Abstract
We analyze the听 capacity 听of Rayleigh block- fading 听尘耻濒迟颈辫濒别- input 听尘耻濒迟颈辫濒别-output ( MIMO )听 channels 听in the noncoherent setting and prove that听 unitary 听space-time modulation (USTM) is not听 capacity - achieving 听when the total number of antennas exceeds the coherence time of the听 fading 听 channel . This situation is relevant for听 MIMO 听systems with听 large 听antenna arrays ( large - MIMO 听systems). Our result settles a conjecture by Zheng & Tse (2002) in the affirmative. The听 capacity - achieving 听 input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a听 unitary 听 isotropically 听 distributed 听random matrix, and a diagonal matrix whose nonzero entries are distributed 听as the square-root of the eigenvalues of a Beta- distributed 听random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in听 large - MIMO 听systems yields a rate gain as听 large 听as 13% for SNR values of practical interest.