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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.


Nominal beam pattern (solid line) and actual beam pattern (dashed line) for oversteered beamforming with Taylor’s weights applied to an end-fire array of eight microphones.
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sensors-15-13477-f015: Nominal beam pattern (solid line) and actual beam pattern (dashed line) for oversteered beamforming with Taylor’s weights applied to an end-fire array of eight microphones.

Mentions: At a frequency of 680 Hz, the inter-element spacing d is equal to 0.05 λ; thus, the nominal array performance for a WNG greater than or equal to 0 dB is as follows. Figure 7 shows that the maximum constrained directivity is 8.62 dB using complex weights and 8.43 dB for oversteering using optimized weights. In the latter case, Figure 8 shows that the oversteering amount should be ε = 1.71. For comparison, if oversteering is used with Taylor’s weights, the maximum constrained directivity is 7.20 dB and is achieved for an oversteering amount ε = 2.25. The nominal beam patterns for these three options are shown in Figure 13, Figure 14 and Figure 15.


Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

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

Nominal beam pattern (solid line) and actual beam pattern (dashed line) for oversteered beamforming with Taylor’s weights applied to an end-fire array of eight microphones.
© Copyright Policy
Related In: Results  -  Collection

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

sensors-15-13477-f015: Nominal beam pattern (solid line) and actual beam pattern (dashed line) for oversteered beamforming with Taylor’s weights applied to an end-fire array of eight microphones.
Mentions: At a frequency of 680 Hz, the inter-element spacing d is equal to 0.05 λ; thus, the nominal array performance for a WNG greater than or equal to 0 dB is as follows. Figure 7 shows that the maximum constrained directivity is 8.62 dB using complex weights and 8.43 dB for oversteering using optimized weights. In the latter case, Figure 8 shows that the oversteering amount should be ε = 1.71. For comparison, if oversteering is used with Taylor’s weights, the maximum constrained directivity is 7.20 dB and is achieved for an oversteering amount ε = 2.25. The nominal beam patterns for these three options are shown in Figure 13, Figure 14 and Figure 15.

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.