Amalgamated CHIRP and OFDM for ISAC

Abstract: Integrated Sensing and Communication (ISAC) requires the development of a waveform capable of efficiently supporting both communication and sensing functionalities. This paper proposes a novel waveform that combines the benefits of both the orthogonal frequency division multiplexing (OFDM) and the chirp waveforms to improve both the communication and sensing performance within an ISAC framework. Hence, a new architecture is proposed that utilizes the conventional communication framework while leveraging the parameters sensed at the receiver (Rx) for enhancing the communication performance. We demonstrate that the affine addition of OFDM and chirp signals results in a near constant-envelope OFDM waveform, which effectively reduces the peak-to-average power ratio (PAPR), a key limitation of traditional OFDM systems. Using the OFDM framework for sensing in the conventional fashion requires the allocation of some resources for sensing, which in turn reduces communication performance. As a remedy, the proposed affine amalgam facilitates sensing through the chirp waveform without consuming communication resources, thereby preserving communication efficiency. Furthermore, a novel technique of integrating the chirp signal into the OFDM framework at the slot-level is proposed to enhance the accuracy of range estimation. The results show that the OFDM signal incorporated with chirp has better autocorrelation properties, improved root mean square error (RMSE) of range and velocity, and lower PAPR. Finally, we characterize the trade-off between communications and sensing performance.

• The paper introduces AAC-OFDM and CM-OFDM, novel waveforms that combine OFDM and chirp signals within the 5G NR resource grid for enhanced sensing and communication in ISAC systems, with significant improvements in range resolution, velocity RMSE, and PAPR reduction.
• Results show that AMC-OFDM provides flexible implementation options at the slot-level and symbol-level which could optimize range resolution and velocity RMSE.
• AAC-OFDM offers 1.7 bits/s/Hz spectral efficiency vs. 1.3 bits/s/Hz for OFDM and CM-OFDM with 25% pilots and achieves 0.02 m/s velocity RMSE & 4.20 m range resolution, compared to 0.38-0.40 m/s and 9.89 m

Motivation and contribution

Integrated Sensing and Communication (ISAC) systems must reconcile two objectives that pull in opposite directions: communication waveforms such as OFDM offer high spectral efficiency but poor autocorrelation properties for radar processing, while chirp/LFM waveforms provide excellent delay–Doppler characteristics but limited data rates. Existing remedies either dedicate resources to sensing — e.g., 5G positioning reference signals (PRS) with comb size 2 consume half the subcarriers [9921271] — or embed information into radar waveforms at the cost of sensing degradation and transceiver complexity. The paper under review proposes a waveform family that combines OFDM and chirp signals within the 5G NR resource grid, aiming to decouple sensing from communication resources entirely.

The work makes four principal contributions: (i) an affine addition of chirp to OFDM (AAC-OFDM) in the time domain, with a systematic treatment of the power-allocation factor $\alpha$; (ii) closed-form derivation of the ambiguity function of AAC-OFDM and of the multiplicative chirp-modulated OFDM (CM-OFDM); (iii) a deterministic PAPR bound yielding a sufficient threshold on $\alpha$ below which AAC-OFDM strictly reduces PAPR relative to OFDM; and (iv) a slot-level versus symbol-level implementation study over the NR frame structure showing that slot-level chirp placement consistently improves range/velocity RMSE.

Waveform design

AAC-OFDM is defined as $a(l) = (1-\alpha)s(l) + \alpha c(l)$, where $s(l)$ is the conventional OFDM time-domain block after IFFT and $c(l)$ is a chirp whose rate is tied to the OFDM subcarrier indices, sweeping bandwidth $B_c = (n_j - n_i)\Delta f$ over duration $T_c$ matched to the OFDM symbol duration $T_o$. The key architectural property is receiver-side: the sensing branch correlates against the chirp template using only knowledge of the chirp rate $\beta$, requiring no pilot subcarriers and no prior knowledge of the transmitted data. This makes AAC-OFDM directly applicable to bistatic sensing, where the receiving base station does not know the payload bits. CM-OFDM, by contrast, multiplies each data symbol by a chirp phase term; its matched filter requires regeneration of the data-dependent template per symbol, so it presupposes knowledge of $X_m(n)$ and is suited to monostatic operation or PRS enhancement.

Sensing metrics follow from the chirp parameters: range resolution $\alpha$0, maximum unambiguous range $\alpha$1, and unambiguous velocity bounded by $\alpha$2. The paper identifies the inherent design dilemma — larger $\alpha$3 improves resolution but shrinks $\alpha$4, while longer $\alpha$5 extends range but compresses the velocity window — and resolves it through the NR-frame-aware implementation described below.

Ambiguity function and PAPR analysis

Expanding the ambiguity integral of AAC-OFDM yields four terms: the chirp self-ambiguity ($\alpha$6, closed-form sinc expression), the OFDM self-ambiguity ($\alpha$7), and two cross terms ($\alpha$8, $\alpha$9) expressible via Fresnel integrals. The weighting $a(l) = (1-\alpha)s(l) + \alpha c(l)$0 only rescales these terms without altering their qualitative structure, which provides a clean analytical handle on the sensing–communication trade-off. The derived CM-OFDM ambiguity exhibits a tilted thumbtack shape due to delay–Doppler coupling, conferring Doppler tolerance inherited from the LFM component.

