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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.


Schematic of oversteered end-fire beamformer for a suitable sampling frequency fs.
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sensors-15-13477-f011: Schematic of oversteered end-fire beamformer for a suitable sampling frequency fs.

Mentions: Figure 11 displays a schematic of the implementation of this beamforming technique. After low-pass filtering (LPF) to avoid aliasing, the N input signals are digitized through analog-to-digital (A/D) converters that sample at a frequency fs = 1/Δ = c/[d(1 + ε)]. If fs is lower than the Nyquist rate, an integer multiple of fs can be set as the sampling frequency. The nth delay τn,ovs given in Equation (7) can be obtained very efficiently by shifting the nth signal by a given number of samples using a digital integer delay line. Before performing the final sum that generates the output signal b(t), the nth signal is multiplied by the real weight coefficient wn. If optimum oversteering performance is desired, the weights wn should be computed by solving Equation (28). Otherwise, the weights can be derived from a traditional weighting window, such as Taylor’s window.


Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

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

Schematic of oversteered end-fire beamformer for a suitable sampling frequency fs.
© Copyright Policy
Related In: Results  -  Collection

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

sensors-15-13477-f011: Schematic of oversteered end-fire beamformer for a suitable sampling frequency fs.
Mentions: Figure 11 displays a schematic of the implementation of this beamforming technique. After low-pass filtering (LPF) to avoid aliasing, the N input signals are digitized through analog-to-digital (A/D) converters that sample at a frequency fs = 1/Δ = c/[d(1 + ε)]. If fs is lower than the Nyquist rate, an integer multiple of fs can be set as the sampling frequency. The nth delay τn,ovs given in Equation (7) can be obtained very efficiently by shifting the nth signal by a given number of samples using a digital integer delay line. Before performing the final sum that generates the output signal b(t), the nth signal is multiplied by the real weight coefficient wn. If optimum oversteering performance is desired, the weights wn should be computed by solving Equation (28). Otherwise, the weights can be derived from a traditional weighting window, such as Taylor’s 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.