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Constellations matched to the Rayleigh fading channel

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2 Author(s)
Girand, X. ; Ecole Nat. Superieure des Telecommun., Paris, France ; Belfiore, J.C.

We introduce a new technique for designing signal sets matched to the Rayleigh fading channel, In particular, we look for n-dimensional (n⩾2) lattices whose structure provides nth-order diversity. Our approach is based on a geometric formulation of the design problem which in turn can be solved by using a number-geometric approach. Specifically, a suitable upper bound on the pairwise error probability makes the design problem tantamount to the determination of what is called a critical lattice of the body S={x=(x1, ···, xn)∈Rn, |Πi=1nxi|⩽1}. The lattices among which we search for an optimal solution are the standard embeddings in R n of the number ring of some totally real number field of degree n over Q. Simulation results confirm that this approach yields lattices with considerable coding gains

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Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 1 )