Capacity and Cutoff Rate of Coded FH/MFSK Communications with Imperfect Side Information Generators

Abslruct-In a coded frequency-hopped M-ary frequency shift-keying (FHlMFSK) communication system, it is known that if perfect side information about the jamming state is available to the decoder, substantial improvement in performance is possible. However, thermal noise, which is present in practical communication systems, can corrupt the jamming state information (JSI). In this paper, when JSI is imperfect due to thermal noise, we calculate the capacities and cutoff rates of the channels as a function of the signal-to-jamming-noise ratio for memoryless, noncoherent FHlMFSK systems under partial-band noise jamming (PBNJ). We consider both soft and hard-decision metrics with perfect, imperfect, and no JSI. Also, we introduce three imperfect JSI generators. The first imperfect JSI generator uses the maximum aposten'ori (MAP) decision rule based on the energy from an FH tone frequency which is near the M-signaling FH tone frequencies. The second decision rule utilizes the MAP rule, but it is based on the total energy received in the M-signaling FH tone frequencies. The third generator has the same decision statistics as the second generator, but its decision rule is an easily implementable suboptimum rule. If hard decisions a r e made and code rates a r e high, e.g., 20.7, then the differences between the imperfect JSI generators and perfect JSI generator can be larger than 1 dB in the signal-to-jamming-noise ratio required to achieve the given capacity or cutoff rate, even though the thermal noise is quite small, e.g., a 25 dB signal-to-thermal noise ratio. If soft decisions a r e made, then the differences between the imperfect and perfect JSI cases a r e negligible.