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**MIMO radar: snake oil or good idea?**

Fred Daum 27 March 2012 Copyright © 2011 Raytheon Company. All rights reserved. Customer Success Is Our Mission is a trademark of Raytheon Company.

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**MIMO* radar vs. phased array radar (SIMO)**

item MIMO radar phased array radar 1. waveforms N orthogonal waveforms transmitted simultaneously from N distinct parts of the antenna one waveform transmitted from the radar (coherently) 2. transmit antenna pattern (array factor) omni directional (except for element pattern or subarray pattern) pencil beam: θ ≈ λ/D 3. transmit antenna gain (array factor) G/N G 4. SNR cT*/N cT 5. time on target (T or T*) full transmit duty cycle (limited by coherence of target & propagation) limited by pencil beam 6. useful range-Doppler space (normalized area) 1/N 1 7. number of degrees of freedom for adaptive nulling NM M *MIMO = multiple input multiple output

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**MIMO Radar – Virtual Array**

ej2p(ft-x/l) ej2p(ft-x/l) q f2(t) q dR dT=NdR … MF MF f1(t) f0(t) … Transmitter: M antenna elements Receiver: N antenna elements q Virtual array: NM elements

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***good cost models for MIMO & SIMO are crucial**

RADAR PERFORMANCE MIMO better than boring old phased array (equal cost, apples & apples comparison)* REFERENCES search (thermal noise only) no (increased angle coverage is cancelled by loss of transmit antenna gain) Friedlander (2009) Chernyak (2008) Rabideau (2011) track (thermal noise only) no (no improvement in SNR & MIMO does not exploit knowledge of target to steer transmit beam) but TWS maybe Vaidyanathan (2010) Li, Stoica & Daum (2010) barrage jamming no (non-responsive jammer doesn’t see waveform diversity) Rabideau (2004) Greenspan (2009) DRFM mainbeam & sidelobe jamming or other responsive jamming (fast set on) passive ranging with network of radars works (but simple multi-static competes well with MIMO also) mitigation of spread Doppler clutter for OTH radar (like ROTHR using TWS) good idea sometimes (SNR loss maybe too high & simple spatial diversity competes well with MIMO) Frazer (2008) Krolik (2004) improved angle measurement accuracy (one-sigma error due to front end noise) factor of √2 to roughly factor of 10 improvement sometimes Tabrikian (2008) adaptive suppression of sidelobes & grating lobes for sparse array MN degrees of freedom vs. only M degrees of freedom helps Chen’s CalTech thesis (2009) relaxed requirement on instantaneous dynamic range against clutter MIMO improves CNR for certain clutter & certain radars & some targets suppression of sea clutter or ground clutter depends on the radar & clutter (GMTI often good but long range fast targets bad) Rabideau (2008) Bliss et al. (2009) Abramovitz & Fraser (2009) face combining for SPY-1, SPY-3, PAVE PAWS, BMEWS, UEWR, AMDR 3 dB to 9 dB better SNR at large scan angles this is multi-static radar not real time MIMO radar (Zatman 2008) multiple radar combining 3 dB to 9 dB better SNR for two radars & more for N radars Coutts, Cuomo, McHarg, Robey, Weikle (2007); but not real time MIMO *good cost models for MIMO & SIMO are crucial

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**MIMO PHASED ARRAY HF OTH radar* (Krolik 2008) target spread Doppler**

clutter MIMO target *issues of sample covariance matrix estimation, SNR loss, competition from non-MIMO spatial diversity, lack of orthogonal waveforms in the real World, loss of useful range-Doppler space, etc.

