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Pareto Sums of Pareto Sets: Lower Bounds and algorithms

algorithmICA 2025年 1-34页

作者： Funke, Daniel Hespe, Demian Sanders, Peter Storandt, Sabine Truschel, Carina KIT D-76128 Karlsruhe Germany Univ Konstanz Univ Str D-78464 Constance Germany

In bi-criteria optimization problems, the goal is typically to compute the set of Pareto-optimal solutions. Many algorithms for these types of problems rely on efficient merging or combining of partial solutions and filtering of dominated solutions in the resulting sets. In this article, we consider the task of computing the Pareto sum of two given Pareto sets A, B of size n. The Pareto sum C contains all non-dominated points of the Minkowski sum M={a+b|a is an element of A, b is an element of B}. Since the Minkowski sum has a size of n(2), but the Pareto sum C can be much smaller, the goal is to compute C without having to compute and store all of M. We present several new algorithms for efficient Pareto sum computation, including an output-sensitive successive algorithm with a running time of O(n log n + nk) and a space consumption of O(n+k) for k = |C|. If the elements of C are streamed, the space consumption reduces to O(n). For output sizes k >= 2n, we prove a conditional lower bound for Pareto sum computation, which excludes running times in O(n(2-delta)) for delta > 0 unless the (min,+)-convolution hardness conjecture fails. The successive algorithm matches this lower bound for k is an element of Theta(n). However, for k is an element of Theta(n(2)), the successive algorithm exhibits a cubic running time. But we also present an algorithm with an output-sensitive space consumption and a running time of O(n(2)logn), which matches the lower bound up to a logarithmic factor even for large k. Furthermore, we describe suitable engineering techniques to improve the practical running times of our algorithms. Finally, we provide an extensive comparative experimental study on generated and real-world data. As a showcase application, we consider preprocessing-based bi-criteria route planning in road networks. Pareto sum computation is the bottleneck task in the preprocessing phase and in the query phase. We show that using our algorithms with an output-sensitive space c

关键词： Minkowski Sum Skyline successive algorithm Fine-grained Complexity

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MIMO Radar Mainlobe Gain Control Design for Co-Existence With Wireless Communication Systems

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IEEE ACCESS 2024年 12卷 65919-65927页

作者： Aldayel, Omar King Saud Univ Dept Elect Engn Riyadh 11421 Saudi Arabia PSATRI Riyadh 13244 Saudi Arabia

We tackle the issue of designing a transmit beampattern for multiple-input multiple-output (MIMO) radar while considering its coexistence with wireless communication systems. Our goal is to design a beampattern that can steer the mainlobe and regulate its gain level toward the desired direction. The significant challenge lies in concurrently enforcing the gain constraint along with the constant modulus constraint on the radar waveform. In our work, we propose a novel approach that entails solving a series of constrained quadratic programs to achieve constant modulus at convergence. Additionally, we demonstrate that each problem in the sequence admits a closed-form solution, ensuring analytical tractability. We assess the effectiveness of our proposed Mainlobe and Interference Control (MAIC) algorithm against state-of-the-art MIMO beampattern design techniques, illustrating that MAIC attains the desired gain level while mitigating interference energy in undesired areas.

关键词： Wireless communication Radar antennas Optimization Interference Millimeter wave radar Microwave antenna arrays MIMO communication Beampattern design co-existence constant modulus electronic steering main lobe energy constraint MIMO radar successive algorithm

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successive algorithm Using Discrete-Time Oscillator Network for Three-Dimensional Image Segmentation

Successive Algorithm Using Discrete-Time Oscillator Network ...

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International Conference on Innovations in Engineering and Technology (ICIET’2013, Bangkok)

作者： Ken'ichi Fujimoto Mio Kobayashi Tetsuya Yoshinaga Department of Systems and Control Engineering Anan National College of Technology

To extract three-dimensional(3D) image regions from a 2D sketch that we roughly draw the outline of target image regions in an image slice, we proposed an algorithm using a discrete-time oscillator network that we have developed. This oscillator network can produce the set of 2D fragments that corresponds to all combinations of 2D image regions. To improve the accuracy of 3D image segmentation, the parameter values of the oscillator network were optimized according to our analyzed results on responses from oscillators. For a 2D rough sketch of target image regions given as the initial reference image, the proposed algorithm successively provides the reference image for the neighbor slice as the fragment that is closest to the reference image for the current slice. Hence, a slice of 3D target image regions is extracted every slice. We also demonstrated that the proposed algorithm worked for 3D medical images.

