Dual-function radar-communication (DFRC) systems offer a promising solution to mitigate spectrum competition and hardware complexity in 5G/6G communication. Orthogonal Frequency Division Multiplexing (OFDM) technology has been commonly employed in current DFRC signals. However, many DFRC signal sequences exhibit poor range sidelobes, making them unsuitable for weak target detection. In this paper, we design encrypted sparse transmitting waveforms to encrypt signals. In the time domain, the DFRC signal's Peak Side Level (DPSL) is minimized to enhance radar detectability, while simultaneously constraining the communication Bit Error Ratio (BER) and the constant envelope value of the signal to maintain communication quality. To address the non-convex optimization problem, we develop a Block Successive Upper-bound Minimization (BSUM) framework, which alternately updates each communication phase location. This framework aims to lower the dual-function cross- and auto-correlation peak sidelobe levels, referred to as the Block Successive Upper bound Minimization for DFRC DPSL (BSUM-DPSL) algorithm. The proposed algorithm's effectiveness is theoretically validated, and simulation results demonstrate that the effectiveness of designed MIMO-OFDM waveform in comparison with other waveforms.
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