We study the problem of orthogonal time frequency space (OTFS) waveform design for joint sensing and communications. Our main objective is to achieve a low peak-to-average power ratio (PAPR) for the OTFS waveform with DFT spread to communication symbols, so that good parameter estimation and bit error rate performances in the presence of phase noise can be obtained for the sensing and communication sides, respectively. To this end, we first devise a symbol pattern scheme with pilot and reference components elaborated in the delay-Doppler domain for the OTFS, with the aim of improving phase noise and channel estimations. Based on this, we then perform power allocations on the designed pattern to further implement the reduction of PAPR for the OTFS waveform. The overall OTFS design is formulated as an optimization problem that incorporates the PAPR metric into the objective function for minimization. By replacing the infinity norm with an equivalent form, we convert the formulated optimization problem into a new tractable form, which allows us to apply majorization-minimization techniques for finding solutions. Our major contributions also lie in elaborating the majorant for the resulting problem and transforming into its dual problem. Simulation results verify the effectiveness of our design.

We study the design of orthogonal frequency division multiplexing (OFDM) waveform for the joint sensing and communications (JSC), whose sub-carriers are to be optimally coded by a set of sequences. To obtain such waveform that simultaneously exploits frequency diversity and modulation flexibility for the JSC, we take the correlation level of waveform for sensing and the orthogonality of modulation sequences for communications into consideration. Specifically, we choose to minimize the integrated sidelobe level (ISL) of the OFDM waveform, and meanwhile, to ensure reasonable constraints enforced on sub-carriers with code modulations. In view of this, an ISL-minimization based design with respect to the modulation sequences is therefore formulated, which is generally non-convex. To tackle it, we introduce virtually auxiliary variables to help reformulate the original optimization problem, and then apply the framework of consensus alternating direction method of multipliers for finding solutions. Our major contributions also lie in elaborating an augmented Lagrangian for the newly obtained optimization problem via a first-order Taylor expansion on its objective function, based on which a closed-form solution is achieved for iterations. Simulation results verify the superiority of our proposed OFDM waveform design.

In this paper, we focus on the multi-waveform design for the joint radar and communications, wherein the elements of waveforms are required to take binary values and to support both good integrated sidelobe level (ISL) and information embedding (IE) performances simultaneously. Since the binary waveform attribute enables limited degrees of freedom for the design, we partially choose to exploit both the phase and index modulations (PIM) of waveform elements to embed communication symbols in the fast-time domain, while we reserve a portion of them to improve the overall ISL of waveforms without PIM. To this end, we divide the fast-time waveforms to be designed into multiple blocks, each of which contains multiple uniform segments. We further develop a rule to instruct the elaboration of segments for IE via PIM within each block, and we leave the remaining segments among blocks unconstrained for the reduction on overall ISL of the binary waveforms. Based on the above, we formulate the design into a non-convex optimization problem that incorporates both the ISL minimization of waveforms and constraints on the fast-time IE. To tackle this problem, we reformulate it into a solvable integer optimization form, for which we employ the coordinate descent framework to find solutions. To make the work complete, we propose an associated method to determine the proper number of IE segments in the waveform design. Simulation results verify the effectiveness of our proposed design.

We study the design of the orthogonal frequency division multiplexing (OFDM) waveform that aims to simultaneously exploit frequency diversities and modulation flexibilities for joint sensing and communications (JSC). Such type of OFDM waveform adopts an optimal coding on subcarriers through a set of pre-designed sequences. To this end, we take into consideration the correlation level, peak-to-average-power ratio (PAPR), and orthogonality of modulation sequences of the OFDM waveform for JSC, based on which we devise two major corresponding designs. Strategically, we choose to minimize the integrated sidelobe level (ISL) of the OFDM waveform to obtain good correlation property in the first type of design, and meanwhile, to enforce reasonable constraints on OFDM subcarriers for achieving strict mutual orthogonality between sequences. For the second type of design, we further incorporate the PAPR reduction on the OFDM waveform into the development for easy practical implementations, wherein the PAPR is treated as either an objective for minimization or a constraint for bounding. Technically, we formulate both types of designs into different optimization problems. To tackle them, we introduce virtually auxiliary variables and reformulate the original problems into tractable forms, wherein the elaboration on constraints are also involved. Then, we apply the consensus alternating direction method of multipliers (ADMM) framework to find solutions, wherein proper augmented Lagrangians are elaborated to facilitate ADMM procedures. Our proposed methods enable closed-form solutions at iterations. For the development of corresponding algorithms, our major contributions also lie in converting the PAPR to a solvable form via an ℓp-norm based approximation and exploring fast implementations to conduct iterations. Simulation results show the superiority of our proposed designs in terms of different aspects.

