Maximum Credible Interference

• Maximum Credible Interference is defined as the highest interference level that remains admissible under application-specific reliability, feasibility, or detection requirements.
• It is quantified through methods such as outage constraints in Poisson wireless networks, feasible cognitive interference regions, and maximum overlap counts in geometric sensor models.
• The concept highlights that interference limits are model-dependent, requiring joint consideration of spatial correlations, exclusion zones, and statistical characterization rather than simple scalar thresholds.

Maximum credible interference is a non-standard but technically useful designation for the largest interference level that remains admissible under an explicit system criterion. Across the cited literature, that criterion is formulated in several distinct ways: an outage-constrained density of simultaneous transmitters in Poisson wireless networks, a receiver-side aggregate interference ceiling derived from allowable degradation, a feasible cognitive-interference region for protecting primary users, a worst-node receiver-interference objective in geometric topology control, a high-quantile aggregate-interference threshold in stochastic cognitive-radio models, or a validated worst-channel anomaly in interference detection. The common structure is always the same: interference is not treated as an unconstrained nuisance term, but as a quantity bounded by reliability, feasibility, or detectability requirements (Tanbourgi et al., 2013, Monemi et al., 2015, Abdulla et al., 2013, 0905.3023, Shin et al., 5 Mar 2026).

1. Conceptual scope and formal meaning

The phrase is absent as a standardized term in most of the underlying papers, but each of them supplies a formal analog. In random wireless networks with maximum ratio combining (MRC), the closest analog is the critical density $\lambda_\epsilon$, defined as the maximum density of simultaneous transmissions such that the outage probability stays below a target $\epsilon$. In coexistence analysis for IEEE 802.20, the analog is the maximum aggregate interference power $I_{\text{agg}}^{\max}$ tolerated by the receiver under a prescribed degradation budget. In underlay cognitive radio networks, the corresponding object is not a scalar threshold at all, but the set of all jointly feasible interference vectors $\mathbf I^{s\rightarrow p}$ satisfying linear protection inequalities. In geometric network design, a related but distinct meaning is the minimum achievable value of the maximum receiver interference, where interference is the number of transmission disks covering a node (Tanbourgi et al., 2013, Abdulla et al., 2013, Monemi et al., 2015, 0802.2134).

Two distinctions are central. First, “maximum” can mean a scalar ceiling, as in $I_{\text{agg}}^{\max}$, or the boundary of a multidimensional feasible set, as in the feasible cognitive interference region (FCIR). Second, “credible” is always criterion-dependent. In outage-based work, it means “consistent with $\mathbb P(\mathrm{SIR}<T)\le \epsilon$.” In coexistence work, it means “consistent with the allowed degradation.” In detection work, it can mean “anomalous enough to exceed threshold and sufficiently corroborated in time or across sensors.” A plausible implication is that maximum credible interference is best understood as a family of admissibility notions rather than a single invariant metric.

2. Outage-constrained interference in stochastic wireless networks

In the Poisson-field MRC model, interference credibility is naturally parameterized by the density $\lambda$ of active interferers. The setup consists of a desired single-antenna transmitter communicating with an $N$-antenna receiver at distance $d$, while interferers form a stationary Poisson point process of density $\lambda$; path loss is $\epsilon$0 with $\epsilon$1, fading is Rayleigh, and the regime is interference-limited. The post-combiner reliability metric is the outage probability

$\epsilon$2

and the critical density is obtained by solving the outage expression for $\epsilon$3. In this framework,

$\epsilon$4

For $\epsilon$5, the paper derives the exact SIR distribution; for $\epsilon$6, it gives min/max-fading bounds and a full-correlation approximation. For the single-antenna case,

$\epsilon$7

This makes the dependence explicit: allowable interferer density decreases as $\epsilon$8, decreases as $\epsilon$9, and increases with a looser outage target $I_{\text{agg}}^{\max}$0 (Tanbourgi et al., 2013).

The same paper shows why correlation matters directly for credible-interference estimation. Because all receive antennas observe interference generated by the same interferer locations, the interference powers across antennas are spatially correlated. The full-correlation approximation is “considerably pessimistic,” producing up to roughly $I_{\text{agg}}^{\max}$1 higher outage probability for typical parameters, whereas the no-correlation model is “significantly optimistic.” Consequently, the former understates the maximum tolerable $I_{\text{agg}}^{\max}$2, while the latter overstates it. The paper also proves that the spatial-contention diversity order

$I_{\text{agg}}^{\max}$3

equals $I_{\text{agg}}^{\max}$4 for $I_{\text{agg}}^{\max}$5, so MRC improves constants but does not improve the outage-versus-density slope beyond first order. For $I_{\text{agg}}^{\max}$6, $I_{\text{agg}}^{\max}$7, $I_{\text{agg}}^{\max}$8, and $I_{\text{agg}}^{\max}$9, the reported critical-density gain over a single-antenna receiver grows sublinearly with $\mathbf I^{s\rightarrow p}$0, and a first-order approximation indicates

$\mathbf I^{s\rightarrow p}$1

This suggests that additional antennas enlarge the credible interference margin, but not with full diversity-order scaling.

