A Novel, Blind, Wideband Spectrum Detection under Non-Flat Spectrum and Fading Scenarios

Abstract

In the field of radio surveillance and cognitive radio, the reception of a signal is usually made in a non-cooperative manner, which means there exists little prior information to detect the signals reliably via a traditional method. At the same time, the prevalent wideband acquisition mode will receive multiple subband signals from homogeneous or heterogeneous systems, leading to deteriorated detection performance under a non-flat spectrum and fading channel. In view of the above concerns, a novel detection algorithm based on the Gaussian hidden Markov model (HMM) is proposed so as to separate the individual sub-band signal from the wideband spectrum accurately in a low signal-to-noise ratio (SNR). The simulated communication signals with spectral fluctuation and multipath fading indicate the superiority and applicability of the proposed algorithm as compared with other detection algorithms. Our algorithm can achieve a 94% detection probability at −10 dB SNR under an additive white Gaussian noise (AWGN) channel and has a nearly ideal receiver operating characteristic (ROC) curve. When faced with a Rayleigh fading channel, it still outperforms other algorithms. The acquired real data also very its practical application with moderate computation complexity and a more stable carrier-frequency estimation.

1. Introduction

With the tremendous increase of wireless service and devices, scarcity in the radio spectrum is becoming more and more significant. However, this phenomenon is largely due to the underutilization of spectral resources. Cognitive radio is a promising technology that allocates the spectrum flexibly and enables opportunistic spectral access by secondary users, which can greatly alleviate the congestion in the spectrum. Spectral sensing is the core task for implementing cognitive radio; its main purpose is to detect the signal from a noisy channel and allocate the unused frequency band to secondary users.

Due to the prevalence of wideband acquisition systems, the received signal will encompass several sub-band signals occupying the non-overlapped portion of the spectrum. The non-cooperative reception mode denotes that little prior information can benefit the detection process. The signal corrupted by noise and fading channel further degrades the detection performance. All of these factors make wideband spectrum detection under non-cooperative situations a challenging but imperative task for spectrum sensing.

Recent research on spectrum detection can be organized into two categories. One of them is based on energy detection, the main idea of which is to locate the sub-band signal using a predetermined threshold. Another widely adopted algorithm is edge detection, which detects the channel boundaries by exploiting the steep transition nature of a bandwidth-limited signal.

A localization algorithm based on double thresholds (LAD) was first proposed to split the narrowband signal from the wideband spectrum [1]; its complexity is remarkably low however. The predetermined thresholds are susceptible to SNR variation, making it hard to select suitable thresholds in practical situations. Adjacent-cluster-combing-based LAD (LAD ACC) has also been proposed to lower the risk of separating one signal into two or more signals, which is the case in original LAD [2]. A histogram-based spectrum segmentation method showed its excellence in locating the channel boundaries for a single-carrier as well as a multicarrier signal [3]; however, three predetermined parameters need extra, prior information to perform the algorithm, signifying its inapplicability under non-cooperative scenarios. Distributed local extension (DLE) in [4] indicated a good level of detection performance with relatively high complexity and extra-experienced parameters.

Most edge detection algorithms have been concentrated on wavelet transform. The wavelet transform multiscale product (WTMP) [5,6,7] and wavelet transform multiscale sum (WTMS) [5,6,7,8] implement edge detection by locating the local maxima of wavelet coefficients. These algorithms may work well at a medium-to-high SNR under the flat spectrum, but when faced with a non-flat spectrum at a low SNR, there will be a great number of spurious edges. A hybrid wavelet transform presented in [9,10] proved its superior detection performance at a low-to-high noise ratio via fine spectrum pre-processing and an extra threshold for eliminating spurious edges at each scale under the flat spectrum.

The others are aimed at detecting the wideband spectrum by locating the edges of the spectrum. The Hilbert transform (HT)-based detection proposed in [11] only works for the flat spectrum; too many spurious edges occurred for modulated communication signals. A recursive time-frequency algorithm in [12] indicated its advantage with modulated signals with gradual roll-off on band edges and a low-duty cycle. Its complexity limits its practical application greatly. An HMM-based wavelet edge detection proposed in [13] proved its effectiveness in the detection of a multicarrier signal; however, it needs prior information about the sub-channel spacing. The state estimation accuracy of HMM in spectrum sensing was comprehensively investigated in [14], which led us to use HMM as a part of our newly proposed algorithm.

Therefore, the proposal of a robust detection algorithm without prior information to adapt to diverse modulation formats with the non-flat spectrum and channel impairment motivated us to do this work.

