Performance evaluation of k out of n detector

In this paper the problem of k out of n detection, between sequence of M random bits is addressed. The main application of the result is in a radar system, when we want to detect a target (with unknown time of arrival (TOA)), using binary integration. Another application is in ESM systems, when the system wants to detect the existence of a swept jammer or a gated noise jammer. But as any other mathematical problem, it may have some other applications. In this paper some simple equations for Pfa and Pd calculation of a detector which detects the existence of sequence of n ones between M random bits, is derived. These equations are then used to find the optimal detector structure in some special cases. Besides, an approximate equation is derived for general case of k out of n detector, and it is shown that, the approximation is almost accurate.