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Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

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

Bottom Line: 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.

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.


Maximum constrained directivity obtained for an end-fire array of N = 8 sensors by imposing WNG ≥ 0 dB using complex weights (solid line) or real weights (dashed line); the directivity obtained using uniform weights (dotted line) is included for comparison.
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sensors-15-13477-f004: Maximum constrained directivity obtained for an end-fire array of N = 8 sensors by imposing WNG ≥ 0 dB using complex weights (solid line) or real weights (dashed line); the directivity obtained using uniform weights (dotted line) is included for comparison.

Mentions: First, we assess the performance of the end-fire array without oversteering when complex or real weight coefficients are used. For a given value of d/λ, the optimum complex weights are computed by setting ε = 0 and solving Equation (23). The optimum real weights are computed by setting ε = 0 and solving Equation (28). CVX software is employed for convex programming [20] on a common PC equipped with an Intel® Core i5 CPU with 2.60 GHz of clock and 12 Gbyte of RAM, and the solution is found in less than 0.2 s. Figure 4 compares the maximum constrained directivities and illustrates the directivity obtainable with uniform weights. In this specific case, the optimum real weights only provide a directivity higher than that obtained by uniform weights for d/λ < 0.22, with a gain that does not exceed 2 dB. In contrast, the complex weights provide a directivity gain of approximately 5 dB over a wide interval of d/λ. The absolute maximum constrained directivity is obtained for d/λ = 0.36 and has a value of 15.3 dB. Because 10 log(N) is 9 dB and 10 log(N2) is 18 dB, the optimum complex weights allow for a robust directivity with an absolute maximum that is significantly higher than N and moderately lower than N2.


Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

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

Maximum constrained directivity obtained for an end-fire array of N = 8 sensors by imposing WNG ≥ 0 dB using complex weights (solid line) or real weights (dashed line); the directivity obtained using uniform weights (dotted line) is included for comparison.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4507652&req=5

sensors-15-13477-f004: Maximum constrained directivity obtained for an end-fire array of N = 8 sensors by imposing WNG ≥ 0 dB using complex weights (solid line) or real weights (dashed line); the directivity obtained using uniform weights (dotted line) is included for comparison.
Mentions: First, we assess the performance of the end-fire array without oversteering when complex or real weight coefficients are used. For a given value of d/λ, the optimum complex weights are computed by setting ε = 0 and solving Equation (23). The optimum real weights are computed by setting ε = 0 and solving Equation (28). CVX software is employed for convex programming [20] on a common PC equipped with an Intel® Core i5 CPU with 2.60 GHz of clock and 12 Gbyte of RAM, and the solution is found in less than 0.2 s. Figure 4 compares the maximum constrained directivities and illustrates the directivity obtainable with uniform weights. In this specific case, the optimum real weights only provide a directivity higher than that obtained by uniform weights for d/λ < 0.22, with a gain that does not exceed 2 dB. In contrast, the complex weights provide a directivity gain of approximately 5 dB over a wide interval of d/λ. The absolute maximum constrained directivity is obtained for d/λ = 0.36 and has a value of 15.3 dB. Because 10 log(N) is 9 dB and 10 log(N2) is 18 dB, the optimum complex weights allow for a robust directivity with an absolute maximum that is significantly higher than N and moderately lower than N2.

Bottom Line: 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.

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.