Our newly proposed algorithm demonstrates that it can detect the sub-band signals reliably for both single-carrier and multicarrier modulated signals. The detection probability is 94% at −10 dB SNR. It can also resist the Rayleigh fading channel with Doppler offset to some extent. The acquired Starlink data also verify the effectiveness of the proposed algorithm.

The remainder of this paper is organized as follows: The signals and previous detection algorithms are analyzed in Section 2. The proposed algorithm is presented in Section 3. A thorough comparison is made in Section 4 to demonstrate the superiority and robustness of the proposed algorithm. Some conclusions are drawn in the last section.

2. Signal and Detection Model

Since we are focusing on wideband spectrum detection for the modulated communication signals, the signals under analysis will first be clearly defined. Afterwards, the applicable detection algorithms for non-cooperative scenarios are presented in detail.

2.1. Signal Model

A non-cooperative scenario means that the modulation format, the carrier frequency, the bandwidth, and the SNR of a modulated communication signal are unknown. An interesting frequency spectrum is known to us. The goals are to detect the sub-band signals accurately and to give an accurate estimation for the carrier frequency. The carrier frequency is a core parameter for deploying automatic modulation classifications in [15,16,17].

The considered communication signals include Phase Shift Keying (PSK), Quadrature Amplitude Modulation (QAM), Gaussian Minimum Shift Keying (GMSK), and Orthogonal Frequency Division Multiplexing (OFDM). All of these signals have been universally adopted by mobile cell systems and satellite communication systems.

PSK is a digital modulation scheme that uses the different phase states of the carrier to characterize digital information. It is expressed as

$$s_{PSK}\left(t\right)=\mathrm{Re}\left(A_m{\displaystyle \sum _n^{}{a}_{n}g\left(t-n{T}_s\right)e^{j\left(2\pi f_{c}t+{\phi }_0\right)}}\right)$$

(1)

where $\mathrm{Re}\left(\cdot \right)$ stands for take the real part of a complex; $A_m$ and $a_n$ are the amplitude, and complex symbols taken from the constellation diagrams, respectively; $g\left(t\right)$ is the pulse shaper with the raised cosine filter; $T_s$ represents the sampling period; $f_c$ denotes the carrier frequency; and ${\phi }_0$ is the initial phase.

QAM is introduced to enable efficient transmission by utilizing joint amplitude and phase modulation to improve noise tolerance. It can be expressed as

$$\begin{array}{r}{s}_{QAM}\left(t\right)=\left[A_m{\displaystyle \sum _n{a}_{n}g\left(t-n{T}_s\right)}\right]\cos \left(2\pi f_{c}t+{\phi }_0\right)\\ +\left[A_m{\displaystyle \sum _n{b}_{n}g\left(t-n{T}_s\right)}\sin \left(2\pi f_{c}t+{\phi }_0\right)\right]\end{array}$$

(2)

where $a_n,b_n\in \left\{2m-1-\sqrt{M}\right\},m=1,2,\dots ,\sqrt{M}$ is the modulation order.

GMSK is composed of a Gaussian low-pass filter and a Minimum Shift Keying (MSK) modulator. The MSK ensures the continuity of the carrier phase, and the Gaussian filtering makes the signal power spectrum more compact and improves spectral utilization. Its expression in the time-domain can be shown as

$$s_{GMSK}\left(t\right)=A_m\cos \left(2\pi f_{c}t+{\phi }_t+{\phi }_0\right)$$

(3)

where ${\phi }_t$ denotes the continuously changed phase over time, which can be expressed as

$${\phi }_t=\pi {\displaystyle {\int }_{-\infty }^t\left[{\displaystyle \sum _n{I}_{n}g\left(\tau -nT\right)}\right]d\tau }$$

(4)

where $I_n\in \left\{-1,1\right\}$, $g\left(t\right)$ is the Gaussian pulse shaping function, and $T$ is the duration of a symbol.

Another widely used component in a multicarrier system is OFDM, which is a multiplexing mode in essence; the baseband modulated symbol sequence is still PSK or QAM. The transmitted signal is written as [18]

$$s_{OFDM}\left(t\right)=\mathrm{Re}\left\{A_m{\displaystyle \sum _{k=0}^{N-1}{\displaystyle \sum _{n\in Z}{d}_{k,n}g\left(t-n\Delta T\right)e^{j2\pi k\Delta F\left(t-n\Delta T\right)}}}\cdot e^{j(2\pi f_{c}t+{\phi }_0)}\right\}$$

(5)

where N is the number of subcarriers, $d_{k,n}$ is the symbol sequence on the kth subcarrier, $\Delta T$ represents time spacing between symbols, and $\Delta F$ denotes the subcarrier spacing.

