Analyses and experimental results for the symmetric nonlinear matched filter (SNMF) and the non-symmetric nonlinear matched filter (nonSNMF) are presented. The properties studied are signal-to-noise ratio (SNR), resolution, and intermodulation. Additionally, for the hard-limiter nonlinearity, optimum threshold selection and probability of error for the SNMF are investigated. The SNMF is composed of a spectral transformation followed by a pointwise nonlinear transformation. This transformation is applied to both the reference signal and the received signal, which is then multiplied in the transform domain. The non-SNMF system involves the nonlinear transformation of only the filter transfer function prior to multiplication with the received signal spectrum. Two major spectral transformations studied are the discrete Fourier transform (DFT) and the real discrete Fourier transform (RDFT). The experimental nonlinear transformation studied is the hard-limiter, while the theoretical analyses assume a general nonlinear transformation with the hard-limiter being a special case. Theoretical and experimental results indicate that the SNMFs have the potential to achieve a high power of resolution and large SNR. In the case of the two-dimensional (2-D) DFT, intermodulation effects should be monitored, while the 2-D RDFT appears to effectively cancel out the intermodulation effects. The selection of the optimum threshold for the hard-limiter SNMF improves the SNR and corresponds to a low probability of error.
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