A key enabler for Cognitive Radio (CR) is spectrum sensing, which is physically implemented by sensor and actuator networks typically using the popular energy detection method. The threshold of the binary hypothesis for energy detection is generally determined by using the principles of constant false alarm rate (CFAR) or constant detection rate (CDR). The CDR principle guarantees the CR primary users at a designated low level of interferences, which is nonetheless subject to low spectrum usability of secondary users in a given sensing latency. On the other hand, the CFAR principle ensures secondary users’ spectrum utilization at a designated high level, while may nonetheless lead to a high level of interference to the primary users. The paper introduces a novel framework of energy detection for CR spectrum sensing, aiming to initiate a graceful compromise between the two reported principles. The proposed framework takes advantage of the summation of the false alarm probability $P_{fa}$ from CFAR and the missed detection probability $(1-P_d)$ from CDR, which is further compared with a predetermined confidence level. Optimization presentations for the proposed framework to determine some key parameters are developed and analyzed. We identify two fundamental limitations that appear in spectrum sensing, which further define the relationship among the sample data size for detection, detection time, and signal-to-noise ratio (SNR). We claim that the proposed framework of energy detection yields merits in practical policymaking for detection time and design sample rate on specific channels to achieve better efficiency and less interferences.

In this paper an upper bound is established for the estimation error of a standard least squares (LS) algorithm used to identify a continuous-time model using filtered, sampled input-output data. It is found that the error has three constituent components due to the initial conditions, observation noise and sample period. In particular, the initial condition bias is bounded by O(1/[N \Delta t]), which requires sufficiently large [N \Delta t] for accurate LS estimation. The theoretical results obtained are confirmed by simulation.

In energy detection for cognitive radio spectrum sensing, the noise variance is usually assumed given, by which a threshold is set to guarantee a desired constant false alarm rate (CFAR) or a constant detection rate (CDR). However, in practical situations, the exact information of noise variance is generally unavailable to a certain extent due to the fact that the total noise consists of time-varying thermal noise, receiver noise, and environmental noise, etc. Hence, setting the thresholds by using an estimated noise variance may result in different false alarm probabilities from the desired ones. In this paper, we analyze the basic statistical properties of the false alarm probability by using estimated noise variance, and propose a method to obtain more suitable CFAR thresholds for energy detection. Specifically, we first come up with explicit descriptions on the expectations of the resultant probability, and then analyze the upper bounds of their variance. Based on these theoretical preparations, a new method for precisely obtaining the CFAR thresholds is proposed in order to assure that the expected false alarm probability can be as close to the predetermined as possible. All analytical results derived in this paper are testified by corresponding numerical experiments.