Active interference cancellation for OFDM spectrum sculpting: Linear processing is optimal

Active interference cancellation (AIC) is a multicarrier spectrum sculpting technique, which reduces the power of undesired out-of-band emissions by adequately modulating a subset of reserved cancellation subcarriers. In most schemes, online complexity is a concern, and thus, cancellation subcarriers have traditionally been constrained to linear combinations of the data subcarriers. Recent AIC designs truly minimizing out-of-band emission shift complexity to the offline design stage, motivating the consideration of more general mappings to improve performance. We show that there is no loss in optimality incurred by constraining these mappings to the set of linear functions.