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Target Detection Performance of Spectrum Sharing MIMO Radars
Awais Khawar, Ahmed Abdelhadi, T. Charles Clancy
TL;DR
The paper addresses target detection when a MIMO radar shares spectrum with a multi-base-station cellular system while shaping its waveform to protect communications. It selects an interference channel, projects the radar waveform into that channel’s null space, and evaluates detection against an orthogonal waveform using GLRT. NSP detection requires 6–13 dB or 3–5 dB additional SNR for 90% detection, depending on the antenna configuration.
Problem
The paper asks how a radar can detect targets while sharing spectrum with cellular systems without causing harmful interference.
Method
The method selects the cellular base station that minimizes waveform degradation, projects the MIMO radar waveform onto its interference-channel null space, and derives GLRT statistics for NSP and orthogonal waveforms.
Results
For 90% detection, NSP waveforms require 6–13 dB additional SNR when N BS < M and 3–5 dB when the radar has the larger antenna array, relative to orthogonal waveforms.
Takeaways & Limitations
Selecting the projection channel is reported to minimize waveform degradation and the additional SNR required for NSP-based target detection.
Abstract
from arXiv · showhide
Future wireless communication systems are envisioned to share radio frequency (RF) spectrum, with other services such as radars, in order to meet the growing spectrum demands. In this paper, we consider co-channel spectrum sharing between cellular systems and radars. We address the problem of target detection by radars that are subject to shape its waveform in a way that it does not cause interference to cellular systems. We consider a multiple-input multiple-output (MIMO) radar and a MIMO cellular communication system with $\mc K$ base stations (BS). We propose a spectrum sharing algorithm which steers radar nulls, by projecting radar waveform onto the null space of interference channel, towards a `selected' BS, thus, protecting it from radar interference. This BS is selected, among $\mc K$ BSs, on the basis of guaranteeing minimum waveform degradation. We study target detection capabilities of this null-space projected (NSP) waveform and compare it with the orthogonal waveform. We derive the generalized likelihood ratio test (GLRT) for target detection and derive detector statistic for NSP and orthogonal waveform. The target detection performance for NSP and orthogonal waveform is studied theoretically and via Monte Carlo simulations.
I. INTRODUCTION
The paper studies radar–cellular spectrum sharing, motivated by growing spectrum demand and concerns about harmful interference. It focuses on target detection for a MIMO radar using waveform projection and compares null-space-projected and orthogonal waveforms.
- Radar–cellular co-channel sharing has received limited attention because of regulatory concerns about harmful interference.
- Growing demand for commercial broadband motivates sharing radar bands with cellular systems, including the proposed 3550–3650 MHz band.
- Large exclusion zones required to protect cellular systems from high-power radar signals can cover populated U.S. regions and undermine commercial deployment.
- The paper examines target detection for a MIMO radar sharing spectrum with a cellular system containing multiple base stations.
- Its approach compares null-space-projected and orthogonal radar waveforms while using the generalized likelihood ratio test for detection.
C. Signal Model
The signal model represents a far-field point-target return from a colocated MIMO radar and adopts simplifying assumptions for propagation, target parameters, and Gaussian noise.
- The transmitted signal is formed from the baseband signals radiated by the M radar transmit elements over the observation interval.
- Transmit and transmit–receive steering vectors and matrices describe the radar array response as a function of target angle θ.
- The received point-target signal includes propagation delays, Doppler shift, and complex amplitude α representing path loss and reflection.
- The model assumes identical path loss across transmit and receive elements under a far-field approximation, with θ denoting azimuth angle.
- After range–Doppler compensation, the received observations follow an independent complex Gaussian model with deterministic unknown target parameters and known noise covariance.
F. Orthogonal Waveforms
The paper uses orthogonal MIMO radar waveforms and models their coexistence with a multi-base-station cellular system through interference channels.
- Orthogonal signals provide transmitter and receiver digital beamforming, improved angular resolution, virtual-array aperture, and more resolvable targets.
- The cellular model contains K base stations, each with N BS transmit and receive antennas and multiple multi-antenna user equipments.
- Signals from user equipments and additive white Gaussian noise contribute to each base station’s received signal.
- The radar–cellular interference model uses K channels H_i, whose entries represent links from radar transmit elements to base-station receive elements.
- Interference-channel elements are modeled as independent, identically distributed circularly symmetric complex Gaussian variables with zero mean and unit variance.
I. Cooperative RF Environment
The radar obtains interference-channel information, constructs null-space projectors through SVD, selects a channel causing minimum waveform degradation, and projects its waveform to avoid interference.
