Sensing Using Coded Communications Signals

Abstract

A key challenge for common waveforms for Integrated Sensing and Communications – widely regarded as a resource-efficient way to achieve high performance for both functionalities – lies in leveraging information-bearing channel-coded communications signal(s) (c.c.s) for sensing. In this paper, we investigate the range-Doppler sensing performance of c.c.s in multi-user interference-limited scenarios, and show that it is affected by sidelobes whose form depends on whether the c.c.s modulates a single-carrier or OFDM waveform. While uncoded signals give rise to asymptotically zero sidelobes due to the law of large numbers, it is not obvious that the same holds for c.c.s, as structured codes (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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\exp ( - O(\text {code rate} \times \text {block length}))$ </tex-math></inline-formula> . Consequently, 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 (i.e., 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 (SIR of −11dB), for both single-carrier and OFDM waveforms.