Ferkans — Interactive Telecom Tutor

What the Chip Has to Do

The previous sections laid out an algorithmic framework: a DD-angle channel model, a covariance SDP for joint beamforming, and an EKF loop for target tracking. This section confronts the practical reality — what those algorithms look like in silicon, what the hardware constraints imply for the algorithms, and where the pragmatic compromises live. The focus is on a 77-GHz automotive ISAC reference design, which has the most mature roadmap.

Definition:
MIMO-OTFS-ISAC Hardware Stack

A MIMO-OTFS-ISAC transceiver consists of four layers:

RF front-end: Phased array with $N_t \times N_r$ antennas, mmWave PA/LNAs, calibration network. Typical mmWave: $N_t = N_r = 16$ - $32$ at 77 GHz, 28 GHz, or 60-120 GHz.
ADC/DAC: Wideband (100 MHz - 2 GHz) converters. Oversampling factor $\beta = 1$ - $2$ per MIMO port.
Digital baseband: FFT, ISFFT/SFFT engines, matrix-matrix multiplication for precoding, compressed-sensing estimator. Parallelized across antenna ports.
Control: Scheduler, beam manager, tracker. Runs SDP-type convex programs on embedded CPU or GPU.

Theorem: Real-Time Compute Budget

For a MIMO-OTFS-ISAC transceiver with $N_t = N_r = 16$ , $M = 256$ , $N = 32$ , $K = 4$ users, $T_{\text{tgt}} = 4$ targets, frame rate $100$ Hz:

Precoding (SDP): $\sim 10^8$ ops per scheduling slot (10 ms): $10^{10}$ ops/sec. Feasible on embedded GPU.
Per-frame detection (MP-OTFS): $\sim 10^7$ ops per frame: $10^9$ ops/sec.
Tracking (EKF): $\sim 10^4$ ops per frame per target: $4 \times 10^6$ ops/sec.
Estimation (DD channel from sensing): $\sim 10^7$ ops per frame: $10^9$ ops/sec.

Total: $\sim 10^{10}$ ops/sec. Within 5-10 W embedded mmWave baseband SoC budget (2024-era: Qualcomm, Infineon prototypes).

MIMO-OTFS-ISAC is compute-feasible at realistic scales. The bottleneck is not raw operation count but memory bandwidth (large DD-channel matrices) and the SDP solver (iterative, hard to parallelize). For deployment-scale systems, SDP is replaced by successive convex approximation or closed-form suboptimal beamformers at runtime; the SDP solution is computed offline and cached as a look-up table indexed by the target scene.

Proof

SDP cost

For $N_t = 16$ , the covariance cone has dimension $136$ . SDP interior-point methods scale $\mathcal{O}(n^{6.5})$ : $136^{6.5} \approx 10^{14}$ — too expensive. In practice, first-order solvers (splitting, ADMM) scale linearly: $\mathcal{O}(n^2 k)$ where $k = 100$ - $500$ iterations, giving $\sim 10^7$ ops/solve.

Detection cost

MP-OTFS: $\mathcal{O}(MN \cdot P)$ per iteration $\times$ 5-10 iterations. For $MN = 8192$ , $P = 8$ : $3 \times 10^5$ per iter, $3 \times 10^6$ per frame.

Tracking cost

EKF: matrix inversions of $4 \times 4$ , propagation: $\mathcal{O}( n_s^3)$ = 64 ops/target. Per 4 targets: 256 ops/frame.

Total

Sum all components at 100 Hz: $\sim 10^{10}$ ops/sec. Feasible on modern automotive SoC (5-10 W thermal budget). $\blacksquare$

,

🔧Engineering Note

Silicon State of the Art (2026)

MIMO-OTFS-ISAC has reached silicon prototype maturity:

77 GHz automotive: Infineon, NXP, Texas Instruments offer $N_t = N_r = 8$ - $16$ arrays with integrated baseband. Throughput 100-500 Mbps data, positional accuracy $\sim 10$ cm. Commercial deployments in premium automotive 2025+.
28 GHz mmWave cellular: Qualcomm, Mediatek, Samsung — BS-side arrays with $N_t = 32$ - $64$ . Research prototypes show joint data + user tracking. Standardization for 6G ISAC expected 2028.
60-120 GHz (WiGig/6G): $N_t = N_r = 16$ - $64$ . Research prototypes. TAsk: healthcare monitoring, high-resolution sensing.

Across vendors, the DD-domain processing has converged as the dominant architectural choice — OFDM-based ISAC is limited by high-mobility cross-talk and Doppler-induced ICI, and the added complexity of per-carrier adaptation exceeds the DD framework's unified approach.

Practical Constraints

•
77 GHz automotive: Infineon/NXP/TI, 8-16 antennas, commercial 2025+
•
28 GHz cellular: 32-64 antennas, 6G standardization 2028
•
60-120 GHz: healthcare/sensing focus
•
Common: DD-domain processing is the dominant architecture

Theorem: Complexity Scaling of MIMO-OTFS-ISAC

For the MIMO-OTFS-ISAC operations, complexity scaling is:

Channel estimation: $\mathcal{O}(P N_t N_r \log(MN))$ per frame (sparse DD-angle, compressed sensing).
Joint beamforming (SDP): $\mathcal{O}(N_t^{3-6} + K^2 N_t)$ per scheduling slot (convex solver cost).
MIMO-OTFS detection (MP): $\mathcal{O}(MN \cdot P \cdot N_r \cdot T_{\text{iter}})$ per frame.
Tracking (EKF): $\mathcal{O}(T_{\text{tgt}} n_s^3)$ per frame.

