Vandermonde frequency division multiplexing for cognitive radio

We consider a cognitive radio scenario where a primary and a secondary user wish to communicate with their corresponding receivers simultaneously over frequency selective channels. Under realistic assumptions that the primary user is ignorant of the secondary user's presence and that the secondary transmitter has no side information about the primary's message, we propose a Vandermonde precoder that cancels the interference from the secondary user by exploiting the redundancy of the cyclic prefix and the frequency selectivity of the channel. Our numerical examples show that VFDM, with an appropriate design of the input covariance, enables the secondary user to achieve a non-negligible rate while generating zero interference to the primary user.