Constellation design for a pcm modem

Abstract

Modem constellations are designed by independently optimizing for each slot of a frame, the distances between constellation points used for that slot. A maximum number of points N(,) are chosen having at least the minimum distance d,without exceeding a power limitation Plim. Using N(,), an attempt is made to increase the d,in the constellation without exceeding Plim. Constellations may be further optimized by, where possible, decreasing N(,) in a particular constellation without affecting the total data rate of the frame. Thus, a maximum potentially achievable data rate Rmax is calculated given the number of points which are in each of the six constellations, and comparing Rmax to a standards-permitted data rate DR; and then, if Rmax exceeds DR, by decreasing N(,) in one or more constellations, provided the decrease in the number of points does not cause a recalculated Rmax to drop below DR. Further optimization is obtained by attempting to increase d,in one or more slots by permitting that slot(s) to exceed Plim, provided the average power of the frame is not exceeded. This is accomplished by finding the slot with the maximum error probability, increasing d,for that slot (while maintaining N(,)) to thereby exceed frame power limitations for that slot, and checking to see whether the changes to the constellation in that slot violates the average frame power limitations. A simple system for checking average constellation power is also provided.