On circularity of complex-valued radar signals

In radars, complex signals arise naturally as a result of a quadrature demodulation or Fourier transform. Also, the Doppler spectrum is not an even function of frequency and the Doppler signal is thus naturally complex. Random complex radar signals used to be automatically assumed to be circular. As a result, most of signal processing algorithms (such as detection and estimation) were derived for circular noises and interferences only. In the recent literature an interest in complex signals that are not circular can be seen. It was noticed that many common signals, particularly in communications, are not circular and processing methods exploiting this noncircularity were presented. In this paper we review complex random signals and their properties of circularity and properness. Then we analyze a few complex-valued signals that arise in radars and show that some of them are indeed noncircular to some extend.