OFDM-ISAC: Integrated Sensing & Communications

4.1  SRS Pilot Extraction

In NR, the Sounding Reference Signal (SRS) is transmitted by the UE on the uplink in a configurable set of OFDM symbols and subcarriers. Because the gNB already knows the exact time-frequency resource grid allocation and the SRS sequence, it can treat each SRS transmission as a known pilot burst and extract a monostatic or bistatic channel estimate purely from the received signal — giving a zero-cost sensing observation piggy-backed on the communication waveform.

SRS Resource Mapping (NR)

SRS occupies the last \(N_{SRS}^{symb} \in \{1,2,4\}\) OFDM symbols of a slot. The comb structure (KTC \(\in \{2,4,8\}\)) interleaves multiple UEs in frequency. For a single UE with comb offset \(k_0\) and starting physical resource block \(n_{PRB,start}\), the set of occupied subcarriers is

where \(N_{RB}^{SRS}\) is the SRS bandwidth in resource blocks and \(K_{TC}\) is the comb size. After reception the gNB extracts the pilot vector \(\mathbf{y}_p \in \mathbb{C}^{M_{SRS}}\) and forms the per-subcarrier channel estimate:

In matrix form, collecting \(L\) consecutive SRS OFDM symbols:

The least-squares channel estimate across all pilot resources is then \(\hat{\mathbf{H}} = \mathbf{Y}\,\mathbf{X}_p^{-1}\). Because \(\mathbf{X}_p\) is diagonal (single-carrier pilots), inversion is trivially element-wise division. The resulting \(\hat{\mathbf{H}}\) represents the delay-Doppler transfer function sampled on the SRS grid — the raw input to all downstream sensing algorithms.

SRS vs DMRS — Sensing Capability Comparison

4.2  Cramér–Rao Bound for Range & Velocity

The Cramér–Rao Bound (CRB) gives the theoretical minimum variance achievable by any unbiased estimator of a deterministic parameter. For OFDM-ISAC the two primary target parameters are the round-trip delay \(\tau\) (mapped to range via \(R = c\tau/2\)) and the Doppler shift \(\nu\) (mapped to velocity via \(v = \lambda\nu/2\)).

Fisher Information Matrix

For a complex Gaussian observation model \(\mathbf{y} \sim \mathcal{CN}(\boldsymbol{\mu}(\boldsymbol{\theta}),\,\sigma_n^2 \mathbf{I})\), where \(\boldsymbol{\theta} = [\tau,\nu]^T\), the Fisher Information Matrix (FIM) is

For an OFDM waveform with \(N\) subcarriers (subcarrier spacing \(\Delta f\), total bandwidth \(B = N\Delta f\)) and \(L\) OFDM symbols (observation time \(T_{obs} = L \cdot T_{sym}\)), the FIM is diagonal (delay and Doppler are asymptotically decoupled) and the CRB simplifies to:

The factor of 3 arises from the second moment of the rectangular spectral / temporal support: for a uniform distribution over \([-B/2, B/2]\), \(\mathbb{E}[f^2] = B^2/12\), so \(8\pi^2 \mathbb{E}[f^2] = 8\pi^2 B^2/12 = 2\pi^2 B^2/3\), and its inverse gives the factor of \(3/(2\pi^2 B^2)\) — which absorbs the 2-way propagation factor to yield (4.5).

CRB vs SNR — Chart

CRB: Range & Velocity Estimation Lower Bound vs SNR (B = 100 MHz, T_obs = 5 ms)

Log-scale CRB curves computed from (4.5) and (4.6). The shaded region marks the NR SRS typical operating SNR (10–25 dB). At 15 dB SNR, range 1-σ bound ≈ 0.12 m and velocity 1-σ bound ≈ 0.06 m/s with these parameters.

4.3  2D-FFT CFAR Detection Pipeline

The canonical NR-ISAC sensing pipeline converts the extracted pilot channel estimates into a Range-Doppler (RD) map via a 2D-IFFT and then applies Constant False Alarm Rate (CFAR) detection to localise targets. The steps below assume \(M\) frequency-domain pilots per symbol and \(L\) consecutive SRS symbols.

Simulated 2D Range-Doppler Map

The heatmap below simulates the output of Step 3 for a 3-target scene: Target 1 at (50 m, +5 m/s), Target 2 at (120 m, −12 m/s), Target 3 at (200 m, +20 m/s). A Gaussian spread models the sinc-like peak after windowing, and a −40 dB noise floor is applied.

