Noise Radar Technology
4.3 MIMO noise radars
received signal component. The ground clutter at the distance of 600 m is also visible, together with the Doppler spread clutter at a distance of up to 150 m, caused by trees and canopy motion. The Doppler spread components can also be atte- nuated, which is described in detail in [54].
The following section will focus on co-located MIMO, which means that the radiators of the antenna array are close enough to each other so that they can observe the object at the same aspect and, thus, the same phase of its scattering coefficient. As a result, coherent beamforming is possible. Another assumption is that the radar works in continuous wave mode. It is not a crucial requirement but it allows the achievement of good integration gain and to avoid distinctive pulse modulation.
The definition of MIMO above says nothing about the potential advantages of this mode over its classical electronically scanned phased-array counterpart which would justify the computational burden of the correlation between received waveforms and all transmit templates, instead of one. To derive them, reasonable criteria for comparison must be set. The following assumptions will be made: there areKtransmit andLreceive antennas, each antenna radiates the same power, and there is a time ofN samples for single integration. Another assumption is that at leastKtransmit beams must be produced to satisfactorily cover the whole azimuth sector.
4.3.1 Signal model
For any array radar, the narrow-band signal reflected from a point scatterer and received by anlth antenna can be described after quadrature de-modulation as
ylðt;f0Þ ¼a0ejwdtXK
k¼1xkðtt0Þ ejwc½tkð Þþtf0 lð Þf0þwlð Þt (4.44) where a0 is the complex amplitude of target reflectivity, xk is the waveform transmitted by thekth antenna,t0is the main time delay,tk andtlare the relative delays between a target placed at anglef0and the subsequent antennas, wcis the carrier angular frequency,wd is the Doppler frequency shift andwlð Þt is additive noise or interference.
This can be simplified by the use of vector notation so that the set of received signals can be described by
yðt;f0Þ ¼a0ejwdtbð Þf0 aTð Þf0 xðtt0Þ þwð Þt (4.45) where
a¼hejwctR1ð Þf;. . .;ejwctRKð ÞfiT
(4.46) and
b¼hejwctT1ð Þf;. . .;ejwctTLð ÞfiT
(4.47) are the steering vectors of the transmit and receive array.
The distinction between a classical phased array and MIMO lies within the form ofxðtÞ. In the first case, this is the same noise realizationx0ðtÞphase shifted at following transmitters according to the weighting vectoraðfTÞ. The weights are
derived from the steering vector corresponding to the wanted illumination angle fT. In the case of MIMO, each entry inxðtÞis an independent noise realization.
The noise radar processing is based on the correlation of the received signal with a template. In the case of MIMO, that can be synthetically written as follows (for simplification, further considerations are limited to a single cell of the cross- ambiguity function):
Zð Þ ¼f0
ð
T0
0
yð Þt xHð Þt dt¼a0bð Þf0 aTð Þf0 RxxþV (4.48) Zis the measurement matrix for a target placed at anglef0. TheRxxis the matrix of the spatial correlation of the transmitted signal, while V is post-integration noise.
When more than one target appears in the examined cell, it is a sum of scaled steering vectors’ products obtained for subsequent target angles that is multiplied by the Rxx correlation matrix instead of one. When a classical phased array is considered, only the correlation withxH0ð Þt is needed in practice but the result must be multiplied by a transmit steering vector to keep the generality of notation.
In the case of MIMO radar, theRxxis diagonal with respect to residuals at the level of the time-bandwidth product below the diagonal.
For a classical phased array, the matrix has a form of aðfTÞaTðfTÞand is singular. The form of the matrix is crucial to the antenna-pattern comparison.
4.3.2 Beamforming and antenna pattern
To perform beamforming, an appropriate criterion regarding its output must be formulated. The most commonly used one is to minimize the output noise with constrained amplitude of the template signalsð Þf at the output:
minh hHð Þf Rhð Þf (4.49)
with constraint hHð Þfsð Þ ¼f 1. The solution to such an optimization problem is given by
hð Þ ¼f ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR1sð Þf sHð ÞfR1sð Þf
p (4.50)
When the MIMO radar is considered, the closed form expression for the output signal-to-noise power ratio can be derived as a ratio of output signal power to the power of noise propagating through the filter. In this case, the spatial correlation matrix of noise Rwill be replaced with the extended auto-correlation Rvv of the vectorized post-correlation noise v. The measurement signal will also be in the vectorized formz.
