The Coprime Array In Its Optimized Version:More Degrees Of Freedom (DOFs) And Reduced Mutual Coupling

The recently proposed coprime array,as an example of a sparse array of antennas,could produce more effective virtual sensors(degrees of freedom(DOFs))than the number of actual sensors being used.The coprime array achieved that by utilizing the coprimality property of two coprime integers M and N to build its two consisting uniform linear subarrays,M-array and N-array,respectively.The N-array is of N sensors with an inter-sensor spacing of M units,while the M-array is of 2M actual sensors with an inter-sensor spacing of N units.In this thesis,a direction of arrival(DOA)estimation based on the optimized coprime array(OpCA)configuration is proposed.The proposed array keeps the N-array untouched,while it shifts all the sensors of the M-array by a specific displacement amount LS towards the positive direction,yielding the Optimized M-array.Different displacement expressions for LS are proposed for the purpose of being applicable to all the possible encountered coprime M and N values.Coprime M and N integers,where M<N,can be classified into five possible types and a proper displacement expression for each is assigned accordingly.Analytically,those displacements are optimized such that the number of the actual sensors for the proposed array is still the same as that for the coprime array,(N+2M-1),via having a common sensor shared between the two subarrays,and the number of central contiguous lags or equivalently virtual sensors,which referred to as the uniform degrees of freedom(DOFs)capacity in the difference coarray,has been enhanced.This enhancement is shown by increasing the one-side uniform DOFs capacity of the coprime array from MN+M-1 to MN+M-1+Ls+M where Ls is the displacement value itself.This enhancement also comes with reducing the number of actual sensor pairs of small separations(small multiples of ?/2),thereby bringing less mutual coupling compared to the coprime array.Numerical simulation results using subspace-based DOA estimation algorithms are provided to demonstrate the effectiveness of the proposed geometry.