Sufficient condition for chaotic maps to yield chaotic behavior after FM

This paper shows that chaotic signals are advantageous over random noise signals for the application of FM signals in radar. The technique described in this paper results in easy generation of constant-envelope wide-band (CEW) signals. A sufficient condition is provided for a chaotic map to yield chaotic behavior after frequency modulation (FM), thus maintaining the wideband characteristics of the modulated signal. The analysis is based on Lyaponov exponents which measure the presence of chaos in the signal. The condition was tested against several maps through simulation. The results are compared to Gaussian distributed frequency modulated (GFM) and uniformly distributed frequency modulated (UFM) signals. The results show that chaotic based frequency modulated (CBFM) signals provide better range resolution than GFM, and equal the range resolution to UFM. Another advantage of chaotic chaos-based frequency modulation (CBFM) signals over UFM signals is that the generation of chaotic signals is easier and cheaper than random noise signals.