Handbook of Cognitive Radio pp 1-34 | Cite as

# Spectrum Sensing, Measurement, and Modeling

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## Abstract

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.

## Keywords

Spectrum Sensing Techniques Cyclostationarity Detection Wideband Sensor Offset Frequency Imperfect Synchronization## Introduction

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”.

- 1.
Include the impairment in the sensing model. Such impairment may be identified through measurements or more practical modeling.

- 2.
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.

- 3.
Develop a compensation algorithm that mitigates the issues introduced by the impairment.

## Spectrum Sensing Techniques

*H*

_{0}stands for the absence of primary user signals, i.e., noise-only samples, and

*H*

_{1}stands for the presence of users, i.e., both noise and signal samples are present. This is a digital implementation, where a test statistic,

*Λ*, is used to process

*N*samples and estimate a desired parameter. Then, the statistic is compared to a predetermined decision threshold. Mathematically, this is expressed as

*λ*is a threshold that can be optimized to attain a certain objective, e.g., meet a false alarm constraint.

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.

### Energy Detection

*r*(

*n*) denote the

*n*-th sample of the received signal; then the energy detector is expressed as

*P*

_{ d }is the probability of detection,

*P*

_{ f }is the probability of false alarm,

*Q*(⋅ ) is the

*Q*-function, and

*Q*

^{−1}(⋅ ) is the inverse

*Q*-function. It can be observed that the performance improves for higher SNR or longer sensing times, i.e., larger

*N*. Note that this expression is assumed to be valid for any SNR value .

### Pilot Detection

*universal*detector, since it does not need any specific signal structure, some practical communication systems deliberately embed signal features to either perform synchronization and acquisition or help improve signal decoding. For instance, in some broadcast communication systems, e.g., digital television, sinewave pilot tones are transmitted for data frame synchronization. Mathematically, the transmitted primary signal can be expressed as [10, 24]

*x*

_{ p }(

*n*) is a known pilot tone,

*x*

_{ d }(

*n*) is the data-carrying signal, and

*ɛ*is the pilot power factor, i.e., the fraction of the total power allocated to the pilot tone. For example, pilots in digital TV signals are 11 dB weaker than the average signal power, i.e.,

*ɛ*≈ 0. 1 [1].

### Cyclostationarity Detection

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 [21].

*cyclic autocorrelation function*(CAF) , where the received signal is correlated with a frequency-shifted version of itself [7]. More formally, the CAF can be estimated using

*N*samples as follows [14, 21]

*α*is the cyclic frequency and

*T*

_{ s }is the sampling period. Once the CAF is computed at the CR receiver, the following test statistic can be performed:

*α*, it can be possible to not only detect signals but also classify them [9, 22].

### 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 [6]. 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 [26], or the presence of spurious harmonics generated from nonlinearities in the receiver front-end [19].

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

*λ*in order to achieve

*any*desired probability of detection. Indeed, it can be observed from the ROC performance of the energy detector in (3) that controlling the sensing time

*N*can help meet any specified (

*P*

_{ d },

*P*

_{ f }) pair. Specifically, the following relation holds

*λ*that achieves a false alarm of

*P*

_{ f }= 0. 05. The threshold is then applied to compute

*P*

_{ d }. From these measurements, the sensing time for a given SNR is derived to achieve a detection performance of

*P*

_{ d }= 0. 9 as shown in Fig. 2. It can be observed that the theoretical scaling law holds for SNR values above − 20 dB. However, as the signal becomes weaker, detection becomes progressively harder, and when the signal is below − 23 dB, the detector cannot sense the signal irrespective of the sensing time, leading to a phenomenon known as the

*SNR wall*[24]. Such deviation illustrates that the energy detector lacks robustness in negative SNR regimes. In addition, the measurements show that the existing sensing model must be revisited to accurately capture the SNR wall phenomenon.

