Probability of Detection

The theoretical foundation for setting detection thresholds. The Neyman-Pearson framework formulates spectrum sensing as a binary hypothesis test designed to maximize Pd subject to an upper-bound constraint on the Probability of False Alarm (Pfa).

• Objective: Maximize Pd for a given Pfa.
• Test Statistic: Compares the Likelihood Ratio to a threshold λ.
• Constraint: Pfa ≤ α (e.g., IEEE 802.22 requires Pfa ≤ 0.1).

This ensures the secondary user is as protective as possible while maintaining a minimum acceptable level of spectrum access opportunity.

The ROC curve is the primary visual tool for evaluating sensing performance. It plots Pd against Pfa as the detection threshold varies, illustrating the inherent trade-off between protection and opportunity.

• Ideal Performance: The curve hugs the top-left corner (Pd=1, Pfa=0).
• Random Guess: A diagonal line from (0,0) to (1,1).
• Area Under the Curve (AUC): A single scalar metric summarizing performance; an AUC of 1.0 is perfect.

Engineers use the ROC to select an operational threshold that meets regulatory Pd requirements while maximizing secondary user throughput.

A fundamental limit caused by noise uncertainty. Below a critical Signal-to-Noise Ratio (SNR), no detector can simultaneously achieve a high Pd and a low Pfa, regardless of sensing duration.

• Mechanism: Imprecision in noise power estimation creates an SNR floor.
• Impact: Energy detection fails reliably below this wall.
• Mitigation: Use feature-based detectors (e.g., cyclostationary detection) that are immune to noise uncertainty.

The SNR wall defines the absolute sensitivity limit of a sensing architecture.

A direct engineering conflict: increasing sensing time improves Pd but reduces the time available for data transmission, lowering secondary user throughput.

• Frame Structure: A cognitive radio divides its frame into a sensing slot and a transmission slot.
• Optimization: Find the optimal sensing duration that maximizes throughput while satisfying a target Pd (e.g., 0.9).
• Result: A shorter sensing time increases throughput but risks missing a primary user, causing harmful interference.

Cooperative Spectrum Sensing (CSS) exploits spatial diversity to dramatically improve Pd in fading channels. Multiple geographically separated nodes observe independent signal fades.

• Hard Fusion (K-out-of-N): Improves Pd by requiring consensus among nodes, mitigating the hidden node problem.
• Soft Fusion: Combines raw energy measurements with optimal weights (e.g., Weighted Gain Combining) for maximum sensitivity.
• Result: A target Pd can be achieved with significantly lower individual node SNR compared to single-node sensing.

Adversarial attacks directly target Pd to either cause harmful interference or deny service.

• Primary User Emulation (PUE): A malicious actor transmits a fake primary signal, forcing legitimate secondary users to vacate the channel (denial of service).
• Spectrum Sensing Data Falsification (SSDF): A Byzantine attack where a compromised node reports false local decisions to a fusion center to corrupt the global Pd.
• Defense: Reputation management and robust fusion rules are required to maintain reliable detection in adversarial environments.

The statistical likelihood that a sensing algorithm incorrectly declares a frequency band occupied when it is actually vacant. This represents a missed transmission opportunity for the secondary user.

• Directly trades off against Probability of Detection
• Governed by the detection threshold
• A high false alarm rate starves the cognitive radio of spectrum access

A graphical plot that illustrates the diagnostic ability of a binary classifier by mapping the Probability of Detection against the Probability of False Alarm as the decision threshold varies.

• The primary evaluation metric for any sensing algorithm
• A curve pushed toward the top-left corner indicates superior performance
• Allows engineers to select an operating point based on regulatory requirements

The optimal detection framework that maximizes the Probability of Detection subject to an upper-bound constraint on the Probability of False Alarm. This forms the theoretical foundation for designing spectrum sensing fusion rules.

• Does not require prior probabilities of occupancy
• Yields the Likelihood Ratio Test (LRT) as the optimal detector
• Directly aligns with regulatory mandates to protect primary users

The fundamental design conflict in cognitive radio where a longer sensing duration improves the Probability of Detection but reduces the time available for data transmission.

• A higher Pd requires more samples, increasing sensing time
• Reduces the secondary user's effective throughput
• Optimized by finding the sensing duration that maximizes throughput while meeting a target Pd

The inherent imprecision in estimating ambient noise power at a receiver, which creates a Signal-to-Noise Ratio (SNR) wall below which reliable detection is impossible regardless of sensing duration.

• Renders energy detection ineffective in low-SNR environments
• Probability of Detection collapses if the threshold is set assuming an incorrect noise floor
• Mitigated by feature detection or cooperative sensing

The complementary event to detection, where a sensing algorithm fails to identify an active primary user. The Probability of Missed Detection equals 1 - Probability of Detection.

• Represents the most dangerous failure mode for a cognitive radio
• Results in harmful interference to the licensed incumbent
• Regulatory bodies often mandate a minimum Pd (e.g., 90% or 99%) to minimize this risk