Bandwidth-Efficient Modulations with More Envelope Fluctuation
Thus far in our discussions, we have focused on constant or quasi-constant envelope modulations many of which, by virtue of their inherent memory, required a trellis decoder (as implemented by the VA ) for optimum reception. In theory, the VA can start producing a ML estimate of the transmitted signal only after observing the channel output corresponding to the entire transmitted signal, resulting in an infinite decoding delay. By decoding delay, we mean the amount of time (typically measured in number of bits) after which one begins to decode. Algorithms such as the truncated VA  can be used to reduce the decoding delay, but, in general, these lead to suboptimum receiver structures.
In certain applications, achieving a finite and small decoding delay is desirable. The natural question to ask is whether the requirement for finite decoding delay imposes constraints on the modulation/demodulation scheme that would reduce its optimality from a power and bandwidth-efficiency standpoint. Furthermore, to what extent would these constraints compromise the constant envelope nature of the transmitted signal set?
The ultimate goal would be to understand the possible trade-offs among minimum Euclidean distance (or, more generally, distance profile), bandwidth (or, more generally, PSD) and decoding delay. Such a goal is beyond the scope of this monograph. Instead, we consider here a reduced goal that investigates ...