Exhaustive Search for Costas-Type Sequences for Multi-Target Recognition

Costas and sonar sequences were respectively introduced in [2] and [10] to deal with the following problem: “An object is moving towards (or away) from an observer, who wants to know effectively the distance to the object and its velocity.” The solution to the problem makes use of the Doppler effect, which states the following: when a signal bounces off a moving target its frequency changes in direct proportion to the velocity of the object relative to the observer. In other words, if the observer sends out a signal towards a moving target, the change between the frequency of the outgoingand that of the returning signal will allow him to determine the velocity of the target, and the time it took to make the round trip will allow him to determine the distance. In a frequency hopping radar or sonar system, the signal consists of one or more frequencies being chosen from a set ff f fmg of available frequencies, for transmission at each of a set ft t tng of consecutive time intervals. For modeling purposes, it is reasonable to consider the situation in whichm n, and where