Conventional scanning radars must rotate at a rate slow enough to allow a number of pulses (typically 20-50 for weather observations) to be transmitted to approximately the same pointing angle. However, since the antenna is continuously rotating, each pulse is actually transmitted to a slightly different direction. Nevertheless, significant overlap in the illuminated volumes (occurring due to finite beamwidth effects) allows the use of these numerous pulses to estimate the reflectivity, radial velocity, and Doppler spectrum width signal moments with estimation errors below the desired thresholds. For WSR-88D radars, these thresholds are typically set to 1 dB1 and 1 m/s for reflectivity and radial velocity, respectively.
Due to the overlap of the resolution volumes and the time required for decorrelation of echoes from atmospheric targets to occur, the echoes from successive pulses are not independent. (In fact, signals with some correlation are required to make Doppler measurements.) To achieve the desired estimation error for reflectivity, the number of pulses required for conventional radar processing is therefore larger than what would be needed if the successive echoes were independent. Time essentially wasted while waiting to acquire the needed independent data could be employed to acquire data from other beam directions by taking advantage of the fast beam steering capability of phased array radars.
Beam Multiplexing (BMX) was recently developed for this purpose (Yu et al., 2007). As illustrated in Figure 4.1b, the general idea is to transmit a small number of pulses (typically two) needed for Doppler measurements in one direction, and then steer the beam to a set of spatially diverse pointing angles. After the atmosphere effects (turbulence, shear) have led to decorrelation of the signal, the beam is directed back to the original pointing angle. Thus, numerous pairs of pulses are gathered from each pointing direction and the moment estimation is then performed. Given the independence of these pulse pairs, the estimation scheme will have significantly lower errors for the same total number of pulses, especially for cases with high signal-to-noise ratio (SNR) and small spectrum widths. As a result, it is possible to either produce moment estimates with lower errors or have a more rapid update with consistent errors.
Figure 4.2 provides examples from the work of Yu et al. (2007). The upper two panels show the reflectivity and radial velocity fields from BMX while the corresponding conventional scanning results are provided in the lower panels. The scan times here are essentially the same for the two different techniques, and the qualitative improvement in the fields is remarkable. A quantitative analysis has shown a 2-4 times possible improvement in scan time (Yu et al., 2007), with a dependence on SNR and other signal characteristics.