Orthogonal modulation, for example, frequency-shift keying (FSK) or pulse-position modulation (PPM), is primarily used in relatively-low-rate communication systems that operate in the power-limited regime. Optimal noncoherent detection of orthogonally modulated signals takes the form of sequence detection and has exponential (in the sequence length) complexity when implemented through an exhaustive search among all possible sequences. In this work, for the first time in the literature, we present an algorithm that performs generalized-likelihood-ratio-test (GLRT) optimal noncoherent sequence detection of orthogonally modulated signals in flat fading with log-linear (in the sequence length) complexity. Moreover, for Rayleigh fading channels, the proposed algorithm is equivalent to the maximum-likelihood (ML) noncoherent sequence detector. Simulation studies indicate that the optimal noncoherent FSK detector attains coherent-detection performance when the sequence length is on the order of 100, offering a 3-5 dB gain over the typical energy (single-symbol) detector. While the conventional exhaustive-search approach becomes infeasible for such sequence lengths, the proposed implementation requires a log-linear only number of operations, opening new avenues for practical deployments. Finally, we show that our algorithm also solves efficiently the optimal noncoherent sequence detection problem in contemporary radio frequency identification (RFID) systems.

Frequency-shift keying (FSK) is an orthogonal modulation technique that is primarily used in relatively low-rate communication systems that operate in the power-limited regime. Optimal noncoherent detection of FSK takes the form of sequence detection and has exponential complexity in the sequence length when implemented through an exhaustive search among all possible sequences. In this work, for the first time in the literature, we present an algorithm that performs generalized-likelihood-ratio-test (GLRT) optimal noncoherent sequence detection of orthogonally modulated signals in flat fading with log-linear complexity in the sequence length. Moreover, for Rayleigh fading channels, the proposed algorithm is equivalent to the maximum-likelihood (ML) noncoherent sequence detector. Finally, we show that our algorithm also solves efficiently the optimal noncoherent sequence detection problem in contemporary radio-frequency-identification (RFID) systems.

Amplitude/phase-shift keying (APSK) is a power- and bandwidth- efficient modulation technique that is robust against high-power- amplifier nonlinear distortion effects and has been adopted in the standard DVB-S2 for digital video broadcasting and interactive broadband satellite services. Differential APSK has been studied as a simple blind alternative that avoids channel estimation and tracking at the receiver. However, if the channel is unknown at the receiver end, then the optimal blind detector takes the form of a sequence detector and has exponential (in the sequence length) complexity when implemented through a conventional exhaustive search among all possible data sequences. In this work, we develop a novel algorithm that has polynomial complexity and performs optimal blind sequence detection of APSK.