MIMO Radar
4.1 INTRODUCTION
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C H A P T E R
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performance of a MIMO radar that transmits signals with arbitrary correlation properties.
A brief discussion of MIMO radar waveforms is provided. Finally, applications of MIMO techniques to particular radar modes are described.
Some key points that will be discussed in this chapter include the following:
• A MIMO radar uses multiple transmit elements that emit independent waveforms and observes the returns from a scene of interest using multiple receive elements.
• A MIMO radar with closely spaced antennas is an extension of the traditional phased array. Standard array configurations preserve receive degrees of freedom by digitizing signals observed by multiple, spatially diverse channels. If a radar could transmit or- thogonal waveforms with spatial diversity, transmit degrees of freedom would also be preserved, leading to a more flexible radar system.
• A MIMO radar with widely separated antennas is an extension of the bistatic radar concept. Each bistatic pair of radars observes a statistically independent realization of target reflectivity that may allow tracking to continue where it would otherwise be interrupted by target fading or an unfavorable geometry.
• The enhanced angular resolution provided by a MIMO radar can be understood by considering how, using multiple transmitted waveforms, a larger virtual array can be synthesized compared with using a single transmit phase center.
• The characteristics of a MIMO radar are described by the correlation between the transmitted signals. A phased array transmits perfectly correlated waveforms to form a narrow, high gain beam. By using uncorrelated waveforms, a MIMO radar trades off this peak gain for a more flexible antenna that can digitally resteer its transmit beam and provide enhanced resolution.
4.1.2 Notation
The conjugate of a scalar, z, is denoted z∗. The Hermitian (conjugate) transpose of a matrix, A, is denoted AH. The pseudoinverse of a matrix, A, is denoted A+. The Kronecker product of two matrices, A and B, is denoted A⊗B. The N×N identity matrix is denoted IN.
Frequently used variables that are found in this chapter include M=number of transmit elements/subarrays
N =number of receive elements/subarrays θ=angle relative to the array (θ =0 is broadside) θ0=angle used for digital beamforming
θ˜0=angle used for analog beamforming
a(θ)=transmit steering vector corresponding to angleθ(length: M) b(θ)=receive steering vector corresponding to angleθ (length: N ) A(θ)=MIMO channel matrix (size: N ×M)
φm(t)=waveform used by transmitter m
(t)=vector of waveforms used by each transmitter (length: M)
y(t ;θ)=vector of signals observed by each receiver for a target at angleθ(length: N ) η (t)=vector of receiver noise signals (length: N )
Rφ =MIMO signal correlation matrix (size: M×M)
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each target will be correlated from element to element. Suppose that only a single target is illuminated and observed by the elements of a MIMO radar. If the elements are widely sep- arated, perhaps distributed among a number of radar platforms, then each transmit/receive pair may observe uncorrelated echoes from the target due to aspect-dependent backscat- tering phenomena. On the other hand, if the elements are colocated on a single platform, they may be suitably close to observe the target from essentially the same aspect.
In a MIMO radar with widely separated antennas, each transmit/receive pair is as- sumed to observe an independent realization of the target reflectivity. This may be consid- ered as an extension of the concept of a bistatic radar system, which consists of a single transmitter and a single receiver that are separated by a great distance, to include the pos- siblity of using multiple transmitters and multiple receivers. This configuration has been called statistical MIMO, since it seeks to exploit this variation to improve detection and estimation performance. The use of widely spaced, multistatic systems was presented in the MIMO context in [6], but such techniques have a long history [7].
Assessing the utility of MIMO with widely separated antennas is not straightforward, since it relies on a system-level analysis to consider trade-offs between coverage rate and tracking utility since multiple radars must cooperate rather than operate independently.
Also, many of the interesting challenges in realizing such systems are concerned with being able to share large volumes of data between distributed radar systems. For these reasons, MIMO radar with widely separated antennas will not be covered in the following discussion. A review of these techniques is provided in [8].
Instead, we will focus on MIMO radars in which the transmit/receive elements are closely spaced. We can therefore assume that the returns due to a particular target are correlated from element to element, which enables coherent processing across the MIMO array. For this reason, MIMO radars with widely separated antennas may be referred to as non-coherent MIMO while those with closely spaced antennas are called coherent MIMO radars.
Conventional array antenna technologies enable digital beamforming on receive by digitizing multiple spatial channels. This allows the receive beampattern to be resteered, but, since the beampattern is the product of the transmit beampattern and the receive beampattern, this has limited utility; a beam cannot be formed in a direction in which no energy was transmitted. Using MIMO techniques, the transmit beampattern may be resteered as well. Just as digitizing multiple channels on receive preserves receive degrees of freedom, transmitting orthogonal waveforms preserves transmit degrees of freedom.
This concept of transmit beampattern flexibility will be developed in the following, as it is key to leveraging MIMO to enhance the capability of a radar system.