Exponential Diversity Achieving Spatio–Temporal Power Allocation Scheme for Fading Channels

In this paper, we analyze optimal (in space and time) adaptive power transmission policies for fading channels when the channel-state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) is available. The transmitter has a long-term (time) average power constraint. There can be multiple antennas at the transmitter and at the receiver. The channel experiences Rayleigh fading. We consider beamforming and space-time coded systems with perfect/imperfect CSIT and CSIR. The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity order if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained in the low SNR region but we get only polynomial diversity in the high SNR region. Another interesting conclusion is that in case of imperfect CSIT and CSIR, knowledge of CSIT at the receiver is very important. Finally, for the optimal power control policy of the uncoded system we find the error-exponents which provide the rate versus diversity-order tradeoff for this policy. This tradeoff is of an entirely different nature than the well-known Zheng-Tse tradeoff.