Sparse Multiple-input Multiple-output Research Articles

Phase Error Correction in Sparse Linear MIMO Radar Based on the Equivalent Phase Center Principle

Multiple-input multiple-output (MIMO) technology is widely used in the field of radar imaging. Array sparse optimization reduces the hardware cost of MIMO radar, while virtual aperture and the equivalent phase center (EPC) principle simplify the radar signal model and reduce the computation and complexity of imaging algorithms. However, the application of sparse array structure and the EPC principle produces a non-negligible phase error, which affects the imaging quality. This paper simplifies the MIMO radar signal model based on the phase center approximation, analyzes the phase error generated by this method, and proposes an improved phase error correction method to solve the problem that the target cannot be well-focused at non-reference distance during imaging. In addition, this paper designs a sparse linear MIMO array with a periodic structure, which reduces the number of transmitting and receiving units, system complexity, and hardware costs. The proposed phase correction method was combined with the wavenumber domain algorithm to simulate and experiment on the designed antenna array, and good experimental results were obtained to verify the effectiveness of the proposed method.

Research on a Near-Field Millimeter Wave Imaging Algorithm and System Based on Multiple-Input Multiple-Output Sparse Sampling

In order to reduce the hardware cost and data acquisition time in near-field scenarios, such as airport security imaging systems, this paper discusses the layout of a multiple-input multiple-output (MIMO) radar array. In view of the existing multi-input multiple-output imaging algorithm, the reconstructed image artifacts and aliasing problems caused by sparse sampling are discussed. In this paper, a multi-station radar array and a corresponding sparse MIMO imaging algorithm based on combined sparse sub-channels are proposed. By studying the wave–number spectrum of backscattered MIMO synthetic aperture radar (SAR) data, the nonlinear relationship between the wave number spectrum and reconstructed image is established. By selecting a complex gain vector, multiple channels are coherently combined effectively, thus eliminating aliasing and artifacts in the reconstructed image. At the same time, the algorithm can be used for the MIMO–SAR configuration of arbitrarily distributed transmitting and receiving arrays. A new multi-station millimeter wave imaging system is designed by using a frequency-modulated continuous wave (FMCW) chip and sliding rail platform as a planar SAR. The combination of the hardware system provides reconfiguration, convenience and economy for the combination of millimeter wave imaging systems in multiple scenes.

Reduced-complexity multiple parameters estimation via toeplitz matrix triple iteration reconstruction with bistatic MIMO radar

In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output (MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovatively addresses the joint estimation of the Direction of Departure (DOD), Direction of Arrival (DOA), and Doppler frequency for incoherent targets. We propose a novel approach that significantly reduces computational complexity by utilizing the Temporal-Spatial Nested Sampling Model (TSNSM). Our methodology begins with a multi-linear mapping mechanism to efficiently eliminate unnecessary virtual Degrees of Freedom (DOFs) and reorganize the remaining ones. We then employ the Toeplitz matrix triple iteration reconstruction method, surpassing the traditional Temporal-Spatial Smoothing Window (TSSW) approach, to mitigate the single snapshot effect and reduce computational demands. We further refine the high-dimensional ESPRIT algorithm for joint estimation of DOD, DOA, and Doppler frequency, eliminating the need for additional parameter pairing. Moreover, we meticulously derive the Cramér-Rao Bound (CRB) for the TSNSM. This signal model allows for a second expansion of DOFs in time and space domains, achieving high precision in target angle and Doppler frequency estimation with low computational complexity. Our adaptable algorithm is validated through simulations and is suitable for sparse array MIMO radars with various structures, ensuring higher precision in parameter estimation with less complexity burden.

