Optimum detection of slow frequency-hopped signals

Optimum detectors have previously been derived for fast frequency-hopped (FFH) signals with M-ary frequency-shift-keyed (MFSK) data modulation received in additive white Gaussian noise (FFH here implies that a single MFSK tone is transmitted per hop), The present paper extends that work to the more analytically complex category of slow frequency-hopped (SFH) signals with multiple MFSK tones per hop. A special subset of the SFH/MFSK format that receives particular attention in the paper is the case of continuous-phase modulation (CPM) for which the carrier phase is assumed to be constant over the entire hop. A fundamental conclusion is that SFW/CPM modulation is advantageous not only to the communicator but also to a sophisticated noncoherent detector. By applying techniques developed in the paper to exploit the continuous-phase characteristic, an intercept receiver of reasonable complexity will perform appreciably better than traditional channelized detectors