Low‐cost message‐driven frequency‐hopping scheme based on slow frequency‐hopping
2018; Institution of Engineering and Technology; Volume: 12; Issue: 4 Linguagem: Inglês
10.1049/iet-com.2017.0390
ISSN1751-8636
AutoresBen Ning, Da Zhong, Lei Guan, Zan Li,
Tópico(s)Advanced Wireless Communication Techniques
ResumoIET CommunicationsVolume 12, Issue 4 p. 485-490 Research ArticleFree Access Low-cost message-driven frequency-hopping scheme based on slow frequency-hopping Ben Ning, Ben Ning State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071 People's Republic of ChinaSearch for more papers by this authorDa Zhong, Da Zhong Data Communication Technology Science and Research Institute, Beijing, 100191 People's Republic of ChinaSearch for more papers by this authorLei Guan, Lei Guan State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071 People's Republic of ChinaSearch for more papers by this authorZan Li, Corresponding Author Zan Li zanli@xidian.edu.cn State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071 People's Republic of ChinaSearch for more papers by this author Ben Ning, Ben Ning State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071 People's Republic of ChinaSearch for more papers by this authorDa Zhong, Da Zhong Data Communication Technology Science and Research Institute, Beijing, 100191 People's Republic of ChinaSearch for more papers by this authorLei Guan, Lei Guan State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071 People's Republic of ChinaSearch for more papers by this authorZan Li, Corresponding Author Zan Li zanli@xidian.edu.cn State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071 People's Republic of ChinaSearch for more papers by this author First published: 26 February 2018 https://doi.org/10.1049/iet-com.2017.0390Citations: 7AboutSectionsPDF 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 This study presents a novel message-driven frequency-hopping (MDFH) scheme leveraging slow frequency-hopping (FH). Since the typical MDFH scheme requires a large amount of detectors to obtain the information that is transmitted through carrier frequency selection, the authors aim at a low-cost MDFH implementation in this study. The basic idea of the proposed FH scheme is to transmit a part of information through the hop rate instead of the carrier frequency selection of an FH signal, which results in reduced hardware cost and better system efficiency. Moreover, a collision-free multi-carrier extension is also introduced in this study. The lower bound on the bit error rate (BER) performance of the proposed scheme is analysed and is verified by numerical results. The numerical results also reveal that the proposed scheme has a better BER and throughput performances than the typical MDFH systems at a low signal-to-noise ratio. 1 Introduction As a well-known spread-spectrum technique, frequency-hopping (FH) is widely used in a variety of military and civilian applications [1]. FH systems can provide secure communication links in the presence of jammings and eavesdroppers since they ramdomly switch their channels based on FH sequences (FHS) [2]. To ensure the communication performance, a great number of channels are adopted in practical FH systems, for example, Bluetooth uses 79 distinct channels [3]. However, in conventional random FH systems [2], each channel is assigned only a relatively narrow bandwidth due to bandwidth limitations of analogue devices. There is no doubt that such an assignment leads to a low data rate in communications [4]. Thus, with the ever-increasing demands of high data rate within a limited bandwidth [5–7], improving the system efficiency of such FH systems is of great importance. In this paper, we propose a novel FH scheme that can improve the system efficiency with low-cost hardware implementation. To increase the system efficiency of the conventional random, a fast FH-based message-driven FH (MDFH) scheme was proposed in [8]. It was reported in [4] that the typical MDFH scheme can significantly increase the system efficiency without extra cost on either bandwidth or power over additive white Gaussian noise (AWGN) channels. Recently, in [9, 10], an extention of the MDFH named multi-carrier anti-jamming MDFH (MC-AJ-MDFH) scheme was proposed and analysed. The MC-AJ-MDFH not only achieves better spectral efficiency and multiple access ability, but also reduces the performance degradation which is caused by jamming [9]. For mobile communications, an MDFH extension which is based on orthogonal frequency division multiplexing was studied in [11]. The basic principle of the MDFH scheme is to convert a part of its data bits referred to as the carrier bits to its FHS. Consequently, the carrier bits can be transmitted through carrier frequency selection at the transmitter, and can be demodulated by a channelised detector at the receiver, which is similar to the structure of a multiple frequency-shift keying system. The ordinary bits are transmitted using conventional