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Non‐cooperative burst detection and synchronisation in downlink TDMA‐based wireless communication networks

2019; Institution of Engineering and Technology; Volume: 13; Issue: 7 Linguagem: Inglês

10.1049/iet-com.2018.5536

1751-8636

Maryam Zebarjadi, Mehdi Teimouri,

Distributed Sensor Networks and Detection Algorithms

IET CommunicationsVolume 13, Issue 7 p. 863-872 Research ArticleFree Access Non-cooperative burst detection and synchronisation in downlink TDMA-based wireless communication networks Maryam Zebarjadi, Maryam Zebarjadi Information Theory and Coding Laboratory, Faculty of New Sciences and Technologies, University of Tehran, IranSearch for more papers by this authorMehdi Teimouri, Corresponding Author Mehdi Teimouri mehditeimouri@ut.ac.ir orcid.org/0000-0003-4662-5535 Information Theory and Coding Laboratory, Faculty of New Sciences and Technologies, University of Tehran, IranSearch for more papers by this author Maryam Zebarjadi, Maryam Zebarjadi Information Theory and Coding Laboratory, Faculty of New Sciences and Technologies, University of Tehran, IranSearch for more papers by this authorMehdi Teimouri, Corresponding Author Mehdi Teimouri mehditeimouri@ut.ac.ir orcid.org/0000-0003-4662-5535 Information Theory and Coding Laboratory, Faculty of New Sciences and Technologies, University of Tehran, IranSearch for more papers by this author First published: 01 April 2019 https://doi.org/10.1049/iet-com.2018.5536Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Blind signal detection is very important in various applications such as cognitive radio, spectrum surveillance, and eavesdropping. This gets trickier when one needs to deal with burst signals (as opposed to continuously transmitted signals) in non-cooperative environments. Here, existing methods for signal detection are studied and developed to use for burst detection. For the special case of downlink time division multiple access (TDMA) burst transmission, performances of these detection methods are improved by proposing a blind synchronisation algorithm which is applied to the output result of detection algorithms. The results of Monte–Carlo simulations demonstrate the performance of the proposed detection and synchronisation algorithms. 1 Introduction Blind signal identification is an important research topic in modern telecommunication technology. Nowadays, non-cooperative signal processing is one of the essential necessities in the design of intelligent receivers [1]. Blind signal detection, blind modulation recognition, and blind channel code reconstruction are three fundamental steps in non-cooperative receivers [2]. Signal detection is the first step in such receivers. All the subsequent steps rely on the results of signal detection phase, so an intelligent receiver must be equipped with an accurate signal detector. Various signal detection methods have been proposed and utilised in different applications. In spectrum sensing technology, various sensing methods are proposed [3]. Energy Detector (ED) is the simplest and the most popular algorithm. In this method, the receiver measures the received signal energy and compares it with a threshold that depends on the noise level [4-12]. ED method does not need to know any information about the signal and the fading channel. However, this method needs to estimate the noise level. As a result, a small error in the estimation of noise level affects the detection result. Methods based on covariance matrix and eigenvalues are proposed for resolving this issue. Signal detection based on the eigenvalues of covariance matrix is investigated by various papers [3, 13-16]. In [17], maximum eigenvalue detector (MED) is proposed. The authors of [18] have suggested the ratio of the maximum eigenvalue to the minimum eigenvalue detector. Cyclostationary features are also proposed for signal detection [19, 20]. However, when the noise is stationary, ED methods outperforms cyclostationary-based methods [21]. Matched filtering detector (MFD) is also considered for signal detection in [22, 23]. MFD has higher accuracy in low signal-to-noise ratio (SNR) conditions, and it is more robust to noise-level uncertainty. However, MFD needs specific knowledge about the transmitted waveform patterns which is the drawback of the method in blind situations. For comprehensive comparisons between various signal detection methods, the reader is referred to [21, 24]. In all the above-mentioned methods, signal-detection process is modelled as a binary hypothesis testing. The null hypothesis is the situation in which only noise is present and the alternative hypothesis is the situation in which signal is received in a noisy environment. This hypothesis testing is suited for environments in which continuous signal is transmitted. Signal detection gets more complicated when one needs to deal with burst signals (as opposed to continuously transmitted signals). In this situation, signal detection is not accomplished only by checking the presence or absence of the signal. In this case, it is also necessary to determine the exact position of bursts. In communications based on burst signals, different users transmit their burst information by using a radio channel and each burst conveys a data packet to a particular receiver. In order to prevent the interference between adjacent bursts, a guard time is usually considered between them. In a non-cooperative environment, the position of the bursts and the guard times must be exactly determined by the receiver without any prior knowledge about signal. So, we can define blind detection of burst signals as determination of the beginning and ending time of all bursts. Since the received signal may contain bursts with different lengths, an efficient detector should have the ability to detect bursts