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arxiv: 2607.00912 · v1 · pith:NUIT2URVnew · submitted 2026-07-01 · 💻 cs.IT · eess.SP· math.IT

Fundamental Limits of Random Downlink Integrated Sensing and Communication over Rician Channels

Marziyeh Soltani , Mahtab Mirmohseni , Rahim Tafazolli , Mark F. Flanagan This is my paper

Pith reviewed 2026-07-02 05:45 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords integrated sensing and communicationRician fadingoutage probabilityCramer-Rao boundbeamformingscaling lawsMIMO
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The pith

Rician channels require new analysis for ISAC outage probabilities because deterministic LoS components create angle-dependent non-i.i.d. random vectors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives communication outage probability and sensing outage probability based on the Cramer-Rao bound for both subspace joint beamforming and linear beamforming in a downlink MIMO ISAC system over Rician fading. It also identifies special cases, bounds, approximations, and large-system high-power scaling laws. A sympathetic reader would care because Rician fading models LoS-dominated deployments where the deterministic component changes reliability compared with Rayleigh fading, and the results show the K-factor affects communication more strongly than sensing with non-monotonic behavior across regimes.

Core claim

For both SJB and LB schemes, communication outage probability and sensing outage probability are derived based on the Cramer-Rao bound, with special cases having simpler expressions; for LB, upper and lower bounds on sensing outage probability and a tractable approximation are obtained; large-system and high-power scaling laws are characterized, showing LB without DPC is interference-limited at high power due to radar self-interference, LB with DPC achieves the best overall performance in strong LoS environments and is the only scheme achieving ultra-high communication reliability in Rayleigh fading, while SJB provides a robust lower-complexity alternative.

What carries the argument

Subspace joint beamforming (SJB) optimal for shared waveform structure and linear beamforming (LB) using separate sensing and communication beamformers, applied to Rician channels whose LoS components produce angle-dependent terms and independent but non-identically distributed random vectors.

If this is right

  • LB without DPC is interference-limited at high power due to radar self-interference.
  • LB with DPC achieves the best overall performance in strong LoS environments.
  • SJB provides a robust lower-complexity alternative across operating conditions.
  • LB with DPC is the only scheme achieving ultra-high communication reliability in Rayleigh fading.
  • The Rician K-factor affects communication more strongly than sensing, with non-monotonic behavior across regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The scaling laws could be used to predict how performance changes when the number of antennas grows without bound.
  • The non-monotonic K-factor dependence suggests there may exist an optimal K-factor value that minimizes outage for a given power level.

Load-bearing premise

The base station to user channel contains both line-of-sight and non-line-of-sight components, with the user line-of-sight angle fixed or random and the target angle following an arbitrary distribution that may be correlated with the user angle.

What would settle it

An experiment that measures communication and sensing outage probabilities in a controlled Rician channel with a known K-factor and known angle distributions, then checks whether the measured values match the paper's closed-form expressions or scaling laws within the stated approximations.

Figures

Figures reproduced from arXiv: 2607.00912 by Mahtab Mirmohseni, Mark F. Flanagan, Marziyeh Soltani, Rahim Tafazolli.

Figure 1
Figure 1. Figure 1: Communication OP (Pout,c(γ)) versus communication threshold (γ) at SJB, communication OP versus communication threshold at LB, and sensing OP Pout,s(ǫ) versus sensing threshold (ǫ) (log scale) at SJB. cross section and path loss effects 1 . We assume that the target and user angles are independent and uniformly distributed over the interval [0, π]. However, our numerical derivations are valid for any arbit… view at source ↗
Figure 3
Figure 3. Figure 3: Sensing OP versus Communication OP in SJB and LB for [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Sensing OP at LB directional imbalance. In [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
read the original abstract

This paper studies the stochastic performance of a downlink multiple-input multiple-output integrated sensing and communication (ISAC) system over Rician fading channels. Rician fading is important in line-of-sight (LoS)-dominated deployments, where a deterministic propagation component can strongly affect sensing and communication reliability. The base station (BS) simultaneously serves a user and senses a target. The BS-user channel contains LoS and non-line-of-sight components. The user LoS angle may be fixed or random, and the target angle may follow an arbitrary distribution potentially correlated with the user angle. Compared with Rayleigh fading, the deterministic LoS component introduces angle-dependent terms and leads to generally independent but non-identically distributed random vectors, requiring new analysis. We analyze two beamforming strategies: subspace joint beamforming (SJB), optimal for the shared waveform structure, and linear beamforming (LB), a practical alternative using separate sensing and communication beamformers. For both schemes, we derive communication outage probability (OP) and sensing OP based on the Cramer--Rao bound (CRB). We also identify special cases with simpler expressions. For LB, we derive upper and lower bounds on sensing OP and a tractable approximation. We characterize large-system and high-power scaling laws. LB without dirty paper coding (DPC) is interference-limited at high power due to radar self-interference. Results show the Rician K-factor affects communication more strongly than sensing, with non-monotonic behavior across regimes. LB with DPC achieves the best overall performance in strong LoS environments and is the only scheme achieving ultra-high communication reliability in Rayleigh fading, while SJB provides a robust lower-complexity alternative across operating conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper studies downlink MIMO ISAC over Rician channels with possibly correlated user/target LoS angles, yielding i.n.i.d. random vectors. It analyzes subspace joint beamforming (SJB) and linear beamforming (LB) schemes, deriving communication and sensing outage probabilities (OP) based on the CRB, special-case simplifications, upper/lower bounds and approximations for LB sensing OP, and large-system/high-power scaling laws. It reports that the Rician K-factor affects communication more than sensing, LB without DPC is interference-limited at high SNR, and LB with DPC performs best in strong LoS while SJB offers a lower-complexity robust alternative.

Significance. If the derivations hold, the work supplies explicit fundamental limits and scaling laws for ISAC under realistic Rician conditions, including the technical step of handling angle-dependent i.n.i.d. vectors. Credit is due for the closed-form/bounded expressions, identification of special cases, and the scaling-law characterizations that quantify regime-dependent behavior and scheme trade-offs.

minor comments (2)
  1. The abstract and introduction would benefit from a brief statement of the main technical novelty (the i.n.i.d. vector analysis) being placed in a dedicated subsection or theorem statement for easier reference.
  2. [§2] Notation for the angle distributions and correlation model could be clarified with an explicit table or diagram in §2 to distinguish fixed vs. random user LoS and arbitrary target distributions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and recommendation of minor revision. No specific major comments were listed in the report, so there are no individual points requiring point-by-point rebuttal or manuscript changes at this stage.

Circularity Check

0 steps flagged

No significant circularity; derivations are self-contained from channel model and CRB

full rationale

The paper performs direct derivations of communication and sensing outage probabilities (plus large-system/high-power scaling laws) for SJB and LB schemes starting from the stated Rician channel model with possible angle correlation. The i.n.i.d. vector analysis, CRB-based sensing metric, and closed-form/bounded expressions are obtained by explicit calculation rather than by fitting parameters, renaming known results, or load-bearing self-citation chains. No step reduces by construction to its own inputs; the central claims remain independent of the paper's own fitted values or prior author results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; full manuscript required to audit modeling assumptions such as angle distributions or CRB applicability.

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discussion (0)

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Reference graph

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