Principles of Modern Radar - Volume 2 1891121537

550 CHAPTER 12 Electronic ProtectionThis resembles Equation 12.7 for the noise jammer except for the last parenthesized terms,which reflect the fact that the jammer is coherent and can recover some or all of the radarcoherent processing gain, nτ B. The duty factor term for the coherent jammer, d j , is notthe actual transmit duty factor but rather the fraction of the radar pulse train that is repeatedback to the radar. Thus if the jammer responds only on alternate pulses, d j = 0.5. Theterm n j in the denominator is the number of range or Doppler cells across which thejammer simultaneously spreads its power. For example, if the jammer puts all of its powerinto one false target occupying a single range-Doppler cell, then n j = 1. If the jammerspreads its power over 10 Doppler filters in a single range cell using DN, then n j = 10.If the jammer spreads its energy over five range cells all within the uncompressed pulsewidth of a pulse compression waveform, then n j = 5. If the latter two conditions arecombined, then n j = 10 × 5 = 50. Note that if the range spacing of the jammer returnsexceeds the radar pulse width, the jammer incurs no penalty in power, as the returns donot simultaneously compete with each other for the HPA’s available power.The formula for a linear repeater is similar, but we must first begin at the radartransmission because the output power of the jammer is proportional to the input power.We can think of the constant-gain repeater as having some internal, electronic smallsignalgain, g j,el , between its receive antenna port and its transmit antenna port, and somemaximum available peak power, P j , in its HPA. As the received signal increases, the outputof the transmitter increases by the small-signal gain g j,el , until eventually the amplifiedsignal reaches the peak output power of the HPA. As the received signal increases beyondthis point, the HPA operates in compression, and the jammer reverts to the constant powerrepeater. The linear repeater jammer level in the constant-gain region, J LIN , is (invokingthe link equation approach)⌊(Pt ) ( ) ⌋λ 2 ( ) λ 2 ( ) d jJ LIN = G tj G j,rx g j,el G j,tx G rj (nτ B)4π Rj4π R j n j= P t G tj G rj λ 4 G j,rx g j,el G j,tx nτ Bd j(4π) 4 R 4 j n j(12.12)The power received by the jammer at its receive antenna port corresponds to thebracketed set of terms in the top line of the equation that begins with the radar transmitpower, P t , and ends with the term G j,rx —the effective jammer receive antenna gain,including losses, at the radar transmit polarization. When we then include the electronicgain g j,el with the bracketed terms, the result is the output power of the jammer transmitter.From there on, the equation is the same as for the constant-power repeater. The jammerpower from a linear repeater is actually the lesser of either J SAT or J LIN in Equations 12.11and 12.12, respectively, as the jammer output power is ultimately limited by the maximumpower available through its HPA.The expressions for JNR for the two repeater modes are obtained by dividing J SATand J LIN by kTFB. The JNR for the coherent jammers has a similar connotation to that ofa noise jammer when DN is used, but for false target techniques the JNR is an indicationof whether the jammer false target is strong enough to be detected by the radar.The expressions for JSR for the two repeater modes are obtained by dividing J SATand J LIN by the target signal, S, of Equation 12.6 (ignoring the loss term, L s , as per