Principles of Modern Radar - Volume 2 1891121537

17.4 Signal Processing Techniques for Reference Signal Cleaning and Reconstruction 769Thus, proper techniques should be applied to remove the multipath contribution onthe reference signal, yielding a pure signal to be used for disturbance cancellation andcross-correlation with the surveillance signal.Specifically, assuming that the PBR is based on FM radio broadcast transmissions,the well-known constant modulus algorithm (CMA) [38, 39] can be exploited to obtain ablind adaptive equalization of the reference signal. This kind of approach is not limitedto our study case, based on FM radio broadcast, but also applies to many of the signalsof opportunity available from both analog and digital broadcast transmission systems.Applying CMA to PBR is considered in [40] for an FM-based PBR and in [13] for a GSMbasedPBR, where only a basic temporal version of the algorithm is applied. References[41, 42] consider the possibility of using a small antenna array for the reception of thereference signal from the transmitter of opportunity, and two additional versions of thealgorithm are used for PBR application along the line suggested in [43–46]: the space-CMA (S-CMA) that operates on the signal samples collected at the different elements ofthe array; and the space-time-CMA (ST-CMA) that operates on the delayed samples ofthe signals collected at the multiple channels.The CMA tries to suppress the additive interference at the input signal by constrainingits output to be a constant modulus signal, accomplished by minimizing the cost functionJ = 1 4 E{[∣ ∣y[n] ∣ ∣ 2 − 1 ]2} (17.20)where E{·} is the statistical expectation, and y[n] is the CMA output at the n-th timeinstant. For the ST-CMA it is given byy[n] =M−1∑m=0 l=0∑L−1w m,l [n] s ref,m [n − l] (17.21)where w m,l [n]isthel-th adaptive weight to be applied on the m-th channel at the n-th timeinstant, and s ref ,m [n] is the reference signal at the m-th channel at the n-th time instant(m = 0,...,M − 1; l = 0,...,L − 1). The corresponding processing scheme is depictedin Figure 17-14. The filter weights to be applied are adaptively updated according to thefollowing strategy:wherew m,l [n + 1] = w m,l [n] − με[n]sref,m ∗ [n − l] (17.22)ε[n] = { |y[n]| 2 − 1 } · y[n] (17.23)and μ is the step-size parameter that determines the rate of convergence and the accuracyof the algorithm. Obviously, using a single-antenna element (M = 1), we come backto the original time-only CMA (T-CMA) that operates as a FIR filter with L taps inthe temporal dimension. The corresponding filter tries to invert the estimated transferfunction of the propagation channel. Using a single tap for each antenna element (L = 1)a space-only version of the algorithm is obtained (S-CMA) that tries to estimate thedirection of arrival (DOA) of the multipath replicas because of the spatial discriminationcapability given by the receiving array. The filter modifies the quiescent antenna patternby synthesizing an equivalent pattern in which zeros are set at given angles correspondingto the DOA of the multipath echoes. Finally, considering multiple antenna elements and