For the sake of simplicity, the signal in the time-domain considered here will be denoted as $s_X\left(t\right)$; the transmitted signal $s_X$ is assumed to have unity energy, and X is the above-mentioned signal format. The transmitted signal will then go through a wireless channel. Therefore, the received signal can be given by

$$r(t)=s_X\left(t\right)\ast h\left(t\right)+w\left(t\right)$$

(6)

where ∗ denotes the convolution operation, $h\left(t\right)$ is the impulse response of the channel, and $w\left(t\right)$ is the white Gaussian noise with a zero mean and variance ${\sigma }^2$.

Apart from the normally assumed flat channel, the fading channel may also come into play in practical situations. Especially for a Rayleigh fading channel with a maximum Doppler shift $f_D$, it can be modelled as shown in the formulation in [19]; the Doppler spectrum in Figure 1 is used to address its impact. When $f_D$ increases, the magnitude of the Doppler spectrum decreases accordingly, leading to a drop in the power of the signal, which directly contributes to deteriorated detection performance.

The frequency domain representation can be given by the Fourier Transformation (FT) of Equation (6)

$$s_r\left(f\right)={\displaystyle \sum _{k=1}^{N_s}{s}_k\left(f\right)}+w\left(f\right) f\in \left[f_0,f_N\right]$$

(7)

where $s_k\left(f\right)$ is the FT of convolution component in Equation (6) for the kth sub-band, $w\left(f\right)$ is the FT of additive Gaussian white noise (AWGN), N_s is the number of sub-band signals, and the interested spectrum is between $f_0$ and $f_N$.

Since the transmitted signal has one unity energy and the amplitude $A_m$ is 1, the SNR $\gamma =E\left({\left|h\right|}^2\right)/{\sigma }^2$; $E\left(\cdot \right)$ means the expectation, and h is 1 for an AWGN channel; h follows the corresponding distribution under a fading channel.

2.2. Detection Algorithm

The spectrum detection problem posed by the wideband is different from that of the narrowband. Narrowband spectrum detection is used to determine whether the one licensed spectral band is occupied or not. However, wideband spectrum detection operates on serval noncontiguous spectral bands, which means we not only need to detect the occupancy of each spectral band, but we must also detect the channel boundaries of each band; therefore, the sub-band signals from homogenous or heterogeneous signals can be separated.

At present, we need to separate each sub-band signal between $f_0$ and $f_N$ without knowing $N_s$, the channel boundaries $\left\{f_1,f_2,\dots ,f_{N-1}\right\}$, or other prior information. Therefore, this is basically a blind detection for multiple sub-band signals, invalidating the cyclostationary detection for a narrowband signal in [20,21] or the machine-learning-based detection in [22,23].

An available practical detection algorithm can be a modified WT inspired by [6,9], LAD ACC in [2], and DLE in [4] under our context. The detailed implementation of these algorithms will be given in the following subsections.

2.2.1. Modified CWT Detection

The authors in [6] have proven the advantages of a mexh wavelet in channel change-point detection, and the authors in [8,9] introduce another threshold to greatly suppress the spurious edges during the continuous wavelet transform (CWT). Inspired by these insights, we formulated a modified CWT detection.

The schematic of the modified CWT detection is illustrated in Figure 2.

The PSD smoothing implemented in the time-frequency domain can be expressed as

$$\left\{\begin{array}{l}\eta =\frac{1}{K}{\displaystyle \sum _{k=0}^{K-1}p\left(n+k\right)}\\ p=\frac{1}{M}{\displaystyle \sum _m{p}_m}\end{array}\right.$$

(8)

where $\eta$ denotes the smoothed power spectrum density (PSD), K is the window length in the frequency domain, and $p_m$ is the periodogram in the m segment of the received signal. M is the total number of segments in the time-domain.

CWT is used to obtain the wavelet coefficients of the smoothed PSD; it can be defined as

$$W_j=\eta \left(n\right)\ast {\psi }_j\left(n\right)$$

(9)

where $W_j$ is the wavelet coefficient, ${\psi }_j$ is a wave with scale j, $j=2^R$, and R is the CWT resolution.

To suppress the spurious edges, the binarization of $W_j$ is made by a threshold $\lambda$, $\lambda =\max \left(W_j\right)+\min \left(W_j\right)/2$. The binarization process is used to set the wavelet coefficients lower than $\lambda$ to 1, as in [9]; the reason for this is that those constant coefficients will not produce any local extrema in the process of a local peak search.

