  This paper develops a low-complexity near-optimal non-coherent receiver for a
multi-level energy-based coded modulation system. Inspired by the turbo
processing principle, we incorporate the fundamentals of bit-interleaved coded
modulation with iterative decoding (BICM-ID) into the proposed receiver design.
The resulting system is called bit-interleaved coded energy-based modulation
with iterative decoding (BICEM-ID) and its error performance is analytically
studied. Specifically, we derive upper bounds on the average pairwise error
probability (PEP) of the non-coherent BICEM-ID system in the feedback-free (FF)
and error-free feedback (EFF) scenarios. It is revealed that the definition of
the nearest neighbors, which is important in the performance analysis in the FF
scenario, is very different from that in the coherent BICM-ID counterpart. The
analysis also reveals how the mapping from coded bits to energy levels
influences the diversity order and coding gain of the BICEM-ID systems. A
design criterion for good mappings is then formulated and an algorithm is
proposed to find a set of best mappings for BICEM-ID. Finally, simulation
results corroborate the main analytical findings.