We study the problem of constant-envelope precoding in massive MIMO communications with interference exploitation, whose main challenge lies in the non-convexity introduced by its constant-modulus constraints. Different from conventional approaches that typically involve constant-modulus approximations, we devise a new method with direct phase manipulations for precoding. To this end, we first formulate the precoding design into an unconstrained phase optimization with a "min-max" scheme, based on which we then apply the majorization-minimization (MM) technique to transform it into a convex minimization problem. For the sake of efficient solutions to this convex optimization, we focus on dealing with its dual problem, whose objective is further transformed into a simple quadratic form by means of elaborating the surrogate for MM. Finally, we arrive to a fast gradient-based solution for iteration. Simulation results show the superiority of our proposed algorithm over the existing methods in terms of different aspects, especially in the context of large-scale optimization.

In this paper, we focus on the orthogonal frequency division multiplexing (OFDM) waveform design for the joint multipleinput multiple-output radar and communications. An efficient method to simultaneously reduce the integrated sidelobe level (ISL) and peak-to-mean envelope power ratio (PMEPR) of OFDM waveforms is proposed from the radar side, which also guarantees high-quality information transmission for communications. Specifically, we exploit the spectral and phase randomness of waveforms to implement fast-time information embedding, based on which we formulate the design into a solvable nonconvex optimization problem. To solve it, we first rewrite its objective function into a quartic form by exploring the inherent algebraic structures and properties, which is then converted to a new quadratic form that is easy to be dealt with. Moreover, we obtain closed-form solutions at each iteration by means of a series of derivations involving majorization-minimization techniques. Simulation results verify the effectiveness of our method over existing works.

We study the problem of jointly designing spatial-slow-time unimodular waveforms and receive adaptive filter for dual-function radar communications with reconfigurable intelligent surface (RIS), which aims to mitigate interference for radar and meanwhile to transfer accurate symbols for communications. Hence, we maximize the signal-to-interference-plus-noise ratio at the radar receiver via devising a joint optimization of the waveform transmission, receive filter, and phase control of the RIS, wherein we enforce mean square error based constraints for communications. A non-convex optimization problem is therefore formulated. To solve it, we choose a cyclic manner that transforms the formulated design into sub optimization problems. In particular, we exploit majorization-minimization techniques followed by the consensus alternating direction method of multipliers for finding solutions to these sub problems. Therein lies a set of properly elaborated surrogate and Lagrangian functions, which finally lead to closed-form expressions for iterations. Simulation results verify the superiority of our proposed algorithm in terms of different aspects.

In this paper, we propose an efficient algorithm for designing large-scale multi-unimodular waveforms with low correlations. Different from existing approaches that commonly involve repetitive projections of complex values into their constant-modulus approximations, we conduct optimizations directly on the phase values of waveform elements. Specifically, we optimize the weighted integrated sidelobe level of waveforms, and formulate such design into an unconstrained optimization problem with respect to phase values of waveform elements. Then, we derive the gradient of the newly formulated objective function, through which we subsequently elaborate its majorant with the support of a properly designed Lipschitz-constant related quantity. Our major contributions also lie in obtaining a closed-form update of phase values that boils down to a gradient-descent regime, and calculating the update with fast implementations. Simulation results verify the superiority of our algorithm over existing state-of-the-art methods.