The local maxima search is done by taking the first derivative of wavelet coefficients; therefore, the boundaries are determined as

$$B_n=\mathrm{maxima}\left(diff\left(W_b\right)\right)$$

(10)

where $W_b$ is the wavelet coefficients after binarization, $B_n$ is the detected local maxima, $diff\left(\cdot \right)$ is the first derivative operation, and $\mathrm{maxima}\left(\cdot \right)$ means the local maximum search.

Since $B_n$ is the frequency index, the frequency edges of a channel can be obtained by multiplying the frequency resolution $R_s$.

The Modified CWT detection can be implemented as the pseudocode in Algorithm 1.

Algorithm 1 Modified CWT detection algorithm

1: Input: time-domain signal $r\left(t\right)$

2: PSD smooth as in Equation (8) 3: compute the wavelet coefficients as in Equation (9) 4: compute the threshold $\lambda$ 5: the binarization of wavelet coefficients if $W_j\le \lambda$ $W_b=1$ else $W_b=W_j$ 6: local maxima search as in Equation (10) 7: the detected frequency boundaries of channel $\widehat{f}=B_n\cdot R_s$

2.2.2. LAD ACC

LAD ACC is an adaptive iteration algorithm used to locate the sub-band signal by comparing the iterative thresholds with the PSD. It is composed of double-threshold iteration, sub-band clustering, sub-band affirmation, and sub-band combination.

The double-threshold iteration is used to perform the forward consecutive mean excision (FCME) algorithm [24] twice to determine the final thresholds; the initial threshold can be written as

$$T_i=-\ln \left(P_{fa}\right)$$

(11)

where $T_i$ is the initial threshold, $P_{fa}$ is the desired false-alarm probability; a lower $P_{fa}$ corresponds to the upper threshold $T_u$, and a higher $P_{fa}$ corresponds to the lower threshold $T_l$.

After the iterations, the final thresholds $T_1$ and $T_2$ can be obtained immediately; the sub-band clustering is used to find the consecutive points whose power are above $T_2$. When the search process is done, the PSD will be segmented into a few clusters, and the sub-band affirmation is used to select the clusters that have at least one point with its power above $T_1$. The sub-band combination denotes that the chosen adjacent clusters can be merged into one if there are only a few points whose power are below $T_2$.

LAD ACC can be implemented as the pseudocode in Algorithm 2. The functions used in Algorithm 2 will not be formally described here; its principles can be found in [2,25].

Algorithm 2 LAD ACC algorithm

1: Inputs: $s_r\left(f\right)$, $T_u$ and $T_l$

2: T1 = function FCME($s_r\left(f\right)$,$T_u$) T2 = function FCME($s_r\left(f\right)$,$T_l$) 3: sub-band clustering: lowerindex = find($s_r\left(f\right)$ > T2) Cluster = function AdjacentCluster(lowerindex) 4: sub-band affirmation: psd = $s_r\left(f\right)$, NBCluster = Cluster(max(psd(Cluster)) > T1) 5: sub-band combination: ACCCluster = function ACC(NBCluster,T2,psd)

After implementing the LAD ACC, the detected number of the sub-band signal will be the size of the ACC Cluster; the detected boundaries will be $\left\{f_1,f_2,\dots ,f_{N-1}\right\}$, so an estimation of the carrier frequency can be obtained as

$${\widehat{f}}_{c,i}=\left(f_i+f_{i+1}\right)/2 \left(i=1,2,\dots ,N-2\right)$$

(12)

2.2.3. DLE

DLE mainly comprises sub-band detection and sub-band mergence to locate the channel edges.

The sub-band detection is implemented in a slipping search method. The spectrum is segmented into 3 parts, as illustrated in Figure 3. The lengths of the left and right window are L_S; the initial search center-point is n_k the length of the body window is 2i, the maximum search length of the body window is L_B; the initial vector sets of the three segments are ${\overrightarrow{n}}_L$,${\overrightarrow{n}}_B$ and ${\overrightarrow{n}}_R$; the corresponding parameters can be found in Table 2.1 in [4].

The mean power of the three vector sets are $m_L$, $m_B$, $m_R$, $P_L=m_B/m_L$, $P_R=m_B/m_R$; a successful detection means that $P_L$ and $P_R$ are both above the predetermined threshold $V_d$. At the same time, if the power of the updated $P_L$ or $P_R$ is below another threshold $V_f$, the search center will be updated again, and the length of the body window will set to 1; therefore, the above-mentioned detection process will restart. To improve the computational efficiency, the times to set I = 1 should be limited.

