The first- and second-order bistatic high frequency radar cross sections of the ocean surface with an antenna on a floating platform are derived for a frequency-modulated continuous wave (FMCW) source. Based on previous work, the derivation begins with the general bistatic electric field in the frequency domain for the case of a floating antenna. Demodulation and range transformation are used to obtain the range information, distinguishing the process from that used for a pulsed radar. After Fourier-transforming the autocorrelation and comparing the result with the radar range equation, the radar cross sections are derived. The new first- and second-order antenna-motion-incorporated bistatic radar cross section models for an FMCW source are simulated and compared with those for a pulsed source. Results show that, for the same radar operating parameters, the first-order radar cross section for the FMCW waveform is a little lower than that for a pulsed source. The second-order radar cross section for the FMCW waveform reduces to that for the pulsed waveform when the scattering patch limit approaches infinity. The effect of platform motion on the radar cross sections for an FMCW waveform is investigated for a variety of sea states and operating frequencies and, in general, is found to be similar to that for a pulsed waveform.

The derivation of high frequency radar ocean surface cross sections has been studied for over four decades. The first-order high frequency radar scatter cross section was developed and analysed in [

All of the models mentioned above were developed specifically for pulsed radar. However, there are inherent disadvantages to using pulsed radar systems. For example, the detectable range capability is determined by the average transmitted power. In a pulsed radar system, both the range resolution and the average transmitted power are dependent on the pulse width. Narrower pulses, bringing better range resolution, require large peak powers to be useful at long range. Compared to this, FMCW radar systems are able to achieve satisfactory range resolution and long range with moderate peak power due to a 100% duty cycle. Thus, in recent years, FMCW radars have been widely used in ocean remote sensing applications.

A good summary of the digital processing of an FMCW signal for radar systems has been reported by Barrick [

In this paper, the first- and second-order bistatic radar ocean surface cross sections for an antenna on a floating platform and incorporating an FMCW source are presented. In Section

By using a small displacement vector,

General (a) first-order and (b) second-order bistatic scatter geometry with antenna motion.

The second-order bistatic received electric field corresponding to the first-order found in (

Following a similar analysis as in [

The current waveform of an FMCW radar may be written as [

It is known from [

After the demodulation preprocess, the exponential factor

Following a similar procedure to the first-order case, the second-order bistatic received electric field with a transmitter on a floating platform for an FMCW waveform may be written as

In developing the ocean radar cross section, a time-varying ocean surface, represented as

After Fourier-transforming the autocorrelation and comparing directly with the radar range equation, the radar cross section,

It is known that the second-order radar cross section contains two portions: an hydrodynamic contribution and an electromagnetic contribution. Using the Fourier coefficient for the second-order ocean waves

Following the same procedure as for the first-order case, based on the total second-order time-varying received electric field (

Based on a Pierson-Moskowitz (PM) ocean spectral model [

Figure

Comparison of the first-order radar cross sections for the FMCW waveform with that for the pulsed waveform.

It is clear that the first-order radar cross section has a certain relationship with the integral limit

Comparison of the side lobe levels of the first-order radar cross sections for the pulsed and FMCW waveform. (a)

By varying the radar bandwidth and keeping the relationships

The effect of the bandwidth on the first-order radar cross sections.

A similar technique is used to simplify and simulate the second-order radar ocean cross section for the FMCW waveform as that for the pulsed waveform in [

Second-order bistatic radar cross section with a transmitter on a floating platform.

The first- and second-order bistatic radar ocean cross sections for an antenna on a floating platform have been presented for the case of an FMCW waveform. In the derivation process, the first- and second-order models begin with the bistatically received electric field equations derived in [

The authors declare that there are no competing interests regarding the publication of this paper.

The work was supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC) under Discovery Grants to Weimin Huang (NSERC 402313-2012) and Eric W. Gill (NSERC 238263-2010 and RGPIN-2015-05289) and by an Atlantic Innovation Fund Award (Eric W. Gill, principal investigator).