Two-dimensional (2D) arrays are fundamental to localization applications. Specifically, sparse arrays can provide superior direction-of-arrival (DoA) estimation performance with limited number of sensors. There has been increased interest in the research community in designing 2D sparse arrays with performance improvement and complexity reduction. The research efforts are uncoordinated resulting in some repetitions and sometimes conflicting claims. After introducing 2D sparse arrays and their importance, this paper establishes the 2D-DoA estimation model and consolidates the performance metrics. An extensive literature overview of sparse arrays for 2D-DoA estimation is presented with an attempt to categorize existing works. The examined arrays include parallel arrays, L-shaped, V-shaped, hourglass, thermos, nested planer, and coprime planner, to name a few. Existing designs are compared in terms of required number of sensors, degrees of freedom (DOF), algorithm used, associated complexity and aperture size. The focus is on describing the sparse arrays, yet some specific details on DoA estimation algorithms are provided for selected array geometries. Fundamental problems of 2D-DoA estimation are outlined and existing solutions to alleviate these problems are discussed. This should be useful in predicting the estimation performance and required complexity; thus, aiding the decision of selecting a sensor geometry for DoA estimation. This review serves as a starting point for researchers interested in exploring or designing new 2D sparse arrays. It also helps to identify the gaps in the field and avoids unnecessary minor design modifications.

Sensor array configurations such as coprime and nested arrays have attracted many researchers because they increase the degree of freedom (DOF). For example, in the direction of arrival estimation, the number of sources that can be estimated is greater than the total number of sensors. This study proposes a multi‐level prime array (MLPA) configuration for sparse sampling that can further increase the DOF. The proposed array uses multiple uniform linear subarrays where the number of sensors in the subarrays is pairwise coprime integers. The inter‐element spacing between the sensors is formulated as a scaled multiple of half‐wavelength where the subarrays share only their first element. For a fixed number of sensors, multiple MLPA configurations can be constructed by controlling the number of sensors in the subarrays or by adjusting the inter‐element spacing. For a given number of sensors, the proposed array has a smaller aperture and achieves more number of unique and consecutive lags compared with coprime arrays. The proposed configuration has limited holes in the difference coarray. The analytical expressions of both the difference coarray and the aperture size are derived. Simulation results confirm the advantage of the proposed configurations compared with the two level coprime arrays.

In this paper, a sparse direction-of-arrival (DOA) estimation based on a shifted coprime array configuration is proposed. The proposed array utilizes two uniform linear arrays (ULAs), one of them is shifted from the other by certain displacement. The displacement is optimized such that the number of lags in the difference coarray is increased. Thus, the value of this displacement changes for different number of sensors. The resulting array is denoted to as shifted coprime array (SCA). Qualitative and quantitative results using Matlab reveal the strength of the proposed configuration. Compared with coprime array with displaced subarrays (CADiS), the proposed SCA has lower aperture and achieved larger number of consecutive lags.

In the literature, antenna arrays for direction of arrival (DOA) estimation are being theoretically optimized to maximize the number of sources that can be estimated for a given number of isotropic elements. In this work, coprime arrays with monopole and patch elements are designed and fabricated to evaluate the impact of antenna directivity and realistic antenna behavior on DOA estimation accuracy. Two DOA estimation algorithms, namely: MUSIC and Lasso are applied where the complex radiation patterns are incorporated within the steering matrix and then the received signal is modified accordingly. With four sources, a root mean square error (RMSE) of around 4 and 1 degrees is achieved at 5 dB with monopole and patch elements, respectively. Furthermore, a software-defined radio (SDR) platform is utilized to experimentally evaluate the real-time performance in realistic environments. It is shown that when the DOA deviates from the boresight, the estimation error increases due to antenna directivity. The performance of the patch array is better than its monopole counterpart due to the inherent multipath mitigation in the directive antennas and polarization purity of the two radiated electric filed components. Experimental results show that the RMSE in the DOA estimation of two sources using coprime array with monopole and patch elements is around 4 and 1 degrees, respectively.

A signal emitter can be located using diverse types of direction finding (DF) techniques. One of the most widely used techniques is the direction of arrival (DOA) estimation using antenna arrays. An array configuration that can increase the degrees of freedom (DOF) or the number of estimated sources is desired. Multi-level prime array (MLPA) uses multiple uniform linear subarrays where the number of elements in the subarrays is pairwise coprime integer. Compared with nested and coprime arrays, MLPA requires smaller aperture size which is important in mobile applications. Different MLPA configurations can be constructed for a given number of antennas and the one that maximizes the DOF is exploited. These configurations have a difference coarray with large number of consecutive lags and few holes. The number of consecutive lags can be increased by properly compressing the inter-element spacing of one subarray under a fixed number of antennas and without changing the aperture size. This paper proposes a new compressed MLPA configuration and demonstrates its performance in sparse DOA estimation. The resultant array, MLPA with compressed subarray (MLPAC), can have a hole-free difference coarray as in nested array case. MLPAC can estimate larger number of sources using both MUSIC and sparse reconstruction algorithms. Mutual coupling between sensors has also been evaluated. Simulation results confirm the achievable DOF and the advantage of the proposed configuration in DOA estimation.