Spreading over OFDM for Integrated Sensing and Communications (ISAC) Ranging: Multi-user Interference Mitigation

In the context of communication-centric integrated sensing and communication (ISAC), the orthogonal frequency division multiplexing (OFDM) waveform was proven to be optimal in minimizing ranging sidelobes when random signaling is used. A typical assumption in OFDM-based ranging is that the max target delay is less than the cyclic prefix (CP) length, which is equivalent to performing a \textit{periodic} correlation between the signal reflected from the target and the transmitted signal. In the multi-user case, such as in Orthogonal Frequency Division Multiple Access (OFDMA), users are assigned disjoint subsets of subcarriers which eliminates mutual interference between the communication channels of the different users. However, ranging involves an aperiodic correlation operation for target ranges with delays greater than the CP length. Aperiodic correlation between signals from disjoint frequency bands will not be zero, resulting in mutual interference between different user bands. We refer to this as \textit{inter-band} (IB) cross-correlation interference. In this work, we analytically characterize IB interference and quantify its impact on the integrated sidelobe levels (ISL). We introduce an orthogonal spreading layer on top of OFDM that can reduce IB interference resulting in ISL levels significantly lower than for OFDM without spreading in the multi-user setup. We validate our claims through simulations, and using an upper bound on IB energy which we show that it can be minimized using our proposed spreading. However, for orthogonal spreading to be effective, a price must be paid in terms of spectral utilization, which is yet another manifestation of the trade-off between sensing accuracy and data communication capacity