Joint design of transmit precoding and antenna selection for multi-user multi-target MIMO DFRC

Dual-function radar and communications (DFRC) systems based on multiple-input multiple-output (MIMO) arrays have received considerable attention in recent years due to their excellent ability to alleviate spectrum congestion. The MIMO DFRC systems enable high-resolution detection of multiple targets while communicating with multiple users simultaneously. However, MIMO arrays require numerous radio frequency (RF) units and suffer a strong mutual coupling among antennas, resulting in significant system overhead and performance degradation, respectively. In light of this, this paper investigates the joint optimization of transmit precoding and antenna selection for MIMO DFRC systems, aiming to improve the angular ambiguity function with a guaranteed communication quality of service (QoS) using a small number of antennas. To address the resultant non-convex optimization problem, both the indirect and direct precoding methods are proposed. In the former, the waveform covariance and antenna selection vector are first jointly optimized via a promoted sparsity along the covariance diagonal, followed by the precoding matrix indirectly derived from the optimal covariance. In the latter, the precoding matrix is directly optimized via an imposed group sparsity under the communication QoS and power constraints. Simulation results demonstrate that the proposed sparse MIMO DFRC system with fewer active antennas can achieve comparable dual-functional performance to that of the full array system.

Hybrid Transceiver Design for Tera-Hertz MIMO Systems Relying on Bayesian Learning Aided Sparse Channel Estimation

Hybrid transceiver design in multiple-input multiple-output (MIMO) Tera-Hertz (THz) systems relying on sparse channel state information (CSI) estimation techniques is conceived. To begin with, a practical MIMO channel model is developed for the THz band that incorporates its molecular absorption and reflection losses, as well as its non-line-of-sight (NLoS) rays associated with its diffused components. Subsequently, a novel CSI estimation model is derived by exploiting the angular-sparsity of the THz MIMO channel. This is followed by designing a sophisticated Bayesian learning (BL)-based approach for efficient estimation of the sparse THz MIMO channel. The Bayesian Cramer-Rao Lower Bound (BCRLB) is also determined for benchmarking the performance of the CSI estimation techniques developed. Finally, an optimal hybrid transmit precoder and receiver combiner pair is designed, which directly relies on the beamspace domain CSI estimates and only requires limited feedback. Finally, simulation results are provided for quantifying the improved mean square error (MSE), spectral-efficiency (SE) and bit-error rate (BER) performance for transmission on practical THz MIMO channel obtained from the HIgh resolution TRANsmission (HITRAN)-database.

Enhanced Automotive Sensing Assisted by Joint Communication and Cognitive Sparse MIMO Radar

Automotive radar is mandated to provide high accuracy direction of arrival (DOA) estimation for safe driving, while remaining a low cost device for feasible mass production. Sparse multiple input multiple output (MIMO) arrays emerge as a primary candidate to meet these requirements. As DOA estimation accuracy is a main indicator of tracking performance, Cramer Rao Bound (CRB) is chosen as the goodness measurement for sparse MIMO array optimization, but its application requires prior information of the road environment. We propose a cognitive sparse MIMO array automotive radar, which “perceives” the road environment via automotive sensing supplemented by co-existed communication from roadside unit to vehicle (R2V). This information is used for co-designing a sparse MIMO array for enhanced automotive sensing and vehicle to roadside unit (V2R) communication. Note that both static RSU and dynamic RSU are usually deployed in Internet of Vehicles (IoV), which can provide continuous transmission coverage and permanent connectivity. The bi-directional communications are integrated into the automotive radar. This is achieved by joint transmit waveform design with spectral nulls for communications and with shared sparse MIMO array co-design for both sensing and high quality V2R communications. Simulation results validate the enhanced automotive sensing performance assisted by the integrated bi-directional communications in the cycle of cognitive-driven optimization.

A dual-resolution unitary ESPRIT method for DOA estimation based on sparse co-prime MIMO radar

