Abstract
We analyze theÌý capacity Ìýof Rayleigh block- fading Ìý³¾³Ü±ô³Ù¾±±è±ô±ð- input Ìý³¾³Ü±ô³Ù¾±±è±ô±ð-output ( MIMO )Ìý channels Ìýin the noncoherent setting and prove thatÌý unitary Ìýspace-time modulation (USTM) is notÌý capacity - achieving Ìýwhen the total number of antennas exceeds the coherence time of theÌý fading Ìý channel . This situation is relevant forÌý MIMO Ìýsystems withÌý large Ìýantenna arrays ( large - MIMO Ìýsystems). Our result settles a conjecture by Zheng & Tse (2002) in the affirmative. TheÌý capacity - achieving Ìý input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of aÌý unitary Ìý isotropically Ìý distributed Ìýrandom matrix, and a diagonal matrix whose nonzero entries are distributed Ìýas the square-root of the eigenvalues of a Beta- distributed Ìýrandom matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM inÌý large - MIMO Ìýsystems yields a rate gain asÌý large Ìýas 13% for SNR values of practical interest.