Ambiguity Function Analysis of Hyperbolic Fractional Fourier Transform in Joint Radar and Communication Applications

The hyperbolic fractional Fourier transform (HFrFT) as a generalized form of the fractional Fourier transform (FrFT) based on complex transform orders is introduced. This paper defines the continuous-time hyperbolic fractional Fourier transform (CHFrFT). Further, a closed form of the discrete hyperbolic fractional Fourier transform (DHFrFT) is derived. The ambiguity function (AF) of the HFrFT signal is calculated, mathematically. The performance of the proposed transform in radar signal processing by analyzing the AF and in wireless communication systems based on the bit error rate (BER) analysis, is evaluated. The simulation result shows that HFrFT can be a suitable technique in joint radar and communication (JRC) applications.