Design of Spectrum Usage Detection in Wideband Spectrum Measurements

We investigate the design of signal processing in wideband spectrum usage (SPU) measurements for efficient and smart dynamic spectrum access (DSA). In particular, we focus on spectrum usage detection (SPUD) in the experimental measurements. The detection results can be exploited to estimate statistics of the SPU. An appropriate design of the SPUD depends on the actual SPU in the target frequency band. There is a broad range of wireless systems in a considered broad measurement frequency band, such as from 60MHz to 6GHz, therefore a general design framework in the measurement frequency band is desired. In the proposed design framework, we at first define two models in terms of the SPU and the SPUD process. In addition, the proposed design procedure determines the adequate choice of parameters for the SPUD model based on given parameters of the SPU model in the target frequency band. Numerical evaluation based on computer simulations shows the validity of the design framework and design procedure. Moreover, a modified duty cycle (DC) estimation method is proposed, which can remove bias errors caused by low time resolution in the SPUD. Numerical evaluation based on experimental measurements demonstrates the practicality of the detection framework and procedure proposed in this work.


I. INTRODUCTION
In the wireless communication field, spectrum scarcity is an urgent issue.Since most of the spectrum has been exclusively assigned to licensed wireless systems, there are not enough spectrum resources for new emerging wireless services.On the other hand, spectrum utilization measurement reports have revealed that the utilization rate of most of the licensed spectrum is not very high in spatial and/or temporal domains [1].One possible solution for this issue is spectrum sharing since it can make the underutilized spectrum resource available to the emerging wireless services [2], [3].In fact, several types of spectrum sharing approaches have been investigated, such as dynamic spectrum access (DSA) [4], [5], licensed shared access (LSA) [6], and spectrum access system with citizens broadband radio service (CBRS) [7], with different types of priorities and licensing.
In DSA, a secondary user (SU) can utilize spectrum licensed to a primary user (PU), as long as the spectrum usage (SPU) by SU does not cause any harmful interference towards the PU [4], [5].There are two important key techniques: spectrum sensing and spectrum management.The spectrum sensing can detect instantaneous status of spectrum and SU can find vacant spectrum.The spectrum management includes spectrum allocation and channel selection to utilize the vacant spectrum efficiently.These key techniques can be designed properly based on PU SPU, which can be characterized by appropriate SPU statistics [8].For example, the knowledge of the duty cycle (DC) can enhance spectrum sensing performance [9]- [11], spectrum management [12]- [15] and channel selection [16].
In [17], the concept of smart spectrum access (SSA), which is an enhanced form of DSA, has been presented.In SSA, the prior information of PU SPU is exploited to enable an enhanced DSA.Two-layered SSA has been proposed as a practical implementation of SSA as shown in Fig. 1.This two-layered SSA concept consists of DSA as the first layer and a spectrum awareness system (SAS) as the second layer.SAS is dedicated for SPU measurements to extract useful PU activity information so that SUs in DSA can be relieved of having to perform energy and time consuming SPU measurements.The SPU information, based on long term, wide band, and broad area spectrum measurements, is stored in a data base.The long term information is processed by adequate SPU modeling to extract a set of parameters sufficiently characterizing the full information (which would be impractical to share) [18].In this paper, we focus on the spectrum measurement which is used to estimate statistical information of SPU based on long term measurements.This is different from the spectrum sensing which attempts to obtain an instantaneous status of SPU.
There have been many SPU measurement campaigns (see [15], [19]- [22] and references therein).Measurement campaigns have shown the DC and measured power of various spectrum bands at various measurement sites [23]- [27].This type of measurement campaigns has simply evaluated spectrum utilization and potential spectrum opportunities (i.e., how much spectrum in a certain dimension, such as time and space, is vacant).In [28], estimation of SPU statistics based on periodic SPUD is investigated.This investigation reveals that the measurement process imposes on accuracy of the estimation.There are also detailed SPU models in time, frequency and space domains, respectively [29]- [32].In these investigations, not only the spectrum utilization ratio, but also the trends and variations of feature quantities of spectrum utilization, such as DC [29], signal strength [31] and busy time (vacant time) [16], [33], have been considered.A probabilistic storage algorithm is also investigated to store a measurement data [34].The proposed algorithm can reduce the storage volume for the spectrum measurement results by approximately 99%.
In most SPU measurements, energy detection (ED) has been employed for SPUD in the time-frequency domain.In ED, averaging the observed power spectrum in the time and frequency domains is typically employed to enhance the detection performance.This area for averaging is referred to as mask in this paper.The mask size affects the detection performance as well as the time and frequency domain resolutions.This implies that the applicable parameters for SPUD and statistics estimation strongly depend on the characteristics of the PU SPU itself.In broadband measurements covering a variety of wireless systems, the SPUD has to be designed by taking into account the heterogeneous features of the systems present in the considered frequency span.However, to the best of the authors' knowledge, this approach has not been deeply investigated.
In this paper, we investigate the design of a SPU measurement by considering the characteristics of the PU SPU.Specifically, we focus on SPUD and the following DC statistics estimation.In SPUD, ED with overlapping fast Fourier transform (FFT), such as Welch FFT, is typically employed [35], [36].Our main contributions are summarized as follows: • A design framework for SPU measurements is proposed.The proposed framework consists of three items: a model of SPU, a model of SPUD, and a design procedure to set adequate parameters for SPUD based on the parameters of the SPU model.This framework has broad utility, which is a desirable aspect for the broadband SPU measurement in SAS.• For the SPUD, the detection performance in terms of detection probability and false alarm probability is used as design criterion.Analysis of the detection performance including effects of correlation in the time samples is derived.This strict analysis enables an optimum parameter setting for SPUD.• The above mentioned analysis may require a large number of significant figures, which may increase the computation time significantly.To address this issue, a deflection coefficient based analysis is also shown.Numerical results will show that design procedure based on the deflection coefficient can reduce complexity of the parameter setting procedure.The remainder of this paper is organized as follows.First, Section II summarizes the considered design framework including the models of SPU and assumed SPUD processing.Section III presents the proposed design procedure for SPUD.Specifically, the design criterion and design procedure to determine the model parameters for the SPUD are shown.In Section IV, a modified DC estimation based on the SPUD results is proposed.In Section V, numerical evaluations

