Principles of Modern Radar - Volume 2 1891121537

132 CHAPTER 4 MIMO RadarFIGURE 4-5MIMO array factoron transmit. Thisexamplecorresponds to anarray with 10subarrays whereeach subarray has20 λ/2 spacedelements.Gain (dB)1050−5Transmit Array FactorPhased ArrayOrthogonal Waveforms−10−15−20−20 −15 −10 −5 0 5 10 15 20Azimuth (deg)Recall that θ 0 is the angle to which the beam is digitally steered and that ˜θ 0 is the directionto which the phased array steered the beam on transmit. The receiver is free to vary θ 0with digital processing, but ˜θ 0 is fixed.As should be expected, the receive gains are identical between the phased array andorthogonal waveforms, but there are two key differences between the transmit gain terms.First, since the phased array transmits a concentrated beam in the direction ˜θ 0 , it is unableto apply any digital steering of the transmit beam; the phased array has already decidedin which direction to send energy. On the other hand, the radar that employs orthogonalsignals is able to resteer the transmit beam to any angle (so long as the subarray patternpermitted energy to be radiated in that direction).However, the cost of doing this is evident. The phased array realizes a transmit beamforminggain that provides an increase in SNR by a factor of M, the number of transmittingsubarrays. This benefit is lost by the radar that uses orthogonal signals.These differences are illustrated in Figure 4-5, where the array factors of a MIMOradar employing orthogonal waveforms as well as a traditional phased array are presented.The performance of an array antenna for use in a radar system is well quantifiedby considering three gain patterns: the steered response, the beampattern, and the pointspread function. These describe the ability of the data collected by the system to be usedto digitally form beams in desired directions with desired properties.The steered response and the beampattern quantify the degree to which the antennacan be digitally steered to an angle of interest as well as the ability to reject returns fromundesired angles. Given an angle of interest, the steered response describes the abilityof the array to observe signals arriving from that direction when the array is steered tothat direction of interest, while the beampattern describes the ability of the array to rejecttargets from other angles [14]. The distinctions between these patterns are summarized inTable 4-1.Let G RX (θ; θ 0 ) be the gain of the receive array in the direction θ when it is digitallysteered to the angle θ 0 . The steered response evaluates this gain for the case when θ = θ 0 ,that is, the gain is evaluated in the direction that the array has been digitally steered. If thearray is steered to the angle θ 0 , then the beampattern evaluated at θ describes how much