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Estimating the direction of arrival (DOA) of source signals is an important research interest in application areas including radar, sonar, and wireless communications. In this paper, the problem of DOA estimation is addressed on concentric circular antenna arrays (CCA) in detail as an alternative to the well-known geometries of the uniform linear array (ULA) and uniform circular array (UCA). We define the steering matrix of the CCA geometry and investigate the performance analysis of the array in the DOA-estimation problem by simulations that are realized through varying the parameters of signal-to-noise ratio, number of sensors, and resolution angle of sensor arrays by using the MUSIC (Multiple Signal Classification) algorithm. The results present that CCA geometries provide higher angle resolutions compared to UCA geometries and require less physical area for the same number of sensor elements. However, as a cost-increasing effect, higher computational power is needed to estimate the DOA of source signals in CCAs compared to ULAs.

The problem of estimating the direction of arrival (DOA) of source signals by sensor arrays has been widely researched for applications such as radar, sonar, and wireless communication technologies. In radar applications as part of military systems, estimating DOAs of signals is crucial to differentiate targets, whereas in communications DOA information provides spatial diversity to increase the number of users communicating simultaneously [

In case of multisource signals, it is inevitable to employ sensor array configurations to estimate the DOA of each signal. Increasing the number of sensors in an array provides a higher signal-to-noise ratio (SNR) by processing the signals received from the sensors in parallel [

There are various techniques in DOA estimation, most of them are either model-based or eigen-analysis-based ones. Model-based techniques, including least mean square (LMS) and sample matrix inversion based algorithms, may have higher computational complexity [

Array geometries impose constraints in DOA estimations. The most important disadvantage of the ULA geometry is that it can only estimate the azimuth angle. To overcome this problem, UCAs have been employed in applications requiring the estimation of both azimuth and elevation angles [

The paper is organized as follows. Section

The observed signal vector

The

As the noise eigenvectors spanning the noise subspace is orthogonal to the columns of the steering matrix

To formulate the DOA estimation problem in a CCA geometry, we need to review the DOA estimation by UCA first. Then, we define the steering matrix of CCA in Section

In DOA estimation by UCA,

Uniform circular array geometry.

CCA geometry is constructed by using concentric UCAs as in Figure

Concentric Circular Array geometry.

In this array structure,

By applying implicit form of (

The simulations are developed in three aspects to observe the behavior of CCAs compared to UCAs in the DOA estimation. These are the effect of SNR, angle resolution, and the number of source signals, respectively.

In this section,

All of the scenarios provide a comparison of the MUSIC algorithm for various SNR values and resolution properties of the source signals in case of CCAs. Section

In this section, the DOA estimation performance of CCAs are investigated for various numbers of sensor elements, SNR values, and angle resolutions by MUSIC algorithm. In the scenarios, Monte-Carlo simulations are realized for all SNR values. The sensor arrays have a total of 7 or 10 elements and for each array geometry SNRs are varied from 5 dB, 10 dB, 15 dB to 20 dB and root mean square error (RMSE) values of the estimations are computed with respect to the given DOA values. The CCA with 7 elements includes two concentric rings with 3 and 4 array elements on each ring, whereas the 10-element arrays have 6 and 4 elements on each ring. In the first ring of the 7-element CCA three sensors are used. The distance between two adjacent elements are chosen as

To analyze the change in the RMSE value with respect to the angle resolution for a fixed SNR, Monte-Carlo simulations are performed for three distinct source signals where the azimuth angle differences are

To analyze the accuracy in DOA estimation with respect to the number of source signals, six different scenarios are considered for the CCA geometry of 7 sensor elements. The number of source signals is varied from 1 to 6 and

When the DOAs of signals are chosen as

Developing an original approach to the estimation of DOAs of target signals, we defined the DOA problem for antenna arrays fitting in a concentric circular geometry and introduced the steering matrix of the CCA. We performed various scenarios to simulate the DOA estimation performance of CCAs. The results of simulations have been analyzed in terms of number of array elements and source signals, as well as SNR values and angle resolutions between the signals.

The simulations show that increasing SNR values and angle differences between the directions of incoming signals causes lower error rates in the DOA estimation. Similarly, increasing the number of antenna elements of CCA has a positive effect on the accuracy of estimations.

While ULAs can only estimate the azimuth angle, CCAs estimate both azimuth and elevation angles. For smaller angle differences among incoming signals, that is, for greater angle resolutions, the CCA provides more accurate estimation results than ULA. However, as the number of terms in the computational steps in the estimation algorithms of CCA and UCA is much more than ULAs, more computational power is needed to realize these algorithms. CCA can have less or similar error rates compared to UCA, for a given number of antennas. CCAs require smaller physical area than UCAs so this gives the CCA an important advantage to be a preferable alternative for using it in mobile applications.

Because of its multidimensional physical geometry, it is possible to generate a lot of scenarios to place the array elements in a CCA for a given number of antenna elements. As a result emanating from this physical realization diversity, it is harder but important to find the optimum solution compared to the ULA and UCA.

In future works, the physical locations of array elements in a CCA may be determined by developing optimization algorithms to achieve more reliable estimates of the parameters related to the DOA problem. This way, estimating accurate DOAs at low SNR values and differentiation of the source signals having small angle resolutions will be possible. Additionally another investigation issue with the CCA geometries will be on the estimation of DOAs of wide band signals.