II. DESIGN FRAMEWORK
We consider SPU measurement based on the two-layered SSA concept, shown in Fig. 1.The spectrum measurement system in SAS consists of several sensors and one fusion center.The main role of the measurement system is to observe the SPU of PUs and to send measurement reports to a database server in the SAS.The measurement systems are deployed in the space domain to observe wide bandwidths (such as from 60MHz to 6GHz) for long time (such as a few dozen days).In this paper, we employ real-time spectrum analyzer Tektronix RSA 6100A as a sensor [18] which can observe large instantaneous bandwidths up to 110 MHz without any time domain gaps between the outputs.Therefore, within the instantaneous bandwidth real-time spectrum analyzer leads to much more accurate results.Most of the measurements to date have used conventional swept spectrum analyzers that can miss signals that occur between the sweeps.For wide-band (several GHz) measurements real time spectrum analyzer utilizing frequency stepping still leads to more accurate results as during the dwell time (which should be set large enough) on each sub-band there are no time domain gaps.In the measurement system, each sensor sends the local measurement information (such as DC estimation) to the fusion center.The fusion center integrates the reported measurement information and sends the integrated information to the database server in SAS.In this paper, we focus on the signal processing for SPU measurement in particular, SPUD, at the sensor.The results of SPUD are used to understand the characteristics of SPU and we investigate a DC estimation method.The measurement frequency bandwidth covers a large variety of wireless systems and the SPUs of these wireless systems are heterogeneous.
In the proposed design framework, we define a model of SPU and a model of SPUD.Each model consists of different  Based on such model parameters, the reasonable parameters for the SPUD can be determined with the proposed design procedure.In the following, both models are presented.

