Title: Design and performance analysis of generalised carrier index <i>M</i> ‐ary differential chaos shift keying modulation
Abstract: IET CommunicationsVolume 12, Issue 11 p. 1324-1331 Research ArticleFree Access Design and performance analysis of generalised carrier index M-ary differential chaos shift keying modulation Guixian Cheng, Guixian Cheng Department of Communication Engineering, Xiamen University, Xiamen, 361005 People's Republic of China School of Physics and Electronic Science, Guizhou Normal University, Guiyang, 550001 People's Republic of ChinaSearch for more papers by this authorLin Wang, Corresponding Author Lin Wang [email protected] Department of Communication Engineering, Xiamen University, Xiamen, 361005 People's Republic of ChinaSearch for more papers by this authorQiwang Chen, Qiwang Chen Department of Communication Engineering, Xiamen University, Xiamen, 361005 People's Republic of ChinaSearch for more papers by this authorGuanrong Chen, Guanrong Chen Department of Electronic Engineering, City University of Hong Kong, Hong Kong, SAR, People's Republic of ChinaSearch for more papers by this author Guixian Cheng, Guixian Cheng Department of Communication Engineering, Xiamen University, Xiamen, 361005 People's Republic of China School of Physics and Electronic Science, Guizhou Normal University, Guiyang, 550001 People's Republic of ChinaSearch for more papers by this authorLin Wang, Corresponding Author Lin Wang [email protected] Department of Communication Engineering, Xiamen University, Xiamen, 361005 People's Republic of ChinaSearch for more papers by this authorQiwang Chen, Qiwang Chen Department of Communication Engineering, Xiamen University, Xiamen, 361005 People's Republic of ChinaSearch for more papers by this authorGuanrong Chen, Guanrong Chen Department of Electronic Engineering, City University of Hong Kong, Hong Kong, SAR, People's Republic of ChinaSearch for more papers by this author First published: 29 May 2018 https://doi.org/10.1049/iet-com.2017.0800Citations: 11AboutSectionsPDF 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 In this study, two generalised carrier index M-ary differential chaos shift keying (CI-MDCSK) schemes are proposed, which combine index modulation with multicarrier M-ary DCSK (MC-MDCSK). At the transmitter, two different index selectors based on two different mapping rulers are employed to select active carriers, where the modulated bits are transmitted by the active carriers through M-ary DCSK modulation, which is based on the Hilbert transform and constellation theory. At receiver, maximum or minimum energy detection is employed to determine the active carriers, where the bits carried on these active carriers are demodulated. The analytical bit error rate (BER) expressions over additive white Gaussian noise as well as multipath Rayleigh fading channels are derived. Simulations are performed with different numbers of carriers and different constellation sizes. Both analytical and simulation results show the superiority of the new schemes in BER performance or spectral efficiency (SE) compared with the MC-MDCSK scheme. Moreover, compared with conventional DCSK, CI-MDCSK schemes owns both better BER performance and SE in some cases, where the constellation is not greater than 8. 1 Introduction In recent years, a new technique was developed for multicarrier communication systems, named index modulation (IM), which transmits information by the indices of subcarriers. Transplanted from spatial modulation [1], communication schemes combining IM with orthogonal frequency division multiplexing (OFDM) [2–10] and spread spectrum [11, 12] have been widely explored. However, these systems still have limitations in wireless communication applications. One of the important design challenges is that the number of subcarrier activation patterns (SAPs) is larger than that of the index symbols. For instance, the index mappers, either look-up table mapper or combinatorial mapper [3], exploits part of the possible SAPs to transmit information, which leads to these systems suffered from the disaster of detecting an invalid SAP. Besides, another improved scheme [7] exploits all the possible SAPs to carry information with non-fixed lengths of index bits, and employs different constellation sizes to maintain fixed length of the transmitted bits for every subblock, which always increases the complexity of the system. Thus, seeking for simplified index selector and detector with practical implementation has become an essential issue for IM-based multicarrier systems. In the past two decades, a great deal of research effort has been devoted to chaos-based communication systems, which results in many digital chaos modulation schemes. Among the proposed schemes, chaos shift keying (CSK) [13, 14] and differential CSK (DCSK) [15–19] attract a lot of attention. In comparison with CSK, DCSK only needs a simple non-coherent demodulator without reproducing an exact replica of