Modeling and Validation of Channel Idleness and Spectrum Availability for Cognitive Networks

The potential of successful cognitive radio networks operating in TV White Spaces (and other future bands re-allocated for unlicensed operation) has led to significant upsurge of interest in their design optimization - particularly those that are cross-layer in nature, involving both MAC protocols as well as physical layer aspects such as channel sensing. Typically, these seek to optimize a network-level metric (notably, aggregate throughput) of secondary (cognitive) network subject to interference constraints on the primary. In turn, this requires suitable sensing by cognitive users to detect availability of primary channels (currently unused by the protected incumbents) for opportunistic usage. To date, most studies have used largely hypothetical assumptions regarding channel idleness and resulting spectrum availability due to primary user dynamics. For example, idleness of channels over any spectrum are typically assumed to be an independent and identically distributed Bernoulli sequence. In contrast, nearly all real-time measurements suggest that channel idleness is frequency dependent, i.e., the probability that a channel is idle depends on the channel location. Cognitive radio research thus increasingly needs more realistic and validated models for channel idleness as the foundation of credible cross-layer analysis; this is the primary contribution of our work. We use two sets of real-time measurements conducted in disparate geographic locations over four distinct time intervals to show that channel idleness is appropriately modeled as independent but non-identical (i.n.i.d.) Bernoulli variables characterized by p_i, the probability of idleness for the i-th channel. We validate that Beta distribution can be used for modeling the variations in channel idleness probabilities; the Beta distribution parameters are estimated from the data to produce the best model fit. Based on the validated i.n.i.d. model, we build a predictive model by computing the availability probability of k channels, i.e, P{N_{idle} = k}, where N_{idle} denotes the number of idle channels over the spectrum of N channels. However, the combinatorial complexity inherent in the computation of P{N_{idle} = k} suggests the need for efficient approximations. We accomplish this by classifying idleness of channels based on the magnitude of p_i, and propose a novel Poisson-normal approximation for computing P{N_{idle} = k}. For validation, the distribution obtained from our technique is compared with the exact distribution and normal approximation using the approximation error criterion.