### Modeling Noise Uncertainty

*σ*

_{ w }

^{2}. However, it is more accurate to assume that such noise samples are instead generated from \(\tilde{w}(n) \sim \mathcal{ N}(0,\tilde{\sigma }_{w}^{2})\) such that

*ρ*≥ 1 is a parameter that quantifies the noise uncertainty. Note that

*ρ*= 1 implies perfect knowledge of the noise variance. In other words, the CR receiver estimates that the noise variance is

*σ*

_{ w }

^{2}, whereas the

*actual*variance is \(\tilde{\sigma }_{w}^{2}\).

*σ*

_{ w }

^{2}becomes an underestimate of the true variance, forcing the CR receiver to more frequently decide that the channel is occupied. Similarly, the lowest probability of detection occurs when the actual noise variance is \(\tilde{\sigma }_{w}^{2} = (1/\rho )\sigma _{w}^{2}\). In this case, the CR receiver overestimates the true variance, leading to increasing the frequency of declaring a channel to be empty. Under such worst-case scenario, it can be shown that the ROC of the energy detector becomes [24]

*ρ*= 1, (11) simplifies to (3). From this expression, the sensing time can be derived to be

*N*→

*∞*when \(\mathop{SNR}\nolimits +1/\rho -\rho = 0\), i.e., there exists an SNR wall where detection below that SNR value becomes impossible. More formally, for

*ρ*> 1, the SNR wall occurs at

*ρ*

_{ dB }= 10log

_{10}(

*ρ*). It is evident that even small uncertainty makes the energy detector poor in highly negative SNR regions. It is also observed that the modified sensing model captures the behavior observed in the experimental study illustrated in Fig. 2.

### Compensating Noise Uncertainty

*w*(

*n*), can be used to estimate the noise variance using the following maximum likelihood (ML) estimator [13]

*H*

_{0}, then the collected samples can, with high accuracy, be declared as noise-only samples, and hence they can be used to update \(\hat{\sigma }_{w}^{2}\) for subsequent energy detection. Such approach can be implemented using the following detector:

*M*, that is triggered infrequently, and energy sensing for duration

*N*, which is triggered frequently. The former is motivated to reliably update the noise variance estimate, which will be used for subsequent fast energy detection.

*M*=

*N*, the sensing time needed to achieve a specific (

*P*

_{ d },

*P*

_{ f }) pair is

*M*=

*N*

^{2}, then \(\sqrt{ \frac{N\cdot M} {N+M}} \approx \sqrt{N}\), i.e., the performance of

*Λ*

_{ E }

^{ ′ }reaches the ideal performance of

*Λ*

_{ E }in the negative SNR regime.

*M*=

*N*or

*M*=

*N*

^{2}, then \(\mathop{SNR}\nolimits _{\mathop{min}\nolimits } \rightarrow 0\) as

*N*→

*∞*, i.e., there is no SNR wall. However, if

*M*is a constant, e.g.,

*M*= 100, then \(\mathop{SNR}\nolimits _{\mathop{min}\nolimits }> 0\) as

*N*→

*∞*.

*P*

_{ f }= 0. 05 and

*P*

_{ d }= 0. 9 when

*Λ*

_{ E }

^{ ′ }is used. As expected, having longer sensing periods to estimate the noise variance, i.e., larger

*M*, improves the performance of the energy detector. However, to mitigate the SNR wall, the noise power estimation period should scale with the duration of the energy detector, e.g.,

*M*=

*N*and

*M*=

*N*

^{2}.

## 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.

*P*

_{ d },

*P*

_{ f }) pair can be shown to be

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

*x*

_{ p }(

*n*) = exp(

*j*(

*ω*

_{ o }

*n*+

*θ*)), where

*ω*

_{0}is the carrier frequency. Suppose there exists a frequency offset,

*ψ*, between the primary transmitter and the CR receiver. This can be modeled by assuming that the pilot tone replica used at the receiver is equal to \(\hat{x}_{p}(n) = x_{p}(n)\exp (j\psi n)\). Using the pilot detector, it can be shown that under

*H*

_{1}

*N*becomes comparable or larger than the period of the frequency offset, then the pilot detector loses its coherent processing gain. In other words, in the presence of frequency offsets, the pilot detector can suffer from the SNR wall, explaining the measured curve in Fig. 7.

