PaperlayerView exact revision on arXiv

Source-linked AI summary

Phased-MIMO Radar: A Tradeoff Between Phased-Array and MIMO Radars

Aboulnasr Hassanien, Sergiy A. Vorobyov

arXiv:0908.2153v1cs.IT

TL;DR

Colocated-antenna MIMO radar can improve angular resolution, while phased-array radar offers coherent transmitting-side processing gain. The paper proposes phased-MIMO radar to combine these advantages, and analytical and simulation results validate its effectiveness.

  • Problem

    Colocated-antenna MIMO radar improves angular resolution, while phased-array radar provides coherent transmitting-side processing gain.

  • Method

    The paper proposes phased-MIMO radar for colocated antennas, combining phased-array and MIMO radar capabilities through jointly used subarrays.

  • Results

    Analytical and simulation results show that phased-MIMO radar combines phased-array and MIMO radar advantages and provides higher resolution capabilities.

  • Takeaways & Limitations

    The phased-MIMO formulation opens a new avenue for MIMO radar developments.

Abstract

from arXiv · show

We propose a new technique for multiple-input multiple-output (MIMO) radar with colocated antennas which we call phased-MIMO radar. The new technique enjoys the advantages of MIMO radar without sacrificing the main advantage of phased-array radar which is the coherent processing gain at the transmitting side. The essence of the proposed technique is to partition the transmitting array into a number of subarrays that are allowed to overlap. Then, each subarray is used to coherently transmit a waveform which is orthogonal to the waveforms transmitted by other subarrays. Coherent processing gain can be achieved by designing a weight vector for each subarray to form a beam towards a certain direction in space. Moreover, the subarrays are combined jointly to form a MIMO radar resulting in higher resolution capabilities. The substantial improvements offered by the proposed phased-MIMO radar technique as compared to previous techniques are demonstrated analytically and by simulations through analysis of the corresponding beampatterns and achievable output signal-to-noise-plus-interference ratios. Both analytical and simulation results validate the effectiveness of the proposed phased-MIMO radar.

I. INTRODUCTION

The paper introduces phased-MIMO radar to combine MIMO waveform diversity and resolution benefits with phased-array coherent transmit processing. It uses overlapping transmit subarrays and analyzes resulting beampattern, SINR, and robustness advantages.

  • Advantages: Phased-MIMO radar retains MIMO benefits including improved angular resolution, more detectable targets, parameter identifiability, and extended array aperture.It also supports existing transmit and receive beamforming techniques and enables overall virtual-array beampattern design.
  • Motivation and contribution: Phased-MIMO radar combines MIMO waveform diversity with phased-array coherent processing to address the latter’s transmit-gain loss.The technique is proposed specifically to overcome MIMO radar’s loss of coherent processing gain and associated beam-shape degradation under RCS fading.
  • Method: The transmitting array is partitioned into overlapping subarrays that coherently transmit mutually orthogonal waveforms.Each subarray uses a weight vector to form a beam in the same spatial direction, while the subarrays jointly form a MIMO radar.
  • Advantages: The technique provides a tradeoff between resolution and robustness against beam-shape loss, while improving robustness against strong interference.These properties are identified among the proposed phased-MIMO radar’s stated advantages over phased-array and MIMO radars.
  • Evaluation: The paper evaluates phased-MIMO radar against phased-array and MIMO radars using beampatterns, achievable output SINRs, and simulations.It also discusses robust/adaptive beamforming and reports significant simulated performance gains over both comparison techniques.

II. MIMO RADAR: PRELIMINARIES

The MIMO radar model uses orthogonal waveforms across colocated transmitting antennas and matched filtering to form an MN-dimensional virtual data vector. With suitable ULA spacing, M+N antennas yield an MN-element virtual aperture, but conventional MIMO lacks transmit coherent processing and has a smaller clear region than phased-array radar.

