Finite rate of innovation channel models and DoF of MIMO multi-user systems with delayed CSIT feedback

Channel State Information at the Transmitter (CSIT) is of utmost importance in multi-user wireless networks, in which transmission rates at high SNR are characterized by Degrees of Freedom (DoF, the rate prelog). In recent years, a number of ingenious techniques have been proposed to deal with delayed and imperfect CSIT. However, we show that the precise impact of these techniques in these scenarios depends heavily on the channel model (CM). We introduce the use of linear Finite Rate of Information (FRoI) signals (which could also be called Basis Expansion Model (BEM)) to model time-selective channel coefficients. The FRoI dimension turns out to be well matched to Degree of Freedom (DoF) analysis since the FRoI CM allows compressed feedback (FB) and captures the DoF of the channel coefficient time series. Both the block fading model and the stationary bandlimited channel model are special cases of the FRoI CM. However, the fact that FRoI CMs model stationary channel evolutions allows to exploit one more dimension: arbitrary time shifts. In this way, the FroI CM allows to maintain the DoF unaffected in the presence of CSIT feedback (FB) delay, by increasing the FB rate. We call this Foresighted Channel FB (FCFB). FRoI CM relates also to (predictive) filterbanks and we work out the optimization details in the biorthogonal case (different analysis and synthesis filters). The FRoIC model with multiple basis functions accommodates FB delay beyond the coherence time and handling of users with unequal coherence times.