chaotic sequences, which makes it more practical [20]. As non-periodic and random-like signals, DCSK possesses excellent auto-correlation and cross-correlation properties which can effectively resist severe multipath fading and jamming. Compared with differential phase shift keying, DCSK is more robust to multipath fading [21]. Due to these advantages, DCSK-based systems have been considered as very good candidates for wireless personal area networks (WPANs) [22]. However, DCSK modulation suffers from two major drawbacks, i.e. relatively low data-rate and the need of a radio-frequency delay line [23]. Many efforts have been made to further improve the DCSK system and some variants of DCSK have been developed. Multicarrier DCSK (MC-DCSK) [24] scheme is one of the most effective DCSK-based systems, which solves both drawbacks as well as effectively improves the energy efficiency (EE). Combining MC-DCSK with IM, a carrier index DCSK (CI-DCSK) scheme [25] was proposed, which employs index selectors having one-to-one mappings between the numbers of the SAPs and index symbols. Compared to the aforementioned index mappers, those index selectors not only can avoid catastrophic results, but also have simpler implementation. It has been shown that CI-DCSK schemes provide a trade-off between error performance and spectral efficiency (SE). In other words, one of the CI-DCSK schemes performs better in BER performance and the other performs better in SE compared with MC-DCSK. Given the advantages of IM for DCSK, there is still an efficient way to increase the data rate and SE of the DCSK system, i.e. extending binary DCSK to the M-ary domain. In the development of DCSK, a lot of researches about M-ary DCSK have been carried out [23, 26–30]. A Walsh code-based M-ary DCSK system [27],which needs perfect synchronisation at the symbol level, employs the orthogonality of a Walsh code sequence to transmit M symbols. As the implementation of the above system is very difficult, two different schemes based on M-ary PSK and M-ary QAM are proposed. One is MPSK/MQAM-based DCSK, which modulates the reference chaotic signal with an M-ary symbol by MPSK or MQAM during the information bearing piece [28]. The other one is M-ary constellation DCSK (MDCSK) [23] modulation, which transmits the M-ary symbols by two orthogonal signals through the constellation theory similar to MPSK for information bearing. Moreover, it is shown in [23] that, compared with MPSK/MQAM-based DCSK, MDCSK has better performance, so MDCSK is the best choice with IM. Due to the benefit of IM and MDCSK, it is necessary to replace the binary DCSK used in CI-DCSK schemes by MDCSK for high data rate, high bandwidth efficiency and good error performance, which are desirable for low-cost, low-power and low-complexity WPAN/WSN applications [31, 32]. However, only the schemes based on IM and binary-DCSK have been studied in [25], while the schemes based on IM and MDCSK remain uninvestigated. In this paper, two simple implementation schemes of carrier index M-ary DCSK (CI-MDCSK) are introduced first, which are considered as generalisation of the CI-DCSK schemes [25]. By choosing different numbers of index bits or different sizes of constellation, both schemes can offer different data rates, EEs and SEs. Then, the analytical BER expressions of the proposed schemes over additive white Gaussian noise (AWGN) channel as well as Rayleigh fading channel are derived. Comparisons between the analytical BER expression and the simulation shows the accuracy of the analytical method. Finally, the two proposed schemes are compared to multicarrier M-ary DCSK (MC-MDCSK), which is generalised MC-DCSK, with the constellation size being enlarged from 2 to M. The contributions of this paper are summarised as follows: (i) Two CI-MDCSK schemes, which employ IM to MC-MDCSK, are proposed. (ii) The analytical BER expressions of the proposed schemes over AWGN channel and multipath Rayleigh fading channel are derived. (iii) Compared to MC-MDCSK scheme with the same number of carriers and the same size of modulation constellation, the performance of the two proposed schemes are better. One of the schemes increases the BER performance, and the other slightly increases both BER performance and SE in some cases. The rest of this paper is organised as follows. In Section 2, the MDCSK encoder and its corresponding decision boundary are presented. In Section 3, two new CI-MDCSK systems are introduced. In Section 4, performance analysis is carried out. Simulation results and discussions are provided in Section 5. Finally, concluding remarks are presented in Section 6. 