Simulated 2D Range-Doppler Map (NR SRS, 100 MHz BW)

Colour scale in dB. Three targets are clearly visible above the −40 dB noise floor. In practice, CFAR detection (Step 4) would threshold this map before peak extraction. Range resolution ≈ 1.5 m; Doppler resolution ≈ 0.43 m/s (with T_obs = 5 ms and λ ≈ 85.7 mm @ 3.5 GHz).

Section 4 — Key Design Takeaways

Study Questions

5.1 Zadoff-Chu Sequences

Zadoff-Chu (ZC) sequences are the mathematical backbone of NR PRACH. Their constant-envelope and perfect periodic autocorrelation properties make them ideal both for random access and — as exploited in ISAC — for unambiguous range and Doppler estimation.

Here \(u\) is the root index (coprime with \(N_{\mathrm{ZC}}\)) and \(N_{\mathrm{ZC}}\) is the sequence length. Key properties:

• Constant envelope: \(|x_u(n)| = 1\) for all \(n\) — the sequence has uniform power, which maximises PAPR efficiency and sensing signal-to-noise ratio.
• Perfect periodic autocorrelation: \(\sum_{n} x_u(n)\,x_u^*(n-k) = N_{\mathrm{ZC}}\,\delta(k)\) for any root \(u\). The energy is concentrated in a single delay bin, giving zero range sidelobes.
• Low cross-correlation between different roots: \(|R_{u,u'}(k)| = \sqrt{N_{\mathrm{ZC}}}\) for \(u \neq u'\), so \(|R|/N_{\mathrm{ZC}} = 1/\sqrt{N_{\mathrm{ZC}}}\). For \(N_{\mathrm{ZC}}=839\) this is \(\approx 0.0346\) — very low.
• Cyclic-shift orthogonality: Cyclic shifts of the same root are orthogonal when the shift exceeds the round-trip delay spread, allowing multiple UEs to share a single root with guaranteed separation.

NR PRACH Format Summary

5.2 ZC-Based Range Estimation

When the gNB receives a reflected PRACH preamble, it cross-correlates the received signal \(y(n)\) with a local replica of the known ZC sequence to form a range profile. The delay bin with maximum correlation energy corresponds to the target round-trip delay.

The corresponding range estimate is simply:

where \(c = 3\times10^8\) m/s. The factor of 2 accounts for the two-way propagation (monostatic sensing scenario).

Cramér-Rao Bound for ZC Ranging

For a ZC preamble of duration \(T_{\mathrm{ZC}}\) with bandwidth \(B\) observed at SNR \(\gamma\), the CRB on delay estimation variance is:

where \(\bar{f}^2 = \int f^2 |X(f)|^2\,df / \int |X(f)|^2\,df\) is the mean-square bandwidth (second spectral moment). For a flat-spectrum ZC preamble, \(\bar{f}^2 \approx B^2/12\). The range CRB is then:

Cyclic Prefix and Unambiguous Range

The PRACH cyclic prefix \(T_{\mathrm{CP}}\) sets the maximum unambiguous round-trip delay: \(\tau_{\max} = T_{\mathrm{CP}}\), giving:

Additionally, the NCS (Ncs — number of cyclic shifts reserved per root) determines the separation between UE preambles in delay space. The unambiguous range from NCS is:

For Format 0 with NCS=13, \(T_s = 1/(15000\times2048)\) s, giving \(d_{\mathrm{NCS}} \approx 22\) km. Any target beyond this distance folds into an ambiguous range bin.

5.3 Multi-Preamble Doppler Estimation

A single PRACH preamble resolves range but not velocity. By observing multiple PRACH transmissions in successive slots, the gNB can extract Doppler information from the phase evolution of the matched-filter output peak across repetitions.

5.4 PUCCH Periodic Sensing

While PRACH is a contention-based transmission, Physical Uplink Control Channel (PUCCH) carries scheduled control information (ACK/NACK, CSI, SR) with a known, regular cadence. For ISAC, PUCCH Formats 2 and 3 are particularly attractive because they use DMRS pilots and span multiple OFDM symbols.

