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Tarek Hassan
Knowledge Hubintegrated sensing and communication3. OFDM Sensing: Turning a Data Signal Into a Radar

integrated sensing and communication learning note

3. OFDM Sensing: Turning a Data Signal Into a Radar

Step by step: how a base station removes its own data from the echo and reads range and speed from an ordinary OFDM signal with two FFTs.

At a glance

  • The BS already knows the dataDividing the echo by the symbols it just sent removes the data and leaves only the channel.
  • Delay and Doppler become phase rampsDelay rotates phase across subcarriers; motion rotates phase across symbols. Two FFTs turn the ramps into peaks.
  • Numerology sets the radarBandwidth sets range resolution, subcarrier spacing sets maximum range, and how many symbols you observe sets velocity resolution.

The Idea in One Sentence

A base station that sends an OFDM signal knows every symbol it put on every subcarrier, so when the signal bounces off a car and comes back, it can divide out its own data and look at what is left: the effect of the car's distance and speed.

No extra radar pulse is needed. This is called communication-centric or OFDM-based sensing, and it is the most practical route to ISAC in cellular networks.

References for this section3

What the Receiver Sees

OFDM sends data on NN subcarriers spaced Δf\Delta f apart, symbol after symbol with period TT. For a single target, the echo on subcarrier kk in symbol mm is

Y[k,m]=α  X[k,m]  e−j2πkΔf τ  e j2πmTfD+W[k,m]Y[k,m] = \alpha \; X[k,m] \; e^{-j2\pi k\Delta f\,\tau} \; e^{\,j2\pi m T f_D} + W[k,m]
  • X[k,m]X[k,m]: the data symbol the base station sent (known to it).
  • α\alpha: echo strength, from the radar equation.
  • τ\tau, fDf_D: round-trip delay and Doppler shift of the target.
  • W[k,m]W[k,m]: noise.

Every useful number is hidden in the two exponentials. The data symbol XX is in the way.

References for this section3

Step 1: Remove the Data

Because the base station knows X[k,m]X[k,m], it simply divides:

H[k,m]=Y[k,m]X[k,m]=α e−j2πkΔf τ e j2πmTfD+W[k,m]X[k,m]H[k,m] = \frac{Y[k,m]}{X[k,m]} = \alpha\, e^{-j2\pi k\Delta f\,\tau}\, e^{\,j2\pi m T f_D} + \frac{W[k,m]}{X[k,m]}

What remains is a grid of numbers, one per subcarrier and symbol, that depends only on the target. With constant-amplitude symbols such as QPSK the noise is not amplified; with higher-order QAM it varies a little from cell to cell.

References for this section3

Step 2: Range From the Subcarriers

Hold the symbol mm fixed and walk along the subcarriers. The phase changes by −2πΔfτ-2\pi\Delta f\tau from one subcarrier to the next: a straight phase ramp whose slope is set by the delay. A farther target makes a steeper ramp.

An inverse FFT across the NN subcarriers turns that ramp into a single peak. The peak's position is the delay, and therefore the range R=cτ/2R = c\tau/2.

References for this section3

Step 3: Speed From the Symbols

Now hold the subcarrier fixed and walk along the symbols. A moving target rotates the phase by 2πTfD2\pi T f_D from one symbol to the next: another phase ramp, this time set by the Doppler shift.

An FFT across the MM symbols turns this ramp into a peak at the Doppler frequency, and therefore at the radial speed vr=fDλ/2v_r = f_D\lambda/2.

Doing both FFTs gives a range–Doppler map: a picture with range along one axis and speed along the other, where each target appears as a bright spot.

References for this section3

Picking the Numbers

The OFDM parameters chosen for communication directly become the radar's specifications:

Radar propertyFormulaSet by
Range resolutionΔR=c2B\Delta R = \dfrac{c}{2B}, with B=NΔfB = N\Delta ftotal bandwidth
Maximum unambiguous rangeRmax⁡=c2ΔfR_{\max} = \dfrac{c}{2\Delta f}subcarrier spacing
Velocity resolutionΔv=λ2MT\Delta v = \dfrac{\lambda}{2MT}total observation time
Maximum unambiguous speedvmax⁡=λ4Tv_{\max} = \dfrac{\lambda}{4T}time between sensing symbols

The interactive map below builds the range–Doppler map from scratch with these exact steps, so you can watch each number change.

OFDM sensing, step by step: from data signal to range–Doppler map

range →↑ approaching radial speed receding ↓0 m/s
Processing step
Bandwidth
Second target
Range resolution c/2B1.50 mmax range c/2Δf = 95.93 m
Speed resolution λ/2MT1.34 m/smax speed λ/4T = ±21.4 m/s
Peak found at38.97 m, 8.0 m/strue: 38.37 m, 8 m/s
Processing gain33.1 dB64 × 32 elements

4. FFT across symbols. An FFT down each column turns the symbol phase ramp into a peak at the target's speed. Each target becomes one bright spot on the range–Doppler map.

H[k,m]=Y[k,m]X[k,m]=∑tαt e−j2πkΔf τt e j2πmTfD,t+W~[k,m]H[k,m] = \frac{Y[k,m]}{X[k,m]} = \sum_{t} \alpha_t\, e^{-j2\pi k\Delta f\,\tau_t}\, e^{\,j2\pi m T f_{D,t}} + \tilde W[k,m]
ΔR=c2B=1.50 m,Rmax⁡=c2Δf=95.93 m,Δv=λ2MT=1.34 m/s,vmax⁡=λ4T=21.4 m/s\Delta R = \frac{c}{2B} = 1.50\ \text{m}, \quad R_{\max} = \frac{c}{2\Delta f} = 95.93\ \text{m}, \quad \Delta v = \frac{\lambda}{2MT} = 1.34\ \text{m/s}, \quad v_{\max} = \frac{\lambda}{4T} = 21.4\ \text{m/s}
64 sensing subcarriers across 100 MHz at 28 GHz, 32 symbols spaced 0.125 ms apart (one sensing symbol per slot). The echo is built from the OFDM model with QPSK data and complex noise, then processed exactly as in the text. Walk through the four steps, then move the target and watch its spot move.
References for this section3

Practical Catches

  • Cyclic prefix: echoes that arrive later than the cyclic prefix leak into the next symbol. A safe sensing range is about c TCP/2c\,T_{\mathrm{CP}}/2, about 88 m for 5G NR at 120 kHz subcarrier spacing (normal cyclic prefix ≈ 0.59 µs).
  • Self-interference: a monostatic base station must listen while it transmits. Its own signal leaks into the receiver millions of times stronger than the echo, so it needs separate antennas, isolation and cancellation (full duplex).
  • Clutter: walls and parked cars produce strong echoes at zero Doppler. Removing the zero-Doppler column, or subtracting a background estimate, reveals the moving targets.
  • Bistatic sensing: if the echo is received by another node, the two must share a clock and know which symbols were sent; small timing offsets show up as range errors.
References for this section3

Takeaway

  • Recipe: divide by the known data, inverse FFT across subcarriers for range, FFT across symbols for speed.
  • Specifications for free: bandwidth, subcarrier spacing and observation time chosen for communication directly fix the radar's resolution and limits.
  • Engineering work: cyclic prefix length, self-interference and clutter decide how well it works in practice.
References for this section3

Check your understanding

0 of 4 answered

  1. Why can a monostatic OFDM base station sense with its own downlink data?

  2. Across subcarriers (for one OFDM symbol), what does a target's delay look like?

  3. Doubling the bandwidth while keeping the number of subcarriers fixed changes what?

  4. How do you get finer velocity resolution?

Complete references and further reading