  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.
