,the communication system is often restricted by other conditions such as space and energy,so it needs to be reduced.The number of array sensors used,while traditional beamforming will be difficult to meet the actual needs,sparse adaptive beamforming algorithms have emerged as the times require.However,in the existing sparse beamforming algorithms,there are usually problems such as poor array sparsity control accuracy,large error in beamforming capability,and slow convergence speed.In response to the above problems,the main work of this article is as follows:（1）In a Gaussian environment,for the practical application of S-band and P-band satellite detection and the precise control of array sparsity,a sparse adaptive beamforming algorithm based on logarithmic cost and approximate ₀l norm（L0-CNLMLS）is proposed.In the traditional mean square error cost function,a more stable and better performance logarithmic cost is introduced to obtain a new minimization optimization problem.And an approximate method of ₀l norm is proposed,which solves the NP-Hard problem of ₀l norm calculation.By Lagrangian multiplier method,the minimization constrained optimization problem is transformed into a minimization unconstrained optimization problem and solved,and the final iterative formula is obtained.In the simulation experiment,based on the quadrature phase shift keying signal input,two array environments（triangular array,TA array and irregular array,IA array）under different application backgrounds were built,and the algorithm was simulated.According to the analysis of the simulation results,it can be proved that the designed L0-CNLMLS algorithm is much better than the other traditional algorithms and related algorithms in recent years in terms of array sparsity control ability and convergence speed.（2）In the impulse noise environment,the minimum log absolute difference adaptive beamforming algorithm（CNLLAD）algorithm suitable for the impulse noise environment and the logarithmic cost and norm-based sparse adaptive beamforming algorithm suitable for the sparse system environment（L0-CNLLAD）.First,the adaptability of the symbol algorithm to impulse noise is introduced,and then the logarithmic cost is introduced into the absolute error cost function to transform the cost function,and the specific derivation formula of the CNLLAD algorithm is obtained.Simulations are carried out from different angles to verify the The feasibility of combining number cost with symbolic function.Since the CNLLAD algorithm cannot be applied to a sparse environment,the approximate norm is used to induce the algorithm to be sparse,and the iterative formula of the sparse adaptive beamforming algorithm L0-CNLLAD is obtained through derivation.Using Bernoulli noise as a prototype to construct an impulse noise environment for simulation experiments,through the comparison and analysis of simulation experiments,it is verified that the L0-CNLLAD algorithm is more adaptable to the impulse noise environment than the LMS algorithms and the sparsity array control ability can also be proved under a variety of array conditions.