Low-Correlation OFDM Waveform Design With Optimally Coded Sub-Carriers for the Joint Sensing and Communications

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.