2 Encoder and decision boundary of MDCSK The MDCSK encoder consists of two independent orthogonal chaotic signals and , which are generated by the chaotic generator and its Hilbert transform, respectively. For simplicity, they are assumed to introduce no extra-delay. They are expressed as and , where is the spreading factor. Utilising and as its horizontal and vertical axes, respectively, the M-ary chaotic symbol () can be mapped to the constellation via , where and represent the orthogonal coordinates of the chaotic symbol [23]. Setting the energy of the reference and information bearing signal equally, it can be verified that the corresponding polar coordinates of are , where and . In MDCSK signal constellation, the signal points are equally spaced on a circle of radius 1 centred at the origin and the Gray code is used in signal assignment. Moreover, the optimum decision boundary for the two adjacent points is a vertical bisector of these adjacent points passing through the origin. Fig. 1 shows a constellation of 8DCSK and its corresponding decision boundaries. Figure 1Open in figure viewerPowerPoint Constellation of 8DCSK and corresponding decision boundaries 3 CI-MDCSK systems In [3], for each subblock of the OFDM-IM system, the index selector maps index bits to a SAP out of possible candidates, where n is the number of all indexed carriers and m is the number of active carriers. The maximum number of index bits carried by selecting m active carriers out of n carriers is given by . Since the number of SAPs is larger than the number of index symbols, a catastrophic result occurs when the receiver detects an invalid SAP [25]. In order to avoid the disaster, it is better to get a one-to-one mapping between SAPs and index symbols, so the formula is revised as . Based on the above formula, two different mapping rules are designed, where in the first rule n is , m is 1, and in the second rule, n is , m is . Combining two mappings with MC-MDCSK, two CI-MDCSK schemes are proposed. n is in both CI-MDCSK schemes, m is 1 in CI-MDCSK1 scheme and m is in CI-MDCSK2 scheme. 3.1 Transmitter Referring to the block diagram in Fig. 2, there are total orthogonal carriers at the transmitter. Among these carriers, one is used to transmit the reference chaotic signal, and the remaining subcarriers indexed from 1 to will be selected to transmit the information-bearing chaotic signals. During the symbol time, p transmitted bits including index bits and modulated bits are put into two bit-to-symbol converters, respectively, which generate one index symbol i () and m modulated symbols labelled as . Moreover, the sequence of modulated symbols are sequentially put into the MDCSK encoder, and the corresponding outputs are labelled as with . Then, the outputs of the MDCSK encoder and the index symbol are put into the index selector, which will generate a sequence of for all the index carriers based on these inputs. In CI-MDCSK1, since the number of active carriers is one, according to the index symbol i, only one modulated symbol is transmitted and the outputs of the index selector will be , where and the others are zero. While in CI-MDCSK2, for the index symbol i and modulated symbols, the index selector will generate symbols as , where Figure 2Open in figure viewerPowerPoint Block diagram of the CI-MDCSK schemes Finally, the chaotic reference signal and the information-bearing signals are generated by pulsing shaping. Therefore, as shown in Fig. 2, the transmitted signal of the CI-MDCSK can be expressed as (1) where , , represents the phase angle of the carrier modulation, is the frequency of the subcarrier, is the square-root-raised-cosine filter and is the chip time. For these CI-MDCSK systems, the subcarriers are orthogonal over the chip duration [24]. 3.2 Receiver In the two schemes, the received signal is expressed as (2) where L is the number of paths, and are the channel coefficient and the path delay of the path, is the convolution operator, is a wideband AWGN with zero mean and power density of and are assumed to be independent Rayleigh distribution random variables. If the number of paths is one, with the channel coefficient being one, it is the AWGN case; otherwise, it is the Rayleigh fading case. This multipath Rayleigh fading channel mode is commonly used in spread-spectrum wireless communication systems [23, 24]. The received signals are first separated by corresponding orthogonal modulated carrier frequencies. After filtered by the matched filters, the signals are sampled at every instant. For each time, the output discrete signals are recorded into two matrices. The reference chaotic signal and its Hilbert transform are stored in matrix , while the data signals are stored in matrix . Finally, is put into the detector. By correlating the information-bearing signal with the reference signal and its Hilbert transform over a symbol time (), the coordinates for symbols are generated and stored in z. In the two schemes, the detector should detect both the index bits and the modulated bits. In CI-MDCSK1, a maximum energy comparator is employed. Obviously, the branch which transmits the maximum energy will be the active carrier. For each symbol time, the comparator first calculates the square sum of every column of z, and then finds the maximum value and its corresponding