### Compensating Frequency Offsets

*M*≪

*N*. This process is repeated

*K*times, and hence in the second stage, the CR receiver noncoherently averages over these collected

*K*blocks, making the total sensing time

*N*=

*K*⋅

*M*. The receiver architecture of the two-stage pilot detector is shown in Fig. 8.

*K*improves the performance with a similar scaling to the energy detector (cf. (3)). Yet, the coherent processing effectively improves the SNR by 10log

_{10}(

*M*)dB. In other words, comparing (24) with (3), it can be observed that under noise uncertainty, which affects nocoherent processing, the enhanced pilot detector moves the SNR wall by 10log

_{10}(

*M*)dB.

*P*

_{ f }= 0. 05,

*ɛ*= 0. 1, and

*N*= 10, 000, where

*K*= 10 and

*M*= 1000. It is clear that the enhanced pilot detector benefits from the coherent processing gains in very negative SNRs, and since

*M*≪

*N*, the robustness against frequency offsets improves.

## 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.

*τ*= 0, which is expressed as

*α*= 0, the cyclostationarity detector simplifies to the energy detector in (2). From this, one can interpret this detector for

*α*≠ 0 as computing the energy of the received signal at a cyclic frequency

*α*. In the presence of noise-only samples, it can be shown that as

*N*→

*∞*then

*R*

_{ r }

^{ α }(0) → 0 for

*α*≠ 0 at all SNRs. That is, the detector can

*theoretically*suppress noise at the negative SNR regime by increasing the sensing time

*N*due to averaging a stationary noise process.

*α*is perfectly known, yet this is difficult to achieve in practice. Specifically, the presence of Doppler shifts, imperfect estimation of carrier frequencies, and the frequency mismatch due to local oscillators all introduce

*cyclic frequency offsets*(CFOs) that can degrade the performance. Such performance degradation is verified experimentally [20]. In particular, a BPSK signal with a symbol period

*T*= 10

*μs*is generated. At the receiver end, the detector in (26) is implemented at

*α*= 1∕

*T*= 100 KHz with a sampling frequency 1∕

*T*

_{ s }= 2 MHz. The cyclic feature of the BPSK signal is analyzed in the presence of different frequency offsets

*Δ*

_{ α }given in units per million (ppm). Figure 10 shows the impact of increasing the sensing time

*N*on the cyclic feature. Interestingly, as the sensing time increases, it becomes harder to detect the cyclic feature. Thus, although increasing

*N*averages the noise process in negative SNR regimes, the cyclic feature becomes harder to detect, leading to an SNR wall phenomenon. The decay in the cyclic feature is theoretically investigated in the next section.

### Modeling Cyclic Frequency Offsets

*Δ*

_{ α }, i.e., the cyclic frequency used is

*r*(

*n*) =

*∑*

_{ m }

*a*(

*mT*

_{ b })

*p*(

*nT*

_{ s }−

*mT*)exp(−2

*πf*

_{0}

*nT*

_{ s }), where

*a*(

*mT*

_{ b }) are data symbols with period

*T*

_{ b }, e.g., for BPSK

*a*(

*mT*

_{ b }) ∈ {+1, −1},

*p*(⋅ ) is a pulse shaping filter, and

*f*

_{0}is the carrier frequency. Then,

*Δ*

_{ α }→ 0. The test statistic to detect the cyclic feature is shown to be [20, 29]

*Δ*

_{ α }≠ 0, the cyclic feature decays as

*N*increases. This makes \(\vert R_{r}^{\hat{\alpha }}(0)\vert\) under

*H*

_{1}to be similar to \(\vert R_{r}^{\hat{\alpha }}(0)\vert\) under

*H*

_{0}, making detection very difficult. Figure 10 shows the theoretical curves of the normalized cyclic feature in the presence of CFOs, which match the results obtained via the experimental study.