Why Periodic PUCCH Enables Sensing

• Predictable scheduling: Semi-persistent PUCCH (configured via RRC) transmits every \(K\) slots deterministically, enabling coherent sensing integration across many periods without coordination overhead.
• Pilot-aided estimation: PUCCH DMRS occupies fixed OFDM symbols within the resource, allowing the gNB to isolate the pilot component and use it as a sensing reference signal independent of the UCI payload.
• Spatial diversity: Multiple UEs transmitting periodic PUCCH on different time-frequency resources provide spatial diversity — the gNB can perform angle-of-arrival estimation by comparing reflections from spatially separated sources.
• Low overhead: PUCCH is already scheduled for communication purposes; sensing is a free by-product with zero additional UL resource cost.

6.1 CSI-RS and PRS Sensing

In monostatic ISAC, the gNB transmits reference signals and listens to its own echoes. CSI-RS (Channel State Information Reference Signal) is the workhorse for monostatic sensing: its structured time-frequency allocation enables coherent channel estimation at the TX itself. PRS (Positioning Reference Signal, defined in 3GPP Rel-16/17) extends this to bistatic/passive scenarios where a separate RX node estimates geometry from the DL transmission.

The PRS sequence is a QPSK-modulated pseudo-random sequence ensuring low PAPR and good autocorrelation properties. For positioning resource \(m\):

where \(c(n)\) is the length-31 Gold code defined in TS 38.211. The constant \(1/\sqrt{2}\) normalises each PRS symbol to unit power.

Reference Signal Comparison

6.2 Full-Duplex Problem & Self-Interference

Monostatic ISAC requires simultaneous TX and RX at the same node — the defining challenge of in-band full-duplex (IBFD). The transmitter leaks directly into the receiver through antenna coupling, PCB paths, and near-field scattering:

The SI cancellation budget is typically decomposed into three domains, each with characteristic limits set by hardware constraints and non-linearities:

• Passive (antenna) isolation: 30–50 dB — achieved by physical separation, cross-polarisation, absorbers, and circulators.
• Analog cancellation: 20–40 dB — reference signal injection in RF domain before the LNA/ADC chain.
• Digital cancellation: 20–40 dB — adaptive filtering on quantised samples; limited by ADC dynamic range and non-linear distortion.

6.3 SIC Stage-by-Stage Analysis

Each cancellation stage must be budgeted carefully. Denote the SI cancellation gains as \(G_{pass}\), \(G_{ana}\), \(G_{dig}\) (linear power ratios). The residual SI variance after all three stages is:

The three-stage pipeline proceeds as follows:

6.4 TDD Guard Period Sensing

In TDD NR, the monostatic sensing window is restricted to the Guard Period (GP) — the brief transition between DL and UL bursts during which no data is scheduled. This avoids the self-interference problem entirely at the cost of limited observation time.

The maximum unambiguous range is set by the round-trip propagation budget during the GP:

For NR \(\mu=1\) (SCS = 30 kHz), one OFDM symbol duration (including CP) is \(T_{sym} \approx 35.7\,\mu s\). A 2-symbol GP gives \(T_{GP} \approx 71.4\,\mu s\), hence \(R_{max} \approx 10.7\) km. Typical deployments use 1–3 GP symbols, yielding 5–16 km range.

TDD Slot Structure — Timing Diagram

DDDSU pattern (3GPP typical). The Special slot (S) contains the GP where monostatic echo reception is possible. GP duration configurable: 1–10 symbols depending on cell size and operator choice.

6.5 Bistatic Downlink Sensing

In bistatic sensing, the transmitter (gNB) and receiver are physically separated — the RX may be a UE in passive-listening mode, a dedicated sensor node, or another base station. There is no self-interference problem because TX and RX are at different locations.

A target at position \(\mathbf{p}\) creates a two-leg propagation path. The bistatic excess delay relative to the direct TX–RX path is:

Loci of constant \(\tau_{bi}\) are ellipses with TX and RX at the foci. The bistatic range (semi-major axis \(a\)) satisfies: \[ 2a = R_{direct} + c\,\tau_{bi}, \qquad R_{bi} = c\,\tau_{bi} \]

