Elie BouDaher

Multi-Frequency Co-Prime Arrays for High-Resolution Direction-of-Arrival Estimation

This paper presents multi-frequency operation for increasing the number of resolvable sources in high-resolution direction-of-arrival (DOA) estimation using co-prime arrays. A single-frequency operation requires complicated and involved matrix completion to utilize the full extent of the degrees of freedom (DOFs) offered by the co-prime configuration. This processing complexity is attributed to the missing elements in the corresponding difference coarray. Alternate single-frequency schemes avoid such complexity by utilizing only the filled part of the coarray and, thus, cannot exploit all of the DOFs for DOA estimation. We utilize multiple frequencies to fill the missing coarray elements, thereby enabling the co-prime array to effectively utilize all of the offered DOFs. The sources are assumed to have a sufficient bandwidth to cover all the required operational frequencies. We consider both cases of sources with proportional and nonproportional power spectra at the employed frequencies. The former permits the use of multi-frequency measurements at the co-prime array to construct a virtual covariance matrix corresponding to a filled uniformly spaced coarray at a single frequency. This virtual covariance matrix can be employed for DOA estimation. The nonproportionality of the source spectra casts a more challenging situation, as it is not amenable to producing the same effect as that of an equivalent single-frequency filled coarray. Performance evaluation of the multi-frequency approach based on computer simulations is provided under both cases of proportional and nonproportional source spectra.

Sparsity-Based Direction Finding of Coherent and Uncorrelated Targets Using Active Nonuniform Arrays

In this letter, direction-of-arrival (DOA) estimation of a mixture of coherent and uncorrelated targets is performed using sparse reconstruction and active nonuniform arrays. The data measurements from multiple transmit and receive elements can be considered as observations from the sum coarray corresponding to the physical transmit/receive arrays. The vectorized covariance matrix of the sum coarray observations emulates the received data at a virtual array whose elements are given by the difference coarray of the sum coarray (DCSC). Sparse reconstruction is used to fully exploit the significantly enhanced degrees-of-freedom offered by the DCSC for DOA estimation. Simulated data from multiple-input multiple-output minimum redundancy arrays and transmit/receive co-prime arrays are used for performance evaluation of the proposed sparsity-based active sensing approach.

Electromagnetic Optimization Using Mixed-Parameter and Multiobjective Covariance Matrix Adaptation Evolution Strategy

Different variations of the covariance matrix adaptation evolution strategy (CMA-ES) are used in the design and optimization of electromagnetic (EM) problems. Two different schemes for the implementation of mixed-parameter CMA-ES and one scheme for the implementation of multiobjective CMAES are presented. Mixed-parameter CMA-ES is attractive in EM optimization when both continuous and discrete design parameters are involved. The first mixed-parameter scheme uses a Poisson mutation operator to update the discrete variables, and the second one forces an integer mutation on discrete variables with small variances. Multiobjective CMA-ES, developed in this paper, optimizes designs with respect to multiple objective functions simultaneously. It ranks the candidate solutions according to two levels: nondominated sorting and crowding distance. Several antenna and microwave design problems are presented to evaluate the performance of these schemes and compare them with other nature-based optimization algorithms.

Mutual coupling effect and compensation in non-uniform arrays for direction-of-arrival estimation

In this paper, we investigate the effect of mutual coupling on direction-of-arrival (DOA) estimation using non-uniform arrays. We compare and contrast the DOA estimation accuracy in the presence of mutual coupling for three different non-uniform array geometries, namely, minimum redundancy arrays (MRAs), nested arrays, and co-prime arrays, and for two antenna types, namely dipole antennas and microstrip antennas. We demonstrate through numerical simulations that the mutual coupling, if unaccounted for, can, in general, lead to performance degradation, with the MRA faring better against mutual coupling than the other two non-uniform structures for both antenna types. We also propose two methods that can compensate for the detrimental effects of mutual coupling, leading to accurate and reliable DOA estimation. Supporting numerical simulation results are provided which show the effectiveness of the proposed compensation methods.