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**MIMO nulls spread Doppler clutter with adaptive transmit pattern**

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**GMTI is often a good niche* application of MIMO radar**

short range long range fast speed targets loss of useful range-Doppler space too much loss of SNR too much & loss of useful range-Doppler space too much slow speed targets GMTI loss of SNR too much *terminology due to Dan Bliss (11 February 2009) at Orlando airport

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**Bliss, et al., “GMTI MIMO radar,” IEEE Waveform diversity Conference, Orlando, Feb. 2009.**

(1) coherent integration time is 5 times longer for MIMO than boring old phased array. (2) surveillance mode. (3) MIMO uses 5 element sparse transmit array, whereas PA uses smaller filled transmit array. (4) both MIMO & PA use 5 element filled receive array. (5) total transmit power is the same for MIMO & PA. (6) frequency = 2 GHz. (7) simulation of textbook clutter (spatially homogeneous)

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**Bliss, et al., “GMTI MIMO radar,” IEEE Waveform diversity Conference, Orlando, Feb. 2009.**

(1) coherent integration time is 5 times longer for MIMO than boring old phased array. (2) surveillance mode. (3) MIMO uses 5 element sparse transmit array, whereas PA uses filled transmit array. (4) both MIMO & PA use 5 element filled receive array. (5) total transmit power is the same for MIMO & PA. (6) theoretical error bound for textbook clutter (spatially homogeneous)

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QUIZ: (1) Why can’t the boring old phased array radar use a pulse-Doppler waveform to get the same 5 times longer coherent integration time as the MIMO radar? (2) Why is the sparse transmit array for the MIMO radar 5 times larger than the transmit array for the boring old phased array radar? (3) Why not compare performance & cost of the MIMO & boring old phased array radar (with 5x larger sparse transmit array or 5x larger filled transmit array) directly? (4) Why not make the receive array 5 times larger, rather than the transmit array? (5) Why not use X-Band or higher frequency rather than L-Band to get much better Doppler resolution & accuracy?

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**signal processing design**

MIMO radar* requires much tighter coupling between design specialties than boring old phased array radars antenna design signal processing design system engineering software design system testing waveform design *also intimidating & complex & risky & 95% snake oil

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**apples & apples analysis!**

Correct apples & apples analysis! Pd=0.9 Phased Array radar Pd=0.99 MIMO radar (from Alex Haimovich, Rick Blum, et al., IEEE Trans. Sig Proc 2006 )

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**Typical Radar Cross Section (RCS) vs. Azimuth Angle**

Radar cross section of the B-26 bomber at 3 GHz as a function of azimuth angle. Source: Introduction to Radar Systems, Merrill I Skolnik, McGraw-Hill, NY, 1962 The target response very complex as a function of aspect due to constructive and destructive interference of scatterers. The statistics of the response over a smallish aspect interval is related to the number of scattering centers. When the ratio of the standard deviation to the mean is large (large variance), it indicates a large number of scattering centers. When small, it indicates that there is one dominant scattering center. From: Introduction to Radar Systems, Merrill I Skolnik, McGraw-Hill, NY, 1962

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(1) Yuri Abramovich & Gordon Frazer, “Bounds on the volume and height distributions for the MIMO radar ambiguity function,” IEEE Signal Processing Letters, 2008. Generalization of Bob Price’s theorem (1965). MIMO has factor of N smaller useful range-Doppler space than boring old phased array. (2) Benjamin Friedlander, “On the relationship between MIMO and SIMO radars,” IEEE Trans. Signal Processing, January 2009. Very clear & explicit quantification of apples & apples performance comparison MIMO vs. PA (3) Victor Chernyak, “About the “new” concept of statistical MIMO radar,” Proceedings of Radar Conference, 2008. Statistical MIMO radar is not “new” and not as good as boring old phased arrays. (4) Victor Chernyak, “Fundamentals of multisite radar systems,” translated from Russian, Gordon & Breach (1998). Russian edition published 1993. Basic reference on multi-radar systems with correct apples & apples comparisons and correct physical models.

