Design of OFDM Waveforms With Subcarrier Interleaving: To Achieve Good PMEPR and SNR Performances for the Joint Radar and Communications

We propose an efficient design for the joint radar and communications through multiple orthogonal frequency division multiplexing (OFDM) waveform transmissions with subcarrier interleaving. Our primary goal is to simultaneously obtain good peak-to-mean envelope power ratio (PMEPR) and periodic correlations of waveforms, and also to achieve reasonable signal-to-noise ratio (SNR) performance for communications. To this end, we devise an optimized scheme for subcarrier interleaving of OFDM, which enables good periodic waveform correlations and successfully avoids possible subcarrier selections resulting in poor SNR performance at users. Based on this scheme, we design multiple OFDM waveforms via minimizing their PMEPR with constraints on the total transmit power and received SNR for users. The design is formulated as a nonconvex optimization problem. To solve it, we first rewrite its objective function into a quartic form by exploring the inherent algebraic structures and their properties. Then, we reformulate the problem into a form that allows for the application of alternating direction method of multipliers (ADMM). Technically, we first introduce virtual auxiliary variables for the ADMM, and then elaborate an augmented Lagrangian for the newly formulated problem. An algorithm that involves closed-form solutions at iterations is finally developed, whose performance is verified by comprehensive simulations.