Simplified Optimum Modulation Indices

The design of a narrowband, phase-modulated, multisubcarrier, phase-coherent, space-communication system requires that the subcarrier modulation indices be kept within close tolerance limits. This need arises since the modulation indices directly affect the division of power among the carrier and subcarriers. If the system is not designed in an optimum manner to handle large tolerance variation, the system performance may degrade sharply in an adverse environment. A universal graphical technique-modulation loss contours-is developed as a design tool for the "optimum" selection of modulation indices. The technique is novel in that it yields solutions directly from the universal curves and does not require the drawing of additional curves. Two criteria of optimization are considered, simultaneous thresholding and minimal sensitivity. The minimally sensitive case is considered as weighted simultaneous thresholding and is solved by the aid of a graphical algorithm. The technique is applicable to k subcarriers (sinusoidal and/or square wave), considering three subcarriers at a time-two subcarriers as direct variables and the third as a parameter-all other subcarriers remaining constant. Previous techniques required trial and error methods, drawing of curves, or computerized search techniques to arrive at the proper modulation indices and maximum tolerance bands. This method allows a quick solution to the tolerance problem and optimum selection of modulation indices, facilitating the design and/or analysis of narrowband PM systems.