### Compensating Frequency Offsets

*N*samples are broken into

*K*blocks, where each one is of length

*M*. In each block of samples, cyclostationarity detection is done, yet

*M*<

*N*, and hence the impact of the CFO is reduced. At the same time,

*K*> 1 in order to average noise. Mathematically, the two-stage detector is given as [21]

*R*

_{ r }

^{ α }(0)

^{ ′ }is given by

*N*samples into several frames can significantly reduce the rate at which the cyclic feature decays, making it more reliable to detect in negative SNR regimes. Figure 12b illustrates the cyclic feature with variations of the CFO, where

*N*= 20, 000. It can be observed that increasing

*K*does not always provide the highest gains. For instance, the cyclic feature is weak for

*K*= 5 when the CFO is small. This emphasizes that the number of samples and how these samples are divided into blocks both affect the performance. This suggests an optimization framework that maximizes the cyclic feature by optimizing

*K*and

*M*[20].

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.

*Δ*

_{ α }= 0 to explicitly understand how the SCO affects the performance of the enhanced cyclostationarity detector. Hence, and similar to the analysis done for the CFO, it can be shown that

*K*= 5. Figure 13a shows the normalized cyclic frequency with variations of the number of samples, whereas Fig. 13b shows the impact of

*δ*, where

*N*= 10, 000. It is assumed that

*α*= 1∕

*T*= 100 KHz and 1∕

*T*

_{ s }= 2 MHz. It is clear that sampling offsets have detrimental effects on the performance.

*K*and

*M*to limit the performance loss due to CFOs and SCOs [21]. An optimization framework can be formulated when these two impairments are modeled as random variables. Figure 14 illustrates the detection performance of the enhanced detector, where both impairments are modeled as zero-mean Gaussian random variables with variances

*σ*

_{ cfo }

^{2}= 2 × 10

^{−4}and

*σ*

_{ sco }

^{2}= 1 × 10

^{−5}. The signal to be detected is assumed to be BPSK with

*α*= 5 MHz, and 1∕

*T*

_{ s }= 10 MHz. Figure 14a shows the simulated ROC performance for different number of frames, where \(\mathop{SNR}\nolimits = -5\) dB. The total sensing window is fixed at

*N*=

*K*⋅

*M*= 5000 samples. It can be observed that the way by which the samples are split is critical to the detector’s performance. Figure 14b shows the detection performance for

*K*= 12 under different SNR regimes. Overall, the detector provides robust performance in negative SNR regimes if

*K*and

*M*are optimized .

## 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.

*channelization*(or filtering) to convert the wideband signal into several narrowbands. Such filtering procedure is nonideal, causing leakage and interference in the channel of interest. In addition, due to the high bandwidth of the signal, the low-power amplifier (LNA) in the RF front-end may be pushed to operate in a nonlinear region, causing the wideband signal to be distorted. These two impairments will be the focus of this section.

### Adjacent Band Interfering Power

*adjacent band interfering power*[26].

#### Modeling Adjacent Interference Power

*r*(

*n*) is a superposition of primary signals corrupted with noise. In other words, let \(w(n) \sim \mathcal{ N}(0,\sigma _{w}^{2})\) be the noise samples; then

*r*(

*n*) =

*∑*

_{ l = 1}

^{ L }

*x*

_{ l }(

*n*) +

*w*(

*n*), where

*x*

_{ l }(

*n*) is the transmitted primary signal over the

*l*-th channel. The received signal can be decoupled into narrowband signals using the frequency domain representation of

*r*(

*n*), which is computed by the normalized fast Fourier transform (FFT) as follows

*k*is the FFT block index,

*m*is the frequency bin, and

*N*

_{ F }is the FFT size. Each channel is represented by

*M*bins. Using Parseval’s theorem, the signal power in the

*l*-th channel can be computed in frequency domain as

*l*-th channel bins. The issue here is that

*R*

_{ k, l }=

*∑*

_{ m }|

*R*

_{ k }[

*m*] |

^{2}is not the power of noise-only samples in case of

*H*

_{0}(or noise-plus-signal samples in case of

*H*

_{1}) since now these samples are corrupted by the adjacent interference. In this case, the variance of the samples under

*H*

_{0}is higher than

*σ*

_{ w }

^{2}, increasing false alarms if the threshold is not corrected. As a result, it is critical to not only reduce the interference but also to estimate it in order to correct the decision threshold.