modulation schemes. Note that only one carrier symbol is transmitted over a hop, and the carrier symbol rate is equal to the hop rate. The great advantages of the MDFH are the ease of frequency synchronisation and the increment of the system efficiency [9]. Typically, the system efficiency is determined by the number of available channels and the hop rate of the system. However, the hop rates of practical FH systems are still limited by the switching speed of their frequency synthesiser. For example, Link 16 [12], an FH-based tactical data link used by North Atlantic Treaty Organisation (NATO), has a hop rate of 76923 hops/s. This means that a 256-channel MDFH system that works at such a hop rate can provide data rate improvement of 76923 bytes/s. Meanwhile, to realise such an MDFH system, a channelised receiver with 256 independent sub-channels needs to be implemented, which is practically intractable for devices that are limited in cost, space or power consumption. By referring MDFH-based schemes, we notice that the basic idea to improve the spectral efficiency of an FH system is to add information to its FHS. Therefore, to deal with these limitations, we alternatively seek for a low-cost approach that utilises the hop rate of the FHS to improve the system efficiency. In this paper, we focus on slow FH systems, which are more preferable than fast FH due to its easy implementation and higher spectrum efficiency. Unlike the typical MDFH scheme that is based on fast FH, we propose a novel MDFH scheme that is based on slow FH. The basic idea of the proposed FH scheme is to make use of the hop rate to transmit information. In the receiver, a detector with only two sub-channels instead of the channelised detector is adopted. The throughput and bit error rate (BER) of the proposed scheme are analysed and simulated. The simulation results show that the proposed scheme not only improves the spectral efficiency, but also significantly reduce the complexity of hardware implementation compared to the conventional fast FH based MDFH scheme. The rest of this paper is organised as follows. Section 2 describes the system model, states our strategy, mathematically formulates the proposed scheme. In Section 3, we analyse the performance of the proposed scheme. Simulation results and discussion are provided in Section 4. Finally, Section 5 concludes this paper. 2 System model In our model, a transmitter and a receiver that are equipped with an omnidirectional antenna are assumed. An original bit stream where '0' and '1' occur with equal probability is formatted into frames, and each frame has size of . The frequency set has K carrier frequencies, and each frequency is marked as a channel with a fixed bandwidth of . Assume that the FHS are known to both of the devices, and for is the lth entry of . The maximal switching speed that our devices allow is , and the minimal hop interval is . Note that for slow FH, it has . The K sub-channels are modelled as AWGN channels with noise power of . The reciprocal of path loss between the two devices is G where . Similar to the MDFH scheme, the original bit stream can be classified into two classes: the ordinary bits and the carrier bits. The ordinary bits are transmitted in the same way as the conventional slow FH, while the carrier bits are transmitted through the dwell time of the carrier. The dwell time is defined as the time during which the symbols are transmitted through a fixed channel. The transmitter and receiver are introduced in Sections 2.1 and 2.2, respectively. 2.1 Transmitter design The structure of the transmitter is shown in Fig. 1, which is similar to the MDFH scheme. We first divide the original bit stream into frames with size of and duration time of which satisifing (1) where is discussed in the left of this paragraph. Let and be the number of hops in a frame and the number of the carrier bits in each block, respectively, the total number of the carrier bits in a frame is . The parameters and are chosen by finding a pair that satisfies For instance, while and . Figure 1Open in figure viewerPowerPoint Structure of the transmitter Then, each block is mapped to a symbol, called carrier symbol, which has a constellation of . Let for denote the carrier symbol that the ith block is mapped to, the dwell time of the lth hop is given as (3) where (4) is the minimal spacing between adjacent carrier symbols. Finally, the waveform of the frame at the transmitter can be describes as (5) where (6) and x(t) is the baseband signal that is generated from the ordinary bits. Without loss of generality, we normalise the signal power of the frame to unity, namely (7) From (5), the carrier frequency with respect to time t can be given as (8) A time–frequency representation of the proposed FH scheme with and is illustrated in Fig. 2. It is proved in Lemma 1 that the hop rate of the proposed FH scheme is guaranteed not to exceed the maximal switching speed . Lemma 1.The propsed FH scheme ensures that the