Reliable Transmission Probability in Wireless Nets

• Reliable Transmission Probability (RTP) is defined as the probability that a user's instantaneous SINR exceeds a required threshold, ensuring effective decoding in interference-prone environments.
• It is computed using explicit closed-form expressions under Rayleigh fading, incorporating variables like base station power, user concurrency, and channel conditions.
• RTP guides system-level optimization by informing resource allocation, user admission control, and dynamic scheduling in intelligent spectrum management frameworks.

Reliable Transmission Probability (RTP) denotes the probability that a legitimate user's communication attains a signal-to-interference-plus-noise ratio (SINR), or a similarly defined quality-of-service threshold, sufficient for successful decoding under the actual network interference, resource scheduling, and channel states. RTP is a central metric in @@@@1@@@@ frameworks, where guaranteeing reliability for legitimate users is critical under both adversarial (eavesdropping, jamming) and benign but unpredictable multi-user wireless environments. The concept is formalized through explicit closed-form expressions in coverage, covert, and spectrum sharing regimes, and used to evaluate, constrain, and optimize system-level performance, user capacity, and spectral efficiency in advanced wireless and cognitive radio networks (Ling et al., 6 Jan 2026).

1. Formal Definition and Role of RTP in Spectrum Systems

In multi-user wireless systems employing dynamic spectrum access and intelligent scheduling, the Reliable Transmission Probability for a user $u$, denoted $P_r(\gamma_u)$, is defined as the probability that the instantaneous SINR of $u$ exceeds a required threshold $\gamma_u$ for accurate decoding:

$$P_r(\gamma_u) = \Pr\{ \mathrm{SINR}_u \ge \gamma_u \}$$

The threshold $\gamma_u$ is typically set by physical-layer modulation/coding constraints or specified Quality of Service (QoS) requirements.

RTP directly quantifies the reliability that can be provided to each user under the actual statistical distributions of channel gains, interference, and any stochastic resource allocation or hopping mechanisms employed by the intelligent spectrum control (ISC) system (Ling et al., 6 Jan 2026). It is the dual of the outage probability in classic wireless theory, but contextualized for modern, AI-driven dynamic access and resource allocation environments.

2. Mathematical Framework and Analytical Expressions

In the ISC-based multi-cell covert communication scenario (Ling et al., 6 Jan 2026), RTP is given an explicit exponential-form closed solution under Rayleigh fading. For a legitimate user's time-frequency hopping and slot assignment induced by a trained ISC scheme, the instantaneous SINR is modeled as:

$$\mathrm{SINR}_u = \frac{m\,p_b}{k\,\sigma_0^2} \sum_{j=1}^{q} \Pr(f_j) |h_{u, f_j}|^2$$

Here, $m$ is the number of base stations, $p_b$ the per-transmission power, $k$ the number of concurrent users, $\Pr(f_j)$ the occupation probability of frequency slot $f_j$, and $|h_{u, f_j}|^2$ is the user’s Rayleigh fading gain (parameter $\omega_u$). The RTP is then

$$P_r(\gamma_u) = \exp\left(- \frac{\gamma_u}{k} \frac{\sigma_0^2}{m\,p_b\,\omega_u}\right)$$

This formula precisely quantifies the reliability loss as a function of user concurrency, system noise, fading severity, base station density, and the ISC-assigned power (Ling et al., 6 Jan 2026).

3. RTP in System Optimization and Capacity Analysis

The RTP functions as both an objective and a constraint in system-level optimization. In covert communications, where both reliability (RTP) and covertness (e.g., eavesdropper’s Detection Error Probability, DEP) must be simultaneously ensured, RTP enters as a constraint:

$P_r(p_b) \ge 1 - \varepsilon_u$

where $\varepsilon_u$ is the maximum tolerable outage probability for user $u$ (Ling et al., 6 Jan 2026). The covert rate maximization problem then seeks the largest possible transmit power $p_b^*$ such that both RTP and covertness constraints are satisfied. If the optimal feasible interval $[p_{\mathrm{low}}, p_{\mathrm{up}}]$ (derived from the RTP and DEP constraints) is non-empty, maximizing the average covert rate becomes possible at $p_b^*=p_{\mathrm{up}}$.

RTP is also pivotal in determining the multi-user capacity under joint reliability and covertness/ISC constraints:

$$N_{\max} = \max\{ k : p_{\mathrm{up}}(k) \ge p_{\mathrm{low}}(k)\}$$

Here, $N_{\max}$ is the largest number of concurrent users that can be accommodated while each maintains the prescribed reliability target (Ling et al., 6 Jan 2026).

4. RTP Under Intelligent Spectrum Control and Comparative Schemes

ISC employs real-time spectrum sensing, AI-driven dynamic slot allocation, and interference avoidance to maximize RTP for all users. By contrast, non-intelligent or fixed allocation schemes (such as artificial noise-aided OFDM) may suffer degradation in RTP due to static resource assignment and inability to avoid jammers or inter-user collisions. ISC can deliver both higher DEP and higher RTP, outperforming traditional benchmarks by actively scheduling users into clean time-frequency slots based on up-to-date sensing and learned models (Ling et al., 6 Jan 2026).

The trade-offs revealed by simulation results include:

• RTP increases with SNR and decreases with the number of concurrent users (due to division of power/interference).
• Accurate spectrum sensing, while potentially consuming more time resources, minimizes slot collisions and jamming events, thus increasing RTP.
• ISC schemes allow for fine-grained shaping of the feasible region for the joint covertness–reliability frontier, affording partial compensation for stricter covert constraints by adapting user hopping patterns and scheduling (Ling et al., 6 Jan 2026).

5. Metrics, Measurement, and Practical Relevance

In both analytical and empirical work, RTP is evaluated via:

• Closed-form expressions (as above) for tractable scenarios with Rayleigh fading and random slot scheduling.
• Monte Carlo simulation matching, especially in the presence of more complex interference models, correlated fading, and adversarial effects (e.g., malicious jammers).

RTP serves as a design and regulatory indicator for system-level provisioning in intelligent spectrum management. Its tractable expressions underpin resource allocation, user admission control, and adaptive slot/power assignment for systems operating under variable interference, multiple access, and dynamic resource environments (Ling et al., 6 Jan 2026).

6. Context in the Broader Spectrum Management Literature

The role of RTP and similar reliability metrics is reinforced across intelligent spectrum access literature:

• In device-to-device scheduling, end-to-end link outage or SINR satisfaction probabilities are central to the reward structure in graph-reinforcement learning–based spectrum scheduling (Shan et al., 2024).
• For RIS-empowered cognitive radio networks, SINR-based guarantees directly enter beamforming and resource allocation optimization, with the equivalent notion of RTP forming the reliability constraint for joint communication-sensing service (Xu et al., 2024).
• Satellite and cognitive radio spectrum management frameworks use RTP or analogous metrics (outage, retainability) as key figures-of-merit in evaluating AI/ML-driven dynamic spectrum management (Silva et al., 30 Aug 2025).

Collectively, RTP—grounded in exact statistical evaluation—operationalizes the reliability dimension of intelligent spectrum control, facilitating rigorous design, analysis, and system-level optimization across advanced wireless scenarios.