Performance analysis of direction of arrival algorithms for smart antenna

ABSTRACT


INTRODUCTION
Currently, many researchers are interested in new technologies such as the Internet of Things and the 5th generation, to track the excessive growth of wireless technologies. This exponential progress generates increased demand for capacity [1], a need for more radio frequencies [2], excessive appeal for signal processing and space constraints [3], which cannot be satisfied using Conventional antennas, despite the improvements made in the coverage area [3]. Moreover, the use of passive antennas leads to a significant energy wastage, a major interference factor in co-channel, which incites researchers to seek alternative strategies to overcome these encountered problems.
Smart antenna technology is considered as the best solution confronting these problems. It can achieve highly efficient network, maximizing the capacity and improving quality and coverage [4,5]. It also referred to adaptive array antennas [6], tends toward creating an adaptive beamforming using a narrow beam in direction of the desired signal while canceling the interference signals. These antennas are used for millimeter waves (mm-wave), Radio Frequency Identification (RFID), Multiple Inputs Multiple Outputs (MIMO), and so on.
Smart antenna system contains two major functions, knowing as the direction of arrival estimation (DOA) and the beamforming given by adaptive algorithms. The classical model of the smart antenna system is considered as showing in Figure 1 [7]. The direction of arrival (DOA) is one of the most challenging problems for locating and tracking multiple moving sources in different areas, such as radar [8], sonor [9], and mobile communications. The location of sources with distributed sensor arrays can be achieved by estimating the direction of arrival of signals from terminal sources [10,11].
Various techniques are used to estimate the direction of arrival, among which are high-resolution methods such as Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) [12], Multiple Signal Classification (MUSIC) [13], Weighted Subspace Fitting (WSF) [14], The Minimum Variance Distortionless Response (MVDR or capon) [15] and beamspace, these techniques have attracted the most interest and has been the subject of many studies [10][11][12][13][14][15], however, none of these studies reached the best performance in smart antennas.
In this paper, we focused on one of the main functions, which is the direction of arrival, and we studied all the possibilities of better performance. To do so, we first investigated the algorithms that we worked with, which are beam scan, MUSIC, root-MUSIC, ESPRIT, capon or MVDR, root-WSF. Then we evaluated our system according to the following criterion: a. The number of array elements b. The number of samples c. The number of signals Finally, we matched the system with the corresponding parameters of smart antenna; in this case, we will work with Wi-Fi parameters as a testing example.

RESEARCH METHOD 2.1. DOA estimation
The main role of the DOA is to estimate the direction of the desired signal by collecting data from the incoming signals received by the antenna array [16]. Adaptive algorithms are the backbone of the smart antenna system. They consist of creating adjustable beams that meet the demands of the system. These algorithms use a set of complex weights to adjust the amplitude or the phase of each elemental antenna of the proposed network. The trained system can only operate by knowing the angles of arrival, where the estimation of the direction of arrival algorithms is then required [17].

Conventional DOA
The conventional DOA beamforming method is also known as the Bartlett method, consist of a power study, in which, over a scan across the angular region of interest, look for the largest output power from the different direction to estimate the desired one [18].
It is also appropriate to proceed to the spatial spectrum method in which the estimation of the direction is made only by corresponding the peak value of the output power with the angle ϴ. The expression of the Bartlett method can be given by: In this expression, a(θ) and RXX represent respectively the array response vector and the autocovariance matrix of the received signal.