A. MODEL OF SPU
Under extremely wide measurement bandwidths, it is difficult to observe the whole bandwidth simultaneously due to the limited capabilities of sensors.Therefore, the whole frequency band is divided into sub-measurement bands.We consider several sub-measurement bands W i where i (i = {1, 2, • • • , I}) is the index number of the sub-measurement band.The partitioning rule for the sub-measurement bands is based on the wireless service and system as well as the capability of the sensor.Specifically, in a sub-measurement band, there may be a target wireless system or several wireless systems sharing the frequency band.This partitioning rule is very natural since the SPU parameters can be determined by the wireless system.The adequate parameters of SPUD are determined for the target wireless system in each submeasurement band.In the numerical evaluations, specific sub-measurement bands, such as LTE-uplink, are considered in Sect.V-C, otherwise a general wireless system is assumed in this paper.
Now we focus on one sub-measurement band with a general wireless system.Typically, there are several channels in the sub-measurement band.Two types of channel configuration are assumed: a non-overlapping channel allocation and an overlapping channel configuration.Examples of both types of channel configuration and channel usage are shown in Fig. 2. The signal area indicates an area occupied by one signal component, such as one data packet, in the time and frequency domain.The channel configuration characterizes the SPU in the frequency domain by the model as shown in Fig. 2, which can be expressed in matrix form as where two edges are used in the frequency domain in each channel.Frequency bands [f L l f H l ] t , where [•] t indicates transposition for a matrix/vector, corresponds to a minimum unit of SPU in the frequency domain and this is denoted by the lth sub-channel.As it can be seen from Fig. 2(b), the division to sub-channels is such that within each sub-channel there is a constant number of systems present.Therefore, the sub-channels that we discuss here can be smaller than the channels used by the PUs.Frequency bands not occupied by signal components, such as guard bands, are not included in F CH .In the SPU measurement, statistics of SPU, such as the DC, in the frequency sub-channel l between f L l and f H l are estimated.
In the time domain, we use the time duration for one continuous spectrum occupation period as a model parameter.The time duration is denoted by T O .This time duration may be time-variant and we use its minimum value, T O,min = min{T O }, to characterize the PU SPU in time domain.In particular, T O,min is used to determine the required time resolution for the SPUD.At the lth sub-channel, the minimum signal area is defined by the minimum time-duration T O,min and the frequency band f H l − f L l , respectively.