column number . So, the index symbol can be determined to be , and the corresponding index bits can be recovered by the symbol-to-bit converter. As for the modulated symbol, based on the two values of the column, i.e. (), the corresponding phase is calculated by . Using the decision boundaries of MDCSK, the modulated symbols are reconstructed and the corresponding modulated bits are recovered by the symbol-to-bit converter. In CI-MDCSK2, as only one carrier is inactive and the others transmit the modulated symbols, a minimum energy comparator is employed. Obviously, the branch which transmits the minimum energy will be the inactive carrier. For each symbol duration, the comparator first calculates the square sum of every column of z, and then finds the minimum value and its corresponding index . Similarly to CI-MDCSK1, based on the index , the index symbol and its corresponding index bits can be recovered. Then, according to the other columns of z, except for the minimum energy column, the decoder recovers the modulated symbols in the same way as CI-MDCSK1, the order of which is consistent with the carrier indices. At last, the modulated bits can be recovered by the symbol-to-bit converter. Above all, for the symbol time, bits will be transmitted by CI-MDCSK1, while bits will be transmitted by CI-MDCSK2. Obviously, CI-MDCSK1 needs more modulation and demodulation operations to transmit the same number of bits, so the CI-MDCSK1 is more complex than CI-MDCSK2. 4 Performance analysis of CI-MDCSK In this section, the analytical BER expressions for the transmitted bits over AWGN channel as well as multipath Rayleigh fading channel are derived. It is assumed that the largest multipath delay is much shorter than the symbol duration, i.e. . Hence, the intersymbol interference is negligible [23, 25]. It is also assumed that the channel is slowly fading and the channel coefficients are constant during the transmission time of a symbol. 4.1 Distributions of energy carried by active and inactive carriers For the chaotic period, two outputs of the active carrier correlators are and , with , while two outputs of the inactive carrier correlators are and , with . Thus [18] (3) (4) (5) (6) where , , and are four independent zero-mean Gaussian noises with the power spectral density of , is caused by the reference carrier, is the Hilbert transform of , and and are caused by the active carrier and the inactive carrier, respectively. For a large spreading factor, the following approximated expression is used [21, 24]: (7) Then, the means and variances of and are approximated as follows [18]: (8) (9) (10) Moreover, the means and variances of the two outputs of the inactive carrier, and , are approximated as follows: (11) (12) (13) where , and is the energy of the reference chaotic signal duration. Note that and are two independent normal random variables with a common variance and different means. The energy carried by the active carrier, defined as , follows non-central chi-square distribution. Also note that and are two independent normal random variables with a common variance and zero mean. The energy carried by the active carrier, defined as , follows central chi-square distribution. 4.2 BER of index bits for CI-MDCSK1/2 For the duration of each symbol, the total number of transmitted bits, p, consists of index bits and modulated bits. 4.2.1 Symbol error rate (SER) of index bits for CI-MDCSK1. When the largest energy carried by the inactive carrier is larger than the energy carried by the only active carrier, an error will occur. Based on the cumulative distribution function (CDF) of the quotient of two random variables, the SER of index bits can be derived as (14) where follows non-central chi-square distribution, , and . As the energy of the inactive carriers are independent and identically distributed (i.i.d.) random variables, is the maximum order statistic, whose CDF is . Thus (15) where is the CDF of , and is the probability density function (PDF) of . Furthermore (16) (17) Substituting and into formula (15), and requiring , the integral is simplified as (18) where , , and is the first kind of zero-order modified Bessel function. 4.2.2 SER of index bits for CI-MDCSK2. When the minimum energy carried by the active carrier is smaller than the energy carried by the only inactive carrier, an error will occur. Based on the CDF of the quotient of two random variables, the SER of index bits can be derived as (19) where , and . As the energy of the active carriers are i.i.d. random variables, is the minimum order statistic, whose CDF is , where . Thus (20) where is the CDF of and is the PDF of . Furthermore (21) (22) Substituting and into formula (20), and requiring , the integral can be simplified as (23) where , and is the first-order Marcum Q-function. 4.2.3 BER of index bits for the schemes. The BER of index bits can be derived as (24) Substituting (18) into (24), the BER of the index bits for CI-MDCSK1 can be derived, while substituting (23) into (24), the BER of the index bits for CI-MDCSK2 can be derived. 