PbS=Nð Þ ¼f hHð Þf z2
hHð ÞfRvvhð Þf (4.51)
By substitutinghwith (4.50), assuming Kronecker’s structure of channel, and exploit- ing the properties of the Kronecker product, (4.51) can be re-formulated as [59]:
bPS=Nð Þ ¼f bHð ÞfRww1Zað ÞfT 2
aHð ÞfT Rxxað ÞfT bHð ÞfRww1bð Þf (4.52) whereRwwis the spatial correlation matrix of noise and interferences. In this form, if Z is replaced with a point response template Sð Þf0 , it is simple to derive theoretical array radiation patterns and quantify the impact of transmitted signal auto-correlation on the radar performance:
Gðf;fT;f0Þ¼GTxð Þf0 aHð Þf0 Rxxað ÞfT 2
aHð ÞfT Rxxað ÞfT GRxð Þf0 bHð Þf0 Rww1bð Þf2
bHð Þf Rww1bð Þf (4.53) When the matrixRxx is replaced with a diagonal one, which is characteristic for the MIMO mode, the transmit part of the expression will take the form of
aHð Þf0 að ÞfT
j j2=K, while in the phased array mode with a strictly correlated set of transmitted signals it isjaHð Þf0 að ÞfT j2=1. This means that in MIMO mode, the achievable signal-to-noise ratio (SNR) is K times smaller due to beamforming properties than in its phased array counterpart. This can be explained quite straightforwardly, since in classical radar, the amplitude of a transmitted signal growsK times due to coherent summation, while in MIMO only medium power grows that much. Therefore, under the same conditions, the shape of the angular response for a single scatterer is exactly the same in MIMO and conventional phase radar, withK-fold gain in favour of the classical solution. An exemplary angular radiation pattern of a 10-by-10 array of omni-directional radiators and a reflecting point placed at the azimuth angle of 0º is presented in Figure 4.20.
30 20 10
–10
G [dB]
–20 –30
–50 0
Object angular position f0 [º]
f, fT
50 Phased MIMO
0
Figure 4.20 Radiation-pattern comparison
4.3.3 Adaptive beamforming
Depending on the knowledge of the spatial interference distribution, different beamforming results may be obtained with (4.53). When the interferences are non- directional and come from receiver noise, theRwwmatrix is diagonal, and it is the conventional beamformer that should be used. When there are directional inter- ferences and matrixRwwis known, then they can be cancelled. The spatial corre- lation matrix of the interferences may be known, for example, when they are stationary and receive-only observation was done. When such a procedure is not possible, one may use theRyymatrix instead ofRww. Such a solution is known as a Capon beamformer or minimum variance distortionless response; however, some authors use different naming conventions. In this case, apart from the interferences, the echo signature is also present in the matrix. Due to the constraint in (4.6), the beamformer does not cancel the useful echo. An example of its use is presented in Figure 4.21 where two objects and interference were placed on a simulated scene with SNR equal to30 dB. The interference was cancelled in both cases but the phased array suffers slight gain degradation in comparison to MIMO. What is worth mentioning is that if the SNR before integration was around 0 dB or higher, the beamformer would allow the separation of two objects with super-resolution for MIMO and spoil the performance for the phased array.
4.3.4 Virtual Nyquist array
In the MIMO radar bibliography, there is a widely spread concept of virtual aper- ture resulting from the spatial convolution of transmit and receive radiators [59,61].
Such convolution has an interesting property when one of the arrays – transmit or receive – is full, which meansl/2 spacing preventing the occurrence of prevents
0
–10 –20
G [dB]
–30
–40
–50 –50 0
Azimuth angle f[º]
50 fi
f0, f1 Phased MIMO
Figure 4.21 Simulated result of Capon beamformer response
aliasing and grating lobes, and the second is sparse in a specific way; namely, the spaces between the radiators are onel/2 slot smaller than the size of the full array.