FIGURE 3: Block diagram of process in a sensor
An outline of the signal processing in each individual sensor is shown in Fig. 3.The received signal is down-converted to baseband signal through the RF (Radio Frequency) and IF (Intermediate Frequency) processing in the sensor.We consider the following model of baseband signal processing in the sensor.An input vector r BB = [r BB,1 , . . ., r BB,N ob ] t represents the observed complex base-band signal where N ob is the number of samples.The measurement frequency band is set to where f s denotes sampling rate, and f c is the center frequency for the sub-measurement band.
For the SPUD, we employ ED implemented with overlapping FFT.The threshold for ED is set based on the Constant False Alarm Rate (CFAR) criterion [37].In the assumed overlapping FFT, power spectrum is obtained by averaging multiple estimations based on overlapping FFTs FIGURE 4: Mask for ED and FFT process with an overlapping [38].The number of samples for one FFT and one Welch FFT using overlapping individual FFTs are denoted by N F F T and N time (N time > N F F T ), respectively, where N F F T is a power of two.The time duration for one overlapping FFT is considered equal to the duration of one time slot.Specifically, N time samples in a time slot are divided into multiple segments with N F F T samples per segment.In the neighboring segments, a part of samples overlap with an overlap ratio equal to γ = 0.5 [38].The relationship among the number of segments in N time , N F F T , and γ is given by In the kth segment, the samples for one FFT is given by (3) The FFT result for r k is where diagonal matrix W represents a window function, such as the Hamming window, and F is a discrete Fourier transform matrix given by where α = exp(2πj/N F F T ).The estimated power spectrum at the kth segment and the bth frequency bin is given by where * indicates complex conjugation and x k,b is the bth sample in the vector x k .
Let us define a tile as a single element of the grid corresponding to one time slot and one frequency bin.The role of SPUD is to recognize the state of each tile: either occupied by a signal component or not.In a typical SPU measurement, the signal occupancy state in each tile corresponding to one frequency bin b and one segment k is detected.On the other hand, we employ mask-based ED and design a mask for ED based on the SPU model parameters T O,min and F CH .Fig. 4 shows the mask and FFT process in one time slot.The mask indicates the area over which the observed power spectrum in the tiles is averaged.The averaged energy is used as a decision variable in ED.The mask is designed for each subchannel as shown for the lth sub-channel in Fig. 4. The shape of the mask is a rectangle and has two components, namely the mask frequency bandwidth and mask time duration [39].These two components are expressed by the number of bins and the number of segments, respectively.The mask time duration is equal to the time slot length N time .For the lth sub-channel [f L l f H l ] t , the mask frequency bandwidth is determined by a region of frequency bins between b L l and b H l , where b L l and b H l are the lower and the upper limits of frequency bins for the lth mask frequency bandwidth, respectively.This means that the frequency bins in the mask bandwidth are fully occupied by signals when signal is present.The matrix of the mask frequency bandwidth for all sub-channels is defined by where l end indicates the number of sub-channels.The ED principle is employed in each mask and the test statistic T ED is given by where M is the set of tiles in the mask and N ave = |M| is the number of tiles in the mask.SPUD is represented by a binary hypothesis problem where hypothesis H 0 indicates that there is no signal component in the mask and H 1 indicates that all tiles in the mask are occupied by signal component.The cases, in which the mask is partially occupied by the signal component are not considered.In Section V, we evaluate the effect of partial occupation on the DC estimation.The SPUD rule is given by where Ĥ is the decision result and η is the threshold for ED.To evaluate the SPUD, we define the detection probability P D as P D = Pr( Ĥ = H 1 |H 1 ) and false alarm probability P F A as P F A = Pr( Ĥ = H 1 |H 0 ).By assuming additive white Gaussian channel noise model, the resulting P F A in the overlapping FFT based ED is given by [40] is an eigenvalue of E x mask,l x H mask,l under H 0 , x mask,l is a vector with the elements x k,b in the mask for the lth sub-channel, and E [•] is the expectation operator.According to the CFAR criterion, η is set to satisfy a target false alarm probability ṖF A .The decision threshold for a target ṖF A can be obtained by solving (8).For the CFAR criterion, noise floor information is necessary to set the threshold for ṖF A .To this end we employ the forward consecutive mean excision (FCME) algorithm for noise floor estimation proposed in [35], [41].The analytical P D is given by [40]  is shown in the appendix.For an adequate SPUD, N F F T and the mask size, i.e., the time slot size N time and mask frequency bandwidth matrix B CH , have to be determined.Therefore, the relevant model parameters of SPUD are N F F T , N time and B CH .The design procedure for these parameters is described in Section III.

