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We propose a novel robust design method to jointly optimize the radar transmit code and receive filter, exploiting the Signal-to-Interference plus Noise Ratio (SINR) at the receiver end as design figure of merit. We confer robustness to our method against uncertainties on the target impulse response (TIR) using a worst-case optimization approach based on two different uncertainty sets. The former is composed of a finite collection of TIRs, obtained by sampling the actual TIR at some aspect angles; the latter is a spherical uncertainty set. We further enforce a peak-to-average power ratio (PAR) constraint to the transmit code, which is very important for radar applications where the transmitter operates close to saturation. The design problem is tackled using a sequential optimization procedure alternating between two semi-definite programming (SDP) problems, followed by randomization steps. Our numerical results highlight the robustness and applicability of the proposed method in different scenarios.

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.

In this paper, under the peak-to-average power ratio (PAR) and energy constraints on the transmit waveforms, a new efficient weighted $\ell _p$ -norm metric (with $p\geq 2$ ) is introduced for colocated wideband/narrowband multiple-input multiple-output radar transmit beampattern matching design. The proposed metric can achieve quasi-equiripple beampattern, which is desirable to improve the robustness of radar systems with imprecise direction information of targets and reduce radar clutter. In addition, mainlobe ripple control, peak sidelobe suppression, and deep null/notch formation can be obtained. On the other hand, the PAR and energy constraints cause the radar waveform losing the degree of freedom to match arbitrary pattern shape, and the desired pattern usually lies in matching an appropriately scaled version of the shape. Thus, a scaling factor is introduced into the proposed metric to tackle the scaling ambiguity problem. The resultant optimization problems are difficult to solve due to the higher order polynomial objective function with coupled scaling factor and waveform matrix, and also the nonconvex PAR constraint. To develop a fast and efficient algorithm, by utilizing the majorization–minimization technique, we decouple the scaling factor and radar waveform matrix variables by a majorization step, derive a new quadratic majorizer to tackle the quadratic function with the matrix variable, and surrogate the nonsmooth nonconvex functions by convex functions. Numerical examples show that the devised approach can synthesize beampattern with lower peak sidelobe level and more flat mainlobe compared to the existing algorithms.

In this paper, we conduct the joint design of transmitting sequence(s) and receiving filters subject to the Peak-to-Average Ratio (PAR) constraint in radar and communications applications. We consider optimizing the worst-case performance and the resulting optimization problem takes a maximin format. We propose two algorithms based on the MM (Majorization–Minimization or Minorization–Maximization) method as opposed to the traditional epigraph-based smooth reformulation. On top of that, both algorithms are guaranteed to converge to a B(oulingand)-stationary solution, and B-stationarity is the appropriate stationarity condition for problems with a nonconvex constraint set. The proposed algorithms successively solve a series of simple convex problems that enjoy low computational complexity. Numerical simulations have shown that the proposed algorithms empirically achieve slightly higher objective values and converge faster in terms of CPU time than the existing methods.

In this paper, we consider the low autocorrelation sequence design problem. We optimize a unified metric over a general constraint set. The unified metric includes the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) as special cases, and the general constraint set contains the unimodular constraint, Peak-to-Average Ratio (PAR) constraint, and similarity constraint, to name a few. The optimization technique we employ is the majorization–minimization (MM) method, which is iterative and enjoys guaranteed convergence to a stationary solution. We carry out the MM method in two stages: in the majorization stage, we propose three majorizing functions: two for the unified metric and one for the ISL metric; in the minimization stage, we give closed-form solutions for algorithmic updates under different constraints. The update step can be implemented with a few Fast Fourier Transformations (FFTs) and/or Inverse FFTs (IFFTs). We also show the connections between the MM and gradient projection method under our algorithmic scheme. Numerical simulations have shown that the proposed MM-based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state-of-the-art algorithms.

In a smart grid network, demand-side management plays a significant role in allowing consumers, incentivized by utilities, to manage their energy consumption. This can be done through shifting consumption to off-peak hours and thus reducing the peak-to-average ratio (PAR) of the electricity system. In this paper, we begin by proposing a demand-side energy consumption scheduling scheme for household appliances that considers a PAR constraint. An initial optimization problem is formulated to minimize the energy cost of the consumers through the determination of the optimal usage power and operation time of throttleable and shiftable appliances, respectively. We realize that the acceptance of consumers of these load management schemes is crucial to its success. Hence, we then introduce a multi-objective optimization problem which not only minimizes the energy cost but also minimizes the inconvenience posed to consumers. In addition to solving the proposed optimization problems in a centralized manner, two distributed algorithms for the initial and the multi-objective optimization problems are also proposed. Simulation results show that the proposed demand-side energy consumption schedule can provide an effective approach to reducing total energy costs while simultaneously considering PAR constraints and consumers' preferences.

PAR-constrained sequences are widely used in communication systems and radars due to various practical needs; specifically, sequences are required to be unimodular or of low peak-to-average power ratio (PAR). For unimodular sequence design, plenty of efforts have been devoted to obtaining good correlation properties. Regarding channel estimation, however, sequences of such properties do not necessarily help produce optimal estimates. Tailored unimodular sequences for the specific criterion concerned are desirable especially when the prior knowledge of the channel is taken into account as well. In this paper, we formulate the problem of optimal unimodular sequence design for minimum mean square error estimation of the channel impulse response and conditional mutual information maximization, respectively. Efficient algorithms based on the majorization-minimization framework are proposed for both problems with guaranteed convergence. As the unimodular constraint is a special case of the low PAR constraint, optimal sequences of low PAR are also considered. Numerical examples are provided to show the performance of the proposed training sequences, with the efficiency of the derived algorithms demonstrated.

In this paper, we study the problem of code design to improve the detection performance of multi-static radar in the presence of clutter (i.e., a signal-dependent interference). To this end, we briefly present a discrete-time formulation of the problem as well as the optimal detector in the presence of Gaussian clutter. Due to the lack of analytical expression for receiver operation characteristic (ROC), code design based on ROC is not feasible. Therefore, we consider several popular information-theoretic criteria including Bhattacharyya distance, Kullback-Leibler (KL) divergence, J-divergence, and mutual information (MI) as design metrics. The code optimization problems associated with different information-theoretic criteria are obtained and cast under a unified framework. We propose two general methods based on Majorization-Minimization to tackle the optimization problems in the framework. The first method provides optimal solutions via successive majorizations whereas the second one consists of a majorization step, a relaxation, and a synthesis stage. Moreover, derivations of the proposed methods are extended to tackle the code design problems with a peak-to-average ratio power (PAR) constraint. Using numerical investigations, a general analysis of the coded system performance, computational efficiency of the proposed methods, and the behavior of the information-theoretic criteria is provided.

Orthogonal frequency division multiplexing (OFDM) has been adopted by several wireless transmission standards. A major disadvantage of OFDM is the large dynamic range of its time-domain waveforms, making OFDM vulnerable to nonlinearities (including clipping effects) of the power amplifier (PA) and causing the PA to yield low efficiency on the RF to dc power conversion. A commonly used metric to characterize a signal's dynamic range is the peak-to-average power ratio (PAR). To suppress the nonlinear effects, one may want to reduce the signal PAR. However, this results in the increase of error vector magnitude (EVM), and may violate the spectral mask. In this paper, we formulate the problem as an EVM optimization task subject to a deterministic PAR constraint and a spectral mask constraint. A low-complexity customized interior-point algorithm is developed to solve the optimization problem. We also discuss extensions of the optimization framework, whereby we optimize the parameters with respect to two metrics on signal-to-noise-and-distortion ratio (SNDR) and mutual information, respectively.