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An angle of arrival (AOA) estimator is presented. Many applications require accurate AOA estimates such as wireless positioning and signal enhancement using space-processing techniques. The proposed AOA estimator depends on the Cholesky decomposition of the received signal autocorrelation matrix. The resultant decomposed matrices are used to modify the crosscorrelation matrix of the received signals at the antenna array doublets. The proposed method is named the Cholesky-decomposition-based-AOA (CDBA) estimator. In comparison with the TLS-ESPRIT algorithm which utilizes the eigenvalue decomposition (EVD) of the received signal autocorrelation and crosscorrelation matrices, the CDBA method has better performance than the TLS-ESPRIT algorithm especially in low signal-to-noise-ratio (SNR) cases. Simulations for the proposed CDBA method are shown to assess its performance.

Accurate estimation of the received signal angle of arrival (AOA) can be very beneficial for signal reception enhancement [

Many AOA estimators were proposed in the literature [

In this paper, an AOA estimator is proposed which enhances the AOA estimation. The proposed method is named the Cholesky-decomposition-based-AOA (CDBA) estimator. The CDBA method utilizes the received signal at the two sides of the antenna array doublets. An autocorrelation matrix of the received signal at one side of the antenna array doublets is calculated. Then, the received signal autocorrelation matrix is decomposed using the Cholesky decomposition. A crosscorrelation matrix between the received signals at both sides of the antenna doublets is calculated. The decomposed matrices of the autocorrelation matrix together with the crosscorrelation matrix are used to form a new matrix from which the AOAs are estimated.

The CDBA method does not require taking the Fourier transform of the received signals nor it requires any iterative or searching procedure to estimate the AOA. Also, in comparison with the well-known TLS-ESPRIT algorithm of [

The paper is organized as follows: Section

This section presents the narrowband received signal model that will be utilized for the AOA estimation. The antenna array is formed from

The AOA is taken between the antenna array axis, and the source signal arrival direction and will be given the notation

The

The received signal vector at the second side of the antenna doublets set will be given the notation

To implement the CDBA method, the crosscorrelation matrix (

Another matrix considered by the CDBA algorithm is the autocorrelation matrix of

Comparing (

Substituting (

Consequently, the EVD of

Substituting (

Now, taking the Cholesky decomposition of

Comparing (

A new matrix

To prove that

Substituting for

Defining the term

Thus, the required AOAs are estimated.

First step: calculate

Second step: calculate

Third step: calculate

Fourth step: calculate the

Fifth step: calculate the eigenvalues of

Sixth step: calculate the AOAs from the

The performance of the AOA estimators in high noise power (low SNR) cases is of interest. A measure of the noise power is the noise variance. A study of the noise variance effect on the performance of the CDBA algorithm is derived and compared with that of the TLS-ESPRIT.

As shown in (

Consider the magnitude of

As for the TLS-ESPRIT algorithm, the AOA estimation starts by taking the EVD of an autocorrelation matrix of the received signals (call it

Comparing

In high noise variance cases, the deviation between the estimated eigenvalues and the true eigenvalues will have a maximum value of 1 in CDBA algorithm, whereas, in the TLS-ESPRIT the deviation will approach

The performance of the proposed CDBA method will be shown in the simulation section (Section

Simulations for the proposed CDBA estimator were completed to assess its performance. The results in this section were averaged over 1000 ensemble runs. The elements of each antenna array were separated by a half-wavelength (i.e.,

Figure

Root mean square error (RMSE) of angle estimation in degrees versus signal-to-noise-ratio (SNR) in dB for

Figure

Root mean square error (RMSE) of angle estimation in degrees versus number of antenna doublets for

Another important issue in comparing AOA estimators is their performance when the AOAs of the received signals are close to each other. Table

Root mean square error (RMSE) of angle estimation in degrees for different AOA separations.

AOA separation |
TLS-ESPRIT | CDBA |
---|---|---|

1^{°} |
11.5223^{°} |
3.1770^{°} |

1.5^{°} |
6.8057^{°} |
1.6336^{°} |

2^{°} |
4.2739^{°} |
0.7330^{°} |

Also, to compare both methods computational complexity, two functions in MATLAB (tic.m and toc.m) were used to measure the time it takes each method to estimate the AOA. The CDBA and the TLS-ESPRIT methods took 0.281 and 0.297 seconds, respectively, to perform one run of AOA estimation for two users. Clearly, this indicates that the CDBA method has less computational complexity than the TLS-ESPRIT method.

In this paper, an AOA estimator is proposed which is named the CDBA method. The CDBA method is applied by taking the Cholesky decomposition of the received signal autocorrelation matrix. The resultant decomposed matrices are used to modify the crosscorrelation matrix of the received signals at the antenna array doublets. The proposed CDBA method has better performance than the TLS-ESPRIT method in estimating the AOAs especially in low SNR cases. The performance of the proposed CDBA method was assessed and compared to the TLS-ESPRIT method.