In this article, a novel structure of sparse co-prime multiple input multiple output (MIMO) radar is proposed. The proposed sparse co-prime MIMO radar employs one co-prime planar subarray (CPSA) as transmit array and multiple separated co-prime planar subarrays as receive arrays. The receive subarrays are deployed separately yielding long aperture baselines to improve the direction of arrival (DOA) estimation accuracies. A dual-resolution 2-D unitary ESPRIT method is derived for DOA estimation based on such sparse co-prime MIMO radar. First, a noncoherent unitary ESPRIT method is employed to yield coarse DOA estimates using the output signals of sparse co-prime MIMO radar noncoherently. Second, a coherent 2-D unitary ESPRIT method is derived to obtain fine DOA estimates and resolve DOA ambiguity utilizing the coarse DOA estimates. The DOA estimation in presence of unknown inter-subarray phase offsets is also addressed. Then an optimization method is developed to select the appropriate shift distances of the receive CPSAs. Finally, the Cramer-Rao Bound (CRB) of DOA estimation is given to evaluate the accuracy of the proposed estimator. Simulation results confirm that the 2-D DOA estimation accuracies of the proposed approach outperform unitary ESPRIT methods employing conventional co-prime MIMO radar and MIMO radar with rectangular arrays.

Height measurement method of monostatic metre wave multiple input multiple output radar based on coprime array

The height measurement algorithm of metre wave multiple input multiple output (MIMO) radar based on uniform linear array (ULA) has some problems, such as a sharp decline of angle measurement accuracy of ultra-low altitude targets and large fluctuation of height measurement with the change of elevation. In order to solve the above difficult problems, starting from the perspective of reducing the influence of multipath effect by array structure, coprime array (CPA) is applied to the height measurement of monostatic metre wave MIMO radar. In this paper, the signal model of monostatic CPA metre wave MIMO radar is established under the condition of flat ground, a height measurement method using physical array is proposed based on the derivation that it is infeasible to use virtual array method for height measurement, it fills the gap of low elevation estimation method based on sparse array metre wave MIMO radar. The proposed method calculates the echo data according to the characteristics of the steering vector of CPA, then obtains the accurate low elevation by using the generalised multiple signal classification algorithm, and finally the target height is obtained by using the geometric relationship. Simulation experiments compare three typical CPAs with ULA using equal array elements, and verify the superiority of height measurement performance of monostatic metre wave MIMO radar based on CPA and the effectiveness of the proposed method.

Sparse Automotive MIMO Radar for Super-Resolution Single Snapshot DOA Estimation With Mutual Coupling

A novel sparse automotive multiple-input multiple-output (MIMO) radar configuration is proposed for low-complexity super-resolution single snapshot direction-of-arrival (DOA) estimation. The physical antenna effects are incorporated in the signal model via open-circuited embedded-element patterns (EEPs) and coupling matrices. The transmit (TX) and receive (RX) array are each divided into two uniform sparse sub-arrays with different inter-element spacings to generate two MIMO sets. Since the corresponding virtual arrays (VAs) of both MIMO sets are uniform, the well-known spatial smoothing (SS) algorithm is applied to suppress the temporal correlation among sources. Afterwards, the co-prime array principle between two spatially smoothed VAs is deployed to avoid DOA ambiguities. A performance comparison between the sparse and conventional MIMO radars with the same number of TX and RX channels confirms a spatial resolution enhancement. Meanwhile, the DOA estimation error due to the mutual coupling (MC) is less pronounced in the proposed sparse architecture since antennas in both TX and RX arrays are spaced larger than half wavelength apart.

Efficient Beamforming Technique Based on Sparse MIMO Array and Spatial Filter Bank

Spatial diversity gained through different beamforming techniques in antenna array is one of the main advantages over the single antenna. Antenna complexity and beamwidth broadening at the scanning angles other than broadside are downsides of antenna arrays that prevent its practical implementation from some applications. In this letter, we propose an efficient beamforming method based on the sparse multiple-input–multiple-output (MIMO) array and spatial filter bank (SFB). The sparse MIMO array produces narrow beams while significantly reduces the number of array elements without compromising system performance. Multiple main beams are chosen from grating lobes by SFB. By combining sparse array geometry and SFB, we can achieve a narrower beamwidth with less antenna elements, multiple beams, and constant beamwidth. The burden of system will be transferred from the frontend hardware to the signal processing back end.