III. DESIGN PROCEDURE FOR THE SPUD
For the design of the SPUD, we use the detection probability P D as the main criterion.Specifically, for a given set of parameters, T O,min and F CH , the proposed design procedure can set the model parameters of SPUD, N F F T , N time , and B CH , to maximize P D .The parameters of SPUD are mainly related to the mask design.The preferred design approach/principle of a mask is that the mask is inside the signal area and covers the minimum signal area (time length: T O,min and frequency width: [f L l f H l ] T ) as much as possible.We now consider the parameter setting for the lth subchannel [f L l f H l ] T based on the mentioned design approach.In this case, model parameters of the SPUD are N F F T , N time , and [b L l b H l ] T .In the lth sub-channel, the frequency domain SPU is expressed by where • is the floor function and • is the ceiling function.
The selected lth mask frequency bandwidth is set to cover a signal area in the frequency domain as large as possible, provided that it is inside the lth sub-channel [f L l f H l ] T .On the other hand, it is difficult to keep the mask inside the signal area in the time domain since the SPU measurement and the observed signal are not synchronized.Therefore, we where R t indicates the possible offset error ratio of T O,min , which typically is R t < 1.Specifically, the maximum allowable overestimation error in time length is R t T O,min in the edge of the signal area.According to this constraint, the time duration of time slot has to be less than R t T O,min .Based on this constraint, N time in the given N F F T can be obtained as Equations ( 11) and (12) indicate that an adequate value of [b L l b H l ] t and N time depends on N F F T .The optimum FFT size N opt F F T is therefore given by N opt F F T = arg max subject to the constraint in (11).An exhaustive search is a straight forward approach to show this optimization problem, however the numerical calculation of ( 9) requires a huge number of significant figures to achieve an accurate calculation.The number of significant figures required for an accurate calculation in ( 9) is about five hundreds.For comparison the double precision floating point numbers typically used for numerical computations have only about fifteen significant figures.For example, in MATLAB, this means that much more costly variable-precision arithmetic needs to be used.
For the issue of computational cost, we also investigate a simpler approach for the model parameter setting.Instead of P D , a modified deflection coefficient D is employed to obtain N opt F F T .The modified deflection coefficient is defined as [42]- [44] where var [•] is the variance function.The analytical derivations of E [T ED |H i ] and var [T ED |H i ] are shown in the appendix.In the design procedure based on D, we also perform an exhaustive search to find N opt F F T .We have discussed the optimum parameter setting for an individual sub-channel.In most cases, there may be multiple sub-channels in the measured sub-band.In this case, we need to consider the worst case to set the value of N F F T .Let D l (N F F T ) denote the achievable modified deflection coefficient with N F F T in the lth sub-channel.The optimum N F F T for the lth sub-channel in the sub-band is obtained as Then, optimum N F F T for the sub-band is  In the case of P D , we can use the same procedure to obtain N opt F F T for the sub-band.

IV. MODIFIED DUTY CYCLE ESTIMATION
In this section, two DC estimation methods are proposed.The first one is conventional DC estimation method used as the reference and the second one is a modified DC estimation method.We consider the estimation of DC in the lth subchannel, where a detection result in the mth mask in the time domain is denoted by In the reference DC estimation method, the DC Ψ R is estimated as where N S denotes the number of decision results.Let S denote a vector S = [S(0), • • • , S(N S − 1)] T .Altered process in the modified DC estimation is explained for S = [0100111110] T as follows.The signal area and detection results in the lth sub-channel are shown in Fig. 5.The signal area in this example is the minimum signal area.In Fig. 5, the left-hand side corresponds to S (before the altered process) and right hand corresponds to the output after the altered process S. In this example, R t = 1/4 is assumed, therefore the mask size in the time domain is approximately one quarter of the time length of the minimum signal area.The altered process extracts the clusters of ones ("1"), which in the example of Fig. 5 there are two clusters in S, i.e., "1" and "11111".In each cluster, the first "1" is changed to "0", which leads to a output vector S = [0000011110] T .There are two aims in the altered process to achieve an accurate DC estimation.If there is a false alarm error, the cluster size may be one.Specifically, the first "1" in S may be a false alarm error and the altered process can remove it.Under high SNR case, even the partially occupied masks will lead to detection, S(m) = 1 and this leads to overestimation in the DC estimation.This is shown as "Mask A" and "Mask B" in the left hand size in Fig. 5.In this example, correct time length is four mask sizes, but estimated time length by the reference DC estimation is five mask sizes (left hand in Fig. 5).As the altered process correctly outputs length of four mask sizes ('11111' was changed to 1111), the altered process can suppress the biased error.This is true also in general case.The reasoning for this process that if we have sufficient SNR, the two partially occupied masks at the beginning and end (Mask A and Mask B in Fig. 5) will be both classified to be '1', leading to overestimation of length.By removing one '1' in the altered process, we recover the true length.
In the modified DC estimation, the estimated DC Ψ M is given by where S(m) is the mth element of S.

