Principles of Modern Radar - Volume 2 1891121537

17.4 Signal Processing Techniques for Reference Signal Cleaning and Reconstruction 767basic processing techniques were introduced with the assumption that no multipath ispresent, it is easy to imagine that the presence of multipath in the reference signal wouldyield significant performance degradation. For this reason, different techniques have beenproposed to remove such undesired contributions from the reference signal. Obviously,these techniques are waveform dependent and might be based on previous literature forboth analog and digital transmissions on channel equalization [37]. Some examples areconsidered in the following for specific modulation types, among the ones more oftenexploited for passive radar systems, with the aim of illustrating the problem and offeringsome useful hints to the design of proper algorithms for reference signal cleaning in PBR.17.4.1 Constant Modulus Algorithm for Reference Signal CleaningUsing Analog ModulationTo investigate the performance degradation of a PBR exploiting a reference signal affectedby multipath, the following model is adopted for complex envelope of the signal collectedat the reference antenna:s ref (t) = A ref d(t) +N M∑m=1A m d(t − τ m ) + n ref (t) 0 ≤ t < T 0 (17.19)where we assume that N M multipath replicas affect the reference signal. In equation(17.19), A ref is the complex amplitude of the direct signal, A m and τ m are the complexamplitude and the delay (with respect to the direct signal) of the m-th multipath replica,respectively, and n ref (t) is the thermal noise contribution. Since the direct signal is receivedby the main lobe of the reference antenna, it is assumed that target and clutter echoes(received from the sidelobes) are negligible.We now consider a simulated PBR study case where an FM radio broadcast transmissionwith bandwidth of 150 kHz is exploited. The received signals are sampled atfrequency f s = 180 kHz. The signal at the surveillance channel consists of direct signalwith a direct signal-to-noise ratio (DNR) of about 61 dB, N S = 13 clutter spikes withclutter-to-noise ratio in the range 40–60 dB and delays of 0.028–0.233 msec, and N T =7 target echoes with different radar cross sections. The direct signal contribution at thereference channel shows a DNR of about 76 dB; different multipath conditions are nowconsidered.Figure 17-12a shows the 2D-CCF obtained for the considered study case after applyingthe ECA operating with K = 45 taps in the absence of multipath in the reference signal.The direct signal and the clutter spikes in the surveillance signal have been correctlyremoved; the obtained clutter attenuation (CA) (i.e., the signal power decrease betweenthe input and the output of the filter) is 54.2 dB. Consequently, all the injected targets areclearly visible as peaks in the 2D-CCF (surrounded by white circles).When the reference signal is affected by multipath, it is likely that the cancellationcapability of the ECA is seriously limited, thus also diminishing its effectiveness fordetecting weak targets, whose level is below the clutter sidelobes. This is demonstrated inFigure 17-12b, where a single multipath replica (N M = 1) is present in the reference signalwith direct signal-to-multipath ratio (DMR) = 5 dB, delay τ 1 = 9/f s , and phase shift φ 1 ≠ A ref − ̸ A 1 = 200 ◦ between direct signal and multipath echo. A strong peak is presentin the 2D-CCF adjacent to the cancellation area, whereas its sidelobes completely masksome targets (discontinuous circles indicate missed detections). The undesired strong peak