  This paper studies enhanced dense code multiple access (DCMA) system design
for downlink transmission over the Nakagami-$m$ fading channels. By studying
the DCMA pairwise error probability (PEP) in a Nakagami-$m$ channel, a novel
design metric called minimum logarithmic sum distance (MLSD) is first derived.
With respect to the proposed MLSD, we introduce a new family of
power-imbalanced dense codebooks by deleting certain rows of a special
non-unimodular circulant matrix. Simulation results demonstrate that our
proposed dense codebooks lead to both larger minimum Euclidean distance and
MLSD, thus yielding significant improvements of error performance over the
existing sparse code multiple access and conventional unimodular DCMA schemes
in Nakagami-$m$ fading channels under different overloading factors.