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(5) Gordon Frazer, et al., “Recent results in MIMO OTH radar,” Proceedings of IEEE Radar Conference, Rome May 2008. Real world system engineering viewpoint on MIMO radar for OTH applications (6) Gordon Frazer, et al., “Spatially waveform diverse radar: perspectives for HF OTHR,” Proceedings of IEEE Radar Conference, Boston April 2007. How to prevent MIMO radar transmitter from melting or exploding (see next chart) (7) Dan Rabideau, “Adaptive MIMO radar waveforms,” Proceedings of IEEE Radar Conference, Rome May 2008. Simple back-of-the-envelope formulas & good solid radar system engineering! (8) Fred Daum, “MIMO radar: snake oil or good idea?” Proceedings of IEEE Asilomar Conference, October 2008. Practical nuts & bolts hard boiled system engineering perspective.

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BACKUP

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**MIT Lincoln Lab radar combining algorithm (Coutts, Cuomo,**

McHarg, Weikle & Robey, IEEE radar conference 2006)

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**MIMO radar waveforms for GMTI**

waveform class distributed clutter point clutter references FDMA (frequency) loss of coherence Rabideau (2008) & Bliss, et al. (2009) CDMA (code) clutter fills the usable range-Doppler space Abramovich & Fraser (2008) Bliss et al. (2009) TDMA (time) very inefficient use of the transmitter DDMA (Doppler) Russians (1980) & Krolik, et al. (2004) space-time waveforms & hybrids of above ??? Rabideau (2008) and Abramovich & Fraser (2008)

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**hot off the press MIMO radar papers:**

(1) Yu, Petropulu & Poor, “MIMO radar & compressive sensing,” (2) Chen & Vaidyanathan, “Compressed sensing in MIMO radar,” (3) Strohmer & Friedlander, “Compressed sensing for MIMO radar,” (4) Willett, et al., “Compressed sensing for MIMO radar,” (5) Vaidyanathan & Pal, “MIMO radar, SIMO radar & IFIR radar,” (6) Hassanien & Vorobyov, “Why the phased-MIMO radar outperforms the phased array and MIMO radars,” 2011.

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**six ways to understand why MIMO improves angular measurement accuracy**

more equations to compute unknowns (MN vs. N) reciprocity of receive & transmit algebra (i.e., compute Cramer-Rao bound for MIMO) geometry (more triangles determine target location more accurately) virtual array antenna patterns (i.e., composite transmit-receive pattern)

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**Bliss, et al., “GMTI MIMO radar,” IEEE Waveform diversity Conference, Orlando, Feb. 2009.**

(1) Coherent integration time is 5 times longer for MIMO than boring old phased array. (2) Surveillance mode. (3) MIMO uses 5 element sparse transmit array, whereas PA uses smaller filled transmit array. (4) Both MIMO & PA use 5 element filled receive array. (5) Total transmit power is the same for MIMO & boring old PA. (6) frequency = 2 GHz.

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**Bliss, et al., “GMTI MIMO radar,” IEEE Waveform diversity Conference, Orlando, Feb. 2009.**

(1) Coherent integration time is 5 times longer for MIMO than boring old phased array. (2) Surveillance mode. (3) MIMO uses 5 element sparse transmit array, whereas PA uses filled transmit array. (4) Both MIMO & PA use 5 element filled receive array. (5) Total transmit power is the same for MIMO & boring old PA.

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Dan Rabideau (2008): To date, the MIMO radar community has largely assumed the use of "orthogonal" waveforms (i.e., waveforms having zero cross-correlation). To approximate orthogonality, some practitioners have proposed waveforms that exhibit both low cross-correlation and low autocorrelation sidelobes. As we shall see, lowering auto/cross correlation levels will indeed reduce decorrelation. However, in many cases this approach still results in unsatisfactory interference rejection levels.

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**Simple back-of-the-envelope formula (Rabideau 2008):**

We can use (4) - (11) to approximate the MCR at high CNR as: MCR == 1-1/(1 + IASR + ICCR)2 where IASR is the integrated autocorrelation sidelobe power ratio, and lCCR is the integrated cross-correlation ratio. For pseudorandom waveforms, IASR ~ (2L - 2)/(2L) , and ICCR ~ (2L -1)/(2L). Hence, (12) predicts an MCR of only -0.5 dB. Computer simulations confirm this prediction.