  • MIMO radar signal model: Orthogonal waveforms are transmitted from the M colocated antennas, and matched filtering recovers the individual waveform returns.The waveform vector satisfies an orthogonality condition, enabling separate recovery of transmitted-waveform returns.
  • MIMO radar signal model: The matched-filtered returns form an MN×1 virtual data vector with target steering vector v(θ)=a(θ)⊗b(θ), plus interference and noise.The virtual steering vector corresponds to a virtual array of MN sensors.
  • Virtual-array geometry: Choosing d_T=Nd_R produces a ULA virtual array of MN elements spaced d_R wavelengths apart, with steering index ζ=mN+n.The transmitting inter-element spacing may exceed half a wavelength without receiving-end ambiguity; the specified choice gives the simplified ULA steering vector.
  • Virtual-array geometry: An MN effective aperture can therefore be obtained using M+N antennas, enabling higher resolution and better detection and estimation performance.These benefits follow from using the virtual data vector for detection and estimation.
  • Limitations: Conventional MIMO does not support coherent transmit beamforming, reducing robustness against sensor noise and RCS fading and producing an M-times-smaller clear region than phased-array radar.The limitation arises because the transmit array cannot perform coherent processing in the stated formulation.

III. PROPOSED PHASED-MIMO RADAR FORMULATIONS

The proposed phased-MIMO formulation partitions the transmitting array into overlapping subarrays that transmit orthogonal waveforms while enabling transmit beamforming. By selecting the number of subarrays, it trades phased-array coherent processing gain against MIMO resolution and related capabilities.

  • Formulation: Phased-MIMO partitions the transmitting array into K overlapping subarrays, each coherently transmitting a distinct waveform and using beamforming weights to form a directional beam.The adopted fully-overlapped partition uses M−K+1 antennas per subarray.
  • Limiting cases: K = 1 reduces the model to conventional phased-array radar, retaining uplink coherent processing gain but yielding an N × 1 received data vector and lower resolution.The coherent processing gain is represented by w^Ha(θ).
  • Limiting cases: K = M reduces the model to unpartitioned MIMO radar, providing the highest possible resolution but no coherent processing gain at transmission.The corresponding data vector has dimension MN × 1.
  • Advantages: The formulation combines MIMO benefits—including angular-resolution improvement, higher target capacity, parameter identifiability, and virtual-aperture extension—with transmit beamforming and coherent-gain optimization.It also supports joint transmit/receive weight design for optimizing the virtual-array beampattern and controlling total transmit power.
  • Tradeoffs and assumptions: Selecting the number of subarrays trades resolution and robustness against beam-shape loss, as well as performance improvements against computational requirements.The formulation assumes nonadaptive subarray selection independent of the target reflection coefficient β(θ).

IV. PHASED-MIMO RADAR TRANSMIT/RECEIVE BEAMFORMING

This section applies and analyzes transmit/receive beamforming techniques for phased-MIMO radar. It compares phased-MIMO, phased-array, and MIMO radars using transmit-receive beampatterns and achievable SINRs, with detailed treatment of non-adaptive methods and brief discussion of adaptive methods.

  • Transmit/receive beamforming: Existing uplink beamforming techniques can be used to design transmitting-array weights that satisfy beampattern and transmit-power requirements.The design is described for different subarrays.
  • Transmit/receive beamforming: The section applies and analyzes transmit/receive beamforming techniques for the proposed phased-MIMO radar.The analysis is formulated for the proposed radar in equation (17).
  • Transmit/receive beamforming: The section examines non-adaptive transmit/receive beamforming in detail and briefly discusses adaptive transmit/receive beamforming for phased-MIMO radar.Non-adaptive methods receive the detailed treatment, while adaptive methods are addressed as a possibility.

A. Non-adaptive Transmit/Receive Beamforming

This section derives non-adaptive transmit/receive beampatterns and output SINR expressions for phased-MIMO radar, then compares them with phased-array and MIMO radar. Fully overlapped partitioning preserves a tradeoff between coherent-processing and waveform-diversity gains while reducing sidelobes.

