On the role of channel side information in cognitive radios

The capacity of cognitive networks is investigated for the scenario in which the cognitive transmitter has full, a-priori knowledge of the primary transmission but does not have a reliable estimate of the channel between the primary transmitter and the cognitive receiver. We focus, in particular, on two channel models: the “Writing Onto Fast Fading Dirt” (WFFD) channel and the Fast Fading Z Cognitive Interference (FFZCI) channel. The WFFD channel is the point-to-point channel in which the channel output is obtained as the sum of the channel input, an interference sequence and a white Gaussian process. The interference sequence is itself obtained as the product of a state sequence, known at the transmitter, and a fading sequence, known at the receiver. In a cognitive network, the state sequence models the transmission from a primary system which is provided to the cognitive transmitter as side information; the fading sequence, conversely, models the channel between the primary system and the cognitive receiver which is unknown at the cognitive transmitter. In this modeling of a cognitive network, the primary transmission strategy is not influenced by the presence of the cognitive user. The FFZCI channel addresses, instead, the scenario in which the primary transmission is aware of the cognitive communication strategy. More specifically, the FFZCI channel is obtained from the WFFD channel by letting the state sequence equal the signal sent by a primary encoder communicating to a primary receiver over an additive white Gaussian noise channel. For this model, the transmission strategy at the primary and cognitive user are jointly designed so as to minimize the effect of the primary transmission over the cognitive user. For both the WFFD and the FFZCI channel, we derive inner and outer bounds to capacity and provide simple conditions under which the two bounds are to within a small gap. These results address the question of how the cognitive transmission can best be pre-coded against the primary signal when only partial knowledge of the primary-to-cognitive channel is available. We show, in particular, that if the fading realizations are sufficiently diverse, then the optimal performance degrades very rapidly as the power of the primary signal increases. This suggests that robust interference pre-cancellation of the primary transmission is substantially unfeasible and that high-quality estimates of the interfering links are required at the cognitive transmitter to take full advantage of the primary system knowledge.