Principles of Modern Radar - Volume 2 1891121537

2.7 Mismatched Filters 79200dB−20−40Matched Filter ISRMatched Filter PSRMismatched Filter ISRMismatched Filter PSR−60−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5FIGURE 2-41 A small fractional Doppler shift has a dramatic impact on MMF performance.The plot shows the degraded performance of the optimized 48-element code and a250-element MISR filter as a function of the number of cycles of Doppler shift across a pulse.f d τwhere W is a diagonal weighting matrix whose elements are the weights assigned to eachsidelobe⎡⎤w 1 0 0 ··· 00 w 2 0 ··· 0W =. 0 0 .. 0 0(2.157)⎢⎥⎣.. . w K +M−2 0 ⎦0 0 0 0 w K +M−1and w>0.For a given code and filter length, the weighted LS (WLS) solution does not achievean ISR lower than the MLS solution, but the sidelobe energy is distributed in a desiredmanner. Consider an application where near-in sidelobes (i.e., those closest to the mainlobe) are more detrimental than distant sidelobes. To create a response with low near-insidelobes, W is defined with the larger weights assigned to the near-in sidelobes. The filterwill suppress the near-in sidelobes at the expense of higher sidelobes elsewhere. A filterused to create this type of response is termed a null-region filter.Figure 2-42 contains the compressed responses for a 130-element null-region filterand an MISR filter both derived for a 64-element MPS code [49]. The code is provided inTable 2-4. For the null-region filter, the 40 sidelobes on either side of the main lobe areassigned a weight of 10, and the remaining sidelobes are assigned a weight of 1. The filtersuppresses the near-in sidelobes to a peak value of approximately –70 dB. The remainingsidelobes approach the levels achieved with the MISR filter. For the null-region filter, ISRand PSR increase by 2.2 dB and 4.6 dB, respectively, and the LPG increases by 0.63 dB.By adjusting the weights assigned to the near-in sidelobes, it is possible to find a balancebetween the suppression achieved in the null region and other performance metrics.2.7.3.5 Reduced Peak Sidelobe FiltersMismatched filters may also be designed to reduce the PSR to a desired level. Such afilter may be obtained using linear programming [32] or through an iterative process [34]