Spectrum sensing is where the focus of cognitive radio research is starting to move towards. It is the capability of a device being aware of the frequency domain, or the radio frequency spectrum, of its surroundings. This can detect various forms of interference. It can be
25 as simple as evaluating where there is high energy in the system or as complicated as detecting unknown modulated signals over random noise.
2.3.3.1. Energy Detection
Energy detection is a signal detection mechanism based on Neyman-Pearson approach [9][10]. The concept of energy detection mechanism is quite simple. The detector computes the energy of the received signal and compares it to certain threshold value to decide whether the desired signal is present or not. The energy of the signal is preserved in both time domain and frequency domain. The time domain representation of this mechanism is shown in Figure 18. The frequency domain representation of this mechanism is shown in Figure 19. Theoretically, whichever representation is used for signal detection and analysis makes no difference in result. However in the former representation a pre-filter matched to the bandwidth of the signal is required. This need makes this representation quite inflexible compared to the frequency domain representation. So, it is intended to use the second representation in near future for analyzing the received signal via simulation.
Figure 18: Time representation of energy detection mechanism
Figure 19: Frequency domain representation of energy detection mechanism
In order to measure the signal energy, the received signal is first sampled, then converted to frequency domain taking FFT followed by squaring the coefficients and then taking the average.
2.3.3.2. Cyclostationary Feature Detection
Cyclostationary feature detection is a method of differentiating primary user signals from noise without prior knowledge of their modulation schemes or protocols. All signals can be modeled as stochastic processes which are probability functions with random variables through
26 time. Stochastic processes are broken up into subcategories based on how random they are. Wide sense stationary processes are stochastic processes with a constant mean such as noise which has zero mean. Cyclostationary processes are stochastic processes with statistical properties that vary cyclically. Modulated signals are cyclostationary processes because they are double sided with sine wave carriers, they have a fixed symbol period, and each modulation type has its own unique cyclostationary features [47].
In a more mathematized definition, cyclostationary processes have periodic autocorrelation functions where wide sense stationary signals do not. This means that the autocorrelation of cyclostationary processes can be written as a Fourier coefficient. The Fourier coefficient form of autocorrelation for cyclostationary processes is expressed in [47];
( )
∫ (
) (
)
(5)
This is called the cycle autocorrelation. If the statistically correlated periodic features in a cyclostationary process repeat every T, then the cycle autocorrelation has a cycle of α. Since the autocorrelation function is a quadratic transform the features of modulated signals that are functions of symbol rate and carrier can be detected.
The cycle autocorrelation is only a time domain transform. This means it falls short in measuring power spectral density of modulated signals. This is because the system is demodulating many different signals. The maximum energy of all the modulated signals is unlikely to be equivalent. Therefore a threshold would only be set by the highest energy signal. The frequency domain equivalent is called the spectral correlation function, which is expressed in [47]: ( ) ∫ ( ) ( ) ( ) ( ) ∫ ( ) ( )
Through Weiner’s relationship, the Fourier transform of cycle autocorrelation is the spectral correlation function. The spectral correlation function is a two dimensional complex transform with to frequency based axis cycle α and frequency f that is used for feature detection [47].
27 To measure spectral correlation of a function, the received signal can be frequency shifted α Hz and –α Hz in two parallel mixers. This searches many different frequencies for possible carriers. After each frequency shifted signal is passed through identical band pass filters, the signal that was frequency shifted –α Hz is then complex conjugated. After the complex conjugation, the two signals match in carriers of both the real and imaginary plane for attempted demodulation. The two signals are then frequency multiplied back together and averaged over a period of time. If the final signal possess a high energy level, this means that the cycle α corresponds to a carrier frequency of a modulated signal [47]. The block diagram is depicted in Figure 20.
Figure 20: Spectral correlation block diagram [5]
The frequency shifting, bandpass filtering and the complex conjugation can all be implemented using a fast Fourier transform for any f and α. To implement the cyclostationary feature detector the received analog signal must be converted to digital. The digital signal is then input into an N point FFT. The conjugate outputs are then correlated and averaged over a period T. The feature detection then senses the peaks for α>0 and can even distinguish between different modulation schemes and protocols with simplified matched filtering [47]. The implementation is depicted in Figure 21.
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2.3.3.3. Matched Filtering
Matched filtering is the optimal method of signal detection since it effectively maximizes received signal to noise ratio. It follows the full cognitive radio model described earlier in that a prior knowledge of the primary user signal at both the physical and medium access control layers is required. This knowledge is the pulse shape that is used for the transmission. The radio has stored memory effectively describing the modulation type, order, pulse shaping and packet format to demodulate the signal. It is also required to synchronize with the carrier and time scheme as well as perform channel equalization [48].
Match filtering takes advantage of the fact that a filter that is the time reverse of the pulse shape used, when convolved with the signal, optimizes the energy of the signal. This is due to the fact that the filter is time reversed again and passed over the system when the convolution occurs. If the filters match, it will be a perfectly constructive superposition. However, a major drawback is the programming of all the different standards into the memory of the radio and dedicating enough receivers to detect all the primary users [48].