Dense MIMO Matrix Lattices and Class Field Theoretic Themes in Their Construction

Since the cyclic division algebras and their orders have become standard material for researchers seeking to construct good MIMO-lattices. The usual construction of the actual lattice corresponds to a cyclic submodule of an order. In a recent submission we studied the problem of identifying those cyclic division algebras that consume the least amount of the available signal space for a given minimum determinant. In this semi-tutorial note some of the material from is recapped together with hopefully illuminating examples. We also motivate our concept of density by previewing upper and lower bounds, and taking a closer look at some of the suggested MIMO-lattices in relation to these bounds.