Array Gain Degradation Research Articles

Analysis of array gain degradation of near-field passive synthetic aperture method

A previous study established a method for localizing low-frequency acoustic sources in the near field using a passive synthetic aperture method [Lei et al., 2015]. Sound fields sampled at different positions (sub-apertures) and times are synthesized to improve the spatial resolution of conventional beamforming. However, in practice, the position errors of the sub-apertures could significantly degrade the performance of the method. In this work, the analysis is extended to measure the sensitivity of the method to the position errors of the sub-apertures using array gain degradation (AGD). First, the position errors in three directions are assumed to be independent and obey the same Gaussian distribution to present a simple expression for AGD. Then, the analysis is generalized to the case of different Gaussian distributions to obtain an expression with explicit physical meaning. The two expressions are verified by simulations and partially validated using the experimental data sampled by a planar array in a semi-anechoic chamber. Finally, the results of localizing the sources on a transformer in a 750 kV substation are revealed.

Affects of nearby bubbles on underwater array gain.

Combining multiple sensor signals coherently (i.e., beamforming) improves spatial or angular resolution and increases signal to noise ratio (SNR). When the array is steered, signals arriving from the steering direction add in phase, while signals arriving from other directions do not (proper choice of signal frequency assumed). Array gain (AG) is a measure of how much the SNR at the array output is increased relative to array input SNR. The degradation in underwater acoustic array AG by scattering from nearby bubbles was measured at the AB Wood tank located at the Institute of Sound and Vibration Research (ISVR), University of Southampton, in June 2008. AG degradation is separate from the effects of bubbles in water to attenuate acoustic signals. Measured statistics of signal phase at the individual sensors show that as bubble density increases, phase differences between the elements increase and AG is degraded. We present a theory and numerical simulation that attributes the phase shifts to scattering from nearby bubbles and provides a way to predict AG degradation from the bubble density. [Work sponsored by the ONR Undersea Signal Processing.]

Measurement and analysis of array gain degradation due to bubble scattering.

When an array is steered in the direction of a signal, array gain (AG) is maximum when the signal is coherent across the array, meaning that the signals add in phase for all elements and the noise or interference is incoherent across the array (i.e., it adds with random phase). For an acoustic array operating in the ocean, we would like to understand the degree to which scattering by nearby bubbles degrades AG. Bubble attenuation can also degrade array performance by attenuating the signal of interest, but that is separate from AG degradation. The degradation of AG due to scattering by nearby bubbles has been measured for different bubble densities. We have analyzed the relationship between bubble density at the array and the degradation in AG. We present probability density functions (pdfs) of signal amplitude and phase at the array elements. The amplitude pdfs can be approximated as a Rayleigh–Rice distribution, and the phase pdfs follow the von Mises distribution. With independence assumed between ampl...

Array gain degradation due to nearby bubbles

Signal‐to‐noise ratio (SNR) is signal power divided by noise power, usually expressed in dB (SNR = 20*log10(Psig/Pnoise). Array gain (AG) is the increase in SNR at an array output relative to that at a single element. AG assumes spatially‐compact signals embedded in spatially‐diffuse noise or interference. When the array is steered in the direction of a signal, AG is maximum when the signal is fully coherent across the array (i.e. the signals add in phase for all elements) while the noise or interference is incoherent across the array (i.e. adds with random phase). For an acoustic array operating in the ocean, we would like to understand the degree to which nearby bubbles degrade AG. Scattering by bubbles represents interference at the array. Bubble attenuation can also degrades array performance by attenuating the signal of interest, but that is separate from AG degradation. Previously we applied the single scattering approximation of Ishimaru (1977, Chap. 6) and found that scattering from bubbles very close to the array can generate correlated interference, thereby decreasing AG. Here we validate the theory using in‐water measurements of AG as the distance of from the array to the bubbles varies. Work sponsored by Office of Naval Research, Code 321 Undersea Signal Processing.

Array gain for a cylindrical array with baffle scatter effects

Cylindrical arrays used in sonar for passive underwater surveillance often have sensors surrounding a cylindrical metal baffle. In some operational sonars, the phones in each stave (i.e., each line of phones aligned with the cylinder axis) are hardwired together so that the array is equivalent to a baffled circular array of directional elements, where each element corresponds to a line array of omnidirectional phones steered to broadside. In this paper a model is introduced for computing the array gain of such an array at high frequencies, which incorporates baffle scatter using infinite, rigid cylinder scattering theory, and with ambient noise described by an angular spectral density function. In practice the phones are often offset from the baffle surface, and the acoustic field sampled by the staves is distorted at high frequencies due to interference between the incident and scattered fields. Examples are given to illustrate the resulting array gain degradation, using three noise distributions that are frequently used in sonar performance modeling: three-dimensional isotropic, two-dimensional isotropic, and surface dipole noise.

Phased array of large reflectors for deep-space communication

In this paper the problem of uplink array calibration for deep-space communication is considered. A phased array of many modest-size reflectors antennas is used to drastically improve the uplink effective isotropic radiated power of a ground station. A radar calibration procedure for the array phase distribution is presented using a number of in-orbit targets. Design of optimal orbit and the number of calibration targets is investigated for providing frequent calibration opportunities needed for compensating array elements phase center movements as the array tracks a spacecraft. Array far-field focusing based on the near-filed in-orbit (low Earth orbit (LEO)) calibration targets is also presented and array gain degradation analysis based on the position error of the array elements and in-orbit targets has been carried out. It is shown that errors in the in-orbit targets positions significantly degrade the far-field array gain while the errors in array elements positions are not very important. Analysis of phase errors caused by thermal noise, system instability, and atmospheric effects show insignificant array gain degradation by these factors

Modal beamforming array gain

In a previous article [T. C. Yang, J. Acoust. Soc. Am. 82, 1736–1745 (1987)], range and depth were successfully estimated by modal beamforming. In this article, the modal beamforming array gain is derived in closed form for a vertical array of N hydrophones. For the case of white noise and a long well-populated vertical array, the array gain nearly equals 10 log N. For the case of colored noise and a finite aperture, finite element vertical array, the array gain degrades from the theoretical by an amount determined by the mode depth amplitudes evaluated at the source and receiver depths and the modal covariance matrix of the noise. Numerical estimates of array gain are given for the FRAM IV vertical array for a colored noise environment in the Arctic sound channel. Approximately 1-dB array gain degradation at 47 Hz is found. Proper array configuration and deployment depth are not only important for optimizing array gain but also critical for maximizing the input signal-to-noise ratio on a vertical array, which together with the array gain determine the array output signal-to-noise ratio.

Modal beamforming array gain

In a previous paper [T. C. Yang, J. Acoust. Soc. Am. 82, 1736–1745 (1987)], range and depth were successfully estimated by modal beamforming. In this paper, the modal beamforming array gain in closed form for a vertical array of N hydrophones is derived. For the case of white noise and a long well-populated vertical array, the array gain nearly equals 10 log N. For the case of colored noise and a finite aperture, finite element vertical array, the array gain degrades from the theoretical by an amount determined by the mode-depth amplitudes evaluated at the source and receiver depths, and the modal covariance matrix of the noise. Numerical estimates of array gain are given for the FRAM IV vertical array for a colored noise environment in the Arctic sound channel. Approximately 1-dB array gain degradation is found at 47 Hz. Proper array configuration and deployment depth is not only important for optimizing array gain but also critical for maximizing the input signal-to-noise ratio on a vertical array, which together with the array gain determines the array output signal-to-noise ratio.