ULA Fitting for Sparse Array Design Shi, Wanlu; Vorobyov, Sergiy A.; Li, Yingsong
IEEE transactions on signal processing,
2021, Letnik:
69
Journal Article
Recenzirano
Odprti dostop
Existing sparse array (SA) geometries, such as coprime and nested arrays, can be regarded as a concatenation of two uniform linear arrays (ULAs). Such arrays lead to a significant increase in the ...number of degrees of freedom (DOF) when the second-order information is utilized, i.e., they provide long virtual difference coarrays (DCAs). Thus, the idea of this paper is based on the observation that SAs can be fitted through the concatenations of sub-ULAs. A corresponding SA design principle, called ULA fitting, is then proposed. It aims to design SAs from multiple sub-ULAs. Towards this goal, a polynomial model for arrays is used, and based on it, a DCA structure is analyzed for the general case when an SA is composed of an arbitrary number of sub-ULAs. ULA fitting enables to transfer SA design requirements, such as hole-free, low mutual coupling, and other requirements, into pseudo-polynomial equation, and hence, find particular solutions. We mainly focus on designing SAs with low mutual coupling and large uniform DOF. Two examples of SAs with closed-form expressions are then developed based on ULA fitting. Numerical experiments verify the superiority of the proposed SAs in the presence of heavy mutual coupling.
ABSTRACT
It is now a widely held view that, in their formation and early evolution, stars build up mass in bursts. The burst mode of star formation scenario proposes that the stars grow in mass via ...episodic accretion of fragments migrating from their gravitationally unstable circumstellar discs, and it naturally explains the existence of observed pre-main-sequence bursts from high-mass protostars. We present a parameter study of hydrodynamical models of massive young stellar objects (MYSOs) that explores the initial masses of the collapsing clouds (Mc = 60–$200\, \rm M_{\odot }$) and ratio of rotational-to-gravitational energies (β = 0.005–0.33). An increase in Mc and/or β produces protostellar accretion discs that are more prone to develop gravitational instability and to experience bursts. We find that all MYSOs have bursts even if their pre-stellar core is such that β ≤ 0.01. Within our assumptions, the lack of stable discs is therefore a major difference between low- and high-mass star formation mechanisms. All our disc masses and disc-to-star mass ratios Md/M⋆ > 1 scale as a power law with the stellar mass. Our results confirm that massive protostars accrete about $40\, -\, 60{{\ \rm per\ cent}}$ of their mass in the burst mode. The distribution of time periods between two consecutive bursts is bimodal: there is a short duration ($\sim 1\, -\, 10~\rm yr$) peak corresponding to the short, faintest bursts and a long-duration peak (at $\sim 10^{3}\, -\, 10^{4} \rm yr$) corresponding to the long, FU-Orionis-type bursts appearing in later disc evolution, i.e. around $30\, \rm kyr$ after disc formation. We discuss this bimodality in the context of the structure of massive protostellar jets as potential signatures of accretion burst history.
Abstract
The FU Orionis–type objects (FUors) are low-mass pre-main-sequence stars undergoing a temporary but significant increase of mass accretion rate from the circumstellar disk onto the ...protostar. It is not yet clear what triggers the accretion bursts and whether the disks of FUors are in any way different from the disks of nonbursting young stellar objects. Motivated by this, we conducted a 1.3 mm continuum survey of 10 FUors and FUor-like objects with ALMA, using both the 7 m array and the 12 m array in two different configurations to recover emission at the widest possible range of spatial scales. We detected all targeted sources and several nearby objects as well. To constrain the disk structure, we fit the data with models of increasing complexity from 2D Gaussian to radiative transfer, enabling comparison with other samples modeled in a similar way. The radiative transfer modeling gives disk masses that are significantly larger than what is obtained from the measured millimeter fluxes assuming optically thin emission, suggesting that the FUor disks are optically thick at this wavelength. In comparison with samples of regular class II and class I objects, the disks of FUors are typically a factor of 2.9–4.4 more massive and a factor of 1.5–4.7 smaller in size. A significant fraction of them (65%–70%) may be gravitationally unstable.
ABSTRACT
3D simulations of high mass young stellar object (HMYSO) growth show that their circumstellar discs fragment on to multiple self-gravitating objects. Accretion of these by HMYSO may explain ...episodic accretion bursts discovered recently. We post-process results of a previous 3D simulation of a HMYSO disc with a 1D code that resolves the disc and object dynamics down to the stellar surface. We find that burst-like deposition of material into the inner disc seen in 3D simulations by itself does not always signify powerful accretion bursts. Only high density post-collapse clumps crossing the inner computational boundary may result in observable bursts. The rich physics of the inner disc has a significant impact on the expected accretion bursts: (1) in the standard turbulent viscosity discs, migrating objects can stall at a migration trap at the distance of a few au from the star. However, in discs powered by magnetized winds, the objects are able to cross the trap and produce bursts akin to those observed so far. (2) Migrating objects may interact with and modify the thermal (hydrogen ionization) instability of the inner disc, which can be responsible for longer duration and lower luminosity bursts in HMYSOs. (3) If the central star is bloated to a fraction of an au by a previous episode of high accretion rate, or if the migrating object is particularly dense, a merger rather than a disc-mediated accretion burst results; (4) Object disruption bursts may be super-Eddington, leading to episodic feedback on HMYSO surroundings via powerful outflows.