4.3 BER for modulated bits The detection of the modulated bits contains two steps: first, demodulate the index symbol by finding the maximum or the minimum energy carrier label; second, demodulate the bits carried by the active carrier through a MDCSK decoder. 4.3.1 CI-MDCSK1. In the first case, when the first detection step is wrong, the probabilities of determining the modulated symbol to the other error cases are the same, so the SER of the decoder is , where M is the size of the constellation employed. Then, the BER of the modulated bits can be calculated (25) In the other case, the first detection is correct, but there is an error detected in the second step. In this case, the BER for the decoder is the same as the BER of MDCSK, which can be deduced from [23] as where Hence, the BER of the modulated bits in this case can be deduced as (26) Based on the above two cases, the BER for the modulated bits is given by (27) where , p and are the same as those in (18). 4.3.2 CI-MDCSK2. In this scheme, when the index symbol detection is wrong, i.e. one of the active carriers is detected as inactive, the only inactive carrier is detected as active. As the modulated bits are sequentially modulated to the active carriers according to the order of the carrier indexes, the modulated bits will be wrongly demodulated if the order of the active carriers is wrongly detected. The probability of wrong detection for all the modulated symbols is , so that the error probability of the modulated bits can be derived as (28) In the second situation, the first detection is correct, but an error is in the second step. In this case, the BER of the decoder is where Hence, the error probability of the modulated bits in this case can be deduced as (29) Combining the above two cases, the BER for the modulated bits is given by (30) where , p and are the same as those in (23). 4.4 BER of the transmitted bits for CI-MDCSK1/2 over AWGN and multipath fading channels In these schemes, the input bits are divided into two kinds of bits, i.e. modulated bits and index bits, so the BERs of the systems is a linear combination of the BER for index bits and modulated bits. It can be derived as (31) Put the BER of index bits and modulated bits for the two schemes into (30), respectively, the BER of the transmitted bits for the CI-MDCSK1/2 schemes over AWGN channel can be derived. Here, only L i.i.d. Rayleigh fading channels are considered. Thus, the PDF of can be written as [21, 24, 33] (32) where is the average bit signal-to-noise ratio (SNR) per channel, and , with and being the energy of a bit. Finally, the BER expression of the CI-MDCSK scheme over multipath Rayleigh fading channel is given by (33) 5 Numerical results and discussions In this section, the BER performances of the transmitted bits for two proposed schemes over AWGN channel and multipath fading channel are discussed. Moreover, the performance comparisons between the proposed schemes and the MC-MDCSK system are presented. In simulation, the logistic map is chosen as the chaotic system for its good performance, and the spreading factor of the systems is set to 80. In the case of multipath Rayleigh fading channel, three paths () are considered, having equal average power gain as , with different time delays and . Note that if the number of the carriers of both CI-MDCSK systems is three, i.e. there is one active carrier and one inactive carrier besides the reference carrier, then the two proposed systems are equivalent. This situation is included in the CI-MDCSK1 system. 5.1 Performance of CI-MDCSK1 The performance of CI-MDCSK1 over AWGN channel is shown in Fig. 3, where the number of index bits is 2, 3 or 5, and the constellation are not . Obviously, the simulation results and the analytical BER expression match very well. Fig. 4 shows the computed results and the simulation results of CI-MDCSK1 over multipath Rayleigh fading channel where they are almost matched. Figure 3Open in figure viewerPowerPoint BER performance of CI-MDCSK1 over AWGN channel Figure 4Open in figure viewerPowerPoint BER performance of CI-MDCSK1 over multipath Rayleigh fading channel The BER performance of CI-MDCSK1 consists of two parts: BER of modulated bits and BER of index bits. Moreover, both of them are directly proportional to the BER performance of CI-MDCSK1. Obviously, BER of modulated bits is directly proportional to the constellation size of the modulated bits, while BER of index bits is directly proportional to the percentage of index bits per symbol. As shown in Table 1, when the constellation size is fixed, with the number of index bits increasing, the percentage of index bits per symbol increases, which is good for the BER performance, hence the performance of the scheme increases. When the number of index bits is fixed, the CI-MDCSK1 performance is affected by both the above two factors. With the constellation size