关键词： Image segmentation discrete-time oscillator network successive algorithm fragment

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Computationally Efficient Direction-of-Arrival Estimation algorithms for a Cubic Coprime Array

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SENSORS 2022年第1期22卷 136-136页

作者： Gong, Pan Chen, Xixin Nanjing Vocat Univ Ind Technol Coll Elect Engn Nanjing 211106 Peoples R China

In this paper, we investigate the problem of direction-of-arrival (DOA) estimation for massive multi-input multi-output (MIMO) radar, and propose a total array-based multiple signals classification (TA-MUSIC) algorithm for two-dimensional direction-of-arrival (DOA) estimation with a coprime cubic array (CCA). Unlike the conventional multiple signal classification (MUSIC) algorithm, the TA-MUSIC algorithm employs not only the auto-covariance matrix but also the mutual covariance matrix by stacking the received signals of two sub cubic arrays so that full degrees of freedom (DOFs) can be utilized. We verified that the phase ambiguity problem can be eliminated by employing the coprime property. Moreover, to achieve lower complexity, we explored the estimation of signal parameters via the rotational invariance technique (ESPRIT)-based multiple signal classification (E-MUSIC) algorithm, which uses a successive scheme to be computationally efficient. The Cramer-Rao bound (CRB) was taken as a theoretical benchmark for the lower boundary of the unbiased estimate. Finally, numerical simulations were conducted in order to demonstrate the effectiveness and superiority of the proposed algorithms.

关键词： direction-of-arrival estimation massive multi-input multi-output Cramer-Rao bound ambiguity elimination total array-based multiple signal classification successive algorithm

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Tractable Transmit MIMO Beampattern Design Under a Constant Modulus Constraint

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第10期65卷 2588-2599页

作者： Aldayel, Omar Monga, Vishal Rangaswamy, Muralidhar Penn State Univ Dept Elect Engn State Coll PA 16801 USA US Air Force RF Exploitat Branch Res Lab Dayton OH 45433 USA

Multiple-input multiple-output (MIMO) radar systems allow each antenna element to transmit a different waveform. This waveform diversity can be exploited to enhance the beampattern design, in particular, effective management of radar radiation power in directions of interest. We address the problem of designing a beampattern for MIMO radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. It is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem. Existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our paper, which involves solving a sequence of convex equality constrained quadratic programs, each of which has a closed form solution and such that constantmodulus is achieved at convergence. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker optimality conditions of the aforementioned hard nonconvex problem. We evaluate the proposed successive closed forms (SCF) algorithm against the state-of-the art MIMO beampattern design techniques in both narrowband and wideband setups and show that the SCF breaks the tradeoff between desirable performance and the associated computation cost.

关键词： MIMO radar wideband beampattern constant modulus successive algorithm SCF

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Adaptive Sequential Refinement: A Tractable Approach for Ambiguity Function Shaping in Cognitive Radar 51

Adaptive Sequential Refinement: A Tractable Approach for Amb...

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51st IEEE Asilomar Conference on Signals Systems and Computers

作者： Aldayel, Omar Guo, Tiantong Monga, Vishal Rangaswamy, Muralidhar Penn State Univ Dept Elect Engn University Pk PA 16802 USA Air Force Res Lab Sensors Directorate Wright Patterson AFB OH USA

ISBN: (纸本)9781538618233

Ambiguity function shaping continues to be one of the most challenging open problems in cognitive radar. Analytically, a complex quartic function should be optimized as a function of the radar waveform code. Practical considerations further require that the waveform be constant modulus, which exacerbates the issue and leads to a hard non-convex problem. We develop a new approach called Adaptive Sequential Refinement (ASR) to suppress the clutter returns for a desired range-Doppler, i.e. ambiguity function response. ASR solves the aforementioned optimization problem in a unique iterative manner such that the formulation is updated depending on the iteration index. We establish formally that: 1.) the problem in each step of the iteration has a closed form solution, and 2.) monotonic decrease of the cost function until convergence is guaranteed. Experimental validation shows that ASR produces a radar waveform with higher Signal to Interference Ratio (SIR) and superior ambiguity function shaping than state of the art alternatives even as its computational burden is orders of magnitude lower.

关键词： Radar signal radar waveform optimization constant modulus successive algorithm

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Transmit MIMO Beampattern Design Under Constant Modulus and Spectral Interference Constraints

Transmit MIMO Beampattern Design Under Constant Modulus and ...

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IEEE Radar Conference (RadarConf)

作者： Aldayel, Omar Monga, Vishal Rangaswamy, Muralidhar Penn State Univ Dept Elect Engn University Pk PA 16802 USA Air Force Res Lab Sensors Directorate Wright Patterson AFB OH USA

ISBN: (纸本)9781467388238

In multiple array radar systems, waveform diversity can be exploited to enhance the beampattern design. However, in a spectrally crowded environment, the spectral shape of radar waveforms must be compatible with civilian and other wireless communication services. We address the problem of designing a beampattern for MIMO radar under a spectral interference constraint. The problem essentially reduces to a constrained design of the radar waveform, where a key open challenge is jointly enforcing the spectral interference constraint in addition to the constant modulus constraint (CMC). A new approach is proposed in our work, which involves solving a sequence of convex Constrained Quadratic Programs, each of which has a closed form solution and such that constant modulus is achieved at convergence. New analytical results are provided in support of the proposed Beampattern design under constant modulus and Interference Constraints (BIC). We evaluate the proposed BIC algorithm against state of the art MIMO beampattern design methods that enforce constant modulus and show that BIC achieves a high fidelity radar beampattern while maintaining low spectral interference in the desired bands.

