Optimal adaptive precoding for frequency-selective Nagakami-m fading channels

DMT transmissions with optimal power and bit loading are suitable for wired-line applications but have high complexity when it comes to wireless time-varying environments. Adaptive modulation on the other hand, assumes that training sequences are available to provide an accurate estimate of the channel parameters, while the channel statistics allow one to evaluate the average performance. Random channel modeling is a powerful tool for assessing wireless systems performance, but can be also be instrumental in optimizing the modulation. We develop optimal loading strategies for frequency selective fading, assuming OFDM modulation and by modeling the channel impulse response as an FIR filter whose taps are 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.