3. Receiver-side interference ceilings and probabilistic protection

In coexistence analysis for IEEE 802.20, the maximum credible interference is formalized as a receiver aggregate-interference threshold derived from allowable degradation. The key relation is

$\mathbf I^{s\rightarrow p}$2

so the tolerated interference ceiling is

$\mathbf I^{s\rightarrow p}$3

In dB form, the benchmark is expressed as

$\mathbf I^{s\rightarrow p}$4

With $\mathbf I^{s\rightarrow p}$5 dB, $\mathbf I^{s\rightarrow p}$6 dB, $\mathbf I^{s\rightarrow p}$7 K, and $\mathbf I^{s\rightarrow p}$8 K, the allowable ratio is

$\mathbf I^{s\rightarrow p}$9

which is approximately $I_{\text{agg}}^{\max}$0 dB relative to receiver thermal noise. The reported tolerated aggregate interference lies roughly in the range $I_{\text{agg}}^{\max}$1 to $I_{\text{agg}}^{\max}$2 dBmW depending on mobility, link direction, bandwidth, and rate point (Abdulla et al., 2013).

Cognitive-radio deployment papers adopt a probabilistic rather than deterministic ceiling. One model uses

$I_{\text{agg}}^{\max}$3

with lognormal shadowing and random distances. In that framework, the practical protection criterion is a tolerated SNR degradation $I_{\text{agg}}^{\max}$4 or a $I_{\text{agg}}^{\max}$5 reliability requirement for the protected receiver. A single-interferer CDF is derived exactly, but for the aggregate the paper argues that the distribution cannot be satisfactorily modeled by a simple lognormal because the random distance factor alters skewness substantially; protection is then enforced by a primary exclusion zone radius $I_{\text{agg}}^{\max}$6 or by REM-based admission control (0905.3023).

A different cognitive-radio aggregate-interference model derives characteristic functions and numerical PDFs for interference under power control or contention control, and then proposes a log-normal approximation for reduced-complexity evaluation. In that setting, a natural interpretation is a high-quantile threshold

$I_{\text{agg}}^{\max}$7

or, under the log-normal fit,

$I_{\text{agg}}^{\max}$8

This suggests that “credible” interference may mean a chosen exceedance percentile rather than a hard worst-case bound, and that the adequacy of log-normal surrogates is model-dependent (Chen et al., 2010).

4. Feasible interference regions in underlay cognitive radio

In underlay cognitive radio networks, maximum credible interference is explicitly non-separable across primary receivers. The paper defines the cognitive interference caused by all secondary users to primary receiving point $I_{\text{agg}}^{\max}$9 as

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$0

and collects these into the vector

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$1

Conventional interference-temperature models assume independent bounds $\mathbb P(\mathrm{SIR}<T)\le \epsilon$2, yielding a box-like admissible region. The paper shows that this is generally incorrect. The true feasible cognitive interference region for uplink cellular CRNs and direct-transmission ad-hoc CRNs is the polyhedron

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$3

with

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$4

The admissible set is therefore the intersection of the nonnegative orthant with coupled linear inequalities, not a Cartesian product of scalar margins (Monemi et al., 2015).

This changes the interpretation of maximum credible interference. The relevant object is the boundary of the FCIR, not an independent per-receiver threshold. A scalar quantity exists only conditionally; for example, when all other cognitive-interference components are zero, the paper defines

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$5

But this is not a general interference temperature limit. If one primary receiver is allowed more interference, the others must generally accept less. The paper’s power-control algorithms use this geometry directly: infeasibility is measured by

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$6

and secondary-user removal is guided by distances to the FCIR boundary rather than by excess over independent box constraints. A common misconception is therefore that protecting every primary receiver can be reduced to independent scalar thresholds. The polyhedral characterization shows that the credible-interference set is fundamentally joint.

5. Geometric maximum interference and random deployment laws

A different literature uses “maximum interference” in a geometric covering sense. In the receiver-interference model for ad hoc and sensor networks, each node $\mathbb P(\mathrm{SIR}<T)\le \epsilon$7 has transmission radius $\mathbb P(\mathrm{SIR}<T)\le \epsilon$8, the symmetric communication graph requires

$\mathbb P(\mathrm{SIR}<T)\le \epsilon$9

and the interference at $\lambda$0 is

$\lambda$1

The objective is to minimize

$\lambda$2

subject to connectivity. Deciding whether a planar point set has a spanning tree with maximum interference at most $\lambda$3 is NP-complete, and the paper notes that one cannot approximate the optimum within a factor less than $\lambda$4 efficiently unless $\lambda$5 (0802.2134).

