Sensing using Coded Communications Signals

A key challenge for a common waveform for Integrated Sensing and Communications (ISAC) - widely seen as an attractive proposition to achieve high performance for both functionalities, while efficiently utilizing available resources -- lies in leveraging information-bearing channel-coded communications signals (c.c.s) for sensing. In this paper, we investigate the sensing performance of c.c.s in (multi-user) interference-limited operation, and show that it is limited by sidelobes in the range-Doppler map, whose form depends on whether the c.c.s modulates a single-carrier or OFDM waveform. While uncoded communications signals -- comprising a block of $N$ i.i.d zero-mean symbols -- give rise to asymptotically (i.e., as $N \rightarrow \infty$) zero sidelobes due to the law of large numbers, it is not obvious that the same holds for c.c.s, as structured channel coding schemes (e.g., linear block codes) induce dependence across codeword symbols. In this paper, we show that c.c.s also give rise to asymptotically zero sidelobes -- for both single-carrier and OFDM waveforms -- by deriving upper bounds for the tail probabilities of the sidelobe magnitudes that decay as $\exp( - O($code rate $\times$ block length$))$. This implies that for any code rate, c.c.s are effective sensing signals that are robust to multi-user interference at sufficiently large block lengths, with negligible difference in performance based on whether they modulate a single-carrier or OFDM waveform. We verify the latter implication through simulations, where we observe the sensing performance (characterized by the detection and false-alarm probabilities) of a QPSK-modulated c.c.s (code rate = 120/1024, block length = 1024 symbols) to match that of a comparable interference-free FMCW waveform even at high interference levels (signal-to-interference ratio of -11dB), for both single-carrier and OFDM waveforms.