MVDR (Capon algorithm)
Minimum Variance Distortionless Response or Capon beamformer is a solution for the conventional beamformer (the Bartlett method) problem caused when the sources to be located are closer than the beamwidth. When the Bartlett method can't separate them, the MVDR technique interferes to solve the problem [19]. The only adjustment made in the conventional beamformer is the additional matrix inversion R xx , in which the Capon spatial spectrum is given by:

MUSIC algorithm
The Multiple Signal Classification (MUSIC) algorithm is widely used in adaptive antennas because of the good result estimating the direction of arrival specifically when the signals are uncorrelated and the number of sources is known [20,21]. This method relies on the Eigenstructure of input covariance matrix [21]. Therefore, we chose to work with the signal value decomposition (SVD) technique, of which the covariance matrix is represented as follows: And 2 represent respectively the signal part and the noise part, where Us is the signal subspace corresponding to Vs and Un is the noise subspace with the noise variance 2 . The expression of normalized MUSIC spectrum is given by: In literature, this expression could be written as:

Root-MUSIC
Root-MUSIC is considered as one of many conversion of MUSIC algorithm, it is based on setting up the roots of a polynomial, this technique aims to decrease the computational complexity and improve its performance. Nevertheless, it is applicable only for a linear array spaced uniformly [17].

ESPRIT algorithm
Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), is a subspace technique, used to estimate the angle of arrival (AOA) by determining the rotational operator Ф [21]. ESPRIT algorithm shows same performance as MUSIC algorithm with slight adjustment. The aims of ESPRIT strategy is to misuse the rotational invariance in the flag subspace, which is made by two clusters with a translational invariance structure [22]. ESPRIT algorithm have several advantages presented in the simplicity of Implementation, producing direction of arrival directly avoiding the search procedure, does not need much computation or storage requirement. Considering a linear array with two doublets and four elements, the two subarrays are received by [21].
2 ( ) = * ∧ * ( ) + 2 ( ) where Where D<M (number of signal hitting the subarrays). The two matrix V 1 and V 2 are creating by two subarrays, in which the eigenvectors are related by a unique nonsingular transformation matrix ф with a unique nonsingular transformation matrix T. Than The eigenvalues of ф (λi) must be equal to the diagonal elements of Λ. Once the eigenvalues are calculated the estimation of the angle of arrival can be made by:

WSF algorithm
Weighted Subspace Fitting (WSF) algorithm is an asymptotically proficient parametric method used for estimating the heights of different scatterers in the same azimuth-range resolution cell [23,24]. Like the MUSIC and ESPRIT algorithms, the WSF algorithm represents a unified approach that also stand in needs of the knowledge of the number of directional sources, and the use of the decomposition technique for eigenvalues. the strongest eigenvectors in a diagonal matrix (̂) and the corresponding eigenvectors in the signal subspace matrix (̂) [25] are used to accomplish this approach. The expression of WSF algorithm can be written as: П ( ) represente The projection matrix onto the column space of a(θ), and W is a weighting matrix to reduce the impact of the subspace swap [26].

Root-WSF algorithm
Root-WSF is the rooting version of Weighted Subspace Fitting, also referred as MODE technique. The aims of this method is to minimize the cost function with [27]. Where: correspond to the asymptotic-optimum weight matrix, 2 is the noise variance and

RESULTS AND ANALYSIS
In order to evaluate the performances of the different direction of arrival algorithms, three scenarios have been made, based on the changing parameters of the number of signals, the number of samples and the number of array elements. For this reason we consider a uniform linear array (ULA) of M the number of elementary antennas with the inter-element spacing of λ/2, where λ is the wavelength of incident radiation, K represents the number of samples or snapshots and the angles of arrival is given by AOA . All the sources are considered uncorrelated with the same frequency of 1 GHz and with identical power. These simulations presented in this section are performed with MATLAB and SIMULINK R2015a.

Result of a spatial spectrum
In this part, we will evaluate the DOA algorithms based on the spatial spectrum study. For that, we proposed a system. The parameters of the proposed system can see in Table 1. The results of these simulations are presented as Figure 2, Figure 3 and Figure 4. The results obtained show three different algorithms. Figure 2 corresponds to the classic Beamforming giving unreliable results, where the proposed arrival angles are not detectable. Figure 3 indicates that the MVDR algorithm provides an acceptable result compared to the conventional algorithm. However, the angle of arrival of ϴ 2 = 0 ° is not conceivable. Figure 4 represents the MUSIC algorithm which gives the sharpest and clearest result among the three AOAs. Therefore, we can certainly conclude that the MUSIC algorithm stipulates the best result.

