Principles of Modern Radar - Volume 2 1891121537

778 CHAPTER 17 Advanced Processing Methods for Passive Bistatic Radar SystemsTABLE 17-5PSLR for Different BWN LengthsFilter Length (L BWN )PSLR (dB)25 26.551 34101 50151 63knowledge of the 11-chip Barker code ACF:⎧∑10⎨ 0 n oddα B [n] = c[k]c[k + n] = 11 n = 0⎩k=0−1 n even(17.25)The BWN is implemented as a transversal lattice filter with impulse response h BWN [n]and total filter length L BWN . Indicating with α BWN [n] = α B [n] ∗ h BWN [n] the output of thisweighting network applied to the 11-chip Barker code ACF, the filter coefficients mightbe found by solving the following constrained optimization problem:{αBWN [0] = max|α BWN [n]| ≤ 1(17.26)To find the solution, each modulus inequality of the system in (17.26) is replaced bytwo linear inequalities, and well-known linear programming algorithms are used. To thispurpose we exploited the CVX MATLAB-based modeling system for convex optimization[50]. By properly selecting the filter length L BWN , different values of the PSLR can beachieved as reported in Table 17-5.The BWN can be applied to the CCF among the surveillance and the reference signalevaluated on a pulse basis before coherent integration over a train of consecutive pulses(see equation (17.24)). To obtain an alternative implementation, the cross-correlationcan be evaluated between the surveillance signal and a BWN prefiltered version of thereference signal. It is to be noticed that, if the filter length is assigned by the specific surveillanceapplication requirements, the optimization required for filter weights evaluation hasto be performed only once.The theoretical performance of the BWN has been analyzed in [18] against simulateddata. Here, the result of the application of the BWN with total length L BWN = 101 isreported in Figure 17-17, compared with the original ACF for a real signal registrationof duration 0.25 s. As expected, the BWN dramatically decreases the ACF sidelobes dueto the Barker code. However, the BWN is not able to obtain the theoretical PSLR of 50dB; this can be explained by observing that the original ACF shows some deviations withrespect to its theoretical version due to the AP and the receiving channel filters that reducethe actual signal bandwidth with respect to its nominal value. Nevertheless, notice thata PSLR greater than 35 dB is obtained that results in a significant increase of the usefuldynamic range.Additional Sidelobes Reduction Filter (ASRF)While the conceived BWN largely reduces the Barker sidelobes, it is ineffective againstthe periodic sidelobe structure due to the nonzero correlation among consecutive symbolsof the beacon frame. Aiming at the detection of targets at delays higher than 0.8 μs (ranges