The pseudocode of DLE has been provided at length in [4]; the sub-band mergence is used to merge the overlapped sub-band into one sub-band. There are three predetermined parameters to run DLE algorithm; the thresholds $V_d$, $V_f$, and the maximum search bandwidth of the body window. As discussed in Section 4, the thresholds are also sensitive to the SNR fluctuation; the maximum search bandwidth should also be adjusted according to the observed spectrum.

3. Proposed Detection Algorithm

The newly proposed HMM-based algorithm is used to locate the sub-band signal by detecting the transition between idle and occupied states. It is a blind detection strategy, and its merit is to locate each sub-band signal by the detection of state transitions without extra traditional thresholds.

The proposed algorithm includes spectral preprocessing in both the time- and frequency-domains; a maximum likelihood estimation-based EM algorithm is used to estimate HMM parameters, a maximum posterior probability (MAP) for state prediction, and a differentiation operation to detect the state change-point.

The spectral preprocessing is the same as that in Equation (8).

The state parameters estimation can be illustrated as shown in Figure 4. The implemented HMM consists of the preprocessed PSD $\eta$ and a hidden state sequence $X$ at frequency index n, $X_n$ = 1 means the sub-band signal is idle, while $X_n$ = 2 means the sub-band signal is active. The initial parameters in $\varphi$ denote the state probability, the state transition matrix, the mean and variance of the Gaussian distribution for the involved states, respectively, with $\mu =\{{\mu }_1,{\mu }_2\}$, $\sum =\{{\sigma }_1^2, {\sigma }_2^2\}$. These parameters can be randomly initialized.

The Baum–Welch algorithm is used to update the initial parameters to obtain ${\varphi }_1$ by the M steps of the EM algorithm, as in [26].

The forward and backward algorithms are used to implement the E steps of the EM algorithm. The procedures can be explained as shown in Figure 5. The parameters in Y represent the log-likelihood estimation, the conditional probability of hidden states, and the conditional probability of observed PSD.

The forward recursion to compute conditional probability $\alpha$ can be expressed as

$${\alpha }_1=diag\left(y_1\cdot \pi \right), {\alpha }_n=diag\left(y_n\cdot G^T\cdot {\alpha }_{n-1}\right)n=2,\dots ,N$$

(13)

where $\alpha$ is a 2 × N matrix, diag(.) means taking the main diagonal element of a matrix, and y is the posterior Gaussian probability density for the input PSD. It is also 2 × N matrices; $y_n$ is a column vector; G denotes the state transition matrices; and (.)^T means the transpose of matrices.

Similarly, the backward recursion to compute conditional probability $\beta$ can be expressed as

$${\beta }_N=1, {\beta }_n=dot\left(G{\beta }_{n+1},y_{n+1}\right) n=N-1,\dots ,1$$

(14)

where $\beta$ is a 2 × N matrix, ${\beta }_n$ is a column vector, and $dot\left(\cdot ,\cdot \right)$ means the dot product operation between two matrices with the same size.

The log-likelihood estimation can be obtained as

$$\log lik={\displaystyle \sum _{n=1}^N\log \left({\displaystyle \sum _{m=1}^2\alpha \left(n,m\right)}\right)}$$

(15)

The EM algorithm compares the log-likelihood estimation between consecutive iterations. The iteration stops when the maximum iteration number is reached or the difference between consecutive likelihood is lower than the threshold.

When the iteration stops, the optimal $\alpha$ and $\beta$ are obtained in the sense of the maximum likelihood. The posterior probability of hidden states can be expressed as

$$gamma=p\left(X_n=i\left|s\left(1:N\right)\right.\right)=dot\left(\alpha ,\beta \right) i=\{1,2\}$$

(16)

where gamma is a 2 × N matrix, indicating the posterior probability of X at each frequency index n.

The MAP is applied to give the state prediction

$$\left\{\begin{array}{ll}{X}_n=1,& if \left(gamma(1,n)\ge gamma(2,n)\right)\\ X_n=2,& otherwise\end{array}\right.$$

(17)

Therefore, the occupied sub-band signals can be detected by the differentiation for the predicted state; the proposed algorithm can be summarized as the pseudocode in Algorithm 3.