V. SIMULATION AND EXPERIMENTAL RESULTS
We first evaluate the SPUD based on the proposed design (design framework and design procedure) and the DC estimation performances by means of computer simulations.Afterwards, we also confirm the practical validity of the proposed design based on experimental SPU measurement results in different wireless systems.
In computer simulations, we consider one sub-channel.The bandwidths of the sub-measurement (all bins in Fig. 4) band and sub-channel are 12.5 and 6MHz, respectively.The sampling rate is equal to 12.5 Msamples/s.The minimum time duration T O,min is set to 50 µsec, which leads to 625 samples in a mask.Since we consider the downconverted signal, the center frequencies for the sub-measurement band and the sub-channel are assumed to be f c = 0 Hz and f (l) c = 0 Hz, respectively, without loss of generality.The assumed signal size is the minimum signal area (i.e.time duration is T O,min ) which corresponds to the worst case for DC estimation.

A. COMPUTER SIMULATIONS (DETECTION PERFORMANCE)
We first evaluate the detection performance of SPUD by means of the miss detection probability which is given by P M D = 1 − P D with a given false alarm probability.In Fig. 6, the P M D performance is shown as a function of SNR for R t = 1/4.There are two types of results: the first one is for fixed FFT size (such as N F F T = 4, 8, 16, 32, 64, 128) and the second one uses N opt F F T with the criteria (13) or (16).In the second type, the optimum N F F T depends on the SNR.We can confirm that N opt F F T based SPUD can always achieve the best detection performance for any SNR.Moreover, the achieved detection performances by ( 13) and ( 16) criteria are the same.This indicates the validity of the efficient design procedure based on the deflection coefficient in (16).To confirm the optimum FFT size, the P M D performance as a function of N F F T is shown in Fig. 7 for the cases of SNR=-2dB (N opt F F T = 16) and SNR=1dB (N opt F F T = 4), respectively.These results show that N opt F F T depends on the SNR.
In Fig. 8, the P M D performance is shown as a function of SNR with R t = 1/16.Again we can confirm the validity of the proposed design procedures since the P M D performance obtained by the proposed design procedures are the best.
In both Figs.6 and 8, there is not any significant performance difference between the P D and D design criteria.An advantage of the D based design procedure is a lower computational cost compared to the P D based design procedure.The computational time ratio of the design procedure based on D to the design procedure based on P D is plotted in Fig. 9.In the criterion based on P D (9), a large number of significant figures, such as 500 digits, is required to avoid not a number (NaN) in a calculation of P D in (9).On the other hand, with the design criterion based on D, double precision floating point numbers are enough.This result indicates that the ratio decreases as R t is reduced.The computational time of the design procedure based on D is at most 10% of the time of the design procedure based on P D .

B. COMPUTER SIMULATIONS (DC ESTIMATION PERFORMANCE)
The reference DC estimation method in (17) and the modified DC estimation method in (18) are evaluated in terms of the DC estimation performance in Fig. 10 for different R t .In the low SNR region (less than -5 dB), large R t can achieve higher detection performance which leads to accurate DC estimation.Notice that large R t values lead to a large number of tiles in the mask, which inherently achieves high detection performance.In the high SNR region, large R t leads to lower time resolution and therefore significantly large bias.For smaller bias the convergent DC estimation, smaller R t is required, which in turn requires high SNR for an accurate DC estimation.
Fig. 11 shows the DC estimation performance of the modified DC estimation method for different R t .They can achieve accurate DC estimation performance compared to the reference DC estimation method in high SNR region.Large R t , such as R t = 1/2, provide a good leading edge in low SNR region but a slightly poor convergence to the true value and vice versa.Therefore, R t = 1/4 is an appropriate option in this case.An advantage of the modified DC estimation is that the biased error can be removed in the high SNR region   (beyond 10 dB) for any R t .
With the reference method (Fig. 10) the estimated DC is accurate only if the SNR takes a particular value, otherwise the estimation is in general very inaccurate due to the false alarms due to the overestimation in the DC estimation.On the other hand, the estimation provided by the modified method (Fig. 11) is very accurate over a wide range of SNR values, provided that the SNR is sufficiently large.This fact indicates that the the modified method can remove the false alarms effectively.