This paper explores nonuniform multiple-input multiple-output (MIMO) sampling and reconstruction of signals with multiple bands in the fractional Fourier domain. We investigate discrete-time fractional Fourier transforms of nonuniformly sampled output signals of MIMO channel and study the resulting fractional spectral aliasing. In order to tackle the problem that the spectral aliasing differs with respect to multiple-output signals, we define combined aliasing boundaries and perform spectrum analysis within the fractional frequency sub-intervals separated by these elaborated boundaries. Moreover, we derive the conditions for combined reconstructing the fractional spectra of the input/output signals of MIMO channel and devise relevant reconstruction methods. Simulation results verify the effectiveness of our proposed methods.

We deal with the problem of unimodular waveform(s) design with low correlation levels for the case of large-scale code lengths that can reach tens of thousands. Our primary goals are to reduce the resulting complexity with high efficiency, and meanwhile, to ensure an integrated sidelobe level (ISL) or weighted ISL (WISL) of waveforms as low as possible. To this end, we study a generic model for the minimization of ISL/WISL, wherein the objective function is formulated to embed a Hadmard product into a high-order matrix norm. Our major contributions lie in the transformation of the objective into a proper form via multiple shift matrices and the reformulation of problem in order to use alternating direction method of multipliers (ADMM) technique. In particular, we introduce a virtual matrix to form an additional equality constraint for ADMM, whose augmented Lagrangian is elaborated to help derive a fast algorithm that iterates with closed-form solutions. Simulation results verify the superiority of our algorithm over existing state-of-the-art algorithms in different aspects.

In this paper, we focus on designing strategies for information embedding (IE) of the joint MIMO radar and communications (JMRC) with subarrays. To fulfill the goal of IE as a secondary function for a MIMO radar with array division, we propose three designs which exploit the phase information conveyed by the construction of subarrays and/or the diversities of beampatterns synthesized by the array. We use the phase differences between subarrays to implement an index modulation for the IE in the first design, while we utilize the invariance property of beampattern rotations in the second design. The third design is a hybrid strategy, which combines the first and second designs together. For each design, the factors that affect the achievable communication data rate are analyzed with detailed derivations. Simulation results verify the effectiveness of our proposed IE designs for the JMRC.

In this paper, we focus on the multiple-waveform design for the joint multiple-input multiple-output radar and communications system, which aims to simultaneously attain low integrated sidelobe level (ISL) of waveforms and accurate fast-time modulation for information embedding (IE). We propose a novel strategy to exploit the attributes of waveform phases with extremely large degrees of freedom for embedding communication symbols, based on which we formulate the generalized waveform design into a nonconvex optimization problem. Our major contribution lies in converting both the ISL related objective and the fast-time modulation related constraints for IE into tractable quadratic forms. To achieve this, we introduce a novel diagonal matrix with Toeplitz blocks to reformulate and then relax the problem into a form that involves the outer product of the waveform vector in its objective. In order to solve this problem, we exploit the majorization-minimization technique to devise an algorithm that enables a closed-form solution at each iteration. Simulation results verify the effectiveness of our design.

This letter proposes new estimations of fractional power spectral density (FrPSD) and fractional correlation function (FrCF) for nonuniform sampling of random signals with non-stationarity and limited bandwidths in the fractional Fourier domain. Unlike previous works, the developed FrPSD and FrCF estimations are capable of dealing with unknown sampling instants. In order to obtain them, we first formulate approximations of FrCF and FrPSD making use of uniform sampling instants. Then we convert the approximate FrPSD to a fractional filtered version of the FrPSD for the original random signal, which does not rely on the sampling instants. With such operations, we propose the FrPSD estimation to cancel the bias of FrPSD approximation by means of a fractional inverse filtering and thereby obtain a high accuracy of it. The FrCF estimation is proposed to be the inverse fractional Fourier transform of the FrPSD, and it serves as the fractional interpolation of the previously obtained approximation of the FrCF. Simulation results show the effectiveness of the proposed estimation methods.

