Analysis of Sensing in OFDM-based ISAC under the Influence of Sampling Jitter

TL;DR

It can be concluded that state-of-the-art hardware enables sufficient communication and sensing robustness against SJ, as RMS SJ values in the femtosecond range can be achieved.

Abstract

To enable integrated sensing and communication (ISAC) in cellular networks, a wide range of additional requirements and challenges are either imposed or become more critical. One such impairment is sampling jitter (SJ), which arises due to imperfections in the sampling instants of the clocks of digital-to-analog converters (DACs) and analog-to-digital converters (ADCs). While SJ is already well studied for communication systems based on orthogonal frequency-division multiplexing (OFDM), which is expected to be the waveform of choice for most sixth-generation (6G) scenarios where ISAC could be possible, the implications of SJ on the OFDM-based radar sensing must still be thoroughly analyzed. Considering that phase-locked loop (PLL)-based oscillators are used to derive sampling clocks, which leads to colored SJ, i.e., SJ with non-flat power spectral density, this article analyzes the resulting distortion of the adopted digital constellation modulation and sensing performance in OFDM-based ISAC for both baseband (BB) and bandpass (BP) sampling strategies and different oversampling factors. For BB sampling, it is seen that SJ induces intercarrier interference (ICI), while for BP sampling, it causes carrier phase error and more severe ICI due to a phase noise-like effect at the digital intermediate frequency. Obtained results for a single-input single-output OFDM-based ISAC system with various OFDM signal parameterizations demonstrate that SJ-induced degradation becomes non-negligible for both BB and BP sampling only for root mean square (RMS) SJ values above 10^-11 s at both DAC and ADC, which corresponds to 0.5*10^-2 times the considered critical sampling period without oversampling. Based on the achieved results, it can be concluded that state-of-the-art hardware enables sufficient communication and sensing robustness against SJ, as RMS SJ values in the femtosecond range can be achieved.

Figures (16)

• Figure 1: Adopted PN model based on the Texas Instruments LMX2594 RF synthesizer ti2019. The double-sided PN PSD is shown in (a), while the integrated PN level as a function of frequency offset (double-sided) for the frequency range of interest assuming BB sampling and $\eta=1$ is presented in (b). In (b), $B/2=250MHz$ is highlighted (– –), as this offset corresponds to the bandwidth $B=500MHz$ listed in Table \ref{['tab:ofdmParameters']}. Finally, the PDF of the PN time series is shown in (c) and the corresponding SJ PDF in (d). Since a critical sampling period of $T_\mathrm{s}=2ns$ was considered, the PDF in (d) is associated with an RMS SJ of 49.44fs.
• Figure 2: Mean EVM obtained with BB sampling as a function of the number of subcarriers $N$. The performed simulations considered $M=128$ OFDM symbols, and SJ RMS values of $[parse-numbers = false]{10^{-14}}{\second}$, $[parse-numbers = false]{10^{-13}}{\second}$, $[parse-numbers = false]{10^{-12}}{\second}$, $[parse-numbers = false]{10^{-11}}{\second}$, and $[parse-numbers = false]{10^{-10}}{\second}$ at both transmitter and receiver. These values correspond to RMS SJs of $0.5\times10^{-5}T_\mathrm{s}$, $0.5\times10^{-4}T_\mathrm{s}$, $0.5\times10^{-3}T_\mathrm{s}$, $0.5\times10^{-2}T_\mathrm{s}$, and $0.5\times10^{-1}T_\mathrm{s}$, respectively. In addition, QPSK ($\CIRCLE$), 16-QAM ($\blacklozenge$), 64-QAM ($\blacksquare$), and 256-QAM ($\bigstar$) modulations were considered. For the results in (a), (b), (c), and (d), $\eta=1$, $\eta=2$, $\eta=4$, and $\eta=8$ were used, respectively.
• Figure 3: Normalized receive QPSK constellations obtained with BB sampling, $M=128$ OFDM symbols, and an RMS SJ of $[parse-numbers = false]{10^{-10}}{\second}$ (i.e., $0.5\times10^{-1}T_\mathrm{s}$). Results are shown for different numbers of subcariers and ZP factors, namely $N=256$ and (a) $\eta=1$, (b) $\eta=2$, (c) $\eta=4$, (d) $\eta=8$, $N=2048$ and (e) $\eta=1$, (f) $\eta=2$, (g) $\eta=4$, (h) $\eta=8$, and $N=16384$ and (i) $\eta=1$, (j) $\eta=2$, (k) $\eta=4$, (l) $\eta=8$.
• Figure 4: EVM at the $n\mathrm{th}$ subcarrier obtained with BB sampling and an RMS SJ of $[parse-numbers = false]{10^{-10}}{\second}$ (i.e., $0.5\times10^{-1}T_\mathrm{s}$), QPSK modulation, and: (a) $N=256$, (b) $N=2048$, and (c) $N=16384$. In all cases, results are shown for $\eta=1$ ($\CIRCLE$), $\eta=2$ ($\blacklozenge$), $\eta=4$ ($\blacksquare$), and $\eta=8$ ($\bigstar$).
• Figure 5: SIR as a function of the RMS SJ obtained with BB sampling, $M=128$ OFDM symbols, QPSK modulation, and (a) $\eta=1$, (b) $\eta=2$, (c) $\eta=4$, and (d) $\eta=8$. In all cases, results are shown for $N=256$ ($\CIRCLE$), $N=2048$ ($\blacklozenge$), and $N=16384$ ($\blacksquare$).