#### Mitigating Adjacent Interference Power

*σ*

_{ I, l }

^{2}, is estimated for each channel, the sensing time needed for each channel to perform a fine PSD estimation is optimized. The PSD estimation can be robustified against power leakages using a windowed FFT instead of using (34). In the windowed FFT, the received samples

*r*(

*n*) are weighted first by a normalized window coefficient

*ω*(

*n*) before computing the FFT. This weighting, however, comes at the expense of reducing the spectral resolution. To maintain a high spectral resolution, a multitap-windowed FFT can be used instead. Mathematically, the multitap-windowed FFT is implemented as [26]

*p*is the tap index and

*P*is the total number of taps. In this case, the multitap-windowed energy detector is expressed as

*N*

_{ l }is the channel-specific sensing time. The sensing time differs across channels depending on the interfering powers in each channel. For a desired (

*P*

_{ f },

*P*

_{ d }) pair and \(\mathop{SNR}\nolimits\) sensitivity,

*N*

_{ l }can be computed as follows:

*μ*is a fitting factor that can be calculated beforehand. This expression can be derived from the detection performance of the multitap-windowed energy detector, which is shown to be [25]

*P*

_{ f },

*P*

_{ d }) = (0. 1, 0. 9) with variations on the interfere-to-noise-power ratio (INR), i.e.,

*σ*

_{ I, l }

^{2}∕

*σ*

_{ w }

^{2}. Three detectors are shown: the multitap-windowed detector; the windowed detector, i.e.,

*P*= 1; and the conventional one, i.e., no windowing is used. It is assumed that \(\mathop{SNR}\nolimits = -5\) dB, and the adjacent interferes are one bin away from the band of interest. It is evident that the multitap-windowed detector provides a significant reduction in the sensing time. Figure 19b shows the false alarm probability with variations of the INR. It is clear that adapting the threshold maintains the false alarm to 0. 1 as desired.

### 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.

*blockers*, located at

*f*

_{ b1}and

*f*

_{ b2}. The signal of interest is located at

*f*

_{0}= 2

*f*

_{ b2}−

*f*

_{ b1}. At the output of the LNA, the blockers introduce IM terms in the same band as the desired signal. These spurious terms remain after downconverting the wideband spectrum into baseband. Hence, the received samples, resulted from digitizing the baseband, are corrupted with the 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.

*x*(

*n*) is the wideband signal and

*w*(

*n*) is an additive white Gaussian noise. Here,

*β*

_{1}and

*β*

_{3}are constants that are characteristics of the receiver front-end. Note that

*β*

_{1}

*x*(

*n*) is the linear term, whereas

*β*

_{3}

*x*(

*n*) |

*x*(

*n*) |

^{2}is the third-order nonlinear term.

*x*

_{ d }(

*n*) is the signal of interest,

*x*

_{ b1}(

*n*) and

*x*

_{ b2}(

*n*) are the two blockers, and

*f*

_{ if }= 2

*f*

_{2}−

*f*

_{1}is the intermediate frequency, where the signal of interest resides. Note that

*x*

_{ d }(

*n*) is present in

*H*

_{1}and absent in

*H*

_{0}, and the CR receiver must determine which hypothesis is true. The challenge here is that in the presence of strong blockers, the IM terms can be stronger than the signal of interest, making the detection difficult.

#### Mitigating LNA Nonlinearities

*f*

_{ b1}, cannot be directly done by measuring the energy in that channel since it does not only contain the blocker signal but also the self-interference as shown in Fig. 20. Indeed, recall the received signal:

*i*-th blocker signal

*x*

_{ bi }(

*n*), and it can be shown that [19]

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.

*θ*is a parameter that can be optimized using an adaptive filter to minimize the IM term. The receiver architecture of this method is shown in Fig. 21.