of different lengths. It also should detect very short guard times. Transient signal detection is a concept which is very relevant to burst detection. Transient signal detection arises in applications such as telemetry and spread spectrum communications. Transient signals are generally considered as short duration signals compared to the observation time. The aim of transient signal detector is to decide whether the observation consists of noise alone or the signal is embedded in noise [25-27]. Various detection schemes have been proposed for this purpose. Selecting an appropriate detection method depends on the amount of knowledge that is available to the detector. Such knowledge includes the arrival time of transient signal, the duration of the transient signal, and the waveform shape of the signal. For instance, matched filtering is the optimal method if the transient signal is known. When the transient signal is partially known, an often used procedure is the likelihood ratio test (LRT). When the signal to be detected is unknown, energy-based detectors become the only choice [25]. In [26], the performance of transient detection based on higher order moments is investigated and a detector based on the third-order absolute moment is proposed. Order statistics (OS)-based signal processing is also applied to transient detection, and it is shown that the duration of an unknown transient signal can be estimated by use of OS technique [27]. In [28], a method based on permutation entropy is introduced for recognition of starting time of a transient signal. GSM signal is used for evaluating the performance of this detection technique where each time slot is considered as a transient signal. Since there is no information available about the frame structure and time slots in a non-cooperative environment, the above-mentioned methods for transient signal detection are not applicable. Moreover, existence of multiple bursts with different lengths is not considered in transient signal-detection formulation. Here, transient signal detection model is generalised and solved for the problem of burst signal detection. In wireless telecommunication networks, burst transmission is usually employed in two different scenarios: first when a contention-based channel access is used in the network (e.g. in IEEE 802.11 [29]) and second when a time division multiple access (TDMA) scheme is implemented (e.g. in GSM standard [30]). Many researches have been done on design of a receiver for TDMA signals in a cooperative environment. For example, the structure of receiver in satellite telecommunications is investigated in [31]; frame and burst acquisition in TDMA satellite communication networks via unique word pattern is considered in [32]; data detection for burst mode signal via polynomial interpolation is proposed in [33]. In [34], energy ratio detector (ERD) is employed for recognition of bursts. However, like all the other methods, it is assumed that the structure of the received signal is known to the receiver. We define burst detection as a problem in which the aim is to find the start and the end of all bursts (i.e. data packets) in an eavesdropped signal. In other words, burst detection can be seen as a generalised transient detection problem where there is more than one transient in the received signal. Besides, the lengths of transients are assumed to be unknown. Despite the importance of this problem, to the best of authors' knowledge, no solid published research is available for blind burst detection in non-cooperative environments. In burst detection context, there are only some rudimentary published researches. For example, in [35], fluctuations of autocorrelation function are used to detect burst signals. The idea is that the autocorrelation function has higher values when the received signal includes burst compared to when only noise is present. However, neither Monte–Carlo simulations nor any performance criterion are presented. Here, autocorrelation detector (ACD), ED, ERD, and maximum to minimum eigenvalue detector (MMED) are modified and generalised for solving the problem of burst detection. The performance of these methods is measured in different scenarios via Monte–Carlo simulation. Despite the acceptable accuracy of the detectors, for the special case of downlink TDMA burst transmission, the performance of detection methods is improved by proposing a blind synchronisation algorithm based on the regularity of the bursts in downlink TDMA structure. The proposed synchronisation algorithm is an iterative algorithm which is applied on the initial detection. The results of simulations demonstrate that the synchronisation algorithm can improve the results of initial detection of ED, MMED, ACD, and ERD. It should be noted again that the problem investigated here is different from the cooperative (i.e. non-blind) TDMA synchronisation in which the TDMA structure and synchronisation patterns are known to the receiver [31-33, 36-38]. In fact, in cooperative communications, some additional bits or specific patterns are generally embedded in the bursts to help the authorised receiver for synchronisation. The rest of this paper is organised as follows. In Section 2, signal model is presented. In Sections 3, ACD, ED, ERD, and MMED are generalised and developed for burst detection. In Section 4, a blind synchronisation algorithm is proposed for downlink TDMA signals based on the regularity of bursts in downlink TDMA structure. Simulation results are presented in Section5. Finally, the paper is concluded in Section 6. 