Optimal Adaptive Precoding for Frequency-Selective Nagakami-m Fading Channels

Discrete Multi-Tone (DMT) systems with optimal power and bit loading are suitable for wired-line applications but have high complexity in wireless links because of the channel uctuations. Adaptive modulation is better suited in wireless communications, assuming that training sequences are periodically transmitted to allow an accurate estimate of the channel parameters. In these applications, random channel modeling is a fundamental tool for assessing wireless systems performance and it can also be incorporated in the derivation of the optimal modulation strategy. In this paper, we develop optimal loading strategies for frequency selective fading, assuming OFDM modulation and modeling the samples of the channel time-varying transfer function as Nagakami-m correlated fading processes. The design minimizes the BER for a given average transmit power. Channel statistics need to be updated at a very slow rate when compared to the exact channel status information (CSI), which reduces complexity of our adaptive OFDM scheme compared to a standard DMT approach. This also alleviates the need of training and allows us to incorporate partial channel knowledge in the design. Interestingly, our derivations identify the optimal solution for the limiting case where the channel transfer function is exactly known at both transmitter and receiver.