  • A. Non-adaptive Transmit/Receive Beamforming: Conventional beamforming is applied at both phased-MIMO transmit and receive arrays to derive and compare beampattern and output SINR expressions.The comparisons include phased-array and MIMO radars.
  • A. Non-adaptive Transmit/Receive Beamforming: The phased-MIMO beampattern is the product of transmit, waveform-diversity, and receive beampatterns, with the first two terms dependent on K and the receive term independent of K.This decomposition focuses beampattern analysis on the K-dependent transmit and diversity terms.
  • A. Non-adaptive Transmit/Receive Beamforming: Phased-array radar has the highest transmit coherent processing gain without diversity gain, whereas MIMO radar has the highest waveform diversity gain without transmit coherent processing gain.Phased-MIMO combines these distinct gain mechanisms through subarray partitioning.
  • A. Non-adaptive Transmit/Receive Beamforming: For fully overlapped ULA subarrays, the phased-MIMO transmit-receive beampattern equals that of a partition with M −K+1 subarrays.This follows from exchanging the roles of the subarray and overlap dimensions.
  • A. Non-adaptive Transmit/Receive Beamforming: Phased-MIMO has a lower highest sidelobe level than phased-array radar, yielding better robustness against interfering targets in the sidelobe area.The section also states that the proposed partitioning is superior to other array-partitioning types based on optimal output SINR comparisons.

1) Dominant noise power:

When interference is negligible because interferers are well separated from the target, noise dominates the interference-to-noise power. Under this condition, phased-array radar is more robust to background noise, while phased-MIMO trades SINR against virtual-array dimension as K increases.

  • Dominant noise power: When interferers are well separated from the target, the interference-to-noise power can be attributed to the noise term alone.Under this assumption, the SINR expressions for phased-array and MIMO radar simplify.
  • Dominant noise power: The phased-array radar is more robust to background noise than the MIMO radar.This conclusion follows from comparing the simplified SINR expressions.
  • Dominant noise power: The ratio η ≜(M −K+1)/M represents the phased-MIMO radar SINR relative to the phased-array radar SINR.The ratio satisfies 1/M ≤η ≤1.
  • Dominant noise power: Increasing K linearly decreases phased-MIMO SNR gain while increasing the dimension of the extended virtual array.This establishes a tradeoff between SNR gain and high-resolution capability.

2) Dominant interference:

Under dominant interference, phased-array and MIMO radars have the same interference robustness, while phased-MIMO radar is capable of better SINR performance than both.

  • Dominant interference:: Phased-array and MIMO radars have the same robustness against interference when noise is negligible relative to interference.The analysis neglects the noise term in the relevant SINR expressions.
  • Dominant interference:: The phased-MIMO radar’s better SINR performance is linked to its lower highest sidelobe level than the phased-array radar.The argument combines the lower highest sidelobe level with the preceding SINR analysis.
  • Dominant interference:: Phased-MIMO radar is capable of providing better SINR performance than phased-array and MIMO radars.The paper states that this observation is verified later using simulation examples.

B. Robust/Adaptive Beamforming · V. SIMULATION RESULTS

The paper develops robust and adaptive receive/transmit beamforming methods for phased-MIMO radar, while simulations compare phased-MIMO, phased-array, and MIMO radars under specified array, interference, and covariance-estimation settings.

