Cubic-complexity optimal noncoherent OOK sequence detection in flat fading

On-off keying (OOK) is a simple orthogonal modulation technique that is primarily used in the noncoherent mode, that is, when the propagation channel is unknown at the receiver. Although the noncoherent OOK detector is usually operated as a simple single-symbol (one-shot) energy detector, it does not take into account memory that is induced by the channel. Hence, optimal noncoherent detection of OOK 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, we present a novel algorithm that performs generalized-likelihood-ratio-test (GLRT) optimal noncoherent sequence detection of OOK signals in flat fading with cubic (in the sequence length) complexity. Moreover, for Rayleigh fading channels, the proposed algorithm is equivalent to the maximum-a-posteriori (MAP) noncoherent sequence detector. Due to its polynomial complexity, the proposed algorithm allows implementation of the optimal sequence detector for large sequence lengths, for which the conventional exhaustive-search approach becomes infeasible. Interestingly, with a large enough sequence length, the noncoherent detector attains nearly-coherent performance, although it does not utilize any knowledge about the propagation channel.