Non-fluctuating target detection in fluctuating K-distributed interference and noise

Abstract

Abstract-This paper deals with the problem of non-fluctuating target detection in the presence of a mixture of heavy tailed K-distributed clutter and independent noise. Prior papers have derived generalized likelihood ratio tests (GLRT) for this problem as well as approximations of the GLRT. These results show the required optimum processing and its vastly different efficiency as compared to similar results derived under standard Gaussian assumptions. In this study we examine the detection performance of several proposed detectors using numerical simulation techniques. We demonstrate their performance under different clutter and noise conditions. We also propose a two-stage detection scheme for a multi-observation multi-channel detection problem.

Sensitivity Analysis of Likelihood Ratio Test in <formula formulatype="inline"><tex Notation="TeX">$K$</tex> </formula> Distributed and/or Gaussian Noise

“…radar returns, and where and stand for the target signature and amplitude, respectively. In [15], we showed that, in contrast to what is commonly admitted, thermal Gaussian noise cannot be ignored, even if clutter to noise ratio is high. Indeed, it was shown that, for heavy-tailed distributions, the detection performance is in fact dominated by a single observation within the i.i.d.…”

“…The normalized matched filter (actually the non coherent integration of the NMF for a single snapshot) is given by (8) Finally, in [15], we discovered that the test statistic in (5) is mostly influenced by the term corresponding to the minimal value of . Let be this snapshot and let us consider the hypothetical test statistic (9) We first study the behavior of the detectors in (5)-(9) under .…”

“…Let . Under the assumption of known , an approximate log-likelihood ratio (LLR) test was derived in [15], given by (5) where (6) Interestingly enough, (5) coincides with the GLR obtained assuming that the variables are deterministic and unknowns [11], while in [15] it was obtained from a large approximation of the modified Bessel function. On the other hand, for the classical problem in (4) the GLR is the matched filter, i.e.…”

“…In the sequel, and similarly to [15], we assume a Gamma distribution for , namely , so that, under , follows a distribution. Let .…”

“…Most often, mainly because the clutter to noise ratio is generally high, it is assumed that thermal noise can be neglected. Manuscript In [15], we considered detection of a fluctuating target in fluctuating -distributed clutter, a problem formalized as (1) where ,…”