Design of Hybrid OFDM-LFM Waveforms With Good Correlation Properties via Optimized Allocations of Frequency Subcarriers and Chirp-Rate Polarities

Modern radar and joint radar-communications increasingly demand waveforms that simultaneously exhibit good correlation performance and flexible frequency agility. To address this need, this article presents the design of multiple hybrid waveforms that combine orthogonal frequency-division multiplexing (OFDM) with linear frequency modulation (LFM), thereby leveraging the complementary advantages of both signaling techniques. In the proposed hybrid OFDM-LFM framework, multiple LFM components derived from a frequency-modulated continuous-wave signal are assigned to different OFDM subcarriers within the available frequency band. The objective is to achieve favorable correlation properties while ensuring sufficient frequency agility among the LFM components through the OFDM structure. Technically, we employ the integrated sidelobe level or peak sidelobe level as the performance metric. Based on this metric, we formulate the hybrid waveform design as an optimization problem, which seeks the optimal allocation of LFM components with bipolar chirp rates across the available subcarriers. The formulation is inherently nonconvex with respect to both carrier frequencies and chirp rates. To address this challenge, we reformulate the problem into an integer programming framework, where the objective is transformed into determining the ordering of carrier frequencies and the polarities of chirp rates for the LFM components across subtime intervals. The resulting problem is further decomposed into two interrelated subproblems, which are solved in a cyclic manner using integer programming techniques enhanced by swarm intelligence. For each subproblem, specialized algorithms based on structured manipulations of permutation matrices are developed. Simulation results validate the effectiveness of our proposed methods and also their superiorities over other methods.