Near Capacity Signaling over Fading Channels using Coherent Turbo Coded OFDM and Massive MIMO

The minimum average signal-to-noise ratio (SNR) per bit required for error-free transmission over a fading channel is derived, and is shown to be equal to that of the additive white Gaussian noise (AWGN) channel, which is $-1.6$ dB. Discrete-time algorithms are presented for timing and carrier synchronization, as well as channel estimation, for turbo coded multiple input multiple output (MIMO) orthogonal frequency division multiplexed (OFDM) systems. Simulation results show that it is possible to achieve a bit error rate of $10^{-5}$ at an average SNR per bit of 5.5 dB, using two transmit and two receive antennas. We then propose a near-capacity signaling method in which each transmit antenna uses a different carrier frequency. Using the near-capacity approach, we show that it is possible to achieve a BER of $2\times 10^{-5}$ at an average SNR per bit of just 2.5 dB, with one receive antenna for each transmit antenna. When the number of receive antennas for each transmit antenna is increased to 128, then a BER of $2\times 10^{-5}$ is attained at an average SNR per bit of 1.25 dB. In all cases, the number of transmit antennas is two and the spectral efficiency is 1 bit/transmission or 1 bit/sec/Hz. In other words, each transmit antenna sends 0.5 bit/transmission. It is possible to obtain higher spectral efficiency by increasing the number of transmit antennas, with no loss in BER performance, as long as each transmit antenna uses a different carrier frequency. The transmitted signal spectrum for the near-capacity approach can be restricted by pulse-shaping. In all the simulations, a four-state turbo code is used. The corresponding turbo decoder uses eight iterations. The algorithms can be implemented on programmable hardware and there is a large scope for parallel processing.