Published in Ross, M.D., & Osborne, W.P. (1995). On the calculation of the exponential bound parameter for phase quantized 8-PSK. IEEE Transactions on Communications, 43(234), 674-676. doi: 10.1109/26.380088 ©1995 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.


The exponential bound parameter is numerically evaluated for 16-zone quantized 8-PSK for signal vectors bisecting decision regions and for signal vectors lying on decision boundaries. For decision regions of equal span, signal vectors lying on decision boundaries are superior, confirming the result of Parsons and Wilson (1990). Signal vectors bisecting decision regions are superior if span of decision regions not containing signal vectors is optimized. Using the partial derivative, it is shown that the optimal configuration depends on SNR. Furthermore, the optimal configuration is not necessarily one in which the decision boundaries are straight lines.