Section 6 — Study Questions

1. TDD R_max: In a TDD NR system with SCS = 30 kHz (\(\mu=1\)) and a 1-symbol guard period, what is \(R_{max}\) for monostatic sensing? (Recall: one NR symbol at \(\mu=1\) has duration \(T_{sym} = 1/(30000) \approx 33.3\,\mu\text{s}\) plus ~20% CP.) Hint: use \(T_{GP} = T_{sym}\) and \(R_{max} = cT_{GP}/2\).
2. Analog SIC necessity: Why is analog SIC required before digital SIC? What fundamental hardware limitation prevents digital-only cancellation from being sufficient? Hint: consider the ADC input power budget and what happens when the SI power exceeds the ADC full-scale range.
3. Bistatic synchronisation: For bistatic sensing, what timing synchronisation accuracy is needed to achieve 1 m absolute range accuracy? How does this compare to the NR frame timing accuracy achievable with PRS (typically ~5 ns at SNR = 0 dB)? At what SNR is PRS timing error < 3.33 ns achievable per 3GPP Rel-17 specs?

7.1 TX → Channel → RX Processing Chain

The OFDM-ISAC sensing chain reuses the communications PHY layer end-to-end. Complex baseband symbols are modulated, pulse-shaped, transmitted, reflected off targets, and then coherently processed at the receiver to extract range, Doppler, and angular information. The received discrete-time signal is modelled as:

where \(\alpha_p\) is the complex reflection coefficient of the \(p\)-th target, \(\tau_p = 2R_p/c\) is the round-trip delay (samples), \(\nu_p = 2v_p f_c/c\) is the Doppler shift (Hz), \(T_s\) is the sampling period, and \(w[n]\sim\mathcal{CN}(0,\sigma_w^2)\) is additive white Gaussian noise. The summation is over all \(P\) scattering paths.

After the 2D-IFFT, the range-Doppler map is:

Each target appears as a 2D impulse at \((\tau_p, \nu_p)\), which after CFAR thresholding yields discrete detections fed into the tracking stage. The pilot-division step normalises out the data symbols, exploiting the known transmit waveform to achieve coherent sensing.

7.2 CFAR Detection

Constant False Alarm Rate (CFAR) detectors adaptively set the detection threshold based on local noise estimates, maintaining a fixed \(P_{FA}\) regardless of clutter level. The cell under test (CUT) is compared against a threshold derived from surrounding reference cells.

Cell-Averaging CFAR (CA-CFAR)

CA-CFAR estimates the noise power from the \(2L\) reference cells (excluding \(G\) guard cells on each side):

where the threshold multiplier \(\alpha\) is chosen to achieve a target \(P_{FA}\):

The false alarm probability for CA-CFAR with \(L\) reference cells is exactly:

A detection is declared when \(|z_{CUT}|^2 > T_{\text{CFAR}}\).

Ordered-Statistics CFAR (OS-CFAR)

OS-CFAR sorts the \(2L\) reference cell samples in ascending order and uses the \(k\)-th order statistic as the noise estimate:

Typical choice: \(k = \lfloor 0.75 \cdot 2L \rfloor\). OS-CFAR is robust to clutter edges and interference spikes that inflate the CA-CFAR noise estimate, at the cost of slightly reduced \(P_D\) in homogeneous clutter.

7.3 MUSIC Direction Finding

After CFAR yields range-Doppler detections, a co-located antenna array estimates the Direction-of-Arrival (DoA) for each detection via the MUSIC (MUltiple SIgnal Classification) algorithm. With an \(M\)-element Uniform Linear Array (ULA) receiving signals from \(K\) point targets, the array output covariance is:

where \(U_s \in \mathbb{C}^{M\times K}\) spans the signal subspace (eigenvalues \(\Sigma_s\)) and \(U_n \in \mathbb{C}^{M\times(M-K)}\) spans the orthogonal noise subspace.

Steering Vector and MUSIC Pseudo-Spectrum

For a ULA with half-wavelength spacing \(d = \lambda/2\), the steering vector for angle \(\theta\) is:

The MUSIC pseudo-spectrum is formed by projecting the steering vector onto the noise subspace:

Sharp peaks in \(P_{\text{MUSIC}}(\theta)\) indicate target angles. The theoretical angular resolution for an \(M\)-element ULA is:

7.4 Kalman Tracking

CFAR detections are discrete, noisy, and possibly missing (misdetections) or spurious (false alarms). A Kalman filter provides a principled recursive estimator that maintains a state estimate and its uncertainty over time, suppressing measurement noise while predicting target motion.

