Wireless communications over rapidly time varying channels Fundamentals of time varying communication channels. Introduction ; The physics of time varying channels ; Deterministic description ; Stochastic description ; Underspread channels ; Parsimonious channel models ; Measurement ; Conclusion Information theory of underspread WSSUS channels. The role of a system model ; A discretized system model ; The large bandwidth regime : diagonalized I O relation ; The large bandwidth regime : I O relation with interference ; The high SNR regime ; Conclusions Algebraic coding for fast fading channels. Introduction ; Product distance based code design ; Lattices ; Algebraic number theory ; Algebraic lattices ; Ideal lattices ; Algebraic rotations with high product distance ; Sphere decoding ; Performance of rotated constellations ; Conclusions Estimation of time varying channels : a block approach. Introduction ; System and channel model ; Channel estimation based on a single block ; Channel estimation based on multiple blocks ; Extension to MIMO systems ; Adaptive channel estimation ; Conclusions Pilot design and optimization for transmission over time varying channels. Introduction ; Pilot design : a framework ; Optimal TDM pilot insertion pattern in single carrier systems ; Alternative pilot insertion strategy : superimposed training ; Resource allocation : amount of training and power optimization ; Pilot design for MIMO channels ; Pilot design for wideband systems ; Conclusion ; The Kalman Filter for TDM training ; Proof of proposition 5.1 ; Proof of Lemma 5.1 ; Proof of theorem 5.1 Equalization of time varying channels. Introduction ; System model ; Coherent equalization ; Noncoherent equalization ; Conclusion ; Derivation of posterior LLR expression (6.36) ; Derivation of the noncoherent MLSD expression (6.73) ; Explanation of EM recursion (6.91) ; Info EM(B) algorithms for noncoherent equalization OFDM communications over time varying channels. OFDM systems ; ICI mitigation techniques ; Time varying channel estimation ; Concluding remarks Multiuser MIMO receiver processing for time varying channels. Introduction ; Multiuser MIMO systems ; Tools for complexity reduction ; Iterative multiuser MIMO time varying channel estimation ; Linear joint antenna multiuser detection ; Nonlinear detection ; Simulation results ; Conclusions ; Computation of the log likelihood ratio (8.44) Time scale and dispersive processing for wideband time varying channels. Introduction ; Narrowband channel characterization ; Wideband delay scale channel characterization ; Wideband dispersive channel characterization ; Underwater wireless communication channels ; Application example