2 Signal model Consider a wireless communication network which employs a burst-mode data transmission scheme. In such network, each user transmits its packets by means of some bursts. The bursts are distributed according to either a predefined rule (e.g. TDMA) or a contention-based channel access method. Assume that the received (i.e. eavesdropped) signal is sampled at a specific sampling rate. So, in burst i, noisy signal samples are received. Usually, a guard time is considered after each burst in order to prevent transmitted bursts from different users overlapping due to different path delays. Assume that the length of guard for burst i is samples. Also, assume that samples are received (i.e. eavesdropped) and there exist bursts in these observations ( depends on ). So, the received signal samples can be modelled as (1)where () are samples of independent complex additive Gaussian noise with known variance per real dimension. Moreover, the values of () are the samples of received bursts. Note that, in this model which is the generalised form of the model proposed in [26] for transient signal detection, bursts samples are aggregated into a single stream . If and the samples of are considered to be consecutively transmitted, transient signal model is obtained. In both predefined and contention-based channel access methods, the number of transmitted bursts may be less than the maximum available bursts. For example, in TDMA channel access method, a user may or may not have a packet to send in its pre-allocated time slots. For TDMA, we define channel occupancy rate (COR) as follows (2)Usually, in TDMA channel access method, the length of all bursts (and likewise the length of all guards) are assumed to be equal. In other words, and for . The aim of the blind receiver is to obtain the values of and the exact position of the bursts in the received samples . In other words, a blind receiver should estimate the start and the end of all bursts (i.e. data packets) in an eavesdropped signal. By using a binary function (denoted by ), the position of bursts can be defined as follows: for the samples corresponding to the bursts, the value of is 1; and for the samples corresponding to the guard times (i.e. noise-only samples), the value of is 0. If we define dummy signal samples corresponding to noise-only samples in (1), we can rewrite (1) as (3)where (4)We call the reference burst position indicator. Let us denote the estimation of the blind receiver about by . In ideal receiver, for . However, in practical situations, and may not be identical functions (see Fig. 1). We propose to use Dice similarity coefficient [39] for evaluating the accuracy of the blind burst detector. Since and are binary functions, we can write Dice similarity coefficient between and as (5) Fig. 1Open in figure viewerPowerPoint Example of dissimilar and It is obvious that in the case of error-free estimation, we have . We can express Dice similarity coefficient in percentage if we multiply both sides of (5) by 100. Although Dice similarity coefficient is a good criterion for evaluating the accuracy of the detector, it is not sufficient. For example, consider a burst signal with very short guard times. If the detector cannot detect the guards in this case, the value of Dice similarity coefficient is still high due to the large number of bursts samples in the signal. So, we employ two other metrics here: error in burst detection and error in guard detection. The error in burst detection, which is denoted by and it is simply called burst error, is obtained by dividing the number of burst samples identified as noise-only samples by the total number of burst samples. Similarly, the error in guard detection, which is denoted by it is simply called guard error, is obtained by dividing the number of guard samples identified as burst samples by the total number of guard samples. 3 Burst detection methods As mentioned earlier, there are many well-known methods for detecting the presence of signal. In this section, four approaches ERD, ED, MMED, and ACD are generalised and developed for burst detection problem. 3.1 Energy ration detector (ERD) ERD utilises the changes in the energy ratio of two adjacent time windows in order to find the burst position function (i.e. ). Let us consider two adjacent windows W1 and W2 with the same length L and slide them along the received signal. Since in the beginning and in the end of the bursts, the energy of the signal changes more intensely, we expect that the ratio of the energies in W1 and W2 take very small or very large values at these boundary points (see Fig. 2). Fig. 2Open in figure viewerPowerPoint ERD functions for finding start and end time of bursts The energy ratio of the first window to the second window is very large when the first window is located entirely in the burst and the second window is placed completely in the guard. On the other hand, at the end of the bursts, this ratio is very small. So, we can employ inverse of this ratio for finding the ending times. In fact, the ratios (6)and (7)are used for locating the start and the end points of bursts, respectively. As it can be seen in Fig. 2, a threshold must be defined in order to locate bursts. Assume that the power of the received signal samples in burst durations is constant and equal to . Moreover, according to (1), the power of noise samples is equal to . So, in the start and in the end points of the bursts, the ratio of energies in the adjacent windows are approximately equal to (8)where SNR is the signal-to-noise ratio in the bursts. We propose to employ (9)as the threshold value for detection, in which is the parameter of the ERD algorithm. ERD algorithm can be described as follows. First, the points of both functions of (6) and (7) with a value higher than the threshold are considered as the set of candidates for the start points (denoted by ) and the set of candidates for end points (denoted by ), respectively. The sets and E are processed as follows. In each neighbourhood of L samples, if there are more than one candidate points in , only the candidate with the maximum value