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**2nd simple back-of-the-envelope formula (Rabideau 2008):**

[for up/down chirps] it can be shown that: MCR ~ 1- (1 + IASR)2 /(1 + IASR + ICCR)2 From (13) we expect an MCR of -1.3 dB. Direct computer simulations also confirmed this value. Note that approximations like (12) and (13) allow us to evaluate entire waveform classes using only gross auto/cross correlation characteristics.

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**Professor Chernyak on statistical MIMO radar:**

There is nothing new in the “statistical MIMO radar concept”….The SIMO radar (with the same total energy) is much better than the MIMO and MISO systems….It is clear that we have a good combination of high incident energy on a target with fluctuation smoothing on the receiving side….The target and signal model suggested by the authors of statistical MIMO radar does not correspond to the physical nature of signal fluctuations at the input of a radar receiver.

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item comments references 1. Loss in SNR Factor of N loss for MIMO Li & Stoica (2009) 2. Loss in useful range-Doppler space Abramovich & Frazer (2008) 3. Cost N antennas, N sites, N² receivers, N waveform generators, calibration of N² channels, data links, complex signal & data processing, testing, etc. Skolnik (1962) 4. Risk Complexity & novelty & tight coupling of designs 5. Melting or explosion of transmitter Energy radiated into imaginary space by standard MIMO design Frazer (2007) 6. Low transmit antenna gain Jamming, radiation hazard, anti-radiation homing missiles, NTIA standards, EMC, ducting 7. Time & frequency agility Decorrelates RCS for phased array (PA) to enhance detection probability 8. Time & frequency agility Decorrelates multipath for PA Barton (1964) 9. Exploit time for tracking Sequence of high gain beams for PA Friedlander (2009) 10. Exploit time for ECCM Sequence of high gain beams to null jammers for PA 11. Range & Doppler resolution for PA Angle resolution is usually irrelevant for resolution of multiple targets 12. Mitigation of multipath for PA Wideband waveforms, adaptive nulling, optimal receive & transmit beams, nonlinear filters Skolnik (2008) 13. Smart design of PA Smart MIMO design vs. dumb PA design 14. Limits on coherent integration time for MIMO to increase SNR Target coherence, propagation path (troposphere & ionosphere & multipath) & transmitter duty cycle 15. Data association errors with MIMO PA is simple & robust Bar-Shalom & Blackman books

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item comments references 1. Loss in SNR Factor of N loss for MIMO Li & Stoica (2009) 2. Loss in useful range-Doppler space Abramovich & Frazer (2008) 3. Cost N antennas, N sites, N² receivers, N waveform generators, calibration of N² channels, data links, complex signal & data processing, testing, etc. Skolnik (1962) 4. Risk Complexity & novelty & tight coupling of designs 5. Melting or explosion of transmitter Energy radiated into imaginary space by standard MIMO design Frazer (2007) 6. Low transmit antenna gain Jamming, radiation hazard, anti-radiation homing missiles, NTIA standards, EMC, ducting 7. Time & frequency agility Decorrelates RCS for phased array (PA) to enhance detection probability 8. Time & frequency agility Decorrelates multipath for PA Barton (1964) 9. Exploit time for tracking Sequence of high gain beams for PA Friedlander (2009) 10. Exploit time for ECCM Sequence of high gain beams to null jammers for PA

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**Please exploit all flavors of diversity, not just waveform diversity**

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item comments references 7. Time & frequency agility Decorrelates RCS for phased array (PA) to enhance detection probability Skolnik (1962) 8. Time & frequency agility Decorrelates multipath for PA Barton (1964) 9. Exploit time for tracking Sequence of high gain beams for PA Friedlander (2009) 10. Exploit time for ECCM Sequence of high gain beams to null jammers for PA 11. Range & Doppler resolution for PA Angle resolution is usually irrelevant for resolution of multiple targets 12. Mitigation of multipath for PA Wideband waveforms, adaptive nulling, optimal receive & transmit beams, nonlinear filters Skolnik (2008) 13. Smart design of PA Smart MIMO design vs. dumb PA design 14. Limits on coherent integration time for MIMO to increase SNR Target coherence, propagation path (troposphere & ionosphere & multipath) & transmitter duty cycle 15. Data association errors with MIMO PA is simple & robust Bar-Shalom & Blackman books

