Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels

We study the problem of modulation and coding for doubly dispersive, i.e., time and frequency selective fading channels. Using the recent result that under-spread linear systems are approximately diagonalized by biorthogonal Weyl-Heisenberg bases, we arrive at a canonical formulation of modulation and code design. For coherent reception with maximum likelihood decoding, we derive the code design criteria as a function of the channel’s scattering function. We use ideas from generalized concatenation to design multilevel codes for this canonical channel model. These codes are based on partitioning a constellation carved out from the integer lattice. Utilizing the block fading interpretation of the doubly dispersive channel, we adapt these partitioning techniques to the richness of the channel. We derive an algebraic framework which enables us to partition in arbitrarily large dimensions.