DOA comparison
In this section, we will analyze the performances of the different DOA algorithms, in order to locate the arrival angles and extract the best method. The proposed system remains the same as shown in Table 1. The Table 2 presents this study. Table 2 is consistent with the study found in the spatial spectrum method, in which the MUSIC algorithm proves its effectiveness. we can also see that other algorithms like ROOT-MUSIC and ROOT-WSF have distinguished themselves by giving good results.

First scenario: Varying the number of elements
After analyzing each DOA estimation algorithm, we will evaluate their performance according to certain criteria. First by changing the number of elementery array M from 6 to 8 then 10. Table 3 gives the results corresponding to two numbers of elementary antennas of 6 and 8. While the number 10 is given by Table 2 where the DOA comparison study was established. We can notice that even by changing the number of antennas, the best results are only provided by ROOT-MUSIC and ROOT-WSF. As a result, the higher the number of antennas, the more accurate the results will be.

2nd scenario: Varying the number of samples
The Table 4 represents the varying number of samples from 100, 500, and 1024, applied in different DOA algorithms. The table corresponding to K = 1024 is the one with the comparison study as shown in Table 2. Like the previous table, the results show that the two algorithms ROOT-MUSIC and ROOT-WSF provide the best results. The ROOT-WSF algorithm gives the most accurate angles of arrival for the three proposed samples. It is also true that the larger the number of samples, the more precise it becomes.

3rd scenario: Varying the number of signals
We will now study the impact of the number of signals on the DOA estimate. The chosen numbers are 2 and 3. From Table 5, we can notice that two signals only need two angles of arrival to function, which is obvious, what is important to note is that for each of the DOA algorithms, we obtain the same result, corresponding to the angles of arrival that we seek. However, when the system switches to three signals, the only algorithms that enable the corresponding detection are ROOT-MUSIC and ROOT-WSF.

Comparaison with other studies
Comparing our study with the related works previously published, we can notice that each of the proposed manuscripts [29][30][31] presents an incomplete study of the direction of arrival estimation algorithms. Therefore, we have tended in this article to complete these works by bringing together all the possibilities offered by the state of the art in order to apply them to new wireless technologies.

Wi-Fi parameter
For this study, we consider the same proposed system given in Table 2. Two Wi-Fi frequencies bands are used: 2.4 GHz and 5 GHz. This analysis is performed only for the algorithms that gave good results found in the previous sections. The three DOA algorithms presented here have the same sensibility to the operating frequency, which is clearly remarkable in Table 6. Besides, the MUSIC algorithm cannot recognize the second angle of arrival at 0°. However, ROOT-WSF algorithm provided the best results with almost no error.

CONCLUSION
The study established in this paper is based on a uniform linear array (ULA) of M antenna elements with the inter-element spacing of λ/2, where all the sources are assumed uncorrelated. We first evaluated the impact of the array elements from 6 to 10, in which the ROOT-MUSIC and the ROOT-WSF algorithms proved their effectiveness. Then we evaluate the impact of the number of sources on the DOA algorithms. The results clearly show that the increase in the number of sources leads to a certain complexity in the proposed DOA algorithms, in this case also, ROOT-MUSIC and the ROOT-WSF algorithms have achieved the best results. Finally, we evaluate the number of snapshots or (number of samples) that gives the identical results.
From this study, it can be seen that ROOT-WSF and ROOT-MUSIC algorithms have provided the best result on the different impacts that we have worked with, therefore, these two techniques will be the most feasible in the upcoming research. As for the operating frequency, the two 2.4GHz and 5GHz Wi-Fi bands gave the best result with the ROOT-WSF algorithm in comparison with the MUSIC and ROOT-MUSIC algorithm. In terms of accuracy, the ROOT-WSF algorithm provides the most accurate detection of the angles of arrival in the three proposed scenarios with almost no error. This makes it the best choice for the implantation in the smart antenna system.