Consequence. Total complexity is $\mathcal{O}(MN \cdot P \cdot N_r)$ dominating — linear in frame size, linear in path count, linear in receive antennas. Scalable to large deployments: 5G NR-scale $MN = 10^5$ , $N_r = 64$ , $P = 10$ : $6 \times 10^7$ ops/frame, $\sim 10^{10}$ ops/sec at 100 Hz frame rate.

The compute scales well because the DD structure exposes the true sparsity ( $P$ paths, not $MN$ channel cells). An OFDM-based ISAC equivalent would scale as $MN \cdot N_t N_r$ — i.e., the channel is not compressed, and all $MN \cdot N_r N_t \approx 10^9$ cells are processed explicitly. The DD-angle representation delivers a $\sim 100$ -fold complexity reduction.

Proof

Per-frame cost

Each of the four operations scales linearly in the main data dimensions, times logarithmic factors for FFT.

Critical scaling

The dominant term is detection (MP): $MN \cdot P \cdot N_r$ .

Per-slot cost

SDP runs per scheduling slot ( $\sim 10$ ms in 5G NR), not per frame. Amortized cost per frame: $10^7/10 = 10^6$ . Acceptable.

Overall

$10^{10}$ ops/sec per transceiver. Feasible on modern SoC. $\blacksquare$

Example: BS Silicon Requirements for Urban ISAC

Design silicon specifications for a 28 GHz urban ISAC BS: $N_t = N_r = 64$ , $M = 512$ , $N = 32$ , $K = 16$ users, $T_{\text{tgt}} = 8$ targets, frame rate 10 Hz (slow-moving urban scene).

(a) Compute the raw operation count per second. (b) State the memory bandwidth requirement. (c) Specify the SoC profile (GPU size, power budget).

Solution

Per-second ops

MIMO-OTFS detection: $MN P N_r = 512 \cdot 32 \cdot 10 \cdot 64 = 10^7$ per frame; $\times 10$ Hz = $10^8$ ops/sec. SDP: $N_t^3 \cdot 100 = 10^5$ per slot; $\times 10$ = $10^6$ ops/sec. Tracking: $T_{\text{tgt}} \cdot 64 = 500$ per frame; $\times 10 = 5 \times 10^3$ ops/sec. Estimation: $MN \cdot P \cdot \log MN = 4 \times 10^6$ per frame; $\times 10 = 4 \times 10^7$ ops/sec. Total: $\sim 1.5 \times 10^8$ ops/sec. Modest.

Memory bandwidth

DD channel matrix: $MN \cdot N_r \cdot N_t$ bytes (complex) = $16 \cdot 64 \cdot 64 \cdot 8 = 4$ MB per frame. At 10 Hz: $40$ MB/s. Easy.

SoC profile

BS baseband: $500$ GFLOPS GPU. Power: 50 W thermal. Budget: $\sim 2000$ GFLOPS/W — well within 2024 embedded GPU specifications. Deployable.

Compute Budget vs System Scale

Show per-frame operation count as a function of $N_t$ (4 to 64) and $MN$ (1024 to 65536). Overlay silicon power envelope (5W, 20W, 100W equivalent throughput budgets) to identify feasible operating regions.

Parameters

Max

N_t

64

Max

MN

32768

P

paths8

Frame rate (Hz)100

Architecture Comparison: OFDM vs MIMO-OTFS ISAC

Metric	OFDM-ISAC (time-multiplexed)	MIMO-OTFS-ISAC (joint)
Comms rate	Good at static	Good at all mobility
Sensing accuracy	Bandwidth-limited range	Bandwidth + frame-duration
Latency	10-20 ms	3-10 ms
Complexity	Low per-op, high total (dense)	Modest (sparse DD)
Doppler robustness	Poor ( $\leq$ 300 km/h)	Excellent (LEO-scale)
Silicon footprint	Smaller (legacy IP)	Modest (new IP 2025+)
Standards	5G NR, 4G LTE legacy	6G candidate (2028+)

Joint ISAC Beam Pattern: $\mathbf{R}_x$ Design

Animation showing the transmit beam pattern as the sensing weight

\alpha

sweeps from 0 (sensing-only) to 1 (comms-only). Users at

\pm 15°, \pm 45°

; targets at

\pm 30°

. Watch the beam carve out nulls toward comms directions when

\alpha

is large and focus toward target directions when

\alpha

is small. The knee point balances both.

Why This Matters: Chapter 14: Sensing-Assisted Communication

This chapter took sensing information as a byproduct of the communication waveform. Chapter 14 reverses the role: use the sensing information to improve the communication channel, closing a feedback loop. Sensing provides target-direction estimates; the scheduler uses these to predict channel variations and preemptively allocate resources. The DD-domain framework makes this loop especially clean: the target scene and the channel model share the same representation.

Hardware and Implementation Considerations