The ambiguity function plays an important role in radar systems. In fact, many radar design problems can be interpreted from the perspective of persuing desired ambiguity functions to adapt to ...various application scenes. In this paper, we consider designing a radar sequence, subject to a peak-to-average power ratio (PAR) constraint, to maximize the signal-to-interference plus noise ratio, which can also be interpreted as designing a sequence with a desired ambiguity function. From an optimization point of view, this is equivalent to optimizing a complex quartic function with the PAR constraint. An efficient algorithm based on the general majorization-minimization (MM) method is developed to solve this problem with guaranteed convergence to a stationary point under some mild conditions. In addition, the unit-modulus constraint, as a special case, is considered and another algorithm is proposed, which is the combination of the general MM and the coordinate descent method. Numerical experiments show that the proposed algorithms can shape a desired ambiguity function based on the prior information, and the performance is much better compared with the existing methods.
The joint design problem for the coexistence of multiple‐input multiple‐output (MIMO) radar and multi‐user multiple‐input‐single‐output (MU‐MISO) communication is investigated. Different from the ...conventional design schemes, which require defining the primary function, we consider designing the transmit waveform, precoding matrix and receive filter to maximize the radar SINR and the minimal SINR of communication users, simultaneously. By doing so, the promising overall performance for both sensing and communication is achieved without requiring parameter tuning for the threshold of communication or radar. However, the resulting optimization problem which contains the maximin objective function and the unit sphere constraint, is highly nonconvex and hence difficult to attain the optimal solution directly. Towards this end, the epigraph‐form reformulation is first adopted, and then an alternating maximisation (AM) method is devised, in which the Dinkelbach’s algorithm is used to tackle the nonconvex fractional‐programing subproblem. Simulation results indicate that the proposed method can achieve improved performance compared with the benchmarks.
In this paper, we consider the joint design of both transmit waveforms and receive filters for a colocated multiple-input-multiple-output (MIMO) radar with the existence of signal-dependent ...interference and white noise. The design problem is formulated into a maximization of the signal-to-interference-plus-noise ratio (SINR), including various constraints on the transmit waveforms. Compared with the traditional alternating semidefinite relaxation approach, a general and flexible algorithm is proposed based on the majorization-minimization method with guaranteed monotonicity, lower computational complexity per iteration and/or convergence to a B-stationary point. Many waveform constraints can be flexibly incorporated into the algorithm with only a few modifications. Furthermore, the connection between the proposed algorithm and the alternating optimization approach is revealed. Finally, the proposed algorithm is evaluated via numerical experiments in terms of SINR performance, ambiguity function, computational time, and properties of the designed waveforms. The experiment results show that the proposed algorithms are faster in terms of running time and meanwhile achieve as good SINR performance as the the existing methods.
For an extended target with different polarimetric responses, one way of improving the detection performance is to exploit waveform diversity on the dimension of polarization. In this article, we ...focus on the joint design of transmit signal and receive filter for polarimetric radars with local waveform constraints. Considering the signal-to-interference-plus-noise ratio (SINR) as the figure of merit to optimize, where the average target-impulse-response matrix within a certain target-aspect-angle (TAA) interval is employed as the target response, the waveform is decomposed and then designed for both horizontal and vertical polarization segments, subject to energy and similarity constraints. An iterative algorithm is proposed based on the majorization–minimization method to solve the formulated problem. The developed algorithm guarantees the convergence to a B-stationary point, where in each iteration, optimal horizontal and vertical transmit waveforms are, respectively, solved by using the feasible point pursuit and successive convex approximation technique. Experimental results show the effectiveness of the proposed algorithm, the robustness of the output SINR against the TAA change, and the advantages of polarization diversity and local design.
The topic of sequence design has received considerable attention due to its wide applications in active sensing. One important desired property for the design sequence is the spectral shape. In this ...paper, the sequence design problem is formulated by minimizing the regularized spectral level ratio subject to a peak-to-average power ratio constraint. Then, two algorithms are proposed by combining both the Dinkelbach's algorithm and the majorization-minimzation (MM) method organically. Specifically, by using the Dinkelbach's algorithm, the challenging fractional programming problem can be handled by solving a series of subproblems, which are further solved via the MM method. The numerical experiments verify the effectiveness of the optimization metric and demonstrate the performance of the proposed algorithms compared with the benchmark.
•We conducted new simulations on S&P 500. From this new simulation, we can see that the portfolio behaves as we expected as it achieves a good tradeoff among different metrics of interest. However, ...since the initial set of assets changes and we have no preporcessing on the large scale data, the performance will deteriorate to some degree as we expect.•We explained some technical points in terms of the proposed algorithm, especially in terms of the efficiency.•We revised some illustrations of the focus of this paper to make our point more clear. This paper proposed a sparse risk parity portfolio and the corresponding fast solving numerical algorithm. The algorithm can design the portfolio weights well with the support of read data simulation.