The resultant convolution produces a uniform dense array of the sizeKL. Such an aperture provides much better angular resolution than two dense arrays with the same number of elements with no grating lobes.
The point is that it is not a feature of the MIMO mode but of the array geo- metry itself [62]. A classical phased array would behave in exactly the same way.
If proper spacing is maintained, nulls of the full array cancel the grating lobes of the sparse one. If the transmit array of classical radar is sparse, apart from the main beam, the energy will be transmitted in unwanted directions according to the grating lobes, but any return from those angles will be nullified by the receive pattern. When the receive array is sparse, there will be grating lobes in the receive pattern but no energy radiated in those directions by the full transmit array. As an illustration, the gain patterns obtained for a 3-by-3 array according to (4.10) are presented in Figure 4.22. The shape is the same and the overall level isK times higher for classical radar, accordingly to the explanation from previous sections.
What is worth mentioning is that such an array configuration works well only for a diagonal interference matrix, since the cancellation of grating lobes consumes all degrees of freedom that could be used for adaptive beamforming.
4.3.5 Benefit of MIMO
The MIMO radar gains considerably when not a single angle but an angular sector observation is performed. The pattern presented in Figure 4.23 is valid for a sce- nario where a conventional array illuminates a single angle for a given time, equal to the acquisition ofNsamples. If it was to coverKangles within the same time, it would have to divide the integration time byK, thus reducing the integration gain
20
10
0
Object angular position f0 [º]
G [dB]
–20
–30
–50 0 50
–10
f, fΤ Phased MIMO
Figure 4.22 Radiation-pattern comparison for virtual Nyquist arrays
from the correlation processing. What is gained from transmit beamforming in comparison to the MIMO is to be lost due to time division between observation angles. The production of multiple beams on receive is in this case redundant, since other directions are not illuminated. The MIMO radar constantly illuminates the whole scene, and a high number of transmit–receive synthetic beams can be pro- duced. Therefore, if a sector observation scenario is considered, the achievable SNR is the same, provided the sector observation time is not excessively long, and target movement does not cause coherency loss.
With equal SNR, there are some undeniable gains from MIMO in the discussed scenario. The first is the extension of integration time, simultaneous for all beams, that results in improved velocity resolution which can be crucial in some applica- tions. The other is the decrease in peak-radiated power and the lack of envelope modulation due to transmit beam sweeping. In the case of CW operation mode, where reflections form strong, close scatterers which can saturate the receiver, an increase in radiated power does not necessarily lead to improved SNR, since the reflected power grows as well. In MIMO, the lack of such spatial power accumu- lation allows the use of a more sensitive receiver without the risk of constant saturation.
There is an interesting analogy between FMCW radar versus CW noise radar and a conventional array versus a MIMO array. The first pair differs in the time–
frequency distribution of radiated power. In FMCW, the power is focused on one point of the spectrum at a time, with the point of focus sweeping through the whole band, while in noise radar it is randomly distributed for the whole integration period. Similarly, in a classical phased array, the focused beam sweeps through the spatial domain, while in CW noise MIMO there is a constant spatially spread
Figure 4.23 MIMO noise radar demonstrator
transmission. To conclude, CW noise MIMO radar is the most energy-spread radar system one can imagine. This feature makes it less prone to being detected and less likely to produce disturbances to other devices sensitive to peak power level.
4.3.6 Experimental results
In order to prove some features of noise MIMO radar, a demonstrator based on a commercial off-the-shelf (COTS) hardware platform and offline processing was developed. It used an arbitrary waveform generator as a transmitter and a vector signal analyser as a receiver, with 50 MHz of instantaneous bandwidth. There were three phase-coherent transmit channels, three receive channels and one reference waveform input allowing digital synchronization between the transmitter and receiver. WiFi sector antennas for 2.4 GHz were used, with a simple front end including amplifiers and a bandpass filter. Each antenna had a width of a single patch radiator along the array axis equal to 6 cm, which allowed for nearlyl/2 spacing. Phase calibration was carried out either using an active corner reflector with Doppler modulation capability, or allowing only relative angular measure- ments of the target. Calibration on a stationary corner reflector turned out to be inaccurate due to the influence of the ground echo from the same range cell. The radar demonstrator on the test site is presented in Figure 4.23.
