Principles of Modern Radar - Volume 2 1891121537

12.3 EW-Related Formulas 547incur the same straddle and signal processing losses as the target return. It is certainlyimportant to keep track of these different losses in actual practice; however, for the sakeof simplicity, we will omit the radar loss terms for the target and jammer in the followingdiscussions.12.3.3 Noise Jammer FormulasThe in-band power of a noise jammer is derived in a manner similar to the signal power inthe radar range equation. In deriving general expressions, we must bear in mind that thejammer is not necessarily co-located with the target, an example being an SOJ. Thus, wemust explicitly distinguish the range to the target from the range to the jammer and theantenna pattern gains toward the target from those toward the jammer. With that in mind,the noise jamming power is given byJ = ( P j G j,tx) ( 14π R 2 j)(λ 2 G rj4π) ( BB j)d j= P j G j,tx λ 2 G r, j Bd j(4π) 2 R 2 j B j(12.7)The parenthesized terms in the top line of the above equation are, from left to right, thejammer effective radiate power (ERP) at the radar polarization (transmit power (P j ) timesantenna gain including losses (G j,tx )); the spherical spreading of the jamming signal atthe radar antenna at range R j ; the capture area of the radar antenna whose receive gaintoward the jammer is G rj ; the fraction of jamming noise spectrum (B j ) that is within theradar waveform bandwidth (B); and the jammer transmit duty factor, d j , which convertspeak power to average power if the jammer is not on continuously. The jammer transmitantenna gain, G j,tx , is the effective antenna gain at the receive polarization of the radarantenna. The duty factor is especially important for fast-blinking noise waveforms butalso accounts for transmitter off-times employed by a transponder during look-throughintervals. The jammer noise bandwidth term, B j , is defined to be greater than or equal to theradar waveform bandwidth, as the noncoherent jammer signal is ultimately decorrelatedby the radar matched filter regardless of its bandwidth.The JNR for a noise jammer is obtained by dividing Equation 12.7 by the noise power,kTFB:JNR = P j G j,tx λ 2 G rj d j(4π) 2 R 2 j B jkTF(12.8)The JNR gives insight into the degradation in radar sensitivity caused by the noise jammer.When the jammer power is comparable to the thermal noise power, a more accuraterepresentation of the relative degradation is the ratio is (J + N)/N.The JSR for a noise jammer is obtained by dividing Equation 12.7 by Equation 12.3(where we ignore the loss term, L s , as per the discussion in Section 12.3.2):JSR = P j G j,tx G rj d j 4π R 4R 2 j B j P t G t G r σ nτ(12.9)Inspection of Equation 12.9 immediately suggests several radar design parameters thatpotentially affect the radar’s vulnerability to noise jamming: ERP, receive antenna gain