New approach to equalizing antenna elements: analysis and performance evaluation

The antenna face of a phased array radar typically consists of several hundred of antenna elements, and they degrade independently. This poses a challenging problem to radar target detection, discrimination, and classification, which rely on adaptive beamforming and assume that the channels are matched to each other. In this research, a channel equalization algorithm is developed compensating for the mismatch between the reference and testing channels using the least-squares error (LSE) criterion. The equalized output is precisely the projection of the reference channel data onto the columns of the equalization matrix, which is solely a function of the testing channel output. Through the analysis of the equalization matrix, the performance metrics including the squares error, instantaneous correlation coefficient, and cancellation ratio (CR) of the proposed equalizer are expressed in closed forms. The analysis also allows us to postulate on the effect of system parameters including: window size, equalizer length, and input signal-to-noise ratio (SNR) on the performance metrics. Extensive Monte Carlo simulations show that higher values of the equalizer length, input SNR, or window size improves the CR; however, once a system parameter approaches a certain threshold, further incrementing the size of these parameters has a diminishing return on system performance. Simulations also reveal that an equalizer with good CR or correlation coefficient results into the equalized testing channel output being almost a replica of the reference channel's output. Correspondingly, degradation in the CR or correlation coefficient affects the equalized testing channel output. The simulation results agree closely with known theoretical analyses. The research in this paper demonstrates the importance of channel equalization and system parameter selection in obtaining a satisfactory antenna elements/subarrays output.