Signal Processing for Cognitive Radios

6POWER SPECTRUM ESTIMATION

6.1 INTRODUCTION

Power spectral density (PSD), or simply the power spectrum, of a signal is a representation of the spread of signal power as a function of frequency. In this chapter, we review basic concepts and techniques of power spectrum estimation that will be useful in subsequent chapters. We limit ourselves to the so-called nonparametric spectrum estimation techniques that do not presume a parameterized form for the signal whose spectrum is to be estimated. The application of interest for us is the wideband spectrum sensing in cognitive radios. In this context, there may be many different signals contained in the signal sensed by a cognitive radio. Hence, assuming a parametric form may not be possible, making nonparametric approaches more suitable.

As we have seen in Chapter 2, cognitive radios are inherently digital devices, and all processing in a cognitive radio is performed on a digital processor called the cognitive engine. Hence, our discussion of power spectrum estimation will also be in discrete time.

Let us start by formally defining the power spectrum of a (power) signal. Suppose that X[n] is a random signal (process) that is second-order stationary, or wide-sense stationary (wss). This means that

(6.1)

and

(6.2)

where X* denotes ...