## 3 Spectrum Sensing for Cognitive Radio
Since it is difficult to design high-resolution A/D converters--the pricing will not follow [PERSON]'s law, it is highly desirable to relax the A/D requirement. Also, the power and A/D complexity rises almost exponentially with the number of bits. There is a synergy between compressed sensing and spectrum sensing. The former enables the use of a bigger signal bandwidth to fully exploit the potential of the 7.5 GHz unlicensed spectrum allocated by FCC. The latter enhances the opportunity of the system to use unoccupied spectra. Operation of WiMax in the 3.5 GHz band is susceptible to interference from UWB devices [89]. Energy-Based SensingThe non-coherent energy based approach does not require _a prior_ knowledge of the signal to detect, and results in far fewer calculations to reach decision, enabling a larger bandwidth to be surveyed at all times. The disadvantages are its lower sensitivity to the weak signal and the requirement for the adaptive threshold setting. Eigenvalue-based sensingThe advantage of the autocorrelation matrix approach is to rely on the spectrum only. Using the Wiener-Khintchine theorem, the autocorrelation estimate at lag \(\tau\) in the band of interest defined by \(\omega_{m}\), \(m\in[1,M]\) is given by [4]  
\[R_{xx}(\tau_{n})=\frac{2}{M}\sum_{m=1}^{M}|S(\omega_{m})|^{2}e^{j2\pi\omega_{m }\tau_{n}} \tag{1}\]where \(\tau_{n}=n\delta t=\frac{n}{F_{s}}\) with \(\delta t\) the sampling period equal to the inverse of the sampling frequency \(F_{s}\). A a result, only the spectrum is used. In other words, the coherent information or phase has been removed. Once the autocorrelation is collected, its matrix can be formed and its eigenvalues can be used to detect the unused/under-used spectrum [90]. Measurement Systems for Sensing  
Measurements of spectrum for interference temperature are basic to cognitive radio, as is channel sounding to wireless communications. A measurement system using spectrum analyzer controlled by Labview has been developed for 9 kHz-26.5 GHz--Figure 6 is a sample of collected data. The delay for each snapshot of the spectrum is in the level of 40 ms. Since sensing window is in the level of 5-25 ms for IEEE 802.22 [34, 35, 36, 38, 39], much quicker measurements are required. For this purpose, we will use real-time spectrum analyzer Tektronix RSA 6114A. Multiple correlated views are available in all domains (frequency, time, amplitude, phase, modulation). The statistics of the spectrum will be essential to future system designs. For example, quickest detection [91] is a framework to incorporate the statistics into the algorithms for wideband (several GHz) spectrum sensing [92]. Preliminary Results and Proposed Tasks  
Roughly speaking, TTU's Lab has developed the necessary equipment infrastructure for long-term research in the area of wideband cognitive radio. The measurement equipment is available for spectrum statistics study. Proposed tasks are to answer the following questions: (1) What are the long-term and short-term statistics of the wideband spectra? (2) How does the statistics change with the geo-location? (3) What algorithms are suitable for wideband spectrum sensing? (4) How is the statistics incorporated into algorithms? How does a CR select the best portions of the spectrum to use [4]? What amount of spectrum will a CR be able to harvest in urban/sub-urban areas? How can a CR limit the risk of using spectrum that only appears to be unused locally but is indeed being used nearby (hidden-node problem)?