An interesting relationship between the probability-constrained and worst-case optimization based robust minimum variance (MV) beamformers has been discovered. It is shown that both in the cases of ...circularly symmetric Gaussian and worst-case distributions of the steering vector mismatch, the probability-constrained robust MV beamforming problem can be tightly approximated as a convex second-order cone programming (SOCP) problem. The latter problem is mathematically equivalent to that resulting from the deterministic worst-case approach and, therefore, probability-constrained beamformers can be interpreted and implemented using their deterministic worst-case counterparts. However, an important advantage of the developed probability-constrained MV beamformers with respect to their standard worst-case counterparts is that the former approaches enable to explicitly quantify the parameters of the uncertainty region in terms of the beamformer outage probability.
In this paper, we address the problem of transmit beamspace design for multiple-input multiple-output (MIMO) radar with colocated antennas in application to direction-of-arrival (DOA) estimation. A ...new method for designing the transmit beamspace matrix that enables the use of search-free DOA estimation techniques at the receiver is introduced. The essence of the proposed method is to design the transmit beamspace matrix based on minimizing the difference between a desired transmit beampattern and the actual one while enforcing the constraint of uniform power distribution across the transmit array elements. The desired transmit beampattern can be of arbitrary shape and is allowed to consist of one or more spatial sectors. The number of transmit waveforms is even but otherwise arbitrary. To allow for simple search-free DOA estimation algorithms at the receive array, the rotational invariance property is established at the transmit array by imposing a specific structure on the beamspace matrix. Semidefinite programming relaxation is used to approximate the proposed formulation by a convex problem that can be solved efficiently. We also propose a spatial-division based design (SDD) by dividing the spatial domain into several subsectors and assigning a subset of the transmit beams to each subsector. The transmit beams associated with each subsector are designed separately. Simulation results demonstrate the improvement in the DOA estimation performance offered by using the proposed joint and SDD transmit beamspace design methods as compared to the traditional MIMO radar technique.
This paper considers a formulation of the robust adaptive beamforming (RAB) problem based on worst-case signal-to-interference-plus-noise ratio (SINR) maximization with a nonconvex uncertainty set ...for the steering vectors. The uncertainty set consists of a similarity constraint and a (nonconvex) double-sided ball constraint. The worst-case SINR maximization problem is turned into a quadratic matrix inequality (QMI) problem using the strong duality of semidefinite programming. Then a linear matrix inequality (LMI) relaxation for the QMI problem is proposed, with an additional valid linear constraint. Necessary and sufficient conditions for the tightened LMI relaxation problem to have a rank-one solution are established. When the tightened LMI relaxation problem still has a high-rank solution, the LMI relaxation problem is further restricted to become a bilinear matrix inequality (BLMI) problem. We then propose an iterative algorithm to solve the BLMI problem that finds an optimal/suboptimal solution for the original RAB problem by solving the BLMI formulations. To validate our results, simulation examples are presented to demonstrate the improved array output SINR of the proposed robust beamformer.
The robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) steering vector is considered in the paper. The common criteria to find the best estimate of the ...steering vector are the beamformer output signal-to-noise-plus-interference ratio (SINR) and output power, while the constraints assume as little as possible prior inaccurate knowledge about the SOI, the propagation media, and the antenna array. Herein, in order to find the optimal steering vector, a beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the SOI is away from the DOA region of all linear combinations of the interference steering vectors. The prior knowledge required is some allowable error norm bounds and approximate knowledge of the antenna array geometry and angular sector of the SOI. It turns out that the array output power maximization problem is a non-convex quadratically constrained quadratic programming problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the SOI steering vector. The results are generalized to the case when an ellipsoidal constraint is considered instead of the similarity constraint, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.
The time division multiple access (TDMA) technique has been applied in automotive multiple-input multiple-output (MIMO) radar. However, it suffers from the transmit energy loss, and as a result the ...parameter estimation performance degradation when the number of transmit elements increases. To tackle these problems, a transmit beamspace (TB) Doppler division multiple access (DDMA) approach is proposed. First, a phase modulation matrix with empty Doppler spectrum is introduced. By exploiting the empty Doppler spectrum, a test function based on sequential detection is developed to mitigate the Doppler ambiguity in DDMA waveform. Then, a discrete Fourier transform (DFT)-based TB in slow-time is formed. The proposed method can achieve waveform diversity in Doppler domain and generate a TB in slow-time that concentrates the transmitted power in a fixed spatial region to improve the transmit energy distribution for automotive MIMO radar, which is favored by medium/long range radar (MRR/LRR) applications. As compared to the conventional TDMA technique, the proposed TB DDMA approach can fully exploit the transmission capabilities of all transmit elements to ensure that the emitted power is efficiently used and inherits easy implementation.Moreover, the proposed TB DDMA method avoids the trade-off between the active time for each transmit antenna element and the frame time due to Doppler ambiguity mitigation. Simulation results verify the effectiveness of the proposed TB DDMA approach for automotive MIMO radar.
Classical methods of DOA estimation such as the MUSIC algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix. For a small number of samples, such methods ...are exposed to performance breakdown, as the sample covariance matrix can largely deviate from the true covariance matrix. In this paper, the problem of DOA estimation performance breakdown is investigated. We consider the structure of the sample covariance matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, the subspace leakage is theoretically derived. We also propose a two-step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced. Furthermore, we introduce a phenomenon named as root-swap which occurs in the root-MUSIC algorithm in the low sample size region and degrades the performance of the DOA estimation. A new method is then proposed to alleviate this problem. Numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods. Moreover, the proposed algorithms are combined with the pseudo-noise resampling method to further improve the performance.
PDF
