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Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

Trucco A, Traverso F, Crocco M - Sensors (Basel) (2015)

Bottom Line: For linear arrays with fixed steering and an inter-element spacing smaller than one half of the wavelength, end-fire steering of a data-independent beamformer offers better directivity than broadside steering.Moreover, we verify that the maximized oversteering performance is very close to the optimum end-fire performance.A numerical simulation is used to perform a statistical analysis, which confirms that the maximized oversteering performance is robust against sensor mismatches.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical, Electronic, Telecommunications Engineering, and Naval Architecture (DITEN), University of Genoa, 5-16126 Genova, Italy. andrea.trucco@unige.it.

ABSTRACT
For linear arrays with fixed steering and an inter-element spacing smaller than one half of the wavelength, end-fire steering of a data-independent beamformer offers better directivity than broadside steering. The introduction of a lower bound on the white noise gain ensures the necessary robustness against random array errors and sensor mismatches. However, the optimum broadside performance can be obtained using a simple processing architecture, whereas the optimum end-fire performance requires a more complicated system (because complex weight coefficients are needed). In this paper, we reconsider the oversteering technique as a possible way to simplify the processing architecture of equally spaced end-fire arrays. We propose a method for computing the amount of oversteering and the related real-valued weight vector that allows the constrained directivity to be maximized for a given inter-element spacing. Moreover, we verify that the maximized oversteering performance is very close to the optimum end-fire performance. We conclude that optimized oversteering is a viable method for designing end-fire arrays that have better constrained directivity than broadside arrays but with a similar implementation complexity. A numerical simulation is used to perform a statistical analysis, which confirms that the maximized oversteering performance is robust against sensor mismatches.

No MeSH data available.


Oversteering amount, ε, that provides the maximum constrained directivity for an end-fire array of N = 8 transducers, which is obtained by imposing WNG ≥ 0 dB for three weighting windows: optimum weights (solid line), uniform weights (dashed line), and Taylor’s weights (dotted line).
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sensors-15-13477-f008: Oversteering amount, ε, that provides the maximum constrained directivity for an end-fire array of N = 8 transducers, which is obtained by imposing WNG ≥ 0 dB for three weighting windows: optimum weights (solid line), uniform weights (dashed line), and Taylor’s weights (dotted line).

Mentions: Figure 5 shows that the oversteering technique performs better than the optimum real weights without oversteering. In particular, Taylor’s window provides advantageous directivity values over a wide interval of d/λ, from 0.05 to approximately 0.42. According to Figure 4 and Figure 5, the performance achieved by real weights (uniform or optimized) without oversteering is poorer than the performance achieved by complex weights or by the oversteering technique; as a result, real weights without oversteering will be disregarded in subsequent investigations. The latter is intended to assess the oversteering with the real weights that maximize the constrained directivity. For a given value of d/λ, the oversteering optimization and the weight computation are performed by the algorithm described in Section 3.3. A discretization step for ε of 0.01 is established, and CVX software is employed for convex programming [20] on the previously mentioned PC, which results in a computation time that does not exceed 4 min. Figure 6 presents the maximum constrained directivities obtained with the oversteering technique using three weighting windows: uniform, Taylor’s, and optimized. The absolute maximum for the constrained directivity (i.e., the performance obtained with the optimum complex weights) is also included for comparison. It is possible to verify that the optimum real-valued weights always provide the best oversteering performance and that the achieved directivity is very close or equal to the absolute maximum. Although the Taylor’s weights provide results that are only slightly poorer over a significant interval of d/λ (from approximately 0.1 to 0.4), the optimized weights ensure the achievement of the maximum constrained directivity achievable by the oversteering technique. In this specific case, for values of d/λ lower than 0.1, the optimized weights provide a significant advantage over traditional weighting windows. To realize this fact, Figure 7 presents a magnification of a portion of Figure 6. Figure 8 presents the oversteering amount ε required to obtain the maximum constrained directivity using uniform, Taylor’s, and optimized weights. In general, the oversteering amount ε necessary to achieve the maximum directivity increases as the spacing d decreases and the allowed interval for ε increases. When d/λ is less than 0.04, the optimized weights achieve the maximum constrained directivity using an oversteering amount that is smaller than those with uniform and Taylor’s weights. Thus, unlike oversteering with traditional weights, the proposed optimization performs best when considering both the oversteering amount and weighting window.


Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

Trucco A, Traverso F, Crocco M - Sensors (Basel) (2015)

Oversteering amount, ε, that provides the maximum constrained directivity for an end-fire array of N = 8 transducers, which is obtained by imposing WNG ≥ 0 dB for three weighting windows: optimum weights (solid line), uniform weights (dashed line), and Taylor’s weights (dotted line).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4507652&req=5

sensors-15-13477-f008: Oversteering amount, ε, that provides the maximum constrained directivity for an end-fire array of N = 8 transducers, which is obtained by imposing WNG ≥ 0 dB for three weighting windows: optimum weights (solid line), uniform weights (dashed line), and Taylor’s weights (dotted line).
Mentions: Figure 5 shows that the oversteering technique performs better than the optimum real weights without oversteering. In particular, Taylor’s window provides advantageous directivity values over a wide interval of d/λ, from 0.05 to approximately 0.42. According to Figure 4 and Figure 5, the performance achieved by real weights (uniform or optimized) without oversteering is poorer than the performance achieved by complex weights or by the oversteering technique; as a result, real weights without oversteering will be disregarded in subsequent investigations. The latter is intended to assess the oversteering with the real weights that maximize the constrained directivity. For a given value of d/λ, the oversteering optimization and the weight computation are performed by the algorithm described in Section 3.3. A discretization step for ε of 0.01 is established, and CVX software is employed for convex programming [20] on the previously mentioned PC, which results in a computation time that does not exceed 4 min. Figure 6 presents the maximum constrained directivities obtained with the oversteering technique using three weighting windows: uniform, Taylor’s, and optimized. The absolute maximum for the constrained directivity (i.e., the performance obtained with the optimum complex weights) is also included for comparison. It is possible to verify that the optimum real-valued weights always provide the best oversteering performance and that the achieved directivity is very close or equal to the absolute maximum. Although the Taylor’s weights provide results that are only slightly poorer over a significant interval of d/λ (from approximately 0.1 to 0.4), the optimized weights ensure the achievement of the maximum constrained directivity achievable by the oversteering technique. In this specific case, for values of d/λ lower than 0.1, the optimized weights provide a significant advantage over traditional weighting windows. To realize this fact, Figure 7 presents a magnification of a portion of Figure 6. Figure 8 presents the oversteering amount ε required to obtain the maximum constrained directivity using uniform, Taylor’s, and optimized weights. In general, the oversteering amount ε necessary to achieve the maximum directivity increases as the spacing d decreases and the allowed interval for ε increases. When d/λ is less than 0.04, the optimized weights achieve the maximum constrained directivity using an oversteering amount that is smaller than those with uniform and Taylor’s weights. Thus, unlike oversteering with traditional weights, the proposed optimization performs best when considering both the oversteering amount and weighting window.

Bottom Line: For linear arrays with fixed steering and an inter-element spacing smaller than one half of the wavelength, end-fire steering of a data-independent beamformer offers better directivity than broadside steering.Moreover, we verify that the maximized oversteering performance is very close to the optimum end-fire performance.A numerical simulation is used to perform a statistical analysis, which confirms that the maximized oversteering performance is robust against sensor mismatches.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical, Electronic, Telecommunications Engineering, and Naval Architecture (DITEN), University of Genoa, 5-16126 Genova, Italy. andrea.trucco@unige.it.

ABSTRACT
For linear arrays with fixed steering and an inter-element spacing smaller than one half of the wavelength, end-fire steering of a data-independent beamformer offers better directivity than broadside steering. The introduction of a lower bound on the white noise gain ensures the necessary robustness against random array errors and sensor mismatches. However, the optimum broadside performance can be obtained using a simple processing architecture, whereas the optimum end-fire performance requires a more complicated system (because complex weight coefficients are needed). In this paper, we reconsider the oversteering technique as a possible way to simplify the processing architecture of equally spaced end-fire arrays. We propose a method for computing the amount of oversteering and the related real-valued weight vector that allows the constrained directivity to be maximized for a given inter-element spacing. Moreover, we verify that the maximized oversteering performance is very close to the optimum end-fire performance. We conclude that optimized oversteering is a viable method for designing end-fire arrays that have better constrained directivity than broadside arrays but with a similar implementation complexity. A numerical simulation is used to perform a statistical analysis, which confirms that the maximized oversteering performance is robust against sensor mismatches.

No MeSH data available.