Error estimate of quadrature sampling system via discrete Hilbert transform

Abstract

Pulse Doppler radar needs accurate measurement of the quadrature sampling system error for error correction to reduce false alarm rate and improve the clutter suppressing performance and the improvement factor. This paper firstly introduces the discrete Hilbert transform to estimate the relative amplitude error and phase error of quadrature sampling system using coherent testing signa1. The error function with respect to each sample is derived theoretically. Computer simulation shows that the theoretical results are effective and accurate. The results can be used to evaluate and correct the errors in the quadrature sampling system to contribute to suppress the background moving clutter and reduce false alarm rate for the pulse Doppler radar.Keywords-relative amplitude error; phase error; error estimate; quadrature sampling system; discrete Hilbert transform I. 0BINTRODUCTION Quadrature sampling system is responsible for converting intermediate frequency (IF) signals into two orthogonal zero-IF digital signals, i.e., inphase and quadrature (I/Q) channel signals. Ideally, the amplitude of I/Q Channels should be equal, and the phase difference between I/Q channels should be 90 0 , and the DC offset should be zero. Unfortunately, perfect balance of amplitude as well as phase of I/Q Channels is nonexistent in an actual system. In an analog coherent quadrature sampling system, due to environmental changes and device aging, the phase error can reach up to 1 0~50 , and the relative amplitude error can reach up to 0.1dB ~ 1dB. The resulting relative mirror image is between -20dB ~-30dB [1]. The existence of the mirror image level will directly restrict the improvement factor, increase the false alarm rate and reduce the clutter suppressing performance of pulse Doppler radar. The system error of the digital coherent quadrature sampling system is relatively small; nevertheless, it still needs accurate measurement of the system error for error correction and increasing the improvement factor. Therefore, it is of concern to calculate the amplitude error and phase error for both analog and digital coherent quadrature sampling system.Computation method for computing the mirror image level, the relative gain error and phase error, and the effective number of bits (ENOB) and the signal to noise ratio (SNR) of A/D converter (ADC) are, respectively, given in [1][2][3]. The method presented in [1] gives an estimation of the relative amplitude error and the phase error for N samples. In this paper, we present a novel method utilizing the discrete Hilbert transform for estimating the relative amplitude error and the phase error, which will give estimation per sample. II. 1BDISCRETE HILBERT TRANSFORMIn the continuous case, the Hilbert transform of a real signal ( )x t is defined aswhere ˆ( ) x t is the Hilbert transform. The Fourier transform of the Hilbert transform is given by [5] where 1 for >0 ( ) 0 for 0 1 for <0 sgn and ( ) X is the Fourier transform of ( ) x t . We associate ( )x t with a complex signal ( ) c x t , defined as...