Adaptive digital beamforming with MMSE technique for polarimetric 2-D phased array weather radar

We have been developing a polarimetric phased array weather radar, which has a dual-polarized antenna with two-dimensional circular planar phase-array elements. It is capable of measuring the 3-D rainfall distribution in less than 10 or 30 seconds in a range of 20 or 60 km, respectively. The radar system use a fan beam, which is main beam having a narrow beam width in azimuth angle and a wider beam width in the elevation angle, as a transmitted waves for rapid scanning observation. A mechanical rotation and an electronic scanning are used in azimuth and elevation angles, respectively. The method of the electronic scanning is termed as a digital beam forming (DBF) method. The DBF method is one of the components to determine an observation accuracy. This paper is focused on a DBF method for the under development radar. DBF is a signal processing method that makes a directional beam pattern. We proposed to apply minimum mean square error (MMSE) method. The precipitation radar signal simulations are carried out to evaluate the effect on the MMSE and to discuss an accuracy of observations. The planar phased array antenna is based on 6992 array elements that are placed in a circular shape. The interval of each element is 16 mm. Operating frequency of the radar is 9.4 GHz. Because the system is under development, the configurations and variables may be changed or optimized in the future. The analysis range for DBF is from -15 to 15° every 1° in both the azimuth and elevation angles, which means the range in the frontal direction of the aperture plane of the antenna. Each antenna element is assumed to be omnidirectional. The fan beam will be used as a transmitted beam pattern. However, we are not considering the transmitted beam pattern, because the transmitted beam pattern has no effect on the result of DBFs. The distributed target consists of precipitation assumed to have a Gaussian distribution. The values of polarimetric variables for the distributed targets are theoretically calculated to be the true values. We compared estimation results with MMSE to those with the conventional DBF method such as Fourier beam forming (FR), to evaluate the effect on DBF. From the results, the mean bias errors of radar reflectivity factor with FR and MMSE were 5.23 dB and 1.34 dB, respectively. In differential reflectivity, the MMSE results also indicate excellent accuracies. The correlation coefficient and the standard deviation of differential reflectivity with MMSE were 0.99 and 0.06 dB, respectively. In specific differential phase with FR and MMSE, the correlation coefficients were 0.73 and 0.96, respectively. In copolar correlation coefficient with FR and MMSE, the correlation coefficients were 0.96 and 0.14, respectively. MMSE's performance was superior to DBF when comparing all polarimetric variables. For actual use, FR with a tapered beam-forming function for side-lobe reduction is used and accuracy is expected to improve. However, it is difficult to estimate the polarimetric variables, especially ofthe copolar correlation coefficient with FR, using low pulse numbers (at least 64). On the other hand, MMSE with 64 pulses has good results for all variables. According to the operation of this radar, it requires a better understanding about the useful pulse numbers. When the antenna is rotary type, several tens of pulses (e.g. 32) are required for rapidly scanning. When the antenna is a fixed mount type, it is capable of using a large number of pulses (e.g. 128). A similar simulation was carried out with a differential number of pulses (i.e. 32 and 128) to consider design and operation of the radar for practical use. The results indicate that the number of pulses is almost independent of the estimated accuracies of MMSE. Considering design and operation of the radar for practical use, it is useful to be independent from the number of pulses with MMSE.