C. MEASUREMENT EXPERIMENT
SPU measurement results (spectrograms and detection results) are shown in Fig. 12   Based on the obtained spectrograms, we can confirm several characteristics of the PU SPU.In the case of LTE, the size of the minimum continuous SPU is 0.18MHz (bandwidth) and time duration of 500 µsec (time duration) as shown in Fig. 13.On the other hand, the measurement result indicates that bandwidth and time duration for one continuous SPU, (e.g., a data packet), vary dynamically.
In the case of DECT, the bandwidth and time duration for one continuous SPU are almost constant.In SCPC/FDMA, the bandwidth is constant, but the time duration varies, and it can fully occupy time domain.
The detection results in Fig. 12 capture the characteristics of the PU SPU and indicate that the SPU measurements can be performed accurately with the proposed design.The design results in Figs. 13  T O,min due to R t = 1/4.The second one is that the number of frequency bins in a sub-channel is approximately seven to eight.This is because an adequate number of bins for a subchannel depends on the SNR as confirmed in Fig. 6 and the target SNR is set to 0 dB for the three cases.
In summary, the results of measurement experiment show that the proposed methods can achieve appropriate detection performance in the various spectrum usage scenarios.This indicates a versatility of the proposed methods.

VI. CONCLUSION
In this paper we have investigated the design of SPUD according to the SPU information.Wide-band SPU measurements cover multiple wireless systems and the characteristic of the PU SPU strongly depends on the wireless system.We have proposed a unified design framework for SPUD.In computer simulations have demonstrated the validity of the proposed design framework, and procedure.The designed SPUD can achieve high detection performance.A strict analysis of detection performance for the model procedure requires a large number of significant figures, which involves a significant computational cost.To address this problem, we employ a deflection coefficient as an approximate criterion.Numerical evaluation show that the design procedure based on the deflection coefficient can achieve a lower computational cost than that of the strict analysis while similar SPUD performance is achieved.We have investigated the trade-off between the detection performance and time resolution in the mask design.Typically, high detection performance can be achieved with a large mask size, however this leads to low time resolution.In the estimation of the SPU statistics, such as DC, a low time resolution causes critical biased errors.To address this problem, a modified DC estimation is proposed.Numerical evaluations prove that the biased errors can be removed by the modified DC estimation method under high SNR.Finally, the proposed design is also evaluated based on three empirical SPU measurement campaigns.The measurement results obtained with the proposed design indicate that the characteristics of the PU SPU can be captured accurately.

APPENDIX A EIGENVALUES AND STATISTICS OF TED
In this appendix, the eigenvalues of E x mask,l x H mask,l in the lth sub-channel under H 0 and H 1 are derived for (8), ( 9) and ( 14) [40].Let y k denote the kth segment of x mask,l , i.e., where F mask is the Fourier transfer matrix for the lth subchannel is given by . . . . . . . . . . . .
E x mask,l x H mask,l can be expressed in terms of y k as A covariance matrix for the pth segment y p and the qth segment y q is then defined as The received signal vector r p is given by r p = s p + z p , where s p and z p are vectors for signal and noise components respectively.Based on the signal model r p = s p + z p , E y p y H q is given by E y p y H q = F mask WE s p s H q WF mask H + F mask WE z p z H q WF mask H . (24) The first and second terms in the right-hand side represent the covariance matrices of signal and noise components, respectively.Each element in z p is a noise signal sample that follows an independent and identically distributed (IID) complex Gaussian distribution with zero mean and variance σ 2 N .Regarding the second term in (24), let δ k be a function defined by z p is a vector with, the sampled noise components as: Therefore, E z p z H q can be expressed as a function of δ k as where ∆ = (q − p)(1 − γN F F T ).A q−p is a function of q − p defined by A q−p = F mask WE z p z H q WF mask H .In the case of q − p ≥ 0, A q−p is given by τ 2,2 • • • τ 2,N f . . . . . . . . . . . .(28) In the case of q − p < 0, A q−p is given by A q−p = A H p−q .Regarding the first term in (24), an assumed model of the signal component in the vector s p is shown as follows.The signal component at the tth time sample is denoted by s(t).This signal is bandlimited to the lth sub-channel in which the center frequency and bandwidth of the sub-channel are denoted by f (l) c and B l .Specifically, s(t) is defined as [45] where s w is the signal component, which follows an IID complex Gaussian distribution with zero mean and variance σ 2 S , w s (i) is a coefficient of the bandlimiting filter, M u : M d is the approximated smallest integer ratio of f s : f By using ρ n−m , E s p s H q can be expressed as Now we define B q−p = F mask WE z p z H q WF mask H , which is also a function of q − p.In the case of q − p ≥ 0, B q−p is given by where w k α (I b +m−1)k w l α −(I b +n−1)l ρ D+l−k (35) Again, in case of q − p < 0, B q−p = B H p−q .The expectation E x mask,l x H mask,l under H 0 is given by while E x mask,l x H mask,l under H 1 is given by Finally, the eigenvalues λ

