Spectrum Sensing, Measurement, and Modeling
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Modeling spectrum sensing is a critical step that paves the way to (i) identify the key impairments that affect the detection performance and (ii) help develop algorithms and receiver architectures that mitigate these impairments. In this chapter, realistic and practical sensing models are presented beyond those developed for classical detection theory. These models capture the impact of different sensing receiver impairments on several detectors such as the energy, the pilot, and the cyclostationarity detectors. Several receiver nonidealities are investigated, including noise uncertainty, imperfect synchronization, and cyclic frequency offsets. In addition, challenges and impairments pertaining to wideband sensing are analyzed, including the presence of strong adjacent interferers as well as the nonlinearities of the receiver RF front-end. From these models, several mitigation techniques are developed to compensate for the presence of the different sensing receiver impairments. Measurements and simulation results are presented throughout the chapter to show the negative impact of such impairments and validate that the developed mitigation techniques provide tangible performance gains.
KeywordsSpectrum Sensing Techniques Cyclostationarity Detection Wideband Sensor Offset Frequency Imperfect Synchronization
A standard cognitive radio (CR) system seeks to identify channels that are not occupied by primary systems so it can access them. Such cognitive and dynamic approach promises to enhance spectrum utilization. For this reason, the CR receiver must be equipped with a spectrum sensor that helps scan a single (in case of narrowband) or multiple (in case of wideband) spectrum bands. The objective of the spectrum sensing receiver is to employ detection algorithms to quickly and reliably detect primary systems and identify available spectral resources.
Among the most popular spectrum sensing techniques proposed in the literature are the energy, pilot, and cyclostationarity detectors. The theoretical detection performance of these detectors has been thoroughly investigated in the literature, yet the derived expressions are assumed to hold under ideal assumptions irrespective of the signal-to-noise ratio (SNR) at the sensing receiver front-end, as will be discussed in section “Spectrum Sensing Techniques”. Indeed, measurements have verified that in negative SNR regimes, many of these assumptions do not hold. In this chapter, more accurate spectrum sensing models are presented, where several receiver impairments are included to better capture the performance attained via experimental studies. Specifically, the energy detector requires noise power estimation, which is commonly assumed to be perfect. Such assumption is dropped, and the detection performance is analyzed in the presence of noise uncertainty. Similarly, pilot and cyclostationarity detectors require tight synchronization to reap the coherent gains achieved via signal feature exploitation. This synchronization is difficult to attain in practice, where frequency, cyclic frequency, and sampling clock offsets are inevitable. Modeling these impairments and studying their impact on energy detection, pilot detection, and cyclostationarity detection will be discussed in details in sections “Energy Detection Under Noise Uncertainty,” “Pilot Detection Under Frequency Offsets,” and “Cyclostationarity Detection Under Imperfect Synchronization”, respectively. Several mitigation algorithms are also presented in their corresponding sections.
While narrowband sensing is fundamental, wideband sensing is a highly desirable feature since it enables the CR receiver to explore more spectral resources and switch between different channels in case some of them become occupied by primary systems. To this end, modeling the wideband sensing problem has been reduced to modeling several narrowband sensing problems by dividing the wideband into many narrowbands. Such approach typically assumes an ideal channelization process, which is infeasible in practice. Indeed, two major bottlenecks arise in wideband sensing. First, a band that is adjacent to other bands with strong signals can suffer from high interference due to the nonideal filter mask in practice, which is commonly assumed to be a brick wall in theory. In addition, strong signals can saturate the RF front-end components such as the low-power amplifier (LNA). This pushes the LNA to operate in a nonlinear region, introducing spurious terms that can affect the detection performance. These two challenges and the mitigation techniques to overcome them will be presented in section “Wideband Sensing: Challenges and Solutions”.
Include the impairment in the sensing model. Such impairment may be identified through measurements or more practical modeling.
For a given detection algorithm, derive the detection performance in the presence of the impairment. The theoretical derivations help identify the key parameters that affect the detection performance.
Develop a compensation algorithm that mitigates the issues introduced by the impairment.
Spectrum Sensing Techniques
There are a plethora of spectrum sensing techniques [2, 11, 23, 28], but the most prominent candidates for practical implementation are the energy detector, the pilot detector, and the cyclostationarity detector, which will be reviewed next.
In the absence of deterministic pilot tones, the CR receiver can instead utilize the inherit features of modulated signals, which exhibit periodic statistical properties [7, 8]. Specifically, many of the modulated signals are second-order cyclostationary, i.e., their means and autocorrelation functions are periodic, where the period depends on the symbol period and the carrier frequency of the signal .
Beyond Classical Detection Theory
Modeling the binary hypothesis testing problem in classical detection theory generally includes many ideal assumptions. For instance, it is commonly assumed that noise samples are generated from a white Gaussian wide-stationary process with a noise variance that is precisely known. This means that the threshold used for the energy detector can be accurately optimized to achieve any desired detection performance. Similarly, for pilot detection, tight synchronization is assumed between the transmitter and the sensing receiver to properly correlate the received signal with a replica of the pilot tone, whereas frequency and clock offsets are neglected in the analysis of cyclostationarity detection.
Such ideal assumptions can be warranted if detection is done in good SNR conditions, where noise estimation and receiver synchronization are more reliable. However, primary user systems require protection even in the worst-case scenarios when the received signal at a CR receiver could be far below noise floor. For example, for a cognitive radio operation in licensed TV bands, IEEE 802.22 working group defined required SNR sensitivities for primary user signals to be − 22 dB for DTV signals and − 10 dB for wireless microphones . Hence, spectrum sensing must be reliable in negative SNR regimes.
