Multiple Frank-Hiemiller Signals for Multiple Access Systems

Abstract

In view of the fact that the Frank-Hiemiller (FH) signal has the property that its periodic autocorrelation is zero, it is desirable to generate multiple FH signals for possible use in a multiple-signal environment and, in particular, in multiple-access communication systems. These multiple FH signals are generated by transformation of an FH matrix whose consecutive rows describe an FH signal. The periodic and nonperiodic autocorrelation and cross correlation of the multiple FH signals are derived, and it is shown that the periodic autocorrelation of multiple FH signals preserves the ideal properties of FH signals and nonperiodic cross correlation is bounded by 1/sin (n/?), where n is the number of phases. In this context, a formula for nonperiodic autocorrelation for FH signals is derived and plots of the autocorrelation of FH signals of length 81 100 and 121 are given. The bound derived for the periodic and nonperiodic cross correlation is applied to find the performance of multiple-access spread-spectrum satellite communications.