  Efficient constellation design is important for improving performance in
communication systems. The problem of multidimensional constellation design has
been studied extensively in the literature in the context of multidimensional
coded modulation and space-time coded MIMO systems. Such constellations are
formally called as lattice codes, where a finite set of points from a certain
high dimensional lattice is chosen based on some criteria. In this paper, we
consider the problem of constellation/signal set design for media-based
modulation (MBM), a recent MIMO channel modulation scheme with promising
theoretical and practical benefits. Constellation design for MBM is
fundamentally different from those for multidimensional coded modulation and
conventional MIMO systems mainly because of the inherent sparse structure of
the MBM signal vectors. Specifically, we need a structured sparse lattice code
with good distance properties. In this work, we show that using an (N,K)
non-binary block code in conjunction with the lattice based multilevel squaring
construction, it is possible to systematically construct a signal set for MBM
with certain guaranteed minimum distance. The MBM signal set obtained using the
proposed construction is shown to achieve significantly improved bit error
performance compared to conventional MBM signal set. In particular, the
proposed signal set is found to achieve higher diversity slopes in the
low-to-moderate SNR regime.