Near-Field Synthetic Spectrum Imaging Algorithm Based on Single-Frequency Sparse MIMO Array

This letter presents a two-dimensional near-field synthetic spectrum imaging algorithm based on a single-frequency sparse multiple-input–multiple-output (MIMO) array. By using an especially defined backward spreading function, the proposed algorithm migrates the scattered wave field under different illuminations. A synthetic spectrum can be obtained by synthesizing the spectrums of these migration results and then interpreted to the final reconstruction. The migration processing enables the algorithm to adapt to arbitrary apertures. Meanwhile, the influences of the limited aperture, the spreading loss, and the wavefront curvature in the near field are considered and compensated. High processing speed is achieved by using a large interpixel spacing during the migration processing and by the fast Fourier transform in the frequency-wavenumber (f-w) domain. Simulations and experiments are carried out, and the results demonstrate both the high-computational efficiency and the high flexibility for arbitrary sparse MIMO array apertures.

Near-Field MIMO-SAR Millimeter-Wave Imaging With Sparsely Sampled Aperture Data

The primary challenge of a cost-effective and low-complexity near-field millimeter-wave (mmWave) imaging system is to achieve high resolution with a few antenna elements as possible. Multiple-input multiple-output (MIMO) radar using simultaneous operation of spatially diverse transmit and receive antennas is a good candidate to increase the number of available degrees of freedom. On the other hand, higher integration complexity of extremely dense transceiver electronics limits the use of MIMO only solutions within a relatively large imaging aperture. Hybrid concepts combining synthetic aperture radar (SAR) techniques and sparse MIMO arrays present a good compromise to achieve short data acquisition time and low complexity. However, compared with conventional monostatic sampling schemes, image reconstruction methods for MIMO-SAR are more complicated. In this paper, we propose a high-resolution mmWave imaging system combining 2-D MIMO arrays with SAR, along with a novel Fourier-based image reconstruction algorithm using sparsely sampled aperture data. The proposed algorithm is verified by both simulation and processing real data collected with our mmWave imager prototype utilizing commercially available 77-GHz MIMO radar sensors. The experimental results confirm that our complete solution presents a strong potential in high-resolution imaging with a significantly reduced number of antenna elements.

Microwave Imaging of Non-Rigid Moving Target Using 2D Sparse MIMO Array

This paper develops a microwave/mmw (millimeter-wave) imaging method for moving objects of non-rigid body which can be used in the heavy traffic scenarios. This method is proposed with a 2D sparse MIMO (multiple-input multiple-output) array composed of two orthogonal linear arrays. In comparison to the RX antennas, a smaller number of TX antennas is used to decrease the data acquisition time of this system when using TDM (time division multiplexing) signal transmitting technique. The 2D sparse MIMO array is deployed with wide-band signals transmitted to reconstruct the backscattering coefficient in 3D space using synthetic aperture imaging technique. Then a series of synthesized 3D snapshot images are generated during the motion of the target. The non-rigid human body target is decomposed into 25 joints tracked by an optical device which is Kinect in this paper. After the decomposition, the movement of each joint can be described as a space-time trajectory tracked by Kinect, providing a preliminary indication of the 3D position of each joint. With the indication, we divide every microwave/mmw image into 25 sub-images corresponding to the joints’ position to form an image sequence of each joint. Subsequently, a segmental joint estimation method is proposed to estimate the accurate motion parameters of each joint from the image sequence. The decorrelation of the images in large angle observation can be significantly reduced by the segmental estimation which leads global optimized motion parameters. Consequently, the estimated parameters are taken into the effective movement compensation of each component. Meanwhile, the image refocusing method is presented to generate the well-focused image of each component. Finally, all the images of components are fused into one image of the whole target to reconstruct the 3D high-resolution image. Imaging simulations and measuring data experiments show that this method is efficient.