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MIMO target “Like traditional STAP methods, the challenge of estimating the clutter covariance matrix from the received data is difficult in slow-time MIMO STAP. Further work is required to determine an appropriate set of training data from which the MIMO adaptive weights can be calculated.” Mecca, Ramakrishnan & Krolik (2008)

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**MIMO for Radar vs. Communication**

Microwave radar HF OTH radar 1. Omni transmit OK? yes! no! Large loss of energy on target in track, which cannot be recovered. yes (track-while-scan) 2. Long time on target? yes (track-while-scan) 3. Long coherence time? no yes (owing to long wavelength) 4. Tolerance for hiatus in music none large some 5. Performance measure Shannon information SNR or SJR or SCR or detection probability or range & angle & Doppler accuracy 6. Exploit frequency agility & time & bandwidth? not generally generally not

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**MIMO target Translation: “Send more money”**

“Like traditional STAP methods, the challenge of estimating the clutter covariance matrix from the received data is difficult in slow-time MIMO STAP. Further work is required to determine an appropriate set of training data from which the MIMO adaptive weights can be calculated.” Mecca, Ramakrishnan & Krolik (ref. 5) Translation: “Send more money”

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Fig. 2. Photograph of the OTHR transmitter array used in the HILOW experiment and taken from directly in front of the array. The array comprises fourteen log periodic dipole array elements arranged as an equi-spaced linear array. The eight center elements were used in the experiment.

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Fig. 3. Spectrogram of the output of one waveform generator and high power amplifier for the case of a staggered linear FMCW waveform set. The signal shown corresponds to one member of the waveform set and is the signal radiated from one transmit array element. dBJ

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Fig. 4. Spectrogram of the received waveform set following two-way propagation. All members of the waveform set are shown. The substantial clutter propagation range depth typical in OTHR is apparent and shows as a “thickening” of each individual chirp. It reduces the time-frequency spacing between members of the waveform set. Such range (and while not shown here, Doppler) spread is typical in OTHR and reduces the practically realisable cardinality of any chosen waveform set.

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Fig. 5. Doppler-delay map for the two-way signal received using a single channel radar receiver. The RD map shows earth return clutter and multi-mode radar measurements of a radar transponder located in the one-hop footprint of the radar. Of particular interest are the first and third (of five) transponder returns, at 8.47ms and 9.01ms delay at approximately 1.7Hz Doppler shift. The receiver signal was processed using multiple matched filters - one per waveform set member - and this diagram corresponds to the RD map in the direction of the peak of a transmitter beam based on maximising the 8.47ms transponder return implemented as a weighted sum of the output of the multiple matched filters.

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**Fig. 6. Transmit beampattern formed at the one-way path receive location**

in the one-hop footprint of the OTHR at a location close to the transponder. The two beampatterns correspond to the 8.47ms and 1.7Hz transponder mode and the 9.01ms and 1.7Hz transponder mode identified in Fig. 5.

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Fig. 7. Transmit beampattern formed at the two-way path OTHR receive location. The two beampatterns correspond to the 8.47ms and 1.7Hz transponder mode and the 9.01ms and 1.7Hz transponder mode identified in Fig. 5.