  • B. Robust/Adaptive Beamforming: Robust uplink beamforming minimizes the beamformer-weight norm while upper-bounding sidelobe levels.The sidelobe bound is controlled by the user-selected parameter δ.
  • B. Robust/Adaptive Beamforming: The robust formulations provide smaller transmit coherent processing gain than phased-array radar because each subarray has a smaller effective aperture.Each subarray therefore produces a wider main beam, trading transmit-beamforming performance for receiving-end benefits.
  • B. Robust/Adaptive Beamforming: Adaptive processing uses an MVDR receive beamformer to minimize interference-plus-noise power while maintaining a distortionless response toward the target.The receive weight vector w_R has dimension KN × 1.
  • B. Robust/Adaptive Beamforming: Because the interference-plus-noise covariance matrix is unavailable in practice, simulations use a target-signal-free sample covariance matrix collected across range bins.The usual snapshot covariance contains the target component, whereas the alternative range-bin collection avoids it.
  • V. SIMULATION RESULTS: The simulations use a ULA of M = 10 omnidirectional transmitting antennas, with two interferers at −30° and −10° and a target arriving from θ_s = 10°.Noise is modeled as a complex Gaussian, zero-mean, spatially and temporally white sequence with identical sensor variances.
  • V. SIMULATION RESULTS: Each example compares phased-MIMO radar with phased-array and MIMO radar, using K = 5 fully overlapped subarrays.Comparisons evaluate transmit/receive beampatterns or output SINRs.
  • V. SIMULATION RESULTS: All methods estimate sample covariance matrices from N = 100 data snapshots, with the MIMO covariance matrix having size 100 × 100.A diagonal loading of 10I is applied to all three radar techniques for fair comparison.
  • V. SIMULATION RESULTS: Output SINRs are computed from 100 independent simulation runs for every tested method.This evaluation is used across all simulation examples.

A. Non-Adaptive Transmit/Receive Beamforming

Non-adaptive beampattern and SINR results show phased-MIMO radar trades modest transmit and diversity-beampattern losses for improved overall sidelobe behavior and waveform-diversity benefits. Across interference conditions, it achieves higher or near-phased-array output SINR while retaining MIMO-like diversity advantages.

  • Example 1: Non-adaptive transmit/receive beampattern without spatial transmit aliasing: Phased-MIMO radar trades a wider main beam and slightly higher sidelobes than phased-array radar for greater waveform-diversity gain.Its transmit beampattern is determined by individual subarray apertures, while its diversity beampattern corresponds to a K-element virtual array.
  • Example 1: Non-adaptive transmit/receive beampattern without spatial transmit aliasing: Phased-MIMO radar has significantly improved overall transmit/receive beampattern shape and lower sidelobe levels than both phased-array and MIMO radars.The overall beampattern is proportional to the multiplication of the transmit and waveform diversity beampatterns.
  • Example 2: Non-adaptive transmit/receive beampattern with spatial transmit aliasing: 5 times: with dT = 5dR and dR = 0.5 wavelength, each transmit and diversity beampattern repeats 5 times through [−π/2, π/2].Spatial aliasing causes large sidelobe variations across the spatial range.
  • Example 2: Non-adaptive transmit/receive beampattern with spatial transmit aliasing: 30 dB: overall-beampattern sidelobes near repeated mainlobes can exceed sidelobes in repeated-sidelobe regions by this amount.The results motivate sidelobe control in MIMO radar transmit/receive beamforming.
  • Example 3: Non-adaptive output SINR: 10 times higher: phased-array radar output SINR than MIMO radar output SINR when INR = −30 dB.Phased-MIMO output SINR is very close to phased-array output SINR while retaining MIMO waveform-diversity benefits.
  • Example 4: Non-adaptive output SINR in the presence of spatially distributed interference: SNR=INR larger than 10 dB: phased-MIMO output SINR outperforms both phased-array and MIMO radars under spatially distributed interference.At low SNR, phased-MIMO output SINR is comparable to phased-array output SINR.

B. Adaptive Transmit/Receive Beamforming

MVDR beamforming shows that phased-MIMO radar combines phased-array robustness with MIMO waveform diversity and adaptive interference rejection. With a single receive antenna, phased-MIMO achieves superior SINR performance by jointly rejecting interference and resisting sensor noise.

