System and method for determining a modulation angle of an information bit in a complex modulated signal

A system for determining a modulation angle of an information bit in a modulated complex signal, the modulation angle lying in one of four quadrants corresponding to angles from zero radians to 2pi radians, the information bit having an associated inphase component I and an associated quadrature component Q, the inphase and quadrature components each having an associated polarity, the system comprising:

• a first stage for determining the inphase component I and the quadrature component Q of the information bit in the modulated complex signal;
• a division stage for determining an absolute ratio of the quadrature component Q to the inphase component I;
• and
• a second stage for determining from the polarity of the inphase and quadrature components the quadrant in which the modulation angle lies;
• a third stage for determining the arctangent of the absolute ratio x of the quadrature component Q to the inphase component I of the transmitted information bit in the modulated signal;
• and
• a fourth stage for determining the modulation angle from the polarity of the inphase and quadrature components and the arctangent of the absolute ratio of the quadrature component Q to the inphase component I of the transmitted information bit in the modulated signal.