In the one-dimensional highway model, the same receiver-interference notion is studied under random deployment. If $\lambda$6 sensors are i.i.d. uniform on $\lambda$7, sorted as $\lambda$8, and each node uses the minimal connectivity-preserving range

$\lambda$9

then the interference at $N$0 is

$N$1

The paper proves

$N$2

indeed more strongly,

$N$3

This is a probabilistic benchmark for the worst receiver overlap under a natural random deployment, contrasting with the $N$4 worst-case behavior possible on a line. A plausible implication is that in this literature “credible interference” is not outage- or SINR-based, but the statistically expected scale of the worst geometric overlap (Kranakis et al., 2010).

6. Detection, cancellation, and sensing-limited interpretations

In GNSS interference monitoring with CYGNSS delay-Doppler maps, the relevant object is not interference power at a victim receiver but a credible worst-channel anomaly. The proposed detector uses the per-epoch maximum DDM noise floor across four simultaneous reflections,

$N$5

with threshold $N$6 dB, and then validates detections through either multi-satellite concurrence,

$N$7

or continuous persistence over a $N$8-second window at $N$9-second sampling. The paper reports that this method flagged $d$0 of total epochs in the Middle East, compared to $d$1 for a mean-based method and $d$2 for NASA’s kurtosis-based flag, and that it detected White Sands events on dates where the comparators produced negligible detections. Here, “credible” is tied to corroboration and persistence rather than to an absolute interference-power ceiling (Shin et al., 5 Mar 2026).

In coherent time-domain cancellation of structured radio-frequency interference, the operative limit is again criterion-dependent. The Demodulation-Remodulation framework models

$d$3

defines the interference rejection ratio

$d$4

and derives it as a function of the estimation variances of amplitude, phase, carrier offset, timing, classification, and symbol decisions. The paper’s main simulation setting shows a noticeable transition around $d$5 dB: below that, symbol errors and poor synchronization dominate; above that, cancellation is mainly limited by parameter-estimation accuracy. This supports an unusual but explicit conclusion: within the model, stronger interference is not less credible for cancellation, but easier to estimate and suppress (Li et al., 20 Dec 2025).

In CP-OFDM sensing beyond the cyclic-prefix limit, a delayed target becomes both weaker and more interfering. The capture fraction is

$d$6

and the interference power induced by a beyond-CP target is

$d$7

The paper states that in high-dynamic-range scenarios this interference can exceed thermal or quantization noise by up to $d$8 dB, while the useful image peak can lose up to $d$9 dB near the maximum unambiguous range. The proposed cleaning methods restore credibility: in measurement results, weak-target image SINR is $\lambda$0 dB for conventional processing, $\lambda$1 dB for JIC-CC, and $\lambda$2 dB for FR-SW, with $\lambda$3 dB used as the reliable-detection threshold (Erdem et al., 23 Feb 2026).

7. Cross-domain implications and recurring misconceptions

Several misconceptions recur across these literatures. The first is that maximum credible interference is always a scalar threshold. In underlay CRNs it is generally a polyhedral set, and in geometric interference problems it is a worst-node overlap count rather than a power or density ceiling (Monemi et al., 2015, 0802.2134). The second is that interference can be characterized independently across diversity branches or protected receivers. Spatial correlation in PPP MRC models invalidates independent-per-antenna surrogates, and coupled FCIR inequalities invalidate independent per-receiver temperature limits (Tanbourgi et al., 2013, Monemi et al., 2015).

A third misconception is that averages are sufficient summaries of harmful interference. The GNSS-R work shows that averaging four simultaneous channels can suppress the signature of a single badly contaminated channel below threshold; the maximum preserves that worst-channel manifestation but requires validation logic to avoid false alarms (Shin et al., 5 Mar 2026). A fourth is that interference tails can always be represented by a simple lognormal. One cognitive-radio shadowing model explicitly shows that distance-weighted aggregate interference is not satisfactorily captured by such a fit, whereas another controlled model uses a log-normal approximation as a reduced-complexity surrogate. This suggests that credible-interference quantification is highly model-dependent (0905.3023, Chen et al., 2010).

Across all cases, the most stable interpretation is operational: maximum credible interference is the largest interference level, vector, density, overlap count, or anomaly statistic that remains compatible with a formally stated protection, feasibility, or detection requirement. Its mathematical representation changes with the system model, but its role does not.