The OFDM Waveform Design With Optimally Coded Subcarriers for Joint Sensing and Communications

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.