Limits...
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 a 10-element array versus the normalized inter-element spacing (i.e., d/λ) for end-fire (solid line) and broadside (dashed line) steering. Optimum weights are computed by imposing WNG ≥ 0 dB and solving Equation (23).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4507652&req=5

sensors-15-13477-f001: Maximum constrained directivity obtained for a 10-element array versus the normalized inter-element spacing (i.e., d/λ) for end-fire (solid line) and broadside (dashed line) steering. Optimum weights are computed by imposing WNG ≥ 0 dB and solving Equation (23).

Mentions: In this context, end-fire steering is frequently preferred to broadside steering [3,4,6] because it enables a significantly higher directivity. In principle, an end-fire array can attain a directivity of N2, where N is the number of sensors [9]. However, to limit the sensitivity to random array errors and sensor mismatches, a constraint on the sensitivity factor, i.e., the inverse of the white noise gain (WNG), can be introduced [2,10,11]. Because random errors and mismatches are uncorrelated between sensors, they serve as spatially white noise [2,10,11]. As a result, the constrained directivity maximization is a classical approach to achieve robust superdirective performance via end-fire arrays [2,10,11]. Although the WNG constraint prevents a directivity of N2, the maximum constrained directivity is often significantly greater than N and is attained for a value of the inter-element spacing d that is greater than zero and smaller than λ/2, where λ is the wavelength. Figure 1 illustrates the maximum constrained directivity versus the inter-element spacing for end-fire and broadside arrays, when N = 10 and WNG ≥ 0 dB. Figure 2 illustrates the maximum constrained directivity versusN for the two steering directions when D = 0.45 λ, where D is the array aperture and when WNG ≥ 0 dB.


Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays.

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

Maximum constrained directivity obtained for a 10-element array versus the normalized inter-element spacing (i.e., d/λ) for end-fire (solid line) and broadside (dashed line) steering. Optimum weights are computed by imposing WNG ≥ 0 dB and solving Equation (23).
© Copyright Policy
Related In: Results  -  Collection

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

sensors-15-13477-f001: Maximum constrained directivity obtained for a 10-element array versus the normalized inter-element spacing (i.e., d/λ) for end-fire (solid line) and broadside (dashed line) steering. Optimum weights are computed by imposing WNG ≥ 0 dB and solving Equation (23).
Mentions: In this context, end-fire steering is frequently preferred to broadside steering [3,4,6] because it enables a significantly higher directivity. In principle, an end-fire array can attain a directivity of N2, where N is the number of sensors [9]. However, to limit the sensitivity to random array errors and sensor mismatches, a constraint on the sensitivity factor, i.e., the inverse of the white noise gain (WNG), can be introduced [2,10,11]. Because random errors and mismatches are uncorrelated between sensors, they serve as spatially white noise [2,10,11]. As a result, the constrained directivity maximization is a classical approach to achieve robust superdirective performance via end-fire arrays [2,10,11]. Although the WNG constraint prevents a directivity of N2, the maximum constrained directivity is often significantly greater than N and is attained for a value of the inter-element spacing d that is greater than zero and smaller than λ/2, where λ is the wavelength. Figure 1 illustrates the maximum constrained directivity versus the inter-element spacing for end-fire and broadside arrays, when N = 10 and WNG ≥ 0 dB. Figure 2 illustrates the maximum constrained directivity versusN for the two steering directions when D = 0.45 λ, where D is the array aperture and when WNG ≥ 0 dB.

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.