  This work deals with turbo coded single user massive multiple input multiple
output (SU-MMIMO) systems, with and without precoding. SU-MMIMO has a much
higher spectral efficiency compared to multi-user massive MIMO (MU-MMIMO) since
independent signals are transmitted from each of the antenna elements (spatial
multiplexing). MU-MMIMO that uses beamforming has a much lower spectral
efficiency, since the same signal (with a delay) is transmitted from each of
the antenna elements. In this work, expressions for the upper bound on the
average signal-to-noise ratio (SNR) per bit and spectral efficiency are derived
for SU-MMIMO with and without precoding. We propose a performance index
$f(N_t)$, which is a function of the number of transmit antennas $N_t$. Here
$f(N_t)$ is the sum of the upper bound on the average SNR per bit and the
spectral efficiency. We demonstrate that when the total number of antennas
($N_{\mathrm{tot}}$) in the transmitter and receiver is fixed, there exists a
minimum value of $f(N_t)$, which has to be avoided. Computer simulations show
that the bit-error-rate (BER) is nearly insensitive to a wide range of the
number of transmit antennas and re-transmissions, when $N_{\mathrm{tot}}$ is
large and kept constant. Thus, the spectral efficiency can be made as large as
possible, for a given BER and $N_{\mathrm{tot}}$.
