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 (Nt), which is a function of the number of transmit antennas Nt. Here f (Nt) 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 (Ntot) in the transmitter and receiver is fixed, there exists a minimum value of f (Nt), 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 Ntot is large and kept constant. Thus, the spectral efficiency can be made as large as possible, for a given BER and Ntot.