Primary User Activity Model

The foundational two-state stochastic process where a channel alternates between BUSY (PU transmitting) and IDLE (spectrum hole) periods.

• Exponential Assumption: Classically models both ON and OFF durations as exponentially distributed random variables for memoryless, tractable analysis.
• Generalized Distributions: Real-world traffic often requires Phase-Type distributions or Hyper-Erlang models to capture the heavy-tailed nature of Wi-Fi or cellular traffic bursts.
• Parameter Estimation: Key parameters like channel idle probability and mean holding time are estimated via Maximum Likelihood Estimation (MLE) on historical sensing data.

Advanced stochastic models that capture the bursty, correlated nature of modern digital communications, moving beyond simple Poisson arrivals.

• Markov Modulated Poisson Process (MMPP): A doubly stochastic process where the Poisson arrival rate of PU packets varies according to an underlying continuous-time Markov chain. Ideal for modeling voice/video codecs.
• Interrupted Poisson Process (IPP): A specific case of MMPP where the arrival rate switches between a fixed positive value and zero, mimicking an ON/OFF source at the packet level.
• Batch Markovian Arrival Process (BMAP): Extends the model to handle batch arrivals, representing the simultaneous transmission of multiple data frames.

A Bayesian framework used when the true channel state is hidden due to sensing errors (missed detections, false alarms). The HMM infers the latent PU activity from noisy observations.

• State Transition Matrix: Defines the probability of the hidden PU state transitioning from IDLE to BUSY.
• Emission Matrix: Models the probability of observing a 'busy' sensor reading given the true hidden state is actually IDLE (false alarm rate).
• Belief State: The cognitive radio maintains a probabilistic belief vector over the channel state, updated recursively using the Forward algorithm with each new sensing sample.

Empirical studies show that Ethernet and WWW traffic exhibit self-similarity, where burstiness persists across multiple timescales, invalidating traditional Poisson assumptions.

• Hurst Exponent (H): A metric where 0.5 < H < 1 indicates long-range dependence. PU models must account for this to avoid underestimating buffer overflow and interference probability.
• Heavy-Tailed Distributions: The Pareto distribution is often used to model ON/OFF periods with infinite variance, capturing the "long memory" of real packet data.
• Fractional Brownian Motion: A Gaussian process used to model aggregated spectrum traffic with long-range dependency for backbone link analysis.

Modern PU models don't just provide a point estimate of the next state; they output a full predictive distribution to quantify risk.

• Gaussian Process Regression: A non-parametric Bayesian method that predicts future channel idle time with a confidence interval, allowing the secondary user to make risk-aware transmission decisions.
• Copula Models: Capture the joint tail dependence between multiple channels. If a high-traffic event occurs on one frequency, a Clayton copula can model the increased probability of simultaneous congestion on a related band.
• Extreme Value Theory (EVT): Specifically models the tail of the distribution to predict the probability of catastrophic, unusually long busy periods that would break a secondary link.

The statistical properties of PU traffic are non-stationary; they change over time due to human activity patterns or network reconfiguration. Static models degrade rapidly.

• Change Point Detection: Algorithms like Bayesian Online Change Point Detection (BOCPD) monitor the streaming sensing data to detect abrupt shifts in the underlying PU traffic model parameters.
• Online Learning: Upon detecting a drift, the model adapts by using a sliding window of recent observations or applying exponential forgetting factors to retrain the Transition Probability Matrix in real-time.
• Ensemble Methods: Maintain a pool of candidate models (e.g., different HMM structures) and dynamically select the one with the highest recent predictive likelihood.

A foundational stochastic process that represents a primary user's channel occupancy as alternating busy (ON) and idle (OFF) periods. The durations of these periods are typically modeled using exponential or phase-type distributions. This model simplifies spectrum prediction into estimating the probability of a state transition, forming the basis for proactive spectrum handoff decisions.

A generalization of the Poisson process where primary user arrivals are governed by an underlying continuous-time Markov chain. The Markov Modulated Poisson Process (MMPP) is a key subclass, capturing bursty traffic patterns where the arrival rate shifts between distinct states. This framework allows a cognitive radio to infer hidden traffic phases from observable channel busy/idle sequences.

A statistical model that treats the true channel occupancy state as a latent variable and the cognitive radio's spectrum sensing result as a noisy observation. HMMs solve three core problems for spectrum mobility:

• Evaluation: Calculating the likelihood of an observed sensing sequence.
• Decoding: Inferring the most likely hidden state sequence (e.g., busy vs. idle).
• Learning: Estimating the transition probability matrix and emission probabilities from data.

A square matrix defining the probabilities of a frequency channel transitioning between idle and busy states at each discrete time step. For a two-state model, it contains four probabilities: P(idle→idle), P(idle→busy), P(busy→idle), and P(busy→busy). This matrix is the core parameter of a Markov chain and is estimated from historical spectrum occupancy data to drive state predictions.

A predicted temporal interval during which a specific frequency channel is forecasted to remain idle with a defined confidence level. A cognitive radio uses this window to schedule a transmission burst without colliding with a returning primary user. The duration of this window is directly derived from the prediction horizon of the underlying forecasting model, such as an LSTM Spectrum Predictor.

A decision-theoretic framework for spectrum access where the true channel state is hidden from the secondary user. The cognitive radio maintains a belief state—a probability distribution over possible channel states—updated via noisy sensor observations. The optimal spectrum handoff policy maximizes long-term reward by balancing exploration (sensing channels) and exploitation (transmitting on predicted idle channels).