of is kept in the set. Similarly, in each neighbourhood of L samples, if there are more than one candidate points in , only the candidate with the maximum value of is kept in the set. In the next step, by starting from the smallest element in , the closest point from with the condition is selected and the detector labels the presence of burst in . Then, in addition to removing and from and , respectively, all the elements in which are smaller than are removed from . If there is no in with the condition , in is removed and no burst will detect corresponding to this point. This process is repeated until is empty. ERD algorithm is shown in Algorithm 1 (see Fig. 3) Fig. 3Open in figure viewerPowerPoint Algorithm 1: ERD algorithm for burst detection In general, since the detection is performed in the non-cooperative environment, there is no prior information about the lengths of the bursts and the guards. Assume that the length L is less than the burst length. So, during the computation of and , one of the following events may occur: Both adjacent windows are entirely in burst samples or they are completely in guard samples. One of the windows includes only guard samples and the other window includes only burst samples. There is only one transition (from 0 to 1, or vice versa) in corresponding to the samples of one of the windows. There are more than one transition in corresponding to the samples of one of the windows. There are no challenges in the case of events i and ii. In fact, most of the detection errors occur when event iii or event iv take place. Error in case iii causes the burst length be estimated larger or smaller than its real length. Event iv occurs when the guard length is too short compared to the window length L. In this case, the detection algorithm may miss the guard and label the noise-only samples as the burst samples. As a result, the length of the sliding window has a great influence on the accuracy of detection. In fact, if the received signal contains short bursts and guards, a short window length should be selected in order to achieve effective detection. On the other hand, short window lengths can lead to many false spikes (i.e. false burst detection) in the detection result , especially in low SNR values. In the latter case, a larger window is not capable of detecting short guards, but it is more suitable for detecting bursts. With regard to above-mentioned issues, we propose to run ERD algorithm with different values of L. Assume that an upper bound on the burst length is known. First we run ERD algorithm with a short window length that is comparatively very smaller than this upper bound. Then, we run ERD algorithm with a long window length that is in order of the upper bound on the burst length. We denote the detection results of these two window sizes by and , respectively. We expect that detects the short guards but it may lead to some false spikes in detection. Accordingly, confirms the bursts presence with more certainty. Combination of these two detections can help us to achieve a better detection result. We propose to use as the combined detection result. In Fig. 4, the proposed method is illustrated. In Fig. 4a, a QPSK modulated signal with raised-cosine pulse shaping is received. The sampling rate is 10 samples per symbol and SNR = −2 dB. The length of bursts varies from 40 to 50 information bits. The length of guards also varies from 2 to 3 bits. First, ERD algorithm is run with L = 10 samples and . The result is achieved which is shown in Fig. 4b. As it can be seen in this case, the detector can detect the short guard time between the two last bursts; however, a falsely detected burst is revealed. The Dice similarity coefficient for the detector is 0.94 in this case. Moreover, and are 0 and 0.09, respectively. In the next step, ERD algorithm is run with L = 100 samples and . The result is achieved which is shown in Fig. 4c. As it can be seen, misses the short guard; however, the presence of bursts are detected efficiently. The Dice coefficient for is 0.98. Moreover, and are 0 and 0.01, respectively. As it is obvious in Fig. 4d, combined result improves the detection result. Dice similarity coefficient for the combined detection is 0.99. The values of and in this case are 0 and 0.007, respectively. In other words, in this example, none of the samples of the bursts are missed. However, a few number of guard samples are detected as burst samples. In Section 5, the performance of the algorithm is evaluated through Monte–Carlo simulations. Fig. 4Open in figure viewerPowerPoint Burst detection by ERD (a) Received signal and reference burst position function, (b) Detection result of window length 10, (c) Detection result of window length 100, (d) Combined detection results 3.2 Energy detector (ED) In general, in ED, the received signal energy is compared with a threshold that depends on noise variance [21]. This method does not need any prior information about signal and is known to have a low computational complexity. We propose to use a sliding window with length L samples in order to make a binary decision about each sample; that is, determine that the sample is a noise-only sample or a burst sample. We start with . When the value of energy in the sliding window is greater than a threshold , increment operation is performed for all the samples j in the sliding window. Finally, when the sliding window reaches to the end of the signal samples, we set for values of k with . In other words, the majority voting mechanism is employed for labelling each point in . In order to determine the decision threshold , we aim to bound false alarm probability. A false alarm occurs when all samples in the window are noise-only, but the window energy is greater than threshold . If we denote false alarm probability by , by using central limit theorem, we can write [40] (10)where . ED algorithm is shown in Algorithm 2 (see Fig. 5). Fig. 5Open in figure viewerPowerPoint Algorithm 2: ED algorithm for burst detection Same as the case for ERD, assume that an upper bound on the burst length is known. First we run ED algorithm with a short window length that is comparatively very smaller than this upper bound. Then, we run ED algorithm with a long window length that is in order of the upper bound on the burst length. We propose to use as the combined detection result. This method is also employed for the detectors proposed in following subsections. 