*P*

_{ f }= 0. 1. It is observed that the detection performance is degraded when the LNA operates in the nonlinear regime, making it critical to compensate for this impairment. Figure 22b shows the probability of detection with variations of the SBR, where the compensation algorithm presented in Fig. 21 is used with adaptive

*θ*[19]. It is assumed that

*N*= 500 and \(\mathop{SNR}\nolimits = 3\) dB. Using the cancellation algorithm, the performance significantly improves particularly when the blocker power is strong relative to the signal power .

## Summary

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.

## References

- 1.ATSC Digital Television Standard (2007) ATSC Std. A/53. http://www.atsc.org/standards.html
- 2.Axell E, Leus G, Larsson EG, Poor HV (2012) Spectrum sensing for cognitive radio: state-of-the-art and recent advances. IEEE Signal Proc Mag 29(3):101–116. doi:10.1109/MSP.2012.2183771CrossRefGoogle Scholar
- 3.Cabric D (2008) Addressing feasibility of cognitive radios. IEEE Signal Proc Mag 25(6):85–93. doi:10.1109/MSP.2008.929367CrossRefGoogle Scholar
- 4.Cabric D, Mishra S, Brodersen R (2004) Implementation issues in spectrum sensing for cognitive radios. In: Proceedings of the 38th Asilomar Conference on Signals, System and Computers (ASILOMAR’04), vol 1, pp 772–776Google Scholar
- 5.Cabric D, Tkachenko A, Brodersen R (2006) Spectrum sensing measurements of pilot, energy, and collaborative detection. In: Proceedings of the IEEE Military Communications Conference (MILCOM’06), pp 1–7Google Scholar
- 6.Chuinard G, Cabric D, Ghosh M (2006) Sensing thresholds. Technical report, EEE 802.22-06/005/r3Google Scholar
- 7.Dandawate AV, Giannakis GB (1994) Statistical tests for presence of cyclostationarity. IEEE Trans Signal Process 42(9):2355–2369. doi:10.1109/78.317857CrossRefGoogle Scholar
- 8.Gardner W (1991) Exploitation of spectral redundancy in cyclostationary signals 8(2):14–36Google Scholar
- 9.Harjani R, Cabric D, Markovic D, Sadler BM, Palani RK, Saha A, Shin H, Rebeiz E, Basir-Kazeruni S, Yuan FL (2015) Wideband blind signal classification on a battery budget. IEEE Commun Mag 53(10):173–181. doi:10.1109/MCOM.2015.7295481CrossRefGoogle Scholar
- 10.Hattab G, Ibnkahla M (2014) Enhanced pilot-based spectrum sensing algorithm. In: Proceedings of the IEEE Biennial Symposium on Communication (QBSC’14), pp 57–60. doi:10.1109/QBSC.2014.6841184Google Scholar
- 11.Hattab G, Ibnkahla M (2014) Multiband spectrum access: great promises for future cognitive radio networks. Proc IEEE 102(3):282–306. doi:10.1109/JPROC.2014.2303977CrossRefGoogle Scholar
- 12.Hossain K, Champagne B (2011) Wideband spectrum sensing for cognitive radios with correlated subband occupancy. IEEE Signal Proc Lett 18(1):35–38. doi:10.1109/LSP.2010.2091405CrossRefGoogle Scholar
- 13.Kay S (1993) Fundamentals of statistical signal processing, vol I – estimation theory. Prentice HallzbMATHGoogle Scholar
- 14.Lunden J, Koivunen V, Huttunen A, Poor HV (2009) Collaborative cyclostationary spectrum sensing for cognitive radio systems. IEEE Trans Signal Process 57(11):4182–4195. doi:10.1109/TSP.2009.2025152MathSciNetCrossRefGoogle Scholar
- 15.Mariani A, Giorgetti A, Chiani M (2011) Effects of noise power estimation on energy detection for cognitive radio applications. IEEE Trans Commun 59(12):3410–3420. doi:10.1109/TCOMM.2011.102011.100708CrossRefGoogle Scholar