关键词： MIMO radar beampattern design spectral interference constant modulus successive algorithm BIC

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successive QCQP Refinement for MIMO Radar Waveform Design Under Practical Constraints

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第14期64卷 3760-3774页

作者： Aldayel, Omar Monga, Vishal Rangaswamy, Muralidhar Penn State Univ Dept Elect Engn University Pk PA 16802 USA US Air Force Res Lab RF Exploitat Branch Dayton OH USA

The authors address the problem of designing a waveform for multiple-input multiple-output (MIMO) radar under the important practical constraints of constant modulus and waveform similarity. Incorporating these constraints in an analytically tractable manner is a longstanding open challenge. This is due to the fact that the optimization problem that results from signal-to-interference-plus-noise ratio (SINR) maximization subject to these constraints is a hard non-convex problem. The authors develop a new analytical approach that involves solving a sequence of convex quadratically constrained quadratic programing (QCQP) problems, which they prove converges to a sub-optimal solution. Because an improvement in SINR results via solving each problem in the sequence, they call the method successive QCQP Refinement (SQR). Furthermore, the proposed SQR method can be easily extended to incorporate emerging requirements of spectral coexistence, as shown briefly in this paper. The authors evaluate SQR against other candidate techniques with respect to SINR performance, beam pattern, and pulse compression properties in a variety of scenarios. Results show that SQR outperforms state-of-the-art methods that also employ constant modulus and/or similarity constraints while being computationally less burdensome.

关键词： MIMO radar waveform design constant modulus similarity constraint successive algorithm phase coding SQR interference constraint cognitive radar

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Tractable MIMO Beampattern Design Under Constant Modulus Waveform Constraint

Tractable MIMO Beampattern Design Under Constant Modulus Wav...

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IEEE Radar Conference (RadarConf)

作者： Aldayel, Omar Monga, Vishal Rangaswamy, Muralidhar Penn State Univ Dept Elect Engn University Pk PA 16802 USA Sensors Directorate Air Force Res Lab Wright Patterson AFB OH USA

ISBN: (纸本)9781509008636

Multiple-Input Multiple-Output (MIMO) radar system allows each antenna element to transmit a different waveform. This waveform diversity can be utilized to enhance the beampattern design, in particular effective management of radar radiation power in directions of interest. In this paper, we address the problem of designing a beampattern for Multiple-Input Multiple-Output (MIMO) radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. Existing beampattern design methods that address constant modulus invariably lead to a stiff trade-off between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our work, which involves solving the hard non-convex problem of beampattern design using a sequence of convex Equality Constrained Quadratic Programs, each of which has a closed form solution. Constant modulus is achieved at convergence, which we prove formally is possible under mild and realistic assumptions. We evaluate the proposed successive closed forms (SCF) algorithm against state of the art MIMO beampattern design techniques and show that SCF breaks the trade-off between desirable performance and the associated computation cost.

关键词： MIMO radar wideband beampattern constant modulus successive algorithm SCF

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SQR: successive QCQP Refinement for MIMO Radar Waveform Design Under Practical Constraints 49

SQR: Successive QCQP Refinement for MIMO Radar Waveform Desi...

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49th Asilomar Conference on Signals, Systems and Computers

作者： Aldayel, Omar Monga, Vishal Rangaswamy, Muralidhar Penn State Univ Dept Elect Engn University Pk PA 16802 USA Air Force Res Lab Dayton OH USA

ISBN: (纸本)9781467385763

We address the problem of designing a waveform for Multiple-Input Multiple-Output (MIMO) radar under important practical constraints, namely the constant modulus and the waveform similarity constraints. Incorporating these constraints in an analytically tractable manner continues to be longstanding open challenge. This is because the optimization problem that results from Signal to Interference plus Noise Ratio (SINR) maximization subject to these constraints is a hard non-convex problem. We develop a new analytical approach that involves solving a sequence of convex Quadratic Constrained Quadratic Programing (QCQP) problems, which we prove converges to a sub-optimal solution. We call the method successive QCQP Refinement (SQR). We evaluate SQR against state of the art in its SINR performance for a practical scenario and show that it outperforms existing methods without incurring a significant computational burden.

关键词： MIMO radar waveform design constant modulus similarity constraint successive algorithm phase coding SQR

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