Near‐optimal detection with constant false alarm ratio in varying impulsive interference

Abstract

As an important class of non-Gaussian statistic model, α-stable distribution has received much attention because of its generality to represent impulsive interference. Unfortunately, it does not have a closed-form probability density function (PDF) except for a few cases. For this reason, suboptimal zero-memory non-linearity (ZMNL) function has to be used as an approximation in designing locally optimal detector, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). To enhance the performance of detectors, the authors first investigate the approximate PDFs for the symmetric α-stable. In particular, a simplified version of Cauchy-Gaussian mixture (CGM) model, called bi-parameter CGM (BCGM) model is detailed. This BCGM model has a concise closed-form, and hence is more tractable than the classical Gaussian mixture model and CGM model. Then based on the preset false alarm ratio (FAR), the test threshold is adaptively evaluated by using BCGM to maintain a constant FAR. The authors further devise an algebraic-tailed ZMNL (AZMNL) with a simplified form. Simulation results show that the detector with AZMNL outperforms the ones with classical Cauchy and GZMNL, and achieves near-optimal performance in varying impulsive interference.

Nonparametric Blind Signal Detection Based on Logarithmic Moments in Very Impulsive Noise

“…us, some locally suboptimal detectors are proposed, such as the soft limiter, hole puncher, and local Cauchy detector [3]. Some detectors based on the approximate expression for the PDF of the SαS distribution are also investigated [7,8].…”

Locally optimal detector design in impulsive noise with unknown distribution

“…Researchers usually chose to study g(x) by approximating the PDF. Figure 1 shows three reported ZMNL functions proposed for symmetric α-stable (SαS) noise, including the algebraic-tailed ZMNL (AZMNL, depending on α, for SαS distribution) [7], the Cauchy ZMNL (CZMNL, for Cauchy distribution α = 1) [8], and the Gaussiantailed ZMNL (GZMNL, independent on α, robust for SαS distribution) [9]. The ZMNL curves in Fig.…”

“…At the breakpoints, natural ZMNLs deduced from heavy-tailed Fig. 1 The LODs for SαS noise and reported ZMNL design [7], for σ = 1 distributions are generally differentiable, while designed ZMNLs may be continuous or discontinuous.…”

“…For instance, Nikais and Shao proposed two kinds of nonlinearity for x / ∈ , including a "hole puncher" to null g(x) and a "clipper" to set g(x) equal to the nearest g(x i ) as constants. The tail of g(x) is also modeled as x 1−α or x −1 in α-stable noise [4,7]. Besides, the breakpoints which connect the tails with the main body are also important for the LOD design.…”

“…For instance, the α-stable noise, which is widely used for modeling the impulse noise, does not provide the PDF in closed form generally [4]. As a result, researchers have developed various ZMNL functions for different α-stable distributions [7][8][9]. However, real-data processing results demonstrate that the impulsive noise does not always strictly obey the for unknown noise PDF.…”