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**Severe degradation due to transmit beamshape loss**

angle estimation accuracy (IEEE Trans Signal Processing Oct 2006) Phased Array Severe degradation due to transmit beamshape loss Explain this intuitively MIMO Subtle detail

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**Both plots are optimistic by two orders of magnitude!**

angle estimation accuracy (IEEE Trans Signal Processing Oct 2006) Both plots are optimistic by two orders of magnitude! Phased Array MIMO

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**phased array MIMO angle estimation accuracy for 2 unresolved**

targets (IEEE Trans SP Oct) phased array MIMO

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**MIMO vs. phased array for jamming**

First, in this example, the 3 dB receive beamwidth is roughly 12 degrees, and therefore an adaptive phased array can easily null a jammer at 45 degrees and detect the (first) target at -60 degrees! Second, the authors assume that the SNR for MIMO and phased array are the same. Third, the authors assume exactly equal amplitudes & phases for all 12 targets (what happens with other phases & amplitudes?). Fourth, the MIMO antenna pattern that is plotted above has no noise, but with only 20 dB SNR, the middle ten targets are all obscured by measurement errors due to noise. Fifth, the Cramer-Rao bound shown above is for the first target, which is the farthest from the jammer, and hence the easiest to detect. Otherwise, this is a fair comparison between MIMO and phased arrays.

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**MIMO vs. phased array for jamming**

First, in this example, the 3 dB receive beamwidth is roughly 12 degrees, and therefore an adaptive phased array can easily null a jammer at 45 degrees and detect the (first) target at -60 degrees! Second, the authors assume that the SNR for MIMO and phased array are the same. Third, the authors assume exactly equal amplitudes & phases for all 12 targets (what happens with other phases & amplitudes?). Fourth, the MIMO antenna pattern that is plotted above has no noise, but with only 20 dB SNR, the middle ten targets are all obscured by measurement errors due to noise. Fifth, the Cramer-Rao bound shown above is for the first target, which is the farthest from the jammer, and hence the easiest to detect. Otherwise, this is a fair comparison between MIMO and phased arrays.

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**MIMO vs. phased array for jamming**

First, in this example, the 3 dB receive beamwidth is roughly 12 degrees, and therefore an adaptive phased array can easily null a jammer at 45 degrees and detect the (first) target at -60 degrees! Second, the authors assume that the SNR for MIMO and phased array are the same. Third, the authors assume exactly equal amplitudes & phases for all 12 targets (what happens with other phases & amplitudes?). Fourth, the MIMO antenna pattern that is plotted above has no noise, but with only 20 dB SNR, the middle ten targets are all obscured by measurement errors due to noise. Fifth, the Cramer-Rao bound shown above is for the first target, which is the farthest from the jammer, and hence the easiest to detect. Otherwise, this is a fair comparison between MIMO and phased arrays.

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**MIMO vs. phased array for jamming**

First, in this example, the 3 dB receive beamwidth is roughly 12 degrees, and therefore an adaptive phased array can easily null a jammer at 45 degrees and detect the (first) target at -60 degrees! Second, the authors assume that the SNR for MIMO and phased array are the same. Third, the authors assume exactly equal amplitudes & phases for all 12 targets (what happens with other phases & amplitudes?). Fourth, the MIMO antenna pattern that is plotted above has no noise, but with only 20 dB SNR, the middle ten targets are all obscured by measurement errors due to noise. Fifth, the Cramer-Rao bound shown above is for the first target, which is the farthest from the jammer, and hence the easiest to detect. Otherwise, this is a fair comparison between MIMO and phased arrays.

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**MIMO vs. phased array for jamming**

First, in this example, the 3 dB receive beamwidth is roughly 12 degrees, and therefore an adaptive phased array can easily null a jammer at 45 degrees and detect the (first) target at -60 degrees! Second, the authors assume that the SNR for MIMO and phased array are the same. Third, the authors assume exactly equal amplitudes & phases for all 12 targets (what happens with other phases & amplitudes?). Fourth, the MIMO antenna pattern that is plotted above has no noise, but with only 20 dB SNR, the middle ten targets are all obscured by measurement errors due to noise. Fifth, the Cramer-Rao bound shown above is for the first target, which is the farthest from the jammer, and hence the easiest to detect. Otherwise, this is a fair comparison between MIMO and phased arrays.

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MIMO Radar MIMO communications is clearly a good idea for certain applications in theory Asserted advantages of MIMO radar Apples & apples comparison of MIMO radar vs. boring old phased array radar New excellent references Story about Russian visitor to Raytheon 25 years ago

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