A key challenge in joint communications and sensing (JCS), a.k.a. integrated sensing and communications (ISAC), is the waveform synthesis that needs to modulate the communication messages and achieve good sensing performance simultaneously. A standard communication waveform could be used for sensing, since the sensing receiver, co-located with the sensing transmitter, knows the communication message and thus the waveform. However, the randomness of communications may result in improper waveforms that have high sidelobes masking weak targets. Therefore, the communication waveform needs to be refined in order to improve the sensing performance. This is similar to the peak-to-average power ratio (PAPR) mit-igation in orthogonal frequency division multiplexing (OFDM), in which the OFDM-modulated waveform needs to be refined to reduce the PAPR. Motivated by the PAPR issue in OFDM, the approach of trellis shaping, which refines the waveform for specific metrics using convolutional codes and Viterbi decoding, is employed for OFDM-based JCS. In such a scheme, the communication data is encoded and then mapped to the constellation in different subcarriers, such that the time-domain sidelobes are reduced. An interesting observation is that the sidelobe reduction in OFDM-based JCS is dual to the PAPR reduction in OFDM, thus sharing a similar signaling structure. Numerical simulations are carried out to demonstrate the validity of the proposed trellis shaping approach.
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