GA Based Estimation of Sparse MIMO Channels with Superimposed Training

Multiple-input multiple-output (MIMO) techniques are foreseen to play a vital role in future 5G cellular networks. This paper presents a novel approach that employs genetic algorithm (GA) to estimate the sparse uplink MIMO channels using superimposed training sequence (SiT). At each transmitter (user) a training sequence is mathematically added with the data bits; thus, avoiding the overhead of dedicated frequency/time slots used for the training. On the receiver side (base station), signals received at all the receive antennas are jointly processed by employing the proposed method to obtain channels’ estimate. Then, a linear minimum mean square error (LMMSE) equalizer estimates the data sequences sent by transmitter. A computer simulation based performance analysis of the proposed method is presented, where performance evaluation is done using metrics of normalized channel mean square error (NCMSE), as well as, bit error rate (BER). A comparative analysis of the proposed method with notable SiT least squares (SiT-LS) and SiT-LMMSE methods in the literature is conducted, which clearly demonstrates that the proposed method outperforms both the existing techniques. DOI: http://dx.doi.org/10.5755/j01.eie.24.6.22294

Off-the-Grid Sparse Imaging by One-Dimensional Sparse MIMO Array

Conventional multiple-input multiple-output (MIMO) technique applied into the millimeter-wave and terahertz (THz) imaging applications would suffer from the large number of array elements due to their short wavelengths. In this paper, to reduce the array elements for azimuth-range imaging, a 1-D sparse MIMO array is introduced that combines with the wideband emitted signal to achieve 2-D imaging in the near field. Provided with these greatly reduced spatial samples measured by the sparse array, an off-the-grid sparse imaging algorithm is proposed to recover the arbitrarily distributed scatterers in a 2-D plane. In particular, the proposed approach takes advantages of the MIMO geometry and matrix pencil (MP) method. It utilizes the echo in wave-number domain which is featured by the MIMO geometry to make a lossless dimension reduction from the 2-D unknown position of each scatterer into a local 1-D frequency. After estimating those local 1-D frequencies by the MP method, an MIMO-structure-determined filter is developed to fulfill the inverse mapping and finally achieve imaging without the pairing problem. Simulations and experiments verify the effectiveness of the proposed approach.

Design of Sparse FIR Decision Feedback Equalizers in MIMO Systems Using Hybrid l₁/l₂ Norm Minimization and the OMP Algorithm.

In this paper, a novel scheme using hybrid l1/l2 norm minimization and the orthogonal matching pursuit (OMP) algorithm is proposed to design the sparse finite impulse response (FIR) decision feedback equalizers (DFE) in multiple input multiple output (MIMO) systems. To reduce the number of nonzero taps for the FIR DFE while ensuring its design accuracy, the problem of designing a sparse FIR DFE is transformed into an l0 norm minimization problem, and then the proposed scheme is used to obtain the sparse solution. In the proposed scheme, a sequence of minimum weighted l2 norm problems is solved using the OMP algorithm. The nonzero taps positions can be corrected with the different weights in the diagonal weighting matrix which is computed through the hybrid l1/l2 norm minimization. The simulation results verify that the sparse FIR MIMO DFEs designed by the proposed scheme get a significant reduction in the number of nonzero taps with a small performance loss compared to the non-sparse optimum DFE under the minimum mean square error (MMSE) criterion. In addition, the proposed scheme provides better design accuracy than the OMP algorithm with the same sparsity level.

Spatially Correlated Sparse MIMO Channel Path Delay Estimation in Scattering Environments Based on Signal Subspace Tracking.

A parametric scheme for spatially correlated sparse multiple-input multiple-output (MIMO) channel path delay estimation in scattering environments is presented in this paper. In MIMO outdoor communication scenarios, channel impulse responses (CIRs) of different transmit–receive antenna pairs are often supposed to be sparse due to a few significant scatterers, and share a common sparse pattern, such that path delays are assumed to be equal for every transmit–receive antenna pair. In some existing works, an exact common support condition is exploited, where the path delays are considered equal for every transmit–receive antenna pair, meanwhile ignoring the influence of scattering. A more realistic channel model is proposed in this paper, where due to scatterers in the environment, the received signals are modeled as clusters of multi-rays around a nominal or mean time delay at different antenna elements, resulting in a non-strictly exact common support phenomenon. A method for estimating the channel mean path delays is then derived based on the subspace approach, and the tracking of the effective dimension of the signal subspace that changes due to the wireless environment. The proposed method shows an improved channel mean path delays estimation performance in comparison with the conventional estimation methods.