Algorithm 3 Proposed algorithm

1: Inputs: preprocessed PSD $\eta$ as in Equation (8)

2: randomly Initialize the HMM parameters $\varphi$ 3: Initialize EM parameters: iter = 1, maxiter = 100, thre = 1 × 10−4, converge = 0 4: function HMMEM($\eta$, $\varphi$, thre, maxiter) 5:  while(iter $\le$ maxiter $\&\&$~converge) 6:  function fwdback($\eta$,$\varphi$) 7:    return Y 8:  end 9:  update $\varphi$ by the Baum–Welch algorithm 10:   prevlog = −inf 11:   function EMconverge (loglik, prevlog, thre) 12:   return converge 13:   end 14:   prevlog = loglik, iter = iter + 1 15:  end 16: gamma is obtained via (16) 17: the hidden state can be determined as (17) 18: The sub-band boundaries $index=diff\left(X\right)~=0$

The sub-band boundaries can be determined by all of the above-mentioned detection algorithms; however, there will be fake noise boundaries for the sub-band at a low SNR. Therefore, the mean power of each detected sub-band signal will be compared with a threshold $T_h$. According to [27], it can be formulated as

$$T_h=Q^{-1}\left(P_f\right)/\sqrt{M}+1$$

(18)

where $P_f$ is the desired false-alarm probability, and M is the number of signal points between the adjacent sub-band.

Therefore, when the mean power of each detected sub-band is above the threshold $T_h$, the signal between the adjacent boundaries is a valid sub-band, and the detection probability is the percentage between the number of valid sub-bands and the number of total sub-bands.

4. Simulation and Experiment Results

The simulation process can be illustrated as shown in the schematic in Figure 6. The generated waveforms include QPSK, QAM, GMSK, and OFDM; each of them includes four sub-band signals. When the waveforms undergo an AWGN channel, the impulse response of the channel is 1; the waveforms are impaired by the Rayleigh fading response under a Rayleigh channel in [19]. The noise is added according to the SNR. The performance metrics are evaluated in terms of sub-band detection probability and the estimation accuracy of carrier frequency.

In most acquisition systems, the received signals are intermediate frequency (IF), which are down-converted by the local mixers. Without loss of generality, it is assumed that the radio carrier frequencies are 810, 820, 830, and 840 MHz, respectively; the corresponding IFs are 10, 20, 30, and 40 MHz. The common simulation parameters include intermediate frequency $f_c$, code rate $R_b$, roll-off factor $\beta$, sampling rate $f_s$, and single length L, which are listed in

Table 1. Common simulation parameters.

fc (MHz)	Rb (MHz)	fs (MHz)	β	L
{10, 20, 30, 40}	1	100	0.35	1 × 105

. The number of Monte Carlo simulations is 500 so as to evaluate the detection performance.

In the time-frequency-domain-smoothing process, the length of each segment of the time-domain signal is L/10 with 50% overlap; the frequency-domain window length is 5, and the step is 2, so the signal frequency resolution is 20 KHz.

First, the advantages of preprocessed PSD in the time-frequency domain are manifested in Figure 7. The simulated QPSK signal consists of 4 sub-band signals; the SNR is −10 dB. The original PSD in Figure 7a was obtained by Fourier transform; the preprocessed PSD in Figure 7b was obtained via Equation (9); its detection performance has been improved under a low SNR scenario without increasing the computational complexity by too much.

To make a fair comparison among our proposed algorithm and the other algorithms presented in Section 2, the preprocessed PSD was applied to all of them.

The main drawbacks of the LAD ACC algorithm are that the initial thresholds $T_u$ and $T_l$ are susceptible to SNR variation, especially in a low SNR region. The detection performance of LAD ACC with 4 QPSK sub-band signals is shown in Figure 8; the PSD presented here is the smoothed PSD via Equation (9); $T_u$ and $T_l$ are set as 2.97 and 1.95 as recommended in [26]; these thresholds are used throughout the paper. The detected sub-band signals are within the adjacent black dotted lines. When the SNR is −8 dB, the first sub-band signal, shown in Figure 8a, is split into 2 signals, and the fourth sub-band signal is not detected. However, when the SNR is −7 dB, the 4 sub-band signals can be all correctly detected.

There are three predetermined parameters to implement the DLE algorithm: the thresholds $V_d$ and $V_f$ and the maximum search bandwidth $B_{\max }$. The DLE algorithm is sensitive to the $B_{\max }$. The DLE detection for QPSK signals is presented in Figure 9 as an example; the imposed SNR is −5 dB; $V_d$ and $V_f$ are set to 2.94 and 0.28, as in [4]. In Figure 9a, the maximum search band is shown as set to 1.5 MHz; the 4 sub-band signals can be correctly detected; the maximum search band is 1.3 MHz in Figure 9b; only the second sub-band signals can be correctly detected.

