A Blind Algorithm Based on Difference of Norms for Equalization of Biorthogonal Signals

Motivated by increasing interest in energy efficient modulations, we investigate a blind algorithm for biorthogonal signaling. While this modulation has historically been considered only for use in narrowband systems without intersymbol interference (ISI), recent attention has been given to its use in ISI channels. Due to the fact that biorthogonal modulation (BOM) results in a source that is not i.i.d., however, classical adaptive equalization techniques cannot be directly applied to equalization of BOM signals. We review the MMSE and LMS-based equalizers, and then identify some peculiarities that arise in blind equalization of BOM signals when compared to more traditional modulations like BPSK. Next, we present a novel blind algorithm, called TROMBONE, for the adaptive equalization of BOM signals. We discuss the convergence properties of this algorithm, and demonstrate its performance with numerical simulations