Principles of Modern Radar - Volume 2 1891121537

2.7 Mismatched Filters 752.6.5 SummaryQuadriphase codes achieve lower spectral sidelobes than traditional phase codes employingrectangular subpulses. The lower sidelobes reduce the potential for EMI. Quadriphasecodes are generated by applying a transformation to the biphase code and using subpulsesshaped as half-cosines. The subpulses are overlapped to create a nearly constant envelope.The peak sidelobe performance is at or near that achieved by the biphase code. At most, thepeak sidelobe increases by 1.48 dB. At the 3 dB point, the main lobe increases by a factor1.9 corresponding to a loss in range resolution. The ambiguity surface of a quadriphasecode may be quite different from that associated with the parent biphase code.2.7 MISMATCHED FILTERS2.7.1 IntroductionPhase codes exhibit a sidelobe response defined by the code sequence. MMFs may beapplied to reduce or shape the sidelobes at the expense of a slight loss in SNR. Thissection examines the design of mismatched filters applied to a phase-coded waveform totailor the sidelobes.2.7.2 Performance MetricsWhen evaluating mismatched filter performance, three metrics are often used: PSR; integratedsidelobe ratio (ISR); and loss in processing gain (LPG). PSR is defined as thesquare of the largest sidelobe divided by the square of the main lobe peak. ISR is theenergy in the sidelobes (i.e. the sum of the squares of all the sidelobes) normalized bythe square of the main lobe peak. LPG is the ratio of the square of the main lobe peakwhen employing mismatched filtering to the square of the main lobe peak when employingmatched filtering and is equivalent to the loss in SNR.2.7.3 Mismatched Filter ApproachesMMFs may be designed to minimize the ISR, to reduce the PSR, or to tailor specific regionsof the sidelobe response. The process of creating a filter is examined in the followingsections.2.7.3.1 Minimum ISR FilterThe lowest ISR known for a binary sequence is –11.49 dB, which is achieved by a13-element Barker code; for longer binary sequences, the lowest achieved ISR is approximately–8 dB [43, 44]. A mismatched filter may be applied that achieves a lower ISRand that in many cases also yields a lower PSR. The filter is derived as the least squaressolution to an overdetermined set of equations used to model a desired sidelobe response.Consider a phase code c k , where k = 0,...,K − 1, and a FIR filter with coefficientsz m where m = 0,...,M − 1 and M ≥ K . The filtered response isK∑−1y n = c k z n−k n = 0,...,(K + M − 2) (2.147)k=0