Sparse reconstruction for direction-of-arrival estimation using multi-frequency co-prime arrays

In this paper, multi-frequency co-prime arrays are employed to perform direction-of-arrival (DOA) estimation with enhanced degrees of freedom (DOFs). Operation at multiple frequencies creates additional virtual elements in the difference co-array of the co-prime array corresponding to the reference frequency. Sparse reconstruction is then used to fully exploit the enhanced DOFs offered by the multi-frequency co-array, thereby increasing the number of resolvable sources. For the case where the sources have proportional spectra, the received signal vectors at the different frequencies are combined to form an equivalent single measurement vector model corresponding to the multi-frequency co-array. When the sources have nonproportional spectra, a group sparsity-based reconstruction approach is used to determine the direction of signal arrivals. Performance evaluation of the proposed multi-frequency approach is performed using numerical simulations for both cases of proportional and nonproportional source spectra.

Towards a dual-function MIMO radar-communication system

Recently, dual-function radar-communication systems in which the radar platform and resources are used for communication signal embedding have emerged as means to alleviate spectrum congestion and ease competition over frequency bandwidth. In this paper, we introduce a new technique for information embedding specific to multiple-input multiple output (MIMO) radar. We exploit the fact that in a MIMO radar system, the receiver needs to know the association of the transmit waveforms to the transmit antennas. However, this association can change over different pulse repetition periods without impacting the radar functionality. We show that by shuffling the waveforms across the transmit antennas over constant pulse repetition periods, a data rate of megabits per second can be achieved for a moderate number of transmit antennas. The probability of error is analyzed and the bounds on the symbol error rate are derived. Simulation examples are provided for performance evaluation and to demonstrate the effectiveness of the proposed information embedding technique.

DOA estimation with co-prime arrays in the presence of mutual coupling

In this paper, we present a method for performing direction-of-arrival (DOA) estimation using co-prime arrays in the presence of mutual coupling. The effects of mutual coupling are first examined for extended co-prime arrays configurations using the Receiving-Mutual-Impedance Method (RMIM). DOA estimation is then achieved by performing a joint estimation of the angles of arrival and the mutual coupling matrix, using the mixed-parameter covariance matrix adaptation evolution strategy. Simulation results demonstrating the effectiveness of the proposed method are provided.

Sparsity-based extrapolation for direction-of-arrival estimation using co-prime arrays

In this paper, we employ a sparsity-based imputation technique to extend the usable portion of the difference coarray of a co-prime array for direction-of-arrival (DOA) estimation. The degrees-of-freedom (DOFs) offered by a co-prime array cannot be fully utilized for subspace-based DOA estimation due to the presence of holes in the corresponding difference coarray. The proposed imputation approach is first employed to fill the holes in the difference coarray, thereby increasing the available DOFs. MUSIC with spatial smoothing is then applied to the combined set of actual and imputed measurements for direction finding. Supporting numerical results are provided that validate the performance enhancements offered by the proposed approach.

Electromagnetic design optimization using mixed-parameter and multiobjective CMA-ES

In this paper, new variations of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are investigated for optimization of electromagnetic design problems. Two variations of the CMA-ES algorithm are presented: mixed-parameter CMA-ES and multiobjective CMA-ES. Examples and results are provided to evaluate the performance of these algorithms.

Inverse Profiling of Inhomogeneous Subsurface Targets With Arbitrary Cross Sections Using Covariance Matrix Adaptation Evolution Strategy

The problem of subsurface inverse profiling of a 2-D inhomogeneous buried dielectric target is addressed in this letter. An iterative optimization technique is proposed that utilizes Covariance Matrix Adaption Evolutionary Strategy (CMA-ES) as its inverse solver and Method of Moments, using Conjugate Gradient-fast Fourier transform, as the forward solver. The numerical results indicate that CMA-ES, as its first reported implementation in buried target reconstruction, can successfully be applied to this challenging reconstruction problem. Also, comparison with Evolutionary Programming and Particle Swarm Optimization indicates that CMA-ES can significantly outperform the other two-optimization techniques in the inhomogeneous subsurface imaging. In addition, examples of various scenarios involving noisy data, lossy targets and multiple targets further demonstrate that CMA-ES can be considered as a robust, simple, and efficient optimization tool in the reconstruction of complex buried targets.