- 16.Paysarvi-Hoseini P, Beaulieu NC (2011) Optimal wideband spectrum sensing framework for cognitive radio systems. IEEE Trans Signal Process 59(3):1170–1182. doi:10.1109/TSP.2010.2096220MathSciNetCrossRefGoogle Scholar
- 17.Pei Y, Liang YC, Teh KC, Li KH (2009) How much time is needed for wideband spectrum sensing? IEEE Trans Wirel Commun 8(11):5466–5471. doi:10.1109/TWC.2009.090350CrossRefGoogle Scholar
- 18.Quan Z, Cui S, Sayed A, Poor H (2009) Optimal multiband joint detection for spectrum sensing in cognitive radio networks. IEEE Trans Signal Process 57(3):1128–1140. doi:10.1109/TSP.2008.2008540MathSciNetCrossRefGoogle Scholar
- 19.Rebeiz E, Ghadam ASH, Valkama M, Cabric D (2015) Spectrum sensing under RF non-linearities: performance analysis and DSP-enhanced receivers. IEEE Trans Signal Process 63(8):1950–1964. doi:10.1109/TSP.2015.2401532MathSciNetCrossRefGoogle Scholar
- 20.Rebeiz E, Urriza P, Cabric D (2012) Experimental analysis of cyclostationary detectors under cyclic frequency offsets. In: Conference on Signals, Systems and Computers (ASILOMAR’12), pp 1031–1035Google Scholar
- 21.Rebeiz E, Urriza P, Cabric D (2013) Optimizing wideband cyclostationary spectrum sensing under receiver impairments. IEEE Trans Signal Process 61(15):3931–3943. doi:10.1109/TSP.2013.2262680MathSciNetCrossRefGoogle Scholar
- 22.Rebeiz E, Yuan FL, Urriza P, Markovi D, Cabric D (2014) Energy-efficient processor for blind signal classification in cognitive radio networks. IEEE Trans Circuits Syst I Regul Pap 61(2):587–599. doi:10.1109/TCSI.2013.2278392CrossRefGoogle Scholar
- 23.Sun H, Nallanathan A, Wang CX, Chen Y (2013) Wideband spectrum sensing for cognitive radio networks: a survey. IEEE Wirel Commun 20(2):74–81. doi:10.1109/MWC.2013.6507397CrossRefGoogle Scholar
- 24.Tandra R, Sahai A (2008) SNR walls for signal detection. IEEE J Sel Top Signal Process 2(1):4–17. doi:10.1109/JSTSP.2007.914879CrossRefGoogle Scholar
- 25.Yu TH, Rodriguez-Parera S, Markovic D, Cabric D (2010) Cognitive radio wideband spectrum sensing using multitap windowing and power detection with threshold adaptation. In: 2010 IEEE International Conference on Communications, pp 1–6. doi:10.1109/ICC.2010.5502024Google Scholar
- 26.Yu TH, Sekkat O, Rodriguez-Parera S, Markovic D, Cabric D (2011) A wideband spectrum-sensing processor with adaptive detection threshold and sensing time. IEEE Trans Circuits Syst I Regul Pap 58(11):2765–2775. doi:10.1109/TCSI.2011.2143010MathSciNetCrossRefGoogle Scholar
- 27.Yu TH, Yang CH, Cabric D, Markovic D (2012) A 7.4-mW 200-MS/s wideband spectrum sensing digital baseband processor for cognitive radios. IEEE J Solid-State Circuits 47(9):2235–2245. doi:10.1109/JSSC.2012.2195933CrossRefGoogle Scholar
- 28.Yucek T, Arslan H (2009) A survey of spectrum sensing algorithms for cognitive radio applications. Commun Surveys Tutor 11(1):116–130. doi:10.1109/SURV.2009.090109CrossRefGoogle Scholar
- 29.Zeng Y, Liang YC (2010) Robustness of the cyclostationary detection to cyclic frequency mismatch. In: 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, pp 2704–2709. doi:10.1109/PIMRC.2010.5671799Google Scholar
- 30.Zou Q, Mikhemar M, Sayed AH (2009) Digital compensation of cross-modulation distortion in software-defined radios. IEEE J Sel Top Signal Process 3(3):348–361. doi:10.1109/JSTSP.2009.2020266CrossRefGoogle Scholar