ALCANCES Y LIMITACIONES

Target RCS Processing gain budget deficit (dB)

(dBm^) 1km 10km 100km 20 55.2 75.2 95.2 25 50.2 70.2 90.2 30 45.2 65.2 85.2 35 40.2 60.2 80.2 40 35.2 55.2 75.2 45 30.2 50.2 70.2 50 25.2 45.2 65.2

Table 2.5. Noise-limited link budget deficits for processing gain against specified target RCS and maximum detection range for Pj=90% and Pfa=10'^.

The conclusion is that for practical radar ranges of 1km to 100km, detection of ship sized targets will require between 25dB and 95dB of signal processing gain. Achievement feasibility and time required for this will next be discussed in Chapter 3.

2.3.3 : Clutter-limited Link Budget

The second limiting factor to reliable target detection is clutter, caused by the extraneous reception of echoes from ground scattering of transmitted signal. We now consider a more realistic situation where the detection performance is limited by unwanted echoes from areas surrounding a target rather than by receiver noise power. In this section, a simple model of clutter is formulated, from which the clutter-limited link budget is derived. The same Gaussian distribution as noise is assumed, so we can apply the same detection criterion as in section 2.3.2.2. In section 2.3.3.1, we note that clutter is distributive, i.e., it is received from all locations because receivers ultimately have non-zero response to all azimuths and time- delays. Azimuth response is determined by antenna radiation pattern, time-delay response is determined by pulse compression. That subject is dealt with in detail in Chapter 3, but in section 2.3.3.2 a simple model of pulse compression output is developed in the first instance to relate clutter levels to a) mainlobe width, and b) mean sidelobe level. In section 2.3.3.3, clutter cell areas are computed from the boundaries of these models to find clutter RCS and hence signal levels as a function of azimuth and time-delay searched by the receiver. Finally, in section 2.3.3.4, we relate all this back to the clutter-limiting criterion above, and conclude what clutter-limited constraints exist on mainlobe width, sidelobe level, and searchable azimuths and time-delays.

2.3.3.1 : Receiver Response to Clutter Echoes

Total clutter power received by the echo antenna is the integral of all unwanted echo signals from all areas weighted by the response functions of the receiver in azimuth and in time- delay. Azimuth response function is determined by the echo antenna radiation pattern while time-delay response function is determined by pulse compression of echoes.

CfiapterZ TrincipCes oftfie (Bistatic d^adar Azimuth response Time delay response Iso-azimuth (beam) contours Target ^ ■«»- Sidelobe clutter Target cell Iso-range (time delay) — contours Mainlobe clutter Rx

Figure 2.5. Origin and detection of clutter by a bistatic radar receiver.

Figure 2.5 illustrates the reception of clutter signals from echoes originating at all receiver

search locations {r,a). Suppose maximum time-delay and azimuth receiver responses occur

at To and respectively, then each response function to clutter at (t,« ) may be written;

= [2.10]

and Gtd(T) = GpGcp(T-To) [2.11]

We use the bistatic radar equation (Eq. 2.2) to calculate partial received clutter power:

^Tx ^p2 Gaz(CX) Gtd(T) X f dCdutter

[2 . 12]

4;r/?R,(T)-

2.3.3.2 : Azimuth and Time-delay Response Models

Here we use known characteristics of azimuth and time-delay properties to construct step functions to model receiver responses. Clutter cell areas (Appendix 2) are calculated to allow one to convert integration of Eq. 2.12 into a summation by defining cells by the step function boundaries in azimuth and time-delay (radial range).

CfiapterZ (Brincipfes of the ‘Bistatic ‘Bg.dar

Azimuth Response M odel

Though the dish ARPs are uncharacterised, typical properties may be anticipated from first principles. Each DBS TV receiver antenna is a 0.6m satellite dish designed to receive TV signals on carriers from 10.75GHz to 12.50GHz, hence the mainlobe width and gain adequately isolates these signals from other satellites 5° adjacent. Parabolic dishes with a weighted feed horn illumination typically have sidelobe levels of -15dBi. It is important to have a small backlobe level on the echo antenna for two reasons: a) to suppress direct reference signal leakage, and b) to shield the echo signal from strong clutter signals originating from the baseline area. In Chapter 4, discussion of the echo antenna installation on the opposite side of a building from the transmitter of opportunity allows one to reasonably disregard the backlobe level. It is therefore assumed that backlobe level is the same as the mean sidelobe level. Hence, we model the ARP by a simple step function model (Figure 2.6a) constructed on three fixed quantities:

• beamwidth, approximately 5°;

• boresight gain, Gr^, approximately 37.5dBi, and;

• peak sidelobe level of a parabolic dish, typically -ISdBi.

Time-delay Response Model

In section 2.2.2.2, the typical DBS TV channel bandwidth was stated to be approximately lOMHz, which with suitable pulse compression leads to typical timing resolutions down to 50ns. However, assuming no Doppler variation in the first instance, echo and clutter powers increase by the same processing gain under pulse compression, so we leave those as unquantified variables. Thus Gtd (Figure 2.6b) is constructed on:

• time-delay resolution, approximately MIB - 50ns, for 5=10M Hz;

• signal processing gain (unspecified SNR, not SCR), G^\

• mean sidelobe level (unspecified), Gtd,si-

Ga +37.5dBi \/ -15.0dBiA 5-0° Mainlobe Mean sidelobe / level

Z

Figure 2.6a. Receiver azimuth response model. Figure 2.6b. Receiver time-delay response model.