On the calculation of the exponential bound parameter for phase quantized 8-PSK

The exponential bound parameter is numerically ‘Odes using Outputs ‘Om a quantized is bounded by: evaluated for 16-zone quantized 8-PSK for signal vectors bisecting For decision regions of equal span, signal vectors lying on decision boundaries are superior, confirming the result of Parsons and Wilson. Signal vectors bisecting decision regions are superior if provided that RO > R. is the length Of the ‘Ode, span of decision regions not containing signal vectors is optimized. decision regions and for signal vectors lying on decision boundaries. Pe I er2 -N[Ro-R] (1) is the number of data bits per symbol, R,, is the exponential a finite set of outputs { z . } , R is calculated from the transition boundaries are straight lines. I O