New Linear Sparse Array Design With Ideal Critical Weights And Increased Degrees Of Freedom

Direction of arrival(DOA)estimation in array signal processing is of paramount significance in order to pinpoint the signal sources precisely.Accurate estimation is an indispensable part of many real-world applications like radar,sonar,microphone array systems,and wireless communications.For robust DOA estimation in the presence of mutual coupling(MC)phenomenon observed to exist among the array sensors and which causes the sensor responses to interfere with each other,a linear sparse array of nonuniform sensors with certain desirable characteristics is required.These characteristics are the existence of a closed-form expression to precisely locate the array physical sensors,the considerably higher number of virtual sensors(or "degrees of freedom(DOFs)")the physical sensors produce and the fewer pairs of physical sensors with small separations(or "inter-sensor spacings").More specifically,the closed-form expression should be scalable for any given number of actual sensors N,and the virtual sensors should be uniformly spaced out by half of the wavelength of the incoming signal(λ/2),such that the virtual array(aka"the difference co-array")can have these virtual sensors as a virtual uniform linear array(ULA)part in the co-array center,since this centering can help to conveniently apply a sub-space-based direction of arrival finding algorithm,such as,multiple signal classification(MUSIC)or estimation of signal parameters via rotational invariance techniques(ESPRIT).Furthermore,besides creating such a uniform linear array part,how the actual sensors are arranged(or "located")should also allow the array arrangement to possess one and only one sensor pair with separations(1 ×λ/2),(2 × λ/2),and(3 ×λ/2),and this is because the mutual coupling phenomenon observed to exist among the array sensors has a severe effect when the two sensors are located close to each other and empirically has no effect when they are far from each other.Compared to the traditional uniform linear array(ULA),which resolves at most N-1 signals using N sensors,co-prime arrays and nested arrays,as novel proposed sparse arrays,achieve a considerable number of resolvable sources.Specifically,with N actual sensors,the co-prime array owns a uniform linear array part of length((N2+4N)/4),while the nested array possesses an((N2/2)+N)-long uniform linear array part.Accordingly,the virtual uniform linear array part of the co-prime array is way less than that of the nested array.Nevertheless,the nested array,in contrast,heavily suffers from severe mutual coupling due to a dense sub-array in its physical configuration.Many arrays out of these two basic arrays have been proposed to address the shortcoming of each.However,neither co-prime-array-based arrays could possess a larger or even an equal ULA part to that of the nested array,nor could nested-array-based arrays possess ideal weight functions for the first three critical separations(i.e.,w(λ/2)=w(λ)=w(3(λ/2))=1)as the co-prime array does.In this thesis,the main goal is to explore a group of new and different sparse arrays,in search of a sparse array that can combine the best features of co-prime and nested arrays to improve the performance of DOA estimation in the presence of mutual coupling.In our first work,we propose a new sparse array that is built based on modifying the prototype of the co-prime array.Different from the co-prime-array-based arrays,which reduce the inter-sensor spacings of the prototype co-prime array(ProCA)to enlarge the virtual uniform linear array part,the proposed array through applying a sequence of displacements to one of the two constituent sub-arrays of ProCA significantly increases the number of uniform degrees of freedom while maintaining the original spacings of ProCA.Specifically,the proposed array design applies the displacements in a systematic procedure to the sensors of one of the two sub-arrays.As a result,the di splacements completely eliminate the redundant virtual sensors between the two sub-arrays and considerably increase their number of uniform degrees of freedom.With no redundant virtual sensors in the resulting difference co-array,the new design is of ideal critical weight functions,and the achievable number of uniform degrees of freedom of the proposed array design,specifically,is((N2/4)+4N+2).Simulation results show that the proposed structure can provide better DOA estimation in the presence of mutual coupling,compared to the augmented co-prime array,co-prime array with compressed sub-arrays,thinned co-prime array and prototype co-prime array with minimum lag redundancy.In our second work,we propose a different new sparse array called dilated nested array(DNA)and construct it in a way that is similar to the way of building the prototype of the nested array so that the proposed dilated nested array has exactly the same uniform linear array part of the nested array but has much fewer sensor pairs with small separations in comparison.Specifically like in NA,in DNA which is made of three subarrays,the second sub-array is nested to the first sub-array.But different from NA,the third sub-array placed beyond the second sub-array to dilate the physical aperture of this latter spaces out the sensors of the array further,hence the fewer sensor pairs with small separations DNA possesses in comparison.Additionally,a displaced dilated nested array(D-DNA)is developed,which involves displacing the third sub-array further from the second.D-DNA proves enhancement in the co-array properties of DNA and simulation results demonstrate that DNA and D-DNA,in particular,provide more accurate estimation performance than the enhanced and generalized co-prime array,extended padded co-prime array,augmented nested array,and super nested array,especially in scenarios where the number of sources contaminated by severe mutual coupling is relatively greater than the number of sensors.In our third work,we propose high-order extensions for the parent dilated nested array,called Qth-order dilated nested arrays(DNAs),where 2 ≤Q ≤Qf+1.While the second sub-array of the parent dilated nested array is sparse because its sensors are safely located far from each other,the sensors of the first and third sub-arrays are closely spaced out by the critical spacing(2 × λ/2).As a result,given its first three weight functions expressed generally as w(1)=1,w(2)=N1+N3-1,and w(3)=1,where N1 and N3 are the numbers of sensors in the first and third sub-arrays,respectively,the parent dilated nested array has a higher number of sensor pairs with separation 2.Through systematic and effective procedures,Qth-order dilated nested arrays,referred to as one-sided dilated nested arrays as well,redistribute the sensors of the third subarray of the parent dilated nested array in a way that the number of uniform degrees of freedom remains unchanged while the number of sensor pairs with separation two is significantly reduced to w(2)=N1-1,without penalizing w(1)and w(3).In this work,through further systematic procedures,super dilated nested arrays,developed from the(Qf+1)th-order dilated nested arrays and referred to as two-sided dilated nested arrays as well,are also proposed to reduce the number of sensor pairs with separation 2 further,through redistributing the sensors of the first sub-array of the parent(Qf+1)th-order dilated nested array,while maintaining the same number of uniform degrees of freedom.As a consequence,the uniform linear array part of the super dilated nested array is still strictly of((N2/2)+N)uniform degrees of freedom whereas the associated first three weight functions become w(1)=w(2)=w;(3)=1.With such a sharp reduction in the weight functions,especially in the weight function of the inter-sensor spacing 2,that is achieved at first by the one-sided dilated nested array,and then the two-sided dilated nested array,without penalizing the other critical weight functions and without affecting the resulting size of the uniform linear array part of parent dilated nested array,super dilated nested arrays combine the best features of co-prime and nested arrays and provide a good balance between the uniform DOF and weight function.As a consequence,compared with robust sparse arrays,such as super nested arrays,maximum inter-sensor spacing constraint arrays,and enhanced and extended generalized co-prime arrays,simulation results show that Qth-order dilated nested arrays and super dilated nested arrays,in particular,demonstrate higher robustness against mutual coupling effects and much more accurate direction of arrival estimation performance in much worse scenarios,where the number of sources is greater than the number of actual sensors and the presence of mutual coupling at the same time is heavily intense.