hop rate in each frame is less than or equal to the maximal switching speed . Proof.According to (3) and (4), the minimal dwell time of the ith hop is for , which means that the switching speed of these hops in each frame cannot exceed . From (3), will be minimised if we maximise for each i. Finally, the maximal can be obtained by setting , which will result in (9) Thus, the swithing speed of each hop does not exceed the maximal switching speed. Figure 2Open in figure viewerPowerPoint Example of time–frequency representation of the proposed FH scheme with and For the branch of the ordinary bits, each ordinary bits are mapped to an ordinary symbol with constellation size of M. In this model, we consider constant-modulus constellations where the energy of each symbol is the same since it is hard to distinguish the amplitude of a non-constant-modulus signal for detectors in the receiver [11]. The symbol rate of the ordinary symbols is given as (10) where denotes the largest integer less than or equal to x and is the bandwidth of a single hop. Equation (10) ensures that the numbers of the symbols that are transmitted in each hop are integers. Moreover, we can choose some that satisfy to achieve (11) Therefore, the frame length can be given as (12) and the maximal bit rate is (13) For the case that and , can be approximated by (14) 2.2 Receiver design The receiver structure is shown in Fig. 3. Since the receiver has full knowledge of , a channelised receiver with full sub-channels is unnecessary. For the proposed scheme, the key to demodulating the transmitted signal is to detect the time at which the carrier frequency hops. Obviously, detecting the switching time needs only two energy detectors; one surveils the energy of the current channel, and the other surveils the energy of the next channel based on . Figure 3Open in figure viewerPowerPoint Structure of the receiver Denote the impluse response of the channels as h(t), the received signal of the frame is given as (15) where is AWGN with power of . For Rayleigh fading channels, h(t) is composed of Gaussian random variables. To derive the lower bound of BER performance, we assume that the channel is ideal, i.e. (16) then the baseband signal through the kth channel at the receiver can be expressed as (17) where is statistically independent white Gaussian noise with power of over the kth channel. The signal-to-noise ratio (SNR) per bit [13] at the receiver is defined as (18) First, the received signal is split in blocks, each of length ; hence, with the sampling rate of , each block contains complex samples. The energy of the bth block over the kth channel is given as (19) where is the discrete form of , namely (20) From (3), the possible dwell time is discrete and has a minimal step of , which is equal to the duration time of the blocks. Thus, we rewrite (19) as the form (21) according to (17). Second, to demodulate the carrier symbols, two energy detectors operating at different frequencies are adopted in the receiver. Without loss of generality, we call these two energy detectors as D1 and D2, which are opterating at and , respectively. Since the first blocks in each hop do not carry any carrier symbol, we concern the blocks that are transmitted after the th block. During the ith hop, the energy of the concerned blocks from D1 and D2 are given as (22) and (23) respectively, where is the mth output from D1, is the mth output from D2 and is the demodulated carrier symbol based on the dwell time of the nth hop. It should be indicated that the previous decisions are employed to calculate the start time of the current hop. Third, the carrier symbol is decided by (24) where is a test statistics given as (25) For convenience, we provide a description of (25) in Fig. 4. Figure 4Open in figure viewerPowerPoint Description of the elements that are used in the test statistics Finally, after a carrier symbol is demodulated, we exchange the names of the two detectors, and let D2 switch to channel . Note that the dwell time of the last hop is not considered because the dwell time of the last hop do not carry any carrier symbol. To demodulate the ordinary symbols, M-ary coherent demodulation [13] is assumed in this paper. 2.3 Extension to multi-carrier FH To further improve the system efficiency, we extend out model to a collision-free multi-carrier scheme in this sub-section. In our multi-carrier scenario, assume that there are frames that need to be transmitted, and the transmitter is capable of transmitting P subcarriers where . For convenience, we consider that K is an integer multiples of P, which ensures that the numbers of the channels are the same for each subcarrier. First, a Latin square [14] is constructed by using (26) where is relatively prime to K, x and y, respectively, denote the row and column of the matrix . Then, to fully exploit the frequency diversity, the frequency set of the pth subcarrier in the qth frame is assigned based on (27) where , and . The frequency set is used