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假定接收阵列的输入为叠加在窄带高斯噪声上的正弦信号,可导出带后置滤波的数字波束形成器的输出功率和输出信噪比,从而不必在频域中进行分析就可进行后面的计算。公式利用了由作者先前给出的量化器函数和最初由达文波特提出的某些功率谱分布因子。本文对这种功率谱分布因子进行了更严密的推导和讨论。对于在相关噪声场中的DIMUS阵列,基于这个公式的数学研究结果表明:除了一些罕见的情况以外,后置滤波通常能改善输出SNR或阵列增益。可以证明,后置滤波增益的大小不仅随阵列输入SNR的变化而变化,而且强热地依赖于阵元间隔与波长的比值,并且只有用削波损耗和噪声相关损耗才能对其进行有意义的解释。特别是用后置滤波对这两种损耗的补偿表明:单元间隔小于二分之一工作波长的接收阵列在某些条件下可以有利于系统的设计。
Assuming that the input of the receive array is a sinusoidal signal superimposed on narrow-band Gaussian noise, the output power and output signal-to-noise ratio of the digital beamformer with postfiltering can be derived so that subsequent calculations need not be done in the frequency domain . The formula takes advantage of the quantizer functions previously given by the author and some of the power spectrum distribution factors originally proposed by Davennett. This paper makes a more rigorous deduction and discussion on this power spectrum distribution factor. For a DIMUS array in a correlated noise field, the mathematical study based on this formula shows that post-filtering generally improves the output SNR or array gain except for some rare cases. It can be shown that the magnitude of the postfiltering gain varies not only with the array input SNR, but also strongly depends on the ratio of the cell spacing to the wavelength, and can be significant only with clipping and noise related losses Explanation. Compensation of these two losses, especially with postfiltering, shows that a receive array with cell spacing less than one-half the operating wavelength can under certain conditions favor the design of the system.