The first task of the radar was to perform imaging of the whole scene within a single integration of 100 ms. The result is presented in Figure 4.24. The empty car park is marked with a dashed line, the active calibrator placed on a car with a triangle and the passive corner reflector with a circle. The positions of buildings are shown with solid rectangles. The seemingly poor quality of the image is fully justified by the system parameters – range resolution and number of array elements.
What is important is that to produce the equivalent with a classical array, one would have to sweep through all the angles with a transmit beam. For the given time slot for the whole scene, the achievable SNR would have been the same.
150
100
Distance y [m] 50
0–100 –50 0
Distance x [m]
50 100 [dB]
0 5 10 15 25 20 30 35 40
Figure 4.24 Image of stationary objects obtained in MIMO mode
Another result was obtained for a moving target – a man with an active signal repeater running radially towards the radar – in two turns at two different angles. In this case, the range-Doppler cell containing the target was extracted, and for each time snapshot range beamforming was done. The echoes from the dominant sta- tionary scatterers were cancelled using a set of lattice filters. An angular response of the man for two runs at different azimuth angles is presented against the theo- retic array response pattern. Since the point-like target was well isolated from the other ones, the measured pattern nearly overlays the theoretical one in Figure 4.25;
the form of one of the patterns extracted was exactly the same as the recording of the scene image. In this case, the radar looked in all directions simultaneously, which allowed multi-angle observation with long integration time and good velo- city resolution. With a classical array counterpart and the same time assigned for the whole-scene observation, the velocity resolution would be three times lower, which in the case of a relatively slow target would cause its overlap by velocity sidelobes of strong stationary targets.
4.3.7 Conclusions
When the task of the radar is to cover a given angular sector in surveillance or search mode, continuous wave noise radar in MIMO mode brings several advan- tages over its phased array counterpart:
● If there areKtransmit beams, and a fixed time to scan the whole sector, the MIMO and phased array achieve the same SNR. The phased array gains on transmit power concentration whereas MIMO makes it up with longer target illumination and effective integration.
10 0 –10 –20 –30
theor.
G [dB]
–40 –50
–50 0
Azimuth angular position [°]
50 f0 = 0°
f0 = –10°
Figure 4.25 Azimuth response of point-like moving object – theoretic and measured
● Longer integration gives better velocity resolution for the whole sector at the same time.
● If the radar is to detect some ephemeral phenomenon at an unknown angle, simultaneous multi-directional observation MIMO mode prevents the radar from missing it.
● In MIMO continuous wave radar, due to multi-directional simultaneous illu- mination, the transmitted peak power and thereby peak power of strong echoes is statisticallyK times smaller for the Gaussian waveform, which improves usage of the vertical range of the radar receiver, resulting in greater obtainable range.
● Lower peak power and lack of modulation caused by the angular beam sweep in MIMO mode may be crucial to the LPI properties of the radar.
● Capon beamformers works better for MIMO but only for high input SNR, barely possible in radar. Otherwise, the spatial resolution is exactly the same in MIMO as it is in a phased array, unless the influence of transmit beamforming is neglected for the phased array.
● The ability to form an extended virtual array improving spatial resolution is not a feature of MIMO but of array geometry itself and can be obtained in a phased array as well.
● In MIMO, the calibration of the transmit array may be done offline, whereas in a phased array it must be assured before transmission.
MIMO needs more independent transmit channels, the data throughput of reference signals isKtimes larger, and instead ofKorLcorrelations,KLmust be calculated.
Moreover, tracking of a single distant object with no masking interference from close objects is done better with a conventional phased array. Before implementing a MIMO noise radar to a particular application, one must consider whether the need for the exploitation of the advantages above is justified.
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