Design and Implementation of Digital Correlator for CAS Synthetic Aperture Radiometer

We present a new method of digital correlation, which uses the technology of direct intermediate frequency or radio frequency sampling and digital phase shift. Digital correlators down-sample IF or RF signals with 3-bit analog-to-digital converters and then delay one sampling interval for quadrature phase shift. Following the same procedure as analog correlation, the digitalized I/Q pairs are processed in a FPGA chip. Analysis and simulations show that sample delay introduces linear phase offset which is proportional to the deviated frequency from the center of digital IF. Derived equation proves that linear phase offset can be compensated simply by a SINC function. Flight tests conducted in April 2004 achieved image as we expected. Introduction Digital radiometry was first proposed by Weinreb in 1961 for use in autocorrelation spectrometers for radio astronomy [1]. Three other applications have arisen since that time: interferometry, polarimetry, and totalpower radiometry (e.g., [2–4]). With the advances of the last 30 years, digital logic has become faster, denser, lower power, and less expensive. The applications of digital radiometry have progressed with these advances from the autocorrelation spectrometers of few megahertz bandwidth (B) to the multigigabit-per-second digital correlators used in microwave polarimetry[5] and interferometry[6]. In addition to the advances in digital logic, improvements in mixed-signal technologies have enabled the use of ultra-fast ADCs for direct sampling of microwave signals. Performance analysis of digital correlator by Ruf[7], Fischman[8] and Piepmeier[9] proves that digital correlator offers compelling advantages for spaceborne microwave radiometry. Several ASIC’s are developed specially for synthetic aperture radiometer(STAR), one of 14 channels by the University of New Mexico Microelectronics Research Center[10]. ASIC spends less power consumption and faster process speed but more expensive. Much more groups build their digital correlator on FPGA for airborne prototype with less financial venture [11]. The microwave receiver in front of digital correlator can be a superheterodyne [3] or an LNA and band-pass filter as in the case of a direct sampling digital radiometer[4]. We present a new digital correlator based on FPGA designed and implemented for CAS synthetic aperture radiometer[12,13]. Sample Delay based Digital Correlation is implemented in this system. Fig.2 shows the basic diagram of SDDC. We expect to demonstrate basic principles of SDDC. Direct IF Sampling and Sample Delay(SDDC) For a specific IF and B, we can simply make the phase shift with digital sample delay instead of quadrature demodulator or analog/digital phase shifter in RF or IF. Under-sampled IF signal is digitalized and its spectrum is down-converted to a lower digital intermediate frequency (DIF), the DIF is determined by both the IF center frequencyfc and the sampling ratefs. If relation between fc, fs and fDIF is as following, { fs = 4fDIF fDIF = mfc − nfs (1) There are four samples for every period offDIF . For the center frequency of DIF, the interval between subsequent samples is π/2, therefore digitalized samples and their one sample delayed version keep a quadrature phase. This is a simple method for digital phase shift to achieve in-phase (I) and quadrature (Q) outputs from each receiver. However, when signal spectrum deviated from center of DIF, there is a linear phase offset φ(ω) proportional to the frequency offset ω from the center of DIF ω0. Both correlation coefficient and phase errors will be introduced by this linear phase offset[14]. In case of the analog signals with linear phase offset, the correlated elements are Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 521 s1 = cos [(ω − ω0)t+ φ1] + j sin [(ω − ω0)t+ φ1 + φ(ω)] s2 = cos [(ω − ω0)t+ φ2] + j sin [(ω − ω0)t+ φ2 + φ(ω)] (2) where φ(ω) = ωπ 2ω0 . The visibility function from a sample delay correlator is