- Interference-channel state information is obtained through feedback from communication systems to support radar interference mitigation.
- The radar seeks a waveform satisfying H_i x(t) = 0, thereby avoiding interference to the selected base station.
- SVD of H_i is used to identify its null space and construct a projection matrix.
- The resulting matrix is an orthogonal projection onto the null space of H_i.
- Among K interference channels, the selected channel minimizes radar waveform degradation in a minimum-norm sense.
- The NSP waveform correlation matrix is no longer identity, and its rank depends on the projection-matrix rank.
C. Spectrum Sharing and Projection Algorithms
The spectrum-sharing algorithms repeatedly obtain interference-channel information, form projection matrices, select the least-degrading projector, and apply null-space projection to the radar waveform.
- At each pulse repetition interval, the radar obtains interference-channel state information for all K channels.
- Algorithm 2 computes null spaces and projection matrices from each base station’s channel matrix.
- Algorithm 1 selects the projection matrix producing the least waveform degradation in a minimum-norm sense.
- The selected projector is applied as x̄(t) = P̄x(t) to produce the null-space-projected waveform.
IV. STATISTICAL DECISION TEST FOR TARGET DETECTION
The paper develops a GLRT-based statistical test for target presence and derives detection statistics for orthogonal and null-space-projected radar waveforms under a tractable single-target model.
- The detection test compares orthogonal and NSP waveforms using the decision of whether a target is present in a range-Doppler cell.
- The hypothesis test distinguishes target absence under H0 from target presence under H1.
- Because target parameters θ and α are unknown but deterministic, the paper uses a GLRT with maximum-likelihood estimates.
- The analysis assumes one target and no interference sources to study NSP effects tractably.
- Karhunen–Loève expansion converts the continuous observation model into discrete coefficients y_z = Q_z(θ)α + n_z.
- The GLRT statistic is calibrated using a desired false-alarm probability, and detection probability is expressed through central and noncentral chi-squared distributions.
A. PD for Orthogonal Waveforms
For orthogonal waveforms, the paper sets the GLRT threshold from a desired false-alarm probability and derives the corresponding detection probability.
- The orthogonal-waveform threshold δ_Orthog is set according to a desired probability of false alarm.
- The resulting probability of detection for orthogonal waveforms is then derived.
B. PD for NSP Waveforms
The paper formulates GLRT-based detection for NSP radar waveforms and sets the NSP detection threshold according to a desired false-alarm probability.
- The GLRT provides the detection statistic for spectrum-sharing waveforms.
- The NSP detection threshold δNSP is set according to the desired probability of false alarm PPF-NSP.
- The paper also derives the probability of detection for orthogonal waveforms.
V. NUMERICAL RESULTS
The numerical study uses Monte Carlo simulations to compare target detection with orthogonal and NSP waveforms under randomly generated interference channels.
- Monte Carlo simulations generate K Rayleigh interference channels and construct their null-space projection matrices.
- The experiments use the MIMO radar system parameters listed in Table II.
A. Performance of Algorithms (1) and (2)
Algorithms (1) and (2) select the interference channel that minimizes waveform degradation, improving NSP detection performance across different radar-array configurations.
- The algorithms select a projection channel that minimizes waveform degradation and thereby maximizes target detection probability.
- 6 dB to 13 dB more SNR is required for 90% detection with NSP than with orthogonal waveforms when NBS < M.
- BS#5 is selected in the NBS < M example because its NSP waveform requires the least additional SNR for 90% detection.
- 3 dB to 5 dB more SNR is required for 90% detection with NSP than with orthogonal waveforms when the radar has the larger array.
- BS#2 is selected in the larger-array example because its NSP waveform requires the least additional SNR for 90% detection.
B. Case 1: dim N[Hi] = 2
Detection probability increases with SNR for both waveforms, but NSP requires more SNR than orthogonal waveforms; the penalty decreases when the radar has more antennas and a larger null space.
- In Case 1, the 2 × 4 interference channel yields a null-space dimension of 2, with PD evaluated across PFA values from 10^-1 to 10^-7.
- In Case 2, the 2 × 8 interference channel yields a null-space dimension of 6, and NSP requires 3.5 to 4.5 dB more SNR than orthogonal waveforms.
- At fixed SNR, orthogonal waveforms detect targets better because NSP removes waveform orthogonality while ensuring zero interference to the selected BS.
- Increasing the radar array enlarges the interference-channel null space and mitigates NSP's detection-performance penalty.
- 9 to 10 dB more SNR is required for NSP to match orthogonal-waveform performance in Case 1.