Abstract
In this chapter, the effect of imperfect training data on feature-based signal detection is explored, as it relates to both training time and detection performance in a cognitive radio system. The improved performance of feature-based detection comes at the cost of either having to know in advance the signal features present in primary user transmissions (an unrealistic assumption) or learning them whilst operating “in the field.” Such learning, however, necessarily takes place with signal sets which do not perfectly represent the features of the primary users' modulated signals. Using a two-stage detector performing both feature training and sensing functions, it is shown in this chapter that reducing the learning time generally results in poorer detection performance and vice-versa. A suitable trade-off between these two outcomes is obtained by optimizing a cost function that takes both factors into consideration. Cyclostationarity detection is specifically considered.
TopBackground: A Model For Training Using Field Characteristics
In supervised learning, learning algorithms require a training set to determine the specific features which may be used for discrimination and classification. In cognitive radio applications, as mentioned previously, it may be required to obtain the training set from field observations. In previous work, training was done for a cyclostationarity detector with a training set containing perfect feature information (Thai & Reisenfeld, 2011). In an operational scenario, a training set would need to be experimentally obtained from channel output signals.
Key Terms in this Chapter
Imperfect Training: Describes a training process for a learning algorithm where there is some uncertainty as to whether or not all of the elements in the training set are truly representative of the features that need to be learned. For example, a feature-based detector that is learning to identify the features in a signal may be presented with observations in the training set where the signal is, in fact, absent.
Signal Detection: The process of deciding whether or not a signal of interest is present in a signal observation. This decision is often made via a hypothesis test, and gathering evidence via a signal detection algorithm to either support the null hypothesis H 0 (hence deciding the signal is absent) or reject it (hence deciding the signal is present, which is the alternative hypothesis H 1 ). In the context of cognitive radios, the ‘signal of interest’ is the transmission of a primary user.
Spectral Correlation Density: A two-dimensional function (in frequency ( f ) and cyclic frequency (a)) of a signal. Conceptually, it provides an indication of the average amount of correlation between the signal’s components at frequencies f + 0.5a, f - 0.5a. Cyclostationary signals have some non-zero values for this function, for a ? 0.
Screening (Training) Detector: A signal detector that is responsible for isolating signal observations which are suitable for use by a learning algorithm. Since no detector is perfect to begin with, this leads to imperfect training.
Feature-Based Detection: A category of signal detection approaches that exploit signal features (beyond its energy) to determine whether or not it is present in a signal observation. Unlike energy detection which makes use of a signal characteristic (i.e. its energy) that is applicable to all signals, different signals may have different features. A feature-based detector must know or learn what these features are, in order to operate without performing redundant computation. Cyclostationarity detection is an example of this type of detection.
Energy Detection: A signal detection approach that use the energy in a signal observation as the sole discriminant to determine whether or not an information-bearing signal is present.
Spectral (Spectrum) Sensing: The task of determining which frequency bands in a cognitive radio’s environment is vacant at a given time. This is generally accomplished by employing signal detection.
Cyclostationarity Detection: A category of signal detection approaches exploiting the presence of certain periodicities which tend to be present in an information-bearing signal, but absent in a signal comprised of only noise. In this chapter, cyclostationarity detection involves exploiting information in a signal observation’s spectral correlation density estimate. It is a form of feature-based detection.
Detection Error Performance Curve: A locus of points that describes how the detector’s probability of false alarm and probability of missed detection vary, parameterized by the detection threshold used. In other words, every point on the curve (an operating point ) represents a different detection threshold.
Signal-to-noise ratio (SNR): In the context of cognitive radios, this is the ratio between the primary user’s signal power as observed by the cognitive radio’s receive antenna during spectrum sensing, and the noise power similarly observed, within a defined frequency band.