1 Introduction
1.1 Background
This thesis dwelt on the development of cognitive radio，specifically, the blindsensing scenario, where energy detector (ED) was used to blindly sense the presence of aprimary user by a secondary user in order to cater for the inefficient use of the radioelectromagnetic wave spectrum. The radio spectrum has frequency range between 3 kHz and300 GHz in the electromagnetic spectrum. Technological advancement in thecommunication, transport, manufacturing, medical, and security industries has brought alongwith it, immense strain on the radio electromagnetic spectrum. The bandwidth frequency ofRF spectrum is very limited therefore there is need to efficiently use this scarce resource. Inthe recent future we will have people fitted with RF transponders to monitor their health.The use of such a technology simply implies more pressure on the spectrum. Many wirelesscommunication systems are switching from wireless telephony to interactive Internet data,and multi-media types of applications, therefore increasing the need for higher data ratetransmissions. As more devices are changing to wireless technology, the demand for highercapacity and data rates becomes a daunting task that requires new innovative technologieswhich can offer ingenious new ways of efficiently exploiting the available radio spectrumresource without congestion. Cognitive radio ⑴，has offered a viable solution to the spectralcongestion problem by introducing the opportunistic usage of frequency bands that are notheavily occupied by licensed users. Licensed users, also referred to as primary users (PU)，are those users that have been given the license to use some specified frequency band by theconcerned national government body e.g.，TV broadcasting stations and radio broadcastingstations. Cognitive radio can successfully determine that a certain part of a radio spectrumband was not occupied and then transmit on those frequencies without interfering with theprimary user. This thesis addressed blind sensing in cognitive radio.
1.2 Motivation
Information or message is usually communicated through a transmitter via the antennasusing carrier waves through some channels that is received at the receiver via antennas aftersome processing, by a recipient. This is an overgeneralization of the communication system,in reality，there is a lot more at stake. In this work we shall refer to information or messageso transmitted as a signal, a digital signal. The signal that is generated at the transmitter isprocessed (digital signal processing) once ready it is transmitted through somecommunication channels to the receiver that performs reverse processes to retrieve it. Digitalsignal processing involves processes like sampling，encoding, equalization, quantization,filtering, modulation, decoding and demodulation， not necessarily in this order. Digitalsignal processing of a given signal is done at the transmitter and encompasses the aboveprocesses like; sampling, encoding, quantization, equalization，filtering and modulation.Once the signal has been digitally processed it is transmitted through communicationchannels via the antenna whence it is propagated through space (air interface) by reflections,refractions, dif&action, satellite, and internet then finally to the receiver. Unlike thetransmitter the receiver down samples the received signal，filters, demodulates, and decodesit to retrieve the information. With the communication system overview completed, the nextquestion that we sought to answer (which motivated us) was how we could blindly detect thesignal at the receiver without knowing anything concerning it like, the noise power，signalpower, and channel characteristics.
Further motivation was derived from the previous work that had been done in cognitiveradio, and specifically in blind sensing where none a priori of the received signal wasrequired. A lot of inspiration was sourced from the simplicity of the energy detector as wellas the researches done to try
