Writing on Fading Paper and Causal Transmitter CSI

A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI - a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm of the bandwidth. Our coding scheme is motivated from the Gel\´fand-Pinsker and dirty paper coding. Nonetheless, our scheme requires only causal transmitter CSI (CSIT) in contrast with Gel\´fand-Pinsker and dirty paper coding, which require non-causal CSIT. A general discrete channel with i.i.d. states is considered later. Each input has an associated cost and a zero cost input "0" exists. The channel state is known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve it. Later, a novel orthogonal coding scheme is proposed for the case of causal CSIT and a condition for equal capacity per unit cost with causal and non-causal CSIT is derived