In addition to the reliable operation under stringent SNR requirements, the CR receiver must seek spectral opportunities over a wide swath of the spectrum, elevating the need for wideband spectrum sensing. The problem of wideband sensing has been typically approached by breaking the spectrum into many narrowband channels, and hence the problem is converted into several binary hypotheses tests, one per channel [11, 12, 16, 17, 18]. Such simplification, however, neglects many design challenges inherited with wideband sensing, including the impact of strong interferers in some channels [26, 27], spectral leakage due to nonideal filters , or the presence of spurious harmonics generated from nonlinearities in the receiver front-end .
The aforementioned design challenges require revisiting the sensing models for two reasons. First, it is important to accurately understand the impact of operating in negative SNR regions with nonideal wideband receiver front-ends on the detection performance. Second, by identifying the key parameters that affect the detection performance, the sensing algorithms can be enhanced to compensate for the different impairments that affect the detection reliability.
Energy Detection Under Noise Uncertainty
Modeling Noise Uncertainty
Compensating Noise Uncertainty
Pilot Detection Under Frequency Offsets
The simplicity of the energy detector comes at the expense of a poor performance in negative SNR regimes. To circumvent this, pilot detection exploits certain signal features to robustify the detection performance, and particularly it relies on pilot tones that are sent alongside data-carrying signals. Indeed, the processing of the received samples via correlation provides coherent gains that make detection of very weak signals possible. However, this coherent processing requires the CR receiver to be in perfect synchronization with the pilot in the received signal.
The deviation of the experimental result from the theoretical curve is explained as follows. Practical receivers have imperfect thus inaccurate oscillators and circuitry, deeming perfect synchronization near impossible, particularly in negative SNR regimes. Typically, synchronization loops can estimate and reliably correct frequency offsets when the SNR at the receiver is positive. However, in negative SNRs these loops are driven by noise and cannot perform robust synchronization. The imperfect synchronization can severely affect the coherent processing gains achieved by correlating the received signal with the pilot tone .
Modeling Frequency Offsets
Compensating Frequency Offsets
Cyclostationarity Detection Under Imperfect Synchronization
Similar to pilot detection, where prior knowledge about pilot tones is needed, cyclostationarity detection requires knowledge about the cyclic frequency of the modulated signal. Such feature exploitation helps robustify detection in negative SNR regimes. However, it is critical to analyze the detection performance when such knowledge is not perfectly known.
Modeling Cyclic Frequency Offsets
Compensating Frequency Offsets
So far, it is assumed that there are no phase offsets between the different blocks, which occur when MαT s is an integer, i.e., the estimation of the CAF is done over an integer number of periods of the cyclic frequency. However, sampling clock offsets (SCOs) resulted in the analog-to-digital conversion stage may prevent coherent integration of the different blocks.
Wideband Sensing: Challenges and Solutions
To realize a full-scale uptake of cognitive radio systems, it is imperative to explore a wide swath of the spectrum in order to identify as many spectral opportunities as possible. Hence, it is critical to equip CR receivers with wideband sensing capabilities, i.e., scanners that can scan many channels in parallel. Not only this provides more bandwidth, and hence more throughput, but also enables the receiver to move from one channel to another when a primary system reappears.
Typically in wideband sensing, the received wideband signal is fed into a filter bank to channelize it into nonoverlapping subbands. In this case, the wideband sensing model becomes a collection of narrowband sensing models. Hence, the impairments discussed in the previous sections can still occur for each subband, e.g., noise uncertainty, imperfect synchronization, frequency offsets, etc.
Adjacent Band Interfering Power
Modeling Adjacent Interference Power
Mitigating Adjacent Interference Power
RF Front-End Nonlinearity
In wideband sensing, the received signal may contain multiple primary user signals. Even if all primary signals are transmitted with the same power, at the CR receiver, these signals can have various power levels, depending on the distance of these users to the CR receiver and channel fading. In the presence of strong signals, the receiver’s LNA may operate in a nonlinear region. Such nonlinearity introduces harmonics and intermodulation (IM) terms.
Modeling LNA Nonlinearities
Different IM terms are generated due to the nonlinearity of the LNA. However, not all these terms affect the received samples. For instance, even-order IM terms lie outside the frequency support of the signal of interest, and hence they can be filtered efficiently. Similarly, odd-order nonlinearities are typically dominated by third-order nonlinearities, making the impact of high odd-order terms, e.g., 5th order and higher, negligible. Hence, only third-order nonlinearities are considered in the subsequent analysis.
Mitigating LNA Nonlinearities
An alternative approach is to cancel the IM terms instead of estimating them since the latter approach typically requires increasing the sensing time to mitigate the presence of interference. Indeed, it is shown in (38) that N l ∝ σ I, l 2∕σ w 2, which shows that higher interference power requires longer sensing duration in order to mitigate it.
Spectrum sensing is an integral component of the cognitive radio system. To this end, modeling the different sensing techniques is critical to ensure reliable detection. While spectrum sensing has been largely studied using the classical detection modeling tools, there are key differences that are inherited to cognitive radio. In particular, spectrum sensing should be robust in negative SNR regimes, where measurements have shown that the detection performance may deviate from that predicted by the theoretical expressions. Indeed, in negative SNRs, noise power estimation becomes difficult and synchronization leads to frequency offsets. In addition, it is shown that converting the wideband sensing problem into several narrowband sensing problems requires additional care due to the adjacent interfering power resulted from the presence of strong signals and the IM terms resulted from the RF front-end nonlinearities.
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