On the PAPR side, under unit average-power normalization of both components, the authors derive the deterministic bound

$a(l) = (1-\alpha)s(l) + \alpha c(l)$1

where $a(l) = (1-\alpha)s(l) + \alpha c(l)$2 is the OFDM peak amplitude and $a(l) = (1-\alpha)s(l) + \alpha c(l)$3 the block correlation between OFDM and chirp. Any $a(l) = (1-\alpha)s(l) + \alpha c(l)$4 guarantees strict PAPR reduction relative to OFDM; in the decorrelated regime this threshold reduces to $a(l) = (1-\alpha)s(l) + \alpha c(l)$5. This is a useful design rule, though it rests on the assumption of equal-power normalization and a unit-modulus chirp.

A complexity analysis shows AAC-OFDM sensing costs $a(l) = (1-\alpha)s(l) + \alpha c(l)$6 complex multiplications plus a one-off template FFT — asymptotically identical to conventional PRS-based OFDM sensing — while CM-OFDM incurs a 50% higher per-symbol cost ($a(l) = (1-\alpha)s(l) + \alpha c(l)$7) because its template must be regenerated per symbol.

Slot-level versus symbol-level implementation

Within the 5G NR frame (120 kHz SCS, 14 symbols/slot), the paper contrasts three chirp-placement modes. Slot-level integration spans $a(l) = (1-\alpha)s(l) + \alpha c(l)$8, extending the maximum unambiguous range by a factor of 14 and improving velocity RMSE through longer coherent integration, consistent with the Cramér–Rao behavior of Doppler estimation. Symbol-level integration widens the unambiguous velocity window for fast targets. A hybrid mode alternates full-slot and single-symbol chirps across a subframe, balancing both objectives while leaving the scheduled data subcarriers untouched. Additionally, the flexibility of AAC-OFDM over the resource grid is tabulated: spanning all 256 subcarriers in one symbol yields 4.88 m range resolution and 350.6 m/s unambiguous velocity, whereas a 2-subcarrier × 14-symbol configuration trades down to 625 m resolution but achieves $a(l) = (1-\alpha)s(l) + \alpha c(l)$9 m unambiguous range. Because the time–frequency slope is held constant across configurations, a single fixed dechirping architecture suffices.

CM-OFDM can also be dropped into existing PRS resource elements (e.g., comb-4 patterns) to sharpen range resolution without disturbing neighboring REs — a compatibility-first enhancement path for deployed systems.

Performance characterization

Simulations use FR2 parameters (24 GHz carrier, 120 kHz SCS, 1024 subcarriers, QPSK, five-tap multipath). The headline numerical findings are:

Metric	Result
PAPR at CCDF $s(l)$0	OFDM/CM-OFDM ≈ 11 dB; AAC-OFDM 10.9/10.1/9 dB for $s(l)$1
Spectral efficiency	AAC-OFDM 1.7 bits/s/Hz ($s(l)$2) vs. 1.3 bits/s/Hz plateau for OFDM/CM-OFDM with 25% pilots
Range resolution ($s(l)$3, one-symbol CPI)	OFDM 9.89 m; CM-OFDM 7.50 m; AAC-OFDM 4.20 m
Velocity RMSE floor (high SNR)	Chirp 0.011 m/s; AAC-OFDM 0.02 m/s; OFDM/CM-OFDM 0.38–0.40 m/s

Three trade-offs deserve emphasis. First, the spectral-efficiency gain of AAC-OFDM stems precisely from its pilot-free operation: OFDM and CM-OFDM sacrifice 25% of subcarriers for sensing, capping throughput, whereas AAC-OFDM carries data on all tones. Second, the sensing penalty of AAC-OFDM when the chirp occupies only one symbol is approximately 5 dB SNR loss relative to OFDM using all symbols as pilots (15 dB at $s(l)$4); slot-level placement largely closes this gap, and for $s(l)$5 AAC-OFDM actually outperforms standard OFDM in range RMSE. Third, BER degrades monotonically with $s(l)$6 since more power diverts from data to the chirp, so $s(l)$7 must be tuned per operating point; the paper suggests $s(l)$8 for balanced performance and adaptive adjustment of $s(l)$9 across detection/tracking phases as a practical control mechanism. Notably, the receiver's dechirp-before-FFT architecture ensures the communication chain remains a standard OFDM receiver, so chirp placement choices affect sensing accuracy but leave communication reliability essentially unchanged.

Limitations and open questions

Several caveats are stated or implicit. The sensing advantage of AAC-OFDM at low $c(l)$0 and short CPIs is real but modest, and the comparison against OFDM/CM-OMF in some figures assumes those schemes use all subcarriers as pilots — a favorable baseline for the competitors that flatters their sensing RMSE. Hardware impairments are analyzed only qualitatively: residual CFO induces a velocity bias $c(l)$1, oscillator phase noise broadens range–Doppler peaks and weakens coherent integration, and bistatic clock drift produces a range bias $c(l)$2; mitigation strategies are sketched but not evaluated quantitatively. All results are simulation-based at a single carrier frequency and channel profile; no measurement validation is provided. The extension to MIMO — where joint angle, range, and Doppler processing and multiuser interference become central — is deferred, as are multi-target detection and tracking in cluttered scenes. Finally, the optimal $c(l)$3 selection is framed as a tuning problem rather than solved via a formal optimization criterion.

Conclusion

This paper contributes a standards-compatible ISAC waveform pair: AAC-OFDM enables pilot-free, data-independent sensing suitable for bistatic operation with controllable PAPR reduction and near-chirp Doppler accuracy, while CM-OFDM offers a drop-in enhancement of existing PRS-based sensing. The slot-versus-symbol implementation study provides actionable guidance for trading range resolution against unambiguous velocity within the NR frame. The principal open problems are quantitative robustness to synchronization and phase-noise impairments, MIMO extension, and multi-target tracking.