State Model

The tracking state vector for a 2D range-angle target is:

State transition (constant-velocity model) with sampling interval \(T\):

where \(q\) is the process noise spectral density (units: m²/s³ or rad²/s³), controlling how quickly the filter adapts to manoeuvres.

Predict Step

Update Step

Given measurement \(\mathbf{z}_k = H\mathbf{x}_k + \mathbf{v}_k\) where \(\mathbf{v}_k\sim\mathcal{N}(0,R)\):

The innovation \(\tilde{\mathbf{z}}_k = \mathbf{z}_k - H\,\mathbf{x}_{k|k-1}\) measures the prediction error; \(K_k\) blends prediction and measurement optimally. The measurement noise covariance is:

where \(\sigma_r\) and \(\sigma_\theta\) are the CFAR range and angle measurement standard deviations, respectively (typically \(\sigma_r \approx \Delta R / \sqrt{2\cdot\text{SNR}}\) and \(\sigma_\theta \approx \Delta\theta_{MUSIC} / \sqrt{2\cdot\text{SNR}}\)).

Study Questions

8.1 MIMO Sensing Channel

In a MIMO-ISAC system the sensing channel is characterized by a matrix \(H_s \in \mathbb{C}^{N_R \times N_T}\) where \(N_T\) is the number of transmit antennas and \(N_R\) is the number of receive antennas. The received signal block is:

where \(L\) is the number of snapshots (OFDM symbols) and \(N\) is additive noise. For a point target at angle \(\theta\) and range \(r\), \(H_s = \sigma_t \, \mathbf{b}(\theta)\mathbf{a}^T(\theta)\) where \(\mathbf{a}(\theta)\) and \(\mathbf{b}(\theta)\) are the transmit and receive steering vectors, respectively.

Virtual aperture and spatial resolution. Coherent MIMO radar synthesizes a virtual array of length:

Angular resolution (3 dB beamwidth of the virtual aperture, ULA with inter-element spacing \(d\)):

8.2 Beampattern Design

The transmit beampattern is the spatial power distribution radiated by the array. Given signal covariance \(R_{XX} = \mathbb{E}[XX^H] \in \mathbb{C}^{N_T \times N_T}\) and the transmit steering vector \(\mathbf{a}(\theta) = \frac{1}{\sqrt{N_T}}[1, e^{j\pi\sin\theta}, \ldots, e^{j(N_T-1)\pi\sin\theta}]^T\), the power pattern is:

A desired (sensing) beampattern \(p_d(\theta)\) is specified (e.g., uniform coverage of a surveillance sector). The covariance design problem is:

The per-antenna power constraint \(\mathrm{diag}(R_{XX}) = \mathbf{p}\) ensures hardware amplifier limits are respected. This is a semidefinite program (SDP) and can be solved efficiently with CVX or similar convex solvers.

8.3 DFRC Precoder Optimization

A Dual-Function Radar-Communications (DFRC) precoder \(W \in \mathbb{C}^{N_T \times K}\) simultaneously serves \(K\) single-antenna downlink users and generates a sensing beam. Let \(W_s \in \mathbb{C}^{N_T \times K}\) be the purely sensing-optimal precoder (from beampattern design). The joint optimization minimizes deviation from the sensing solution while enforcing comms quality:

where the SINR of user \(k\) under zero-forcing / beamforming is:

8.4 Massive MIMO Degrees of Freedom

As \(N_T \to \infty\) with fixed \(K\) users, the law of large numbers gives channel hardening and favorable propagation. Key asymptotic results:

• Communications DoF: \(K\) spatial streams (limited by the number of users, not antennas).
• Sensing DoF: \(N_T - K\) remaining spatial dimensions are free for sensing without harming comms.
• Beamwidth: \(\Delta\theta = \lambda/(N_T d) \to 0\) — pencil beams with negligible inter-beam interference.

Near-field sensing at mmWave (XL-MIMO). When the target distance \(r \lesssim 2 D^2/\lambda\) (Fraunhofer distance, \(D = N_T d\)), the wavefront curvature across the array is non-negligible. The near-field steering vector encodes both angle and range:

This enables 3D (angle + range) sensing from a single aperture — a key capability of XL-MIMO ISAC at mmWave frequencies.

