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.

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.

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.

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.