A novel computationally efficient method for jointly designing the space-(slow) time (SST) transmission with unimodular waveforms and receive adaptive filter is developed for different radar configurations. The range sidelobe effect and Doppler characteristics are considered. In particular, we develop a novel approach for jointly synthesizing unimodular SST waveforms and minimum variance distortionless response receive adaptive filter for two cases of known Doppler information and presence of uncertainties on clutter bins. Corresponding non-convex optimization problems are formulated and efficient algorithms are derived. The main ideas of the algorithm developments are to decouple composite objective function of the formulated problems, generate minorizing surrogates, and then solve the joint design problem iteratively, but in closed-form for each iteration by means of minorization - maximization technique. The proposed algorithms demonstrate good performance and have fast convergence speed and low complexity.

A new method for designing single/multiple unimodular waveforms with good weighted correlation properties, which is based on minimizing the weighted integrated sidelobe levels of waveforms, is developed. The main contributions of the paper lie in formulating the objective as a quartic form where Hadamard product of matrices is involved, converting the non-convex quartic optimization problem into a quadratic form and then solving it by means of majorization-minimization technique which seeks to find the solution iteratively. Corresponding algorithm enables good weighted correlations of the designed waveforms and shows fast convergence compared with existing methods.

We address the problem of terrain-scattered jammer suppression in multiple-input multiple-output (MIMO) radar using space-(fast) time adaptive processing (SFTAP). The correlation function of jamming components after matched filtering at the receiving end of MIMO radar is derived, and its relationship to the correlation matrix of the transmitted waveforms is established. This correlation function serves as a theoretical measure of evaluating the matched filtering effect on the received jamming signals. We propose a minimum variance distortionless response (MVDR) type SFTAP design by taking into account the factors of waveform-introduced range sidelobes and cold clutter stationarity over different pulse intervals. A closed-form solution to this design is derived by means of the method of Lagrange multipliers. We also propose a relaxed SFTAP design by modifying the constraints of the MVDR type design. Both proposed SFTAP designs can support further slow-time Doppler processing procedure. Simulation results show the validity of our SFTAP designs.

In this paper, the problem of joint hot and cold clutter mitigation in the context of transmit beamspace (TB)-based multipleinput multiple-output (MIMO) radar is studied. The TB-based MIMO radar enables special spatio-temporal structure and low rank of clutter covariance matrices. To efficiently mitigate the hot clutter such as terrain scattered multipath jamming concentrated in the sector-of-interest and the enhanced cold clutter due to transmit energy focusing, we resort to three-dimensional (3D) space-time adaptive processing (STAP) technique. A new 3D STAP method is proposed, which significantly reduces the computational complexity. We show from interference mitigation perspective that the TB-based MIMO radar enables superior output signal-to-interference-plus-noise ratio to that of its traditional MIMO radar counterpart.

The problem of jammers suppression in colocated multiple-input multiple-output (MIMO) radar is considered. We resort to reduced dimension (RD) beamspace designs with robust-ness/adaptiveness to achieve the goal of efficient jammers suppression. Specifically, our RD beamspace techniques aim at designing optimal beamspace matrices based on reasonable tradeoffs between the desired in-sector source distortion and the powerful jammer (possibly in-sector) attenuation when conducting the jammers suppression. These designs are cast as convex optimization problems which are derived using second-order cone programming. Meanwhile, we study the MUSIC-based direction-of-arrival estimation performance of the proposed beamspace designs by comparing to the conventional algorithms. Moreover, we demonstrate that the capability of efficient powerful in-sector jammers suppression using these designs is unique in MIMO radar.

An ambiguity function (AF) for the multiple-input multiple-output (MIMO) radar with correlated waveforms is derived. It serves as a generalized AF for which the phased-array and the traditional MIMO radar AFs are important special cases. A simplified expression for the AF for the case of far-field targets and narrow-band waveforms is also derived. We establish relationships between the generalized MIMO radar AF metric and the previous works on AF including the Woodward's AF and the AF defined for the traditional colocated MIMO radar. Moreover, we compare the AF of the MIMO radar with correlated waveforms with the squared-summation-form AF definition. Simulation results show that the generalized MIMO radar AF achieves lower relative sidelobe level with proper design of the waveform correlation matrix or, equivalently, the transmit beamspace matrix.