Douglass Alexander S, Dowling David R
Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
J Acoust Soc Am. 2019 Jul;146(1):122. doi: 10.1121/1.5114811.
Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029] is a nonlinear, out-of-band signal processing technique used to beamform non-zero bandwidth signals at below-band frequencies. This is accomplished with the frequency-difference autoproduct AP(Δω)=P(ω)P(ω), a quadratic product of complex field amplitudes that mimics a genuine field at the difference frequency, Δω=ω-ω. For frequency-difference beamforming, AP(Δω) replaces the in-band complex field in the conventional beamforming algorithm. Here, the near-field performance of frequency-difference beamforming is evaluated in the presence of 1 to 30 high-contrast spherical scatterers with radius a placed between, and in the plane defined by the source and a 12-element linear receiving array with element spacing d. Based on the center frequency wave number, k, of the 150-200 kHz frequency sweep source signal, the scatterers are large, ka ≈ 15; the array is sparse, kd = 37; and the average source-to-receiver distance is up to 4.3 mean-free-path lengths. Beamforming results from simulations and experiments show that in-band beamforming loses peak-to-sidelobe ratio and fails to reliably locate the source as the scatterer count increases. Using the same signals, frequency-difference beamforming with difference frequencies from 5 to 25 kHz localizes sources reliably with higher peak-to-side-lobe ratios, though with reduced resolution.
频差波束形成[阿巴迪、宋和道林（2012年）。《美国声学学会杂志》132卷，3018 - 3029页]是一种非线性带外信号处理技术，用于在低于频段的频率上对非零带宽信号进行波束形成。这是通过频差自乘积AP(Δω)=P(ω)P(ω)实现的，它是复场幅度的二次乘积，模拟了差频Δω=ω - ω处的真实场。对于频差波束形成，AP(Δω)取代了传统波束形成算法中的带内复场。在此，在1到30个半径为a的高对比度球形散射体存在的情况下，评估频差波束形成的近场性能，这些散射体置于源与一个12元线性接收阵列之间以及由源和该阵列所定义的平面内，该接收阵列的阵元间距为d。基于150 - 20 kHz扫频源信号的中心频率波数k，散射体较大，ka≈15；阵列稀疏，kd = 37；源到接收器的平均距离可达4.3个平均自由程长度。模拟和实验得到的波束形成结果表明，随着散射体数量增加，带内波束形成会失去峰旁瓣比，并且无法可靠地定位源。使用相同信号时，差频在5到25 kHz的频差波束形成能够以更高的峰旁瓣比可靠地定位源，不过分辨率有所降低。