8.5 MUSIC AoA Estimation with ULA

MUSIC (MUltiple SIgnal Classification) exploits the eigenstructure of the spatial covariance matrix. Given \(L\) snapshots at the \(M\)-antenna receiver:

EVD: \(\hat{R} = E_s \Lambda_s E_s^H + E_n \Lambda_n E_n^H\) where \(E_s \in \mathbb{C}^{M \times P}\) spans the signal subspace (\(P\) targets) and \(E_n\) spans the noise subspace. MUSIC pseudo-spectrum:

Peaks of \(P_{\mathrm{MUSIC}}(\theta)\) give AoA estimates. With \(M = 16\) antennas and sufficient SNR, MUSIC resolves targets separated by as little as 3°, well below the Rayleigh limit of \(\approx 6.4°\) for a 16-element ULA.

8.6 Visualizations

8.7 Study Questions

9.1 Fisher Information Matrix

The Fisher Information Matrix (FIM) provides the fundamental lower bound on the variance of any unbiased estimator. For a parameter vector \(\boldsymbol{\xi} = [\xi_1, \xi_2, \ldots, \xi_p]^T\), the \((i,j)\) entry of the FIM is defined as the negative expected curvature of the log-likelihood:

For complex Gaussian observations \(\mathbf{y} \sim \mathcal{CN}(\boldsymbol{\mu}(\boldsymbol{\xi}), C)\) with signal-dependent mean and known covariance \(C\), the FIM takes the compact form:

The Cramér-Rao Bound (CRB) states that the variance of any unbiased estimator \(\hat{\xi}_i\) satisfies:

Joint Delay-Doppler FIM for OFDM Sensing

For an OFDM waveform with \(N\) subcarriers (spacing \(\Delta f\)) and \(M\) symbols (PRI \(T_s\)), the received signal from a target at delay \(\tau\) and Doppler shift \(\nu\) is:

where \(\alpha\) is the complex target reflectivity, \(s_{k,m}\) is the transmitted symbol on subcarrier \(k\), symbol \(m\), and \(n_{k,m} \sim \mathcal{CN}(0, \sigma_n^2)\). Stacking into the joint parameter vector \(\boldsymbol{\xi} = [\tau, \nu]^T\) and computing the partial derivatives yields the \(2\times2\) FIM:

9.2 CRB vs SNR Analysis

For an OFDM system with \(N\) subcarriers carrying pilots at frequencies \(\{f_k\}\) with powers \(\{p_k\}\), define the effective mean-square bandwidth and observation duration:

The one-sided range (delay) and velocity (Doppler) CRBs become:

Pilot Power Allocation: Uniform vs Edge-Weighted

9.3 Sensing-Comms Pareto Frontier

Consider a total transmit power budget \(P\) split between communication and sensing waveforms with splitting factor \(\alpha \in [0,1]\): \(P_c = \alpha P\) and \(P_s = (1-\alpha)P\). The joint ISAC optimization problem can be stated as a bi-objective program:

For the scalarized single-parameter sweep, comms spectral efficiency (Shannon capacity with interference-free AWGN channel) and range CRB are:

The Pareto frontier is the set of operating points \((C(\alpha), \sigma_r^2(\alpha))\) as \(\alpha\) sweeps \([0,1]\). Three canonical operating regimes are identified:

9.4 Practical Considerations

Coherent vs Incoherent Integration

When multiple OFDM symbols (pulses) illuminate the same target, SNR can be accumulated. The improvement depends on whether phase coherence is maintained across pulses:

Coherent integration provides a linear (10 dB/decade) gain vs. the \(\sqrt{N}\) (5 dB/decade) gain of incoherent integration. However, coherence requires:

• The target's Doppler phase to remain predictable over the coherent processing interval (CPI).
• CPI \(\ll T_{\mathrm{coherence}} \approx 1/B_D\) where \(B_D\) is the target's Doppler spread.
• Oscillator phase noise below the inter-symbol phase rotation threshold.

Mismatched Filter and Sidelobe Masking

In practice, the sensing matched filter is implemented via 2D-IFFT over the delay-Doppler grid. Imperfect windowing produces range/velocity sidelobes. For a rectangular window:

Sidelobe masking occurs when a weak target falls within the sidelobe zone of a strong nearby target. The masking threshold in range is approximately:

When is Coherent Integration Feasible?