3.3 Maximum to minimum eigenvalue detector (MMED) Covariance matrix of the received signal is introduced to resolve the deficits of energy detector [21]. When covariance matrix is employed for signal detection, there is no need to estimate the noise level. Consider the following vectors for consecutive samples of the signal: (11) (12) (13)where superscript T denotes the matrix transpose. Covariance matrices for the above-defined vectors can be written as (14) (15) (16)where is identity matrix with size and superscript H denotes the matrix conjugate transpose. It can be easily seen that (17)The ratio of the maximum eigenvalue to the minimum eigenvalue of the covariance matrix can be used as a measure of signal presence [18]. Assume that and are the maximum eigenvalues of and , respectively. Also, assume that and are the minimum eigenvalues of these covariance matrices. Using (17), it can be shown that (18) (19)It is obvious that when the observations are noise-only samples, we have . So if there is no signal in observations, then , otherwise . Therefore, by defining a threshold value , we can say that if , signal is present. The threshold value can be determined according to the false alarm probability. Now, let us return to the problem of burst detection. We start with . Consider a sliding window of length L samples from the signal model in (1). Denote these samples by , , …, . For these samples, we can write the elements of the sample autocovariance matrix of as follows (20)where . We denote the maximum and the minimum eigenvalues of by and , respectively. If , we can assume that signal is present. In this case, the increment operation is performed for all the samples j in the sliding window. If the false alarm probability is , we can write [17] (21)where is the cumulative distribution function (CDF) of Tracy–Widom distribution of order 2. Finally, when the sliding window reaches to the end of the signal samples, we set for values of k with . In other words, the majority voting mechanism is employed for labelling each point in . MMED algorithm is shown in Algorithm 3 (see Fig. 6). Fig. 6Open in figure viewerPowerPoint Algorithm 3: MMED algorithm for burst detection 3.4 Autocorrelation detector (ACD) Sample autocovariance values in (20) can be used in another way to determine if the observed samples in a window are noise-only. Consider a sliding window of length L samples from the signal model in (1). Denote these samples by , , …, . For these samples, compute the sample autocovariance values of for and using (20). It is obvious that there are only unique values , , …, among these sample autocovariance values, since the value of depends only on . The sample autocorrelation values can be written as follows (22)If the observed samples , , …, are noise-only samples, we expect that the values of are independent and normally distributed with mean 0 and variance [41]. This means that for large values of L, we expect that the sample autocorrelation values are very small. On the other hand, for burst samples, we expect that autocorrelation values are larger compared to noise-only samples. We propose to consider only . So, if the value of is larger than a predefined threshold , we assume that the observed samples in the current window are burst samples. If we denote false alarm probability by , we can write (23)ACD algorithm is shown in Algorithm 4 (see Fig. 7). Fig. 7Open in figure viewerPowerPoint Algorithm 4: ACD algorithm for burst detection 4 Downlink TDMA burst synchronisation As stated in the previous section, by employing one of the developed detectors ERD, ED, MMED, and ACD, burst signals can be detected as the binary function . In the special case of Downlink TDMA burst transmission, the obtained can be improved. In this section, we propose a blind synchronisation algorithm which is applied to the outputs of the developed detection algorithms. This iterative algorithm which works based on the regularity of the bursts in downlink TDMA structure improves the performance of the detection algorithm. Since the initial detection is performed in non-cooperative environment, the synchronisation algorithm must also perform in the same situation. As in downlink TDMA transmission, the bursts have the same lengths and they follow a regular pattern, the aim of the blind synchroniser is to find the closest TDMA structure to the detected . In such a regular and arranged structure, the distance between the starting times of successive bursts is an integer multiplication of the time slot duration. Let us denote the estimation of the blind synchroniser about by . In fact, the blind synchroniser takes as its input and obtains . For a perfect synchronisation, we expect . TDMA burst structure can be defined with three parameters: one of the start times of bursts denoted by , time slot duration denoted by , and burst duration denoted by . We call such TDMA structure, a structure. It is obvious that . The proposed iterative algorithm is as follows. First, the most frequent value among burst lengths is selected as the initial burst length . Moreover, the starting time of the first burst with length is selected as the initial start time . In order to set , we perform the following method. For each possible value of