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The two-sample locally optimum rank detector test statistics for composite signals in additive, multiplicative, and signal-dependent noise are obtained in this letter. Compared with the structure of the one-sample locally optimum rank detector, that of the two-sample locally optimum rank detector is shown to be simpler, although it needs more computations. It is known that there is a trade-off of computational complexity and structural simplicity between the one- and two-sample detectors.
The locally optimum rank detector achieves a simpler detector structure when reference observations, in addition to regular observations, are available. Without reference observations, we have to use the sign statistics of regular observations, and using the sign statistics results in a complex detector structure. Instead, more computations are necessary to deal with additional reference observations.
The one-sample locally optimum rank detector test statistics for composite signals in multiplicative and signal-dependent noise are obtained. Since the one-sample locally optimum rank detector makes use of the sign statistics of observations as well as the rank statistics, both 'even' and 'odd' score functions have to be considered. Although the one-sample locally optimum rank detector requires two score functions while the two-sample detector requires only one score function, the one-sample detector requires fewer calculations since it has to rank fewer observations.