For vehicular targets at \(f_c = 28\) GHz with radial velocity \(v\), the Doppler shift is \(f_D = 2v f_c/c\). The coherence time is \(T_c \approx 1/(2B_D)\). For a single point target at known velocity, the CPI can span several milliseconds. For extended or fluctuating targets (Swerling models), envelope fluctuation limits effective CPI to \(T_c\), beyond which non-coherent combining is preferred. OFDM has the advantage that the pilot phase is deterministic, enabling phase-coherent accumulation across symbols up to the channel coherence time.

10.1 TS 22.837 Service Requirements

3GPP TS 22.837 defines the service requirements for Integrated Sensing and Communication (ISAC) in 5G NR. These KPIs set hard targets that physical-layer designs must meet across heterogeneous deployment scenarios.

10.2 TR 38.837 Findings (Rel-18 Study Item)

3GPP TR 38.837 documents the Rel-18 ISAC Study Item outcomes, establishing the feasibility baseline for NR-based sensing and identifying the priority issues for the subsequent Rel-19 Work Item.

10.3 3GPP Release Timeline

ISAC standardisation follows a phased incremental approach within 3GPP, building on positioning enhancements from Rel-17 and maturing through Rel-19/20 work items.

10.4 6G Outlook — ISAC as a Native Service

The IMT-2030 framework (6G) elevates ISAC from an add-on capability to a first-class design goal. Sensing performance targets are orders of magnitude beyond current 5G NR.

10.5 Open Research Challenges

Despite rapid progress, several fundamental challenges remain open for the research community before ISAC can be deployed at scale.

Study Questions

1. CRB vs TS 22.837 indoor range requirement: TS 22.837 requires \(\sigma_r \leq 1\,\text{m}\) indoors. For NR at \(B = 100\,\text{MHz}\) with flat spectrum, the effective RMS bandwidth is \(\sigma_B = B/\sqrt{12} \approx 28.9\,\text{MHz}\). The range CRB is \(\sigma^{CRB}_r = c / (4\pi\sigma_B\sqrt{2\,\text{SNR}})\). Substituting: \(\sigma^{CRB}_r \approx 0.83 / \sqrt{2\,\text{SNR}}\,\text{m}\). For the 1 m requirement, \(\sqrt{2\,\text{SNR}} \geq 0.83\), i.e., \(\text{SNR} \geq -1.6\,\text{dB}\). This appears achievable, but practical NR pilots occupy only a fraction of the bandwidth (every 4th subcarrier for SRS), reducing \(\sigma_B\) by \(\sim 2\times\) and requiring SNR > 4 dB — tight but feasible for indoor small-cell deployments.
2. Half-duplex constraint on monostatic range: A gNB transmitting sensing pulses in DL cannot simultaneously receive echoes. The receiver switches on only after the TX guard period. For 30 kHz SCS, GP \(\approx 35.7\,\mu\text{s}\), giving blind range \(R_{blind} = c \cdot T_{GP}/2 \approx 5.4\,\text{km}\). Targets closer than \(R_{blind}\) produce echoes that arrive while the gNB is still transmitting — these are completely masked. For urban macro cells (ISD \(\sim 500\,\text{m}\)), this is not an issue; for short-range applications (factory, gesture), a full-duplex or bistatic architecture is mandatory.
3. Incremental (3GPP) vs native (6G) ISAC tradeoffs: The incremental 3GPP approach reuses existing OFDM waveforms and reference signals, enabling ISAC deployment on installed base without hardware changes — low cost, fast time-to-market, backward compatible. The native 6G approach co-designs waveform, multiple access, and beamforming from scratch for joint optimality, achieving superior performance (sub-cm range, full-duplex) but requires a clean-slate deployment with new devices and infrastructure. The incremental approach incurs a persistent performance penalty from CP overhead, half-duplex constraint, and suboptimal sensing waveforms; the native approach risks fragmentation if 6G standardisation timelines slip or market adoption is slow.

Notebook Summary — Key Formulas by Section

Quick-reference table covering all ten sections of this OFDM-ISAC notebook. Each row gives the section topic, the single most important formula, and a brief interpretation.

This appendix traces the complete standardization journey of Integrated Sensing & Communications through 3GPP — from the first workshop discussions to the active Rel-19 Work Item and the 6G horizon. Each milestone links to the responsible working group and the key output document.

Key 3GPP Documents

Standardization Gantt