The choice of wavelet basis has a significant impact on the detection performance of the Modified CWT algorithm. The detection performance of Modified CWT is presented in Figure 10 as an example; the imposed SNR is −10 dB; the mexh wavelet in Figure 10a gives a right detection. However, the coif4 wavelet in Figure 10b cannot detect the first two sub-band signals. In line with [6], mexh will be chosen as the wavelet basis throughout the paper.

The proposed algorithm does not need any predetermined parameters. The simulated signal comprises 4 OFDM signals at −10 dB; Figure 11a shows the result under an AWGN channel. Figure 9b shows the result with a Rayleigh fading channel; the maximum Doppler offset is 15 Hz; it can be seen that both of them can detect the sub-band signals correctly; however, the amplitude of the signal in Figure 11b drops about 1 dB compared to that in Figure 11a. It can be inferred from Figure 1 that the detection performance will degrade greatly when the Doppler offset is outside of a certain range.

The ROC [28] is universally utilized to characterize the detection performance in terms of false-alarm probability and detection probability.

The ROC curves of the considered signals are depicted in Figure 12. The imposed SNR is −13 dB under an AWGN channel, as illustrated in Figure 12. The ROC curves of different detection algorithms indicate a consistent detection performance, regardless of modulation formats. It can be also observed that none the detection models behave well enough. When the false alarm probability is 0.1, the detection probability of the proposed algorithm is about 43%, which is 12% higher than that of Modified CWT. Not all of the detection models can be applied in practical situations at this SNR.

A single metric called the “area under curve” (AUC) [29], in accordance with that shown in Figure 12, is extracted to characterize the detection performance. The AUCs of the different detection models at −13 dB are listed in

Table 2. Results of the AUC for different detection algorithms.

Detection Algorithms	Proposed	Modified CWT	LAD ACC	DLE
AUC	0.7656	0.7084	0.6767	0.5753
	0.7610	0.7023	0.6665	0.5627
	0.7534	0.6954	0.6666	0.5620
	0.7624	0.6997	0.6723	0.5667

. The AUC values of each detection algorithm corresponds to the modulation format, as shown in Figure 12. It can be seen that the AUC values are almost identical for a given detection algorithm for the four modulation formats; for the sake of brevity, only the detection performance of QPSK will be presented henceforth. In fact, this also holds for the other modulation formats we describe here.

The ROC curves at −10 dB SNR are also presented in Figure 13; the proposed algorithm shows the highest performance, and the Modified CWT also shows a good detection performance. When the false-alarm probability is 0.01, the proposed detection probability is 94%, which satisfies the specified 90% detection probability, as required by IEEE 802.22 for spectrum sensing [30]. There is a distinct performance improvement compared with the AUCs in the first row of Table 2; the AUCs of the detection models here are 0.9957, 0.8992, 0.9852, and 0.7321, respectively.

The relationship between detection probability and SNR values is shown in Figure 14; the false-alarm probability is set to 0.01. It can be shown that the proposed algorithm has a distinct advantage in a low SNR region. When the SNR is −5 dB, the detection probabilities of all of the detection models are 100%; the detection algorithms can all detect the sub-band signals reliably.

Another evaluation metric is the estimation accuracy of carrier frequency; the estimated carrier frequencies can be obtained immediately via Equation (12), which can be helpful for blind demodulation.

The carrier-frequency estimation accuracy of different detection algorithms at SNR = −5 dB under the AWGN channel are presented in

Table 3. Results of the carrier-frequency estimation accuracy.

Detection Algorithms	Proposed	Modified CWT	LAD ACC	DLE
Average (MHz)	9.97	9.98	9.98	9.98
	19.98	19.98	19.98	20.00
	29.97	29.98	29.98	29.97
	39.97	39.98	39.98	39.95
Standard Derivation (KHz)	0.63	9.57	10.98	78.75
	1.95	8.71	12.70	93.49
	0.63	8.78	12.80	83.33
	1.67	9.74	9.15	101.99

. The real carrier frequencies of the 4 sub-band signals are 10, 20, 30, and 40 MHz. Considering our spectrum resolution is 20 KHz, the carrier-frequency estimation errors of the detection algorithms are within 3 times the spectrum resolution; it can also be noticed that the proposed algorithm has the smallest standard derivation, indicating a more robust level of carrier-frequency estimation as compared with the other detection algorithms.

