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The Generaliszed Multifrequency Signals on a Basis of Number-Theoretical Distributions of Frequencies


B.G. Sverdlov, V.V. Chapursky

The concept for the generalized multifrequency signal (GMS) as a burst of monopulse multifrequency pulses is introduced. The general expression for bidimentional “delay – speed” ambiguity function (AF) of GMS signal is received at any time-frequency base of a signal. AF of various types of such signals are investigated and compared at a classical uniform grid of frequencies and at use of optimum in number-theoretical sense frequency distributions – Golomb rulers and Costas arrays, based on the theory of Galois fields of prime numbers. It is established, that distributions of frequencies according to Golomb rulers instead of uniform grids of frequencies in GMS burst with not overlapped frequency bands of pulses results in improvement of structure and a level of lateral lobes in delay section of AF and practically does not influence levels of collateral ambiguity lobes in speed section of AF. In both variants of frequencies distributions it was received practical absence of ambiguity on a delay (range) within the limits of duration of a burst. Other useful quality of the given signals is the high delay resolution of a burst as a whole, adequate to the increased common frequency band of a burst. For GMS burst signals it is investigated distributions of a grid of groups of frequencies from one pulse to another according to Costas arrays instead of regular uniform grids of frequencies and grids of frequencies according to Golomb rulers at not over-lapped frequency bands of pulses. Such distributions result in improvement of structure and reduction of lateral and collateral lobes levels in AF sections on speed up to acceptable values. Thus there is a further reduction of a maximum collateral lobe levels in AF section on a delay. However, the structure of the main lobe of delay section remains practically the same, as well as at absence of Costas permutations. For improvement of structure of the main lobe of AF section on delay at preservation of "good" properties of section on speed the combination of Costas and Golomb distributions of frequencies in GMS burst is applicable. Thus narrow false lateral lobes of a low level within the limits of the main lobe are absent, and instead of them appear randomized lobes with approximately triangular envelope in twice pulse duration interval and approximately twice lower mean level of maxima, than in the previous case. AF sections on speed keep the good properties achieved due to distribution of pulses frequencies in a burst according only to Costas array.
June 24, 2020
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