Effects of frequency instability caused by phase noise on the performance of the fast FH communication system

In this paper, we newly analyze the effect of phase noise in the frequency synthesizer on the performance of fast frequency-hopping (FFH)/M-ary noncoherent frequency-shift keying (M-NCFSK) system. The symbol-error probability (SER) of the frequency-hopping spread-spectrum (FHSS) system is derived when the noncoherent FSK demodulation with the square-law detector is considered. Also, the effect of phase noise on the performance of the FFH/M-NCFSK system is analyzed in terms of phase noise power spectrum and frequency-hopping spacing, as well as the diversity level. The required signal-to-noise ratio (SNR) to meet P_s=10^-3 is about 11.8 dB when the standard frequency deviation is about 31.623 kHz and the frequency-hopping spacing in the FFH/2-NCFSK system is 400 kHz. So, it is found that there is about 0.8-dB power penalty than the phase noise-free system. Similarly, there is about 0.7-dB power penalty in the FFH/4-NCFSK system. SER performance is changed with the standard frequency deviation, but SER is nearly independent of the modulation level. As the diversity level is increased from 1 to 4, frequency diversity effect is trivial in the lower SNR below 6 dB, but is considerably improved in the higher SNR.