Based on the characteristics of the thresholds of two detection schemes employing locally optimum test statistics, a sequential detection design procedure is proposed and analyzed. The proposed sequential test, called the sequential locally optimum test (SLOT), inherently provides finite stopping time (terminates with probability one within the finite horizon), and thereby avoids undesirable forced termination. The performance of the SLOT is compared with that of the fixed sample-size test, sequential probability ratio test (SPRT), truncated SPRT, and 2-SPRT. It is observed that the SLOT requires smaller average sample numbers than other schemes at most values of the normalized signal amplitude while maintaining the error performance close to the SPRT.

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.

When orignal signals are contaminated by both additive and signal-dependent noise components, the test statistics of locally optimum detector are obtained for detection of weak composite signals based on the generalized Neyman-Pearson lemma. In order to consider the non-additive noise as well as purely-additive noise, a generalized observation model is used in this paper. The locally optimum detector test statisics are derived for all different cases according to the relative strengths of the known signal, random signal, and signal-dependent noise components. Schematic diagrams of the structures of the locally optimum detector are also included. The finite sample-size performance characteristics of the locally optimum detector are compared with those of other common detectors.