  • Example 5: MVDR beamforming employing multiple transmit multiple receive antennas: In multiple-transmit/multiple-receive operation, all radar techniques place nulls at powerful-interference locations, while phased-MIMO and phased-array radars maintain lower sidelobes than MIMO radar.The phased-MIMO radar therefore has almost the same robustness against sensor noise as phased-array radar while retaining waveform diversity.
  • Example 5: MVDR beamforming employing multiple transmit multiple receive antennas: Phased-MIMO radar exhibits SINR performance very close to phased-array radar and substantially better MVDR output SINR than MIMO radar.The phased-array advantage is attributed to transmit coherent processing, while phased-MIMO combines phased-array and MIMO benefits.
  • Example 6: MVDR beamforming employing multiple transmit single receive antennas: With one receive antenna, phased-array radar cannot reject powerful interference because its received-data dimension is 1 × 1.MIMO and phased-MIMO radars support adaptive reception through the larger-dimensional virtual extended array created by transmit waveform diversity.
  • Example 6: MVDR beamforming employing multiple transmit single receive antennas: Both MIMO and phased-MIMO radars reject interference effectively, but phased-MIMO has lower sidelobes and higher sensor-noise robustness than MIMO radar.MIMO radar suffers from poor performance because it lacks robustness against sensor noise.
  • Example 6: MVDR beamforming employing multiple transmit single receive antennas: Phased-MIMO radar achieves SINR performance superior to both phased-array and MIMO radars by combining interference rejection with sensor-noise robustness.Phased-array performs very poorly because it cannot reject strong interference, whereas MIMO performs better through adaptive rejection.

VI. CONCLUSIONS

The paper proposes phased-MIMO radar, which partitions a colocated transmitting array into potentially overlapping subarrays that transmit mutually orthogonal waveforms coherently. By combining subarray beamforming with joint MIMO processing, the technique combines phased-array and MIMO advantages, achieves higher resolution, and shows superior performance in simulations.

  • Technique: Phased-MIMO radar partitions the transmitting array into overlapping subarrays for colocated MIMO radar.The subarrays are allowed to overlap.
  • Technique: Each subarray coherently transmits a waveform orthogonal to those transmitted by other subarrays.This preserves waveform orthogonality while enabling coherent transmission within each subarray.
  • Processing: Subarray weight vectors form directional beams, while joint subarray processing creates a MIMO radar with higher resolution capabilities.The subarrays are combined jointly after directional beamforming.
  • Findings: The proposed technique combines the advantages of phased-array and MIMO radar and therefore has superior performance.The conclusion explicitly characterizes the combined performance as superior.
  • Validation: Simulation results confirm the theoretical observations and demonstrate the effectiveness of phased-MIMO radar.The formulation also opens a new avenue in MIMO radar developments.

APPENDIX A: PROOF OF PROPOSITION 2

The appendix proves that the phased-MIMO radar beampattern has a lower highest sidelobe than the phased-array radar beampattern. The proof uses Fourier-transform expressions, sidelobe properties, and bounds for different subarray-size cases to establish the required inequality.

  • Proof of Proposition 2: The appendix establishes that the phased-MIMO radar’s highest sidelobe is lower than the phased-array radar’s highest sidelobe.This is the inequality stated as Proposition 2 and is concluded after proving (58).
  • Proof of Proposition 2: Fourier-transform analysis expresses the square roots of both sides of (58) using Dirac-delta functions, convolution, and sinc functions.The derivation introduces interelement spacing d, wavelength λ, and sinc(κΩ).
  • Proof of Proposition 2: For K = 1, corresponding to phased-array radar, the beampattern has higher sidelobes than all cases with K > 1.This observation from H_K(Ω) supports the proposition’s sidelobe comparison.
  • Proof of Proposition 2: For κ = 2, no sidelobes exist; κ = 3 has one sidelobe at Ω = π; and κ ≥ 4 produces multiple sidelobes.For κ ≥ 4, the sidelobe closest to the main lobe is the highest peak sidelobe.
Loading 0908.2153v1…