516 zyxwv ON THE SECOND-ORDER HIGH FREQUENCY BISTATIC GROUND WAVE RADAR CROSS SECTION OF THE OCEAN SURFACE E.W. Gill’ and J. Walsh1,2 ‘Faculty of Engineering and Applied Science, MUN, St. John’s, NF 2Northern Radar Systems Limited, St. John’s, NF ABSTRACT The electric field equation is presented for the scat- tering of high frequency radiation (3-30 MHz) from a patch of ocean when the source and the receiver are not cdocated. Describing the ocean surface by a Fourier series with time-varying coefficients, the bistatic cross section to second order in scatter is developed and com- pared to existing monostatic models. 2. THE SECOND-ORDER HF BISTATIC CROSS SECTION OF THE OCEAN SURFACE Figure 1 depicts the case where double scattering oc- curs on the patch of ocean formed by the overlapping transmit and receive beams. Gill [6] shows that for a pulsed dipole source the expression for the second-order scattered field, (E&)zl(t), normal to a random, slightly rough, time-varying surface may be written as 1. INTRODUCTION Since the early 1970’s, much effort has been given to examining the scatter mechanism for high frequency (HF) electromagnetic (EM) radiation interacting with the surface of the ocean, the latter being an example of time-varying randomly-rough surfaces of high conduc- tivity. HF ground wave radar (GWR) cross sections of the ocean surface for monostatic operation have a p peared in the literature as early zyxwvut as 1972 [l], and sub- sequent analyses [2], based on the scattering theory of Walsh [3], have provided more thorough descriptions of the monostatic problem. In this paper, Walsh’s approach [3, zyxwvu 41 is applied again to operation in a marine environment but for the bistatic case zyxwvutsrq - i.e. the radar transmitter and receiver are not cdocated as for the monostatic case (see Figure 1). While the first-order bistatic problem is addressed by Walsh zyxwvutsrq et zyxwvutsrqponm al. [5], here the problem is extended to second-order. Seeking an asymptotic expression for the second- order scattered electric field via a stationary phase in- tegration indicates at least two distinct features impor- tant to the total scatter. One of these is due to a double scatter on a “patch” of ocean at a distance from both the transmit and receive sites, while the other involves a single scatter very near the transmitter with that ra- diation again scattering from the “patch” before being received. This paper addresses the first feature. In equation (l), the various parameters are as follows (also, see Figure l(a)): 70 is the intrinsic impedance of free space; At is the length of the dipole antenna; z lo is the magnitude of the dipole current; IC0 (= ?) is the free space wavenumber of the transmitted radia- tion, WO being the radian frequency and c the speed of light; Apszl (= zyxw y) is the effective radial extent of the scattering patch, with 70 being the pulse duration of the radiated signal; ps2, = (p2 +p20)/2, p2 and p20 be- ing, respectively, the distance from the transmitter and receiver to the scattering patch; poq1 = c[t - (70/2)]/2; zy p is the distance from the transmitter to the receiver; ~Pz~,~~ and 1PgprW2 are the Fourier coefficients of the surface components whose waye vectors and angular frequencies are zyxw I?, and w1 and K2 and w2, respectively; the time, t, variation of the surface is introduced by virtue of the exponential term, ej(wl+wa)t; =y21 is the electromagneticcoupling coefficient; q5bo is the effective bistatic angle formed by p02 or p020 and the normal to the ellipse with focii at (0,O) and (p,O), while ,002 CCECE’97 0-7803-3716-6 /97/$5.00 0 1997 IEEE