Coding Requirements for Multiple - AntennaChannels with Unknown Rayleigh Fading

Multiple transmitter and receiver antennas can boost the reliability and capacity of wireless fading channels. When the channel is unknown to the transmitter and receiver, it is known that the fading coherence time in a piecewise-constant fading channel ultimately limits the channel capacity. In this work, we examine coding requirements for the unknown fading channel by computing the random coding error exponent. We show that the fading coherence time also plays a fundamental role in the error exponent, by proving that the error exponent is not increased by having more transmitter antennas than the number of samples in the coherence time. The signal structure that maximizes the exponent is computed and is shown to be very similar to the signal structure that achieves capacity. We calculate the minimum coding block length requirements as a function of probability of error for various fading coherence times. We conclude that coding over a certain number of independent fades is always needed to guarantee low probabilities of error, regardless of the coherence time.