The above-shown detection performance under the AWGN channel is a baseline used to address the impact under a fading channel. The Rayleigh fading channel with AWGN is investigated here to research performance degradation.

The detection performance under a flat fading channel with a maximum Doppler offset f_D is shown in Figure 15. The false-alarm probability is 0.01. When f_D is 30 Hz, the detection probability at −10 dB of the proposed algorithm is still above 90%; however, when f_D increases to 50 Hz, a distinct drop can be observed, from 94% to 70%; therefore, it can endure the Rayleigh channel with a Doppler offset to some extent.

Real data acquired from the Starlink satellite is also utilized to test the detection performance in real-time. The sample rate is 2.4 GHz; the acquired signals are segmented into 500 frames; each frame has a length of 1 × 10⁴; the original radio frequency spectrum is presented in Figure 16.

It can be seen that there are 4 sub-band signals in the observed spectrum; the SNRs of these signals are all above −5 dB; in fact, the SNR of each sub-band can be estimated according to [31]; the mean SNRs of the sub-band for the 500 signal frames are 8.9, 17.1, 37.3, and 7.6 dB. The spectrum resolution is 4.8 MHz.

The parameters of the detection algorithms are all the same as before, except that the maximum search band of the DLE is extended to 200 MHz according to the observed wideband sub-band shown in Figure 16. The detected sub-band channels of the algorithms are shown in Figure 17; this also holds for the other detection algorithms; the spectrum in the solid blue line is the smoothed PSD; the spectrum between the adjacent black dotted lines is the detected sub-band; the spectrum between the sub-band signals is the white space, which can be allocated to secondary users if necessary.

Since the SNR of all 4 of the sub-bands are well above −5 dB, the detection probabilities of all of the algorithms are 100%. The overall detection performance is listed in

Table 4. Overall detection performance of different algorithms.

Detection Algorithms	${\widehat{\mathit{f}}}_{\mathit{c}}$ (GHz)	$\mathit{\sigma }\left({\widehat{\mathit{f}}}_{\mathit{c}}\right)$ (MHz)	${\mathit{P}}_{\mathit{d}}$	$\overline{\mathit{T}}$ (ms)
Proposed	14.36, 15.03 15.30, 15.42	1.77, 1.92 1.77, 2.18	1	1.77
Modified CWT	14.35, 15.04 15.31, 15.44	9.85, 2.20 3.14, 4.19	1	1.59
LAD ACC	14.36, 15.04 15.31, 15.42	1.78, 2.19 4.19, 4.04	1	0.67
DLE	14.37, 15.04 15.31, 15.42	4.62, 1.93 2.37, 5.88	1	6.48

. ${\widehat{f}}_c$ is the estimated carrier frequencies of each of the 4 sub-band signals; $\sigma \left({\widehat{f}}_c\right)$ is the standard derivation of ${\widehat{f}}_c$; $P_d$ is the detection probability; and $\overline{T}$ is the mean detection time for the 500 signal frames.

It can be seen in Table 4 that the proposed algorithm has a moderate level of computational complexity with the lowest carrier-frequency-estimation error; the DLE algorithm has the highest complexity, and LAD ACC has the lowest complexity.

From the above analysis, we can see that the advantage of the proposed algorithm is its superior detection performance in the low SNR region without any predetermined parameters, and it can also be applied in real-time.

5. Discussion

A novel, blind, detection for wideband spectrum sensing is proposed for the purpose of reliably detecting the non-overlapped sub-bands within the wideband spectrum without setting some predetermined parameters. It has been demonstrated that the proposed algorithm outperforms energy detection algorithms, such as LAD ACC and DLE under the AWGN channel and a moderate Rayleigh fading channel, as well as the wavelet-based detection algorithm. First, the proposed algorithm is a totally blind detection without extra, handcrafted, prior parameters, implying its potential application under non-cooperative scenarios. Secondly, the proposed algorithm can achieve a 94% detection probability at −10 dB SNR; it indicates a huge detection advantage in the low SNR region and gives an accurate carrier-frequency estimation with high stability over other detection models in the non-cooperative context. Thirdly, the acquired Starlink data validate its real-time application with a moderate complexity and a more stable carrier-frequency estimation. Last but not least, the proposed algorithm can only tolerate the Doppler offset within a small range; future work can be accomplished by utilizing some channel-estimation methods to compensate for the impact of the Doppler offset, which can counterbalance the adverse impact imposed by the Doppler offset. Therefore, the detection performance under the Rayleigh channel with the Doppler offset will hopefully be further improved.