Compressive Spectrum Sensing: Wavelet-Based Compressive Spectrum Sensing in Cognitive Radio

Introduction

The problem of spectrum scarcity has become of critical importance with the increase in the number of wideband communication systems. The main goal of cognitive radio is to efficiently utilize the spectrum by allowing unlicensed (secondary) users to opportunistically access licensed parts of the spectrum that are momentarily unoccupied by licensed (primary) users. In order to avoid interference with primary users, secondary users must sense the spectrum in order to determine which parts of the spectrum are unoccupied by primary users, these unoccupied frequency bands are called spectrum holes (Haykin, 2005; Ma & Juang, 2009). The goal of spectrum sensing is to identify these spectrum holes. Spectrum sensing methods have evolved from using tunable band pass filters to sense one narrowband frequency at a time to more efficient methods like wavelet edge detection and compressive sensing.

For narrowband systems, a tunable band pass filter (BPF) operating at a narrowband range can be used to sense the spectrum, one band at a time. For wideband systems, an early approach was to use a series of narrowband BPFs. In this case the filter range of each BPF is preset. However, this architecture requires a large number of components and therefore increases the cost and complexity of the system (Divakaran, Manikandan, & Hari, 2011; Polo, 2011). Another method is the windowed Fourier transform, otherwise known as the Short Time Fourier Transform (STFT). The Fourier transform gives time averaged values for the frequency components of the signal but does not provide information on the time of occurrence of these frequencies, but using the STFT, the signal is first divided into smaller time segments using a suitable window function, then the Fourier transform of each of these segments is obtained. Breaking the signal into smaller segments and identifying the frequency components of each time segment provides time resolution, however, it suffers low frequency resolution, high variance of estimated power spectrum as well as side lobes of large magnitude (Divakaran, Manikandan, & Hari, 2011; Merry & Steinbuch, 2005).

The periodogram is another method quite similar to the STFT, where the spectrum signal is truncated using a rectangular window function, and the spectral density plot is obtained by squaring the Fast Fourier Transform (FFT) of the truncated signal. This method suffers from spectral leakage and lack of time-frequency localization due to the truncation of the signals which results in a Dirichlet Kernel in the frequency domain (Haggstrom, 2016). To alleviate the shortcomings of the periodogram; multi-taper spectral estimation can be used as an alternative, since it reduces spectral leakage by using multiple orthogonal filters. Multi-taper refers to the method used for estimating power spectra using an orthogonal set of data tapers, such as Slepian sequences, which allow us to trade spectral resolution for reduced variance of the estimate without compromising its bias (Divakaran, Manikandan, & Hari, 2011; Wang & Zhang, 2009). However, this method involves excessive computations and cannot completely eliminate the spectral leakage problem while better methods can.

When the information of the primary user signal is known to the cognitive user, the optimal detector in stationary Gaussian noise is the matched filter, which maximizes the received signal-to-noise ratio (SNR); this is known as coherent detection. Such information includes the preamble, signaling information for synchronization, pilot patterns for channel estimation, and modulation orders of the transmitted signal. The matched filter method is fast and achieves optimum performance but its main disadvantage is its dependence on primary user information as well as hardware complexity. Moreover, in case of channel fading, time dispersion and Doppler shifts may affect synchronization and ultimately the performance of the matched filter (Bagwari & Singh, 2012; Divakaran, Manikandan, & Hari, 2011).