Multiple input multiple output radar imaging based on multidimensional linear equations and sparse signal recovery

Multiple input multiple output (MIMO) radar forms large virtual aperture and improves the cross-range resolution of radar imaging. Sparse signal recovery algorithms can be used to improve image quality of target with sparse property in spatial domain. Conventional sparse signal recovery-based MIMO radar imaging method rearranges the received two-dimensional (2D) or 3D signals into a vector, then linear equations describing the relation between the received signal and the reflectivity of the scatterers are solved. However, this method occupies huge memory spaces and increases the computational load. In this study, by introducing synthetic codes, multidimensional linear equations of MIMO radar imaging are derived, which occupy less memory spaces and cost less computationally. A L 1 L 0 norms homotopy sparse signal recovery algorithm for multidimensional linear equations is used to recover the image. Simulation results verify the high efficiency of using multidimensional linear equations.

Compressed Sensing of Sparse Multipath MIMO Channels with Superimposed Training Sequence

Recent advances in multiple-input multiple-output (MIMO) systems have renewed the interests of researchers to further explore this area for addressing various dynamic challenges of emerging radio communication networks. Various measurement campaigns reported recently in the literature show that physical multipath MIMO channels exhibit sparse impulse response structure in various outdoor radio propagation environments. Therefore, a comprehensive physical description of sparse multipath MIMO channels is presented in first part of this paper. Superimposing a training sequence (low power, periodic) over the information sequence offers an improvement in the spectral efficiency by avoiding the use of dedicated time/frequency slots for the training sequence, which is unlike the traditional schemes. The main contribution of this paper includes three superimposed training (SiT) sequence based channel estimation techniques for sparse multipath MIMO channels. The proposed techniques exploit the compressed sensing theory and prior available knowledge of channel's sparsity. The proposed sparse MIMO channel estimation techniques are named as, SiT based compressed channel sensing (SiT-CCS), SiT based hardlimit thresholding with CCS (SiT-ThCCS), and SiT training based match pursuit (SiT-MP). Bit error rate (BER) and normalized channel mean square error are used as metrics for the simulation analysis to gauge the performance of proposed techniques. A comparison of the proposed schemes with a notable first order statistics based SiT least squares (SiT-LS) estimation technique is presented to establish the improvements achieved by the proposed schemes. For sparse multipath time-invariant MIMO communication channels, it is observed that SiT-CCS, SiT-MP, and SiT-ThCCS can provide an improvement up to 2, 3.5, and 5.2 dB in the MSE at signal to noise ratio (SNR) of 12 dB when compared to SiT-LS, respectively. Moreover, for $$\mathrm {BER}=10^{-1.9}$$BER=10-1.9, the proposed SiT-CCS, SiT-MP, and SiT-ThCCS, compared to SiT-LS, can offer a gain of about 1, 2.5, and 3.5 dB in the SNR, respectively. The performance gain in MSE and BER is observed to improve with an increase in the channel sparsity.

Structured compressive sensing‐based non‐orthogonal time‐domain training channel state information acquisition for multiple input multiple output systems

In practical multiple input multiple output (MIMO) systems, accurate knowledge of the channel state information (CSI) is a prerequisite to guarantee the system performance. The conventional CSI acquisition methods for MIMO system usually rely on the orthogonal (either time- or frequency-domain) training sequences (TSs) to estimate the channel associated with each transmit–receive antenna pair, which is not spectrally efficient. This study proposes a non-orthogonal time-domain training-based CSI acquisition approach for MIMO systems under the framework of structured compressive sensing. By exploiting the spatial–temporal correlations of the sparse MIMO channels, a spatially–temporally spARsity-adaptivE-simultaneous orthogonal matching pursuit algorithm is proposed, which could use the inter-block interference free region of very small dimension within the received TS to recover the multiple channels. Furthermore, the proposed algorithm could utilise the priori channel partial common support to improve the recovery probability and reduce the complexity. Simulation results show that the proposed scheme has better performance and higher spectral efficiency than the conventional MIMO schemes, which might be an appealing solution for the future wireless communications.