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G. Tauböck:
"A maximum entropy theorem for complex-valued random vectors, with implications on capacity";
Talk: IEEE Information Theory Workshop 2011, Paraty, Brasilien; 10-16-2011 - 10-20-2011; in: "Proceedings IEEE ITW 2011", (2011), 375 - 379.

Recent research has demonstrated significant achievable performance gains by exploiting circularity/non-circularity or properness/improperness of complex-valued signals. In this paper, we investigate the influence of theses properties on important information theoretic quantities such as entropy and capacity. More specifically, we prove a novel maximum entropy theorem that is based on the so-called circular analog of a given (in general, non-Gaussian) complex-valued random vector. Its introduction is supported by a characterization theorem that employs a minimum Kullback-Leibler divergence criterion. As an application of this maximum entropy theorem, we show that the capacity-achieving input random vector is circular for a broad range of multiple-input multiple-output (MIMO) channels including coherent and noncoherent scenarios. This result does not depend on a Gaussian assumption and thus provides a justification for many practical signalling/coding strategies, regardless of the specific distribution of the channel parameters.

complex-valued; circular; proper; MIMO; entropy; Kullback-Leibler divergence; capacity

http://publik.tuwien.ac.at/files/PubDat_203454.pdf