to assign frequencies in multi-carrier cases. The pth subcarrier in the qth frame is uniformly and randomly selected from . Equation (27) also gives that , which ensures that each subcarrier has at least two choices. Due to the properites of Latin squares, each subcarrier has the same probability of accessing each channel in every K frames, and the subcarriers are transmitted without collision. A simple proof is given as follows. Proof.Due to is a Latin square, each frequency occurs exactly once in each row and exactly once in each column. In our FH model, varies from 0 to during each K frames. Thus, for any , with occupies rows during each K frames. Since the pth subcarrier is uniformly selected from , each subcarrier has the same probability of accessing each channel in every K frames, and the subcarriers are transmitted without collision. Finally, The bit rate of the multi-carrier scheme is given as (28) and the maximum value can be obtained by substituting into (28), which is given as (29) Furthermore, the assignment strategy can be also extended to multi-user cases. 3 Performance analysis 3.1 BER analysis Since for are influenced by the previous decisions according to (22)–(24), the existence of the different dwell time causes memory in carrier symbol transmission. Besides, an error in the carrier bits means the receiver switches its channel at a wrong time, which leads to more errors in ordinary bits. Therefore, it is difficult to give an analytic BER performance of the proposed scheme. For this reason, this paper discusses the lower bound on the BER performance. The errors can be classified into three categories: the ordinary bit error that occurs in conventional transmission, the carrier bit error and ordinary bit error that are caused by incorrect switching time estimations. We first analyse the errors occuring in the carrier bits. For the case that the received signal switch from to at the th possible time where , the outputs of D1 and D2 satisfy (30) and (31) where denotes the non-central chi-squared distribution with x degrees of freedom and non-centrality parameter of y. Due to the complex samples in , the degrees of freedom in (30) and (31) are . Substituting (30) and (31) into (25) gives (32) where denotes the doubly non-central F-distribution [15], which can be obtained by dividing a ramdom variable (RV) that satisfies by another RV that satisfies . Since the analytical result of (33) is difficult to obtain, we use numerical approaches to calculate to show the performance [16]. Suppose that the last carrier symbol is recovered correctly, the probability of a correct carrier symbol decision is obtained as (34) The probability of carrier symbol errors occuring in a frame follows the binomal distribution, which has an expectation of (35) where denotes the expectation operator. Thus, the expectation of the carrier bits errors occuring in a frame, denoted as , is given as (36) according to the results in [13]. Second, we analyse the ordinary bit error that is caused by a wrong switching time. Note that the BER of the ordinary bits is affected by not only errors that occur in conventional transmission but also the errors that are casued by the wrong switching time. For a switching that occurs at the mth possible switching time, there are ordinary symbols that are transmitted between the mth and th possible switching time, which leads to an average of errors in the ordinary bits. As a result, let be number of the ordinary bits error that is caused by a wrong switching time, we have (37) For the ordinary bits that are transmitted in a frame, the expectation of number of errors except the errors caused by the wrong switching time is given as (38) where is the BER of the conventional transmission. Finally, the lower bound on the BER is (39) 3.2 Throughput and hardware complexity A comparison of throughput and hardware complexity of some mentioned schemes is listed in Table 1. It should be indicated that the variables are chosen to maximise the results or to achieve the best case, e.g. we use instead of . The throughput is defined as the maximum bit rate, and the hardware complexity is compared based on the number of receiving channels that are required in a receiver. Table 1 shows that the hardware complexity of the proposed scheme is lower that that of the typical MDFH, and the same result holds for their MC extensions. The comparison of the throughput gives that different schemes make use of different additional parameters to improve their throughput, hence, it is a problem concerned with the hardware configuration. Table 1. Comparison of the maximum throughput and hardware complexity Scheme Throughput Receiving channel(s) proposed 2 proposed with MC extension MDFH [4] K MC-AJ-MDFH [9] K RFH [2] 1 4 Numerical results In this section, the performance of the proposed FH scheme is evaluated and compared with that of the MDFH and conventional FH schemes. First, Fig. 5 is provided to have a straightforward comparison of