Principles of Modern Radar - Volume 2 1891121537

9.2 Digital Beamforming Fundamentals 405element-level DBF on transmit any necessary phase shifts or time delays can be performedin the distributed WFGs.The DBF architecture enables the use of a number of array signal processing techniquesthat can enhance the capability of a radar, including the following:1. Digital resteering of beams on receive for improved search occupancy2. Adaptive cancellation for jammer and electromagnetic interference (EMI) mitigation3. High-resolution angle estimation of both targets and jammers for improved metricaccuracyIn addition, wideband DBF array designs can potentially replace costly analog time-delayunits, which are typically a significant source of error, with effectively infinite precisiondigital time delay. A DBF array is also more robust to receiver failures because only theportion of the array feeding that receiver is lost as opposed to an entire sum or monopulsedifference beam in a conventional analog array.If there is a receiver at every element as shown in Figure 9-1, then any amplitudeweighting used to control sidelobes and any phase weighting (or time delay for wideband)used to steer beams can be performed in the digital computer. Amplitude weights, phaseweights, and time delays can be applied digitally with less error than can be achieved withanalog components while greatly simplifying the front-end analog hardware.The fundamental operation of the DBF processor is to weight and sum the I/Q samplesfrom the spatial channels to produce beams. If the complex amplitude and phase weightingfor the k-th element, x k ,isgivenbythen the beam output, y, is given bywherey =w k = a k e jϕ k(9.1)M∑wk ∗ x k = w H x (9.2)k=1⎡ ⎤w 1w 2w = ⎢ ⎥⎣ . ⎦ , andw M⎡ ⎤x 1x = x 2⎢ ⎥⎣ . ⎦x M(9.3)In addition to performing the weight and sum beamforming, the beamforming processormay also perform other functions such as equalization of the receiver channels and timedelaysteering for wideband operation (see Figure 9-2). The receiver channel equalizationis necessary to match their frequency responses over the bandwidth as closely as possibleto enable good jammer cancellation.Time-delay steering is necessary to prevent the beam from squinting in angle as afunction of frequency during wideband operation. In a digital system, the simplest wayto delay signals would be to shift the digitized data by multiples of the sampling period.Unfortunately for typical ADC sampling rates and radar operating frequencies, sampleshifting does not provide enough granularity for time-delay steering a phased array. Forexample, ADC sampling rates from 10 to 100 MHz result in sampling period of 100 to1 nsec. If the time delay needs to be done only at a subarray level, then the time delay can