FIGURE 1 :
FIGURE 1: Concept of two-layered smart spectrum access (SSA) Non-overlapping channel allocation (b) Overlapping channel allocation

FIGURE 2 :
FIGURE 2: Two types of channel allocation and example of channel usage in the time-frequency domain samples (r BB ) where λ (H1) k is an eigenvalue of E x mask,l x H mask,l under H 1 and the signal component is assumed to be Gaussian signal.A detailed analytical derivation of the eigenvalues λ (H0) k and λ (H1) k This work is licensed under a Creative Commons Attribution 4.0 License.For more information, see https://creativecommons.org/licenses/by/4.0/.This article has been accepted for publication in a future issue of this journal, but has not been fully edited.Content may change prior to final publication.Citation information: DOI 10.1109/ACCESS.2019.2938549,IEEE Access Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS set a constraint in terms of possible offset error due to the asynchronicity operation as

FIGURE 5 :
FIGURE 5: Input (left-hand) and output (right-hand) for altered process in the modified DC estimation

FIGURE 6 :FIGURE 7 :
FIGURE 6: P M D performance as a function of SNR with R t = 1/4 and P F A = 0.01 for different FFT sizes

FIGURE 8 :
FIGURE 8: P M D performance as a function of SNR with R t = 1/16 and P F A = 0.01 for different FFT sizes

FIGURE 9 :
FIGURE 9: Computational time ratio of D to P D as a function of R t performance

FIGURE 10 :
FIGURE 10: Duty Cycle estimation (reference method) as a function of SNR for different R t , the conventional DC estimation is used.

FIGURE 11 :
FIGURE 11: Duty Cycle estimation (modified method) as a function of SNR for different R t , the modified DC estimation is used.

FIGURE 13 :
FIGURE 13: F CH , B CH , and mask design in sub-band LTEuplink

FIGURE 14 :
FIGURE 14: F CH , B CH , and mask design in sub-band DECT

FIGURE 15 :
FIGURE 15: F CH , B CH , and mask design in sub-band SCPC/FDMA and an element in y k , x k,b , in the frequency region b L l ≤ b ≤ b H l .Let N f denote the number of bins in the frequency region, i.e., N f = b H l − b L l + 1.The FFT output for y k is given by y

2 h
bandlimiting filter coefficient w s (i) is set to;w s (i) = M d /M u L i=−L (h(i)) sinc(x) = sin(πx)/(πx), I 0 β 1 − (l/L) 2 /I 0 (β)indicates Kaiser window, I 0 is modified Bessel function of the first kind and zeroth order, and β is a shape parameter for the window.The covariance between s(m) and s(n), is given byE [s(m)s * (n)] = σ 2 S L l=−L w s (i)w s (M d (n − m) + i) • exp −2πj f c − f (l) c f s (n − m) = σ 2 S ρ n−m .