Maximum-Likelihood Noncoherent PAM Detection

Sequence detection offers improved error-rate performance over conventional symbol-by-symbol detection when channel knowledge is not available at the receiver end. However, maximum-likelihood (ML) noncoherent sequence detection is proven to be notoriously intractable in many communication settings. In this work, we develop a new ML sequence detector for pulse-amplitude modulation (PAM) or quadrature-amplitude modulation (QAM) transmissions in unknown Rayleigh fading. Our detector identifies the ML sequence with overall polynomial complexity. This is possible via an auxiliary-angle approach that unlocks a low-rank property of the ML detection problem, reduces the exponential-size set of solution sequences to a polynomial-size set of candidates, and guarantees that the ML sequence is always contained in this substantially smaller set.