Signal generation for extended hyperbolic congruential frequency hop codes

Frequency hop codes represent a class of codes in which the signal is transmitted as a sine wave whose frequency, at any time, is one of a set of possible discrete values. This paper describes a new method for the efficient generation of a family of hop code signals, defined upon extended hyperbolic congruences, enabling them to be of practical importance. The extended hyperbolic congruential (EHC) coding scheme is implemented with minimal hardware by optimizing the two processes needed in the synthesis of the code words, i.e., generation of the constituent sine waves, and evaluation of the sequence in which they follow each other/spl minus/which is defined by a function called the placement operator. The constituent sine waves are generated by characterizing them as phase increments. This enables a simplified hardware implementation with an adder and an accumulator. Since all frequency hop codes require a set of sine waves, this method can be utilized in other frequency-hopping schemes. The placement operator is calculated by showing that module addition can replace the module multiplication required in the process. This result can also be applied to conventional hyperbolic congruential codes. These design innovations significantly reduce the complexity of the design and are illustrated in a VLSI extended hyperbolic congruential hop code transmitter implemented in 2.0 /spl mu/m CMOS technology.<>