Since the 2008 financial crisis, risk management has become more important and portfolio approaches, such as the minimum-variance and equally weighted portfolios, have gained popularity. However, such portfolios still do not diversify the risk in the true sense. Recently, risk parity portfolios has been receiving significant interest from both the theoretical and practical perspectives due to its advantages in the diversification of (ex-ante) risk contributions among assets. However, this portfolio type usually results in nonzero weights in all the assets, which implies high transaction cost in practice. In addition, focusing only on the risk aspect can make this type of portfolio unsatisfactory if other performance factors, e.g., annual yield, are considered. In this paper, we jointly consider asset selection and risk diversification via imposing sparsity and risk parity regularization in the portfolio problem formulation, which turns out to be a general and flexible portfolio framework. Then we propose an efficient sequential algorithm based on the successive convex optimization framework. The numerical results on historical data show that our portfolio approach, compared with benchmark portfolios, can achieve a good balance among asset selection, risk diversification and other evaluation criteria, and achieves the best performance on profit and loss (P&L) and/or drawdown.
This paper focuses on optimal time-of-arrival (TOA) sensor placement for multiple target localization simultaneously. In previous work, different solutions only using non-shared sensors to localize ...multiple targets have been developed. Those methods localize different targets one-by-one or use a large number of mobile sensors with many limitations, such as low effectiveness and high network complexity. In this paper, firstly, a novel optimization model for multi-target localization incorporating shared sensors is formulated. Secondly, the systematic theoretical results of the optimal sensor placement are derived and concluded using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), based on rigorous geometrical derivations. The reachable optimal trace of Cramér-Rao lower bound (CRLB) is also derived. It can provide optimal conditions for many cases and even closed form solutions for some special cases. Thirdly, a novel numerical optimization algorithm to quickly find and calculate the (sub-)optimal placement and achievable lower bound is explored, when the model becomes complicated with more practical constraints. Then, a hybrid method for solving the most general situation, integrating both the analytical and numerical solutions, is proposed. Finally, the correctness and effectiveness of the proposed theoretical and mathematical methods are demonstrated by several simulation examples.
Extremely low-resolution (e.g. one-bit) analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) can substantially reduce hardware cost and power consumption for MIMO radar ...especially with large scale antennas. In this paper, we focus on the detection performance analysis and joint design for the MIMO radar with one-bit ADCs and DACs. Specifically, under the assumption of low signal-to-noise ratio (SNR) and interference-to-noise ratio (INR), we derive the expressions of probability of detection (<inline-formula><tex-math notation="LaTeX">\mathcal {P}_{d}</tex-math></inline-formula>) and probability of false alarm (<inline-formula><tex-math notation="LaTeX">\mathcal {P}_{f}</tex-math></inline-formula>) for one-bit MIMO radar and also the theoretical performance gap to infinite-bit MIMO radars for the noise-only case. We further find that for a fixed <inline-formula><tex-math notation="LaTeX">\mathcal {P}_{f}</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">\mathcal {P}_{d}</tex-math></inline-formula> depends on the defined quantized signal-to-interference-plus-noise ratio (QSINR), which is a function of the transmit waveform and receive filter. Thus, an optimization problem arises naturally to maximize the QSINR by joint designing the waveform and filter. For the formulated problem, we propose an alternatin g wavefo r m and filt e r d e sign for QSINR maximiza t ion (GREET). At each iteration of GREET, the optimal receive filter is updated via the minimum variance distortionless response (MVDR) method, and due to the difficulty in global optimality, an alternating direction method of multipliers (ADMM) based algorithm is devised to efficiently find a high-quality suboptimal one-bit waveform. Numerical simulations are consistent to the theoretical performance analysis and demonstrate the effectiveness of the proposed design algorithm.
Beam-hopping (BH) technology, integral to multi-beam satellite systems, adapts beam activation to the variable communication demands of terrestrial users. The optimization of power allocation and ...beam illumination scheduling constitutes the core design challenge in BH systems, especially under the constraint on a limited number of simultaneously active beams due to restricted radio frequency chain availability. This paper proposes a two-stage BH design solution, which minimizes energy consumption in BH satellite communications while accommodating the heterogeneous demands of users. The first stage addresses the coupling variables of power and beam status by recasting the allocation and scheduling problem through a statistical lens, thus breaking down the intricate relationship between variables. To manage the resulting non-convex challenge, we propose an iterative method that capitalizes on the optimality conditions inherent to this problem. This method is designed to procure a statistically-informed solution that aligns with our reformulated interpretation. Subsequently, the second stage maps this solution into a concrete beam illumination schedule, employing binary quadratic programming techniques. A penalty-based iterative method is applied, ensuring convergence to a locally optimal solution. Through numerical simulations, the proposed framework has been validated for its efficacy in improving energy efficiency and accurately matching demands.
In polarimetric radars, corresponding to the polarized antennas, exploiting waveform diversity along the polarization dimension becomes accessible. In this article, we aim to maximize the ...signal-to-interference plus noise ratio (SINR) of a polarimetric radar by optimizing the transmit polarimetric waveform, the power allocation on its horizontal and vertical polarization segments, and the receiving filters jointly, subject to separate (while practical) unit-modulus and similarity constraints. To mitigate the SINR sensitivity on Target-Aspect-Angle (TAA), the average Target-Impulse-Response Matrix (TIRM) within a certain (TAA) interval is employed as the target response, which leads to an average SINR as the metric to be maximized. For the formulated nonconvex fractional programming problem, we propose an efficient algorithm under the framework of the alternating optimization method. Within, the alternating direction method of multiplier (ADMM) is deployed to solve the inner subproblems with closed form solutions obtained at each iteration. The analysis on computational cost and convergence of the proposed algorithm is also provided. Experiment results show the effectiveness of the proposed algorithm, the robustness of the output SINR against the TAA uncertainty, and the superior performance of polarimetric power adaption.