throughput. The result is based on Table 1 with , and baud. It can be seen that the throughput of the proposed scheme with MC extension is the largest. Since MC extension is employed, the MC-AJ-MDFH scheme also reaches a high throughput among the compared schemes. The throughput of the MDFH scheme is the lowest, which is caused by a low switching speed. Figure 5Open in figure viewerPowerPoint Comparison of the throughput between different systems Second, to show the BER performance of the proposed scheme, we consider a Bluetooth system where , and . The modulation of the conventional transmission is M-ary phase-shift keying with coherent demodulation. The MC extension of the proposed scheme is not tested in simulation because each subcarrier is independent to other, which result in the same BER performance as the scheme without the MC extension. Based on the parameters referred to Bluetooth [3], the simulation set-up of the proposed scheme is listed in Table 2 where we provide three groups of parameters to show the performance of the proposed scheme. The RFH system is configured with . It is known that Bluetooth is based on slow FH, and the parameters are unfair to the MDFH scheme, hence, the parameters for the MDFH system are modified to achieve the same throughput as the group 1, which is given as , and hops/s. Table 2. Simulation set-up Parameter Group 1 Group 2 Group 3 21 21 21 11 11 11 6 6 9 M 4 16 4 The comparison of BER performance is shown in Fig. 6 where both the theoretical lower bound on BER and the corresponding experimental results are provided. In Fig. 6, the RFH system has the same performance as the group 2. The reason is that the bit rate of the carrier bits is relatively slow, thus making difficult to be interfered by noise. In other words, almost all carrier bits are correct in these cases, and the BER is mainly dependent on the constellation size M. The same conclusion holds for the result of group 1 and group 3. In group 3, since the system is configured with instead of , the bit rate of the carrier bits is higher than that of the group 1, which leads to a lower SNR per bit, thus, increasing the BER. Although the BER of the RFH and group 2 are the same, the throughput of group 2 has an improvement of 4571.4 bits/s. The BER of the MDFH system is larger than the result of the group 1 at a low , but decreases rapidly at . Moreover, it is obvious that all the experimental results are higher than or equal to the corresponding lower bound, and the curves between the experimental results and corresponding lower bound are closed to each other. Therefore, the derivation of the lower bound is verified. From Fig. 6, we can find that the experimental and theoretical curves are nearly coincident for higher SNR. As we dicussed above, the carrier bits are more reliable than the ordinary bits. For higher SNR, only few errors occurs in the carrier bits transmission. In this case, the system BER is mainly determined by the ordinary bits transmission, and the experimental and theoretical curves coincide with each other. Figure 6Open in figure viewerPowerPoint Comparison of the BER performance under AWGN channel In addition, the BER performance under flat Rayleigh fading channel is also provided in Fig. 7. Due to Rayleigh fading environments, non-coherent demodulation is assumed in this simulation. From Fig. 7, the performance of RFH is the worst since other schemes treat some of their bits as carrier symbols which is more reliable through Rayleigh fading channels. Note that the performance of Group 1 is very close to that of Group 3 when SNR goes to large. This implies that their carrier symbols can be transmitted correctly at a high SNR, and the errors occur in ordinary symbols. Figure 7Open in figure viewerPowerPoint Comparison of the BER performance under Rayleigh fading channel 5 Conclusions In this paper, we propose a novel MDFH scheme based on slow FH. The basic idea of the proposed scheme is to transmit a part of information through the hop rate or dwell time of an FH signal. The proposed scheme can improve the system efficiency while significantly reduce the hardware complexity compared to the typical MDFH scheme. To further improve the system efficiency, a collision free multi-carrier extension is introduced. We compare the maximum throughput and hardware complexity between the proposed and MDFH schemes. The lower bound on the BER performance of the proposed scheme is analysed and verified. Moreover, the results show that the BER performance of our system is better than that of the typical MDFH system under the same throughput at low SNR. 6 Acknowledgments This work was supported by the National Natural Science Foundation of China (nos. 61631015 and 61501354), China Postdoctoral Science Foundation (no. 2016M592755) and the Fundamental Research Funds of the Ministry of Education (no. JB160117). The authors thank Miss Saotome for her valuable comments and suggestions. 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