  This paper investigates the limits of information transfer over a fast
Rayleigh fading MIMO channel, where neither the transmitter nor the receiver
has the knowledge of the channel state information (CSI) except the fading
statistics. We develop a scalar channel model due to absence of the phase
information in non-coherent Rayleigh fading and derive a capacity supremum with
the number of receive antennas at any signal to noise ratio (SNR) using
Lagrange optimisation. Also, we conceptualise the discrete nature of the
optimal input distribution by posing the optimisation on the channel mutual
information for $N$ discrete inputs. Furthermore, we derive an expression for
the asymptotic capacity when the input power is large, and compare with the
existing capacity results when the receiver is equipped with a large number of
antennas.