increasing, the percentage of index bits decreases, which degrades the performance of the CI-MDCSK1. However, as shown in Figs. 3 and 4, the performance of CI-4DCSK1 outperforms CI-DCSK1, since 4DCSK outperforms DCSK for large spreading factors () [23]. While for other constellation size, with the constellation size increasing the Euclidean distance of MDCSK becomes smaller, which will also degrade the performance of CI-MDCSK1. Table 1. Parameters of CI-MDCSK1 under different constellation sizes and differentnumbers of index bits number of the index carriers 5 33 5 33 5 33 5 33 number of index bits 2 5 2 5 2 5 2 5 size of the constellation M 2 2 4 4 8 8 16 16 number of modulated bits 1 1 2 2 3 3 4 4 number of transmitted bits p 3 6 4 7 5 8 6 9 percentage of index bits per symbol 0.67 0.83 0.5 0.714 0.4 0.625 0.33 0.56 number of the transmitted bits per subcarrier 0.6 0.18 0.81 0.21 1 0.24 1.2 0.27 5.2 Performance of CI-MDCSK2 The performance of CI-MDCSK2 over AWGN channel is shown in Fig. 5, where the number of index bits is 2, 5 or 6, and the constellation are not . Obviously, the simulation results and the analytical BER expression match very well. In Fig. 6, the computed results and the simulation results of CI-MDCSK2 over multipath Rayleigh fading channel are almost matched with each other. Figure 5Open in figure viewerPowerPoint BER performance of CI-MDCSK2 over AWGN channel Figure 6Open in figure viewerPowerPoint BER performance of CI-MDCSK2 over multipath Rayleigh fading channel The BER performance of CI-MDCSK2 consists of two parts: BER of modulated bits and BER of index bits. Moreover, both of them are directly proportional to the BER performance of CI-MDCSK2. Similarly, BER of modulated bits is directly proportional to the constellation size of the modulated bits, and BER of index bits is directly proportional to the percentage of index bits per symbol. As presented in Table 2, when the constellation size is fixed, with the number of the index bits increasing, the percentage of index bits per symbol reduces, which is not good for the BER performance, hence the performance of the scheme decreases. When the number of carrier is fixed, with the constellation size enlarging, the change of the BER performance is the same as that of CI-MDCSK1. Table 2. Parameters of CI-MDCSK2 under different constellation sizes and differentnumbers of index bits number of index carriers 5 33 5 33 5 33 5 33 number of index bits 2 5 2 5 2 5 2 5 size of the constellation M 2 2 4 4 8 8 16 16 number of modulated bits 3 31 6 62 9 93 12 124 number of transmitted bits p 5 36 8 67 11 98 14 129 percentage of index bits per symbol 0.4 0.139 0.25 0.075 0.182 0.051 0.143 0.039 number of the transmitted bits per subcarrier 1 1.09 1.6 2.03 2.2 2.97 2.8 3.76 5.3 BER comparisons with MC-MDCSK and DCSK MC-MDCSK is extended from MC-DCSK, where the modulation is MDCSK instead of binary DCSK. In such a system, one carrier is used to transmit the reference chaotic signal and remaining carriers transmit the M-ary DCSK signals. With the number of the carriers increasing, the performance of MC-MDCSK is improved as less reference energy is used to transmit one bit [24]. However, the improvement is limited as shown in Fig. 7, where the number of carriers (P) is more than 17. Thus, in the comparison between CI-MDCSK2 and MC-DCSK, the number of carriers is set to be larger than 17. Figure 7Open in figure viewerPowerPoint Performance comparisons between MC-MDCSK over AWGN channel with different carrier numbers (P) 5.3.1 CI-MDCDK1 compared with MC-MDCSK. Fig. 8 shows the comparison of BER performance between CI-MDCSK1 and MC-MDCSK, with the same number of carriers and the same constellation size. It is obvious that the BER performance of CI-MDCSK1 outperforms that of MC-MDCSK in high SNR region. The phenomenon can be interpreted as that the CI-MDCSK1 sacrifices SE for BER performance. Moreover, the correct decision probability for the state of index carriers increases in the high SNR region, which improves the BER performance. Figure 8Open in figure viewerPowerPoint Performance comparisons between MC-MDCSK and CI-MDCSK1 over the AWGN channel with the same number of carriers and constellation size 5.3.2 CI-MDCDK2 compared with MC-MDCSK. If the number of the total carriers and the constellation size employed in the two systems are the same and the number of the index bits is larger than , i.e. , then the SE of CI-MDCSK2 is not less than the SE of MC-MDCSK. For instance, when 4DCSK is used in both systems, if , the SE of CI-4DCSK2 is larger than the SE of MC-4DCSK. Fig. 9 shows the BER performance comparisons of MC-MDCSK and CI-MDCSK2 with the same number of carriers and constellation size. If , the conclusions can be derived as follows. First, if , SE of CI-4DCSK2 is better than that of MC-4DCSK and BER performance of CI-4DCSK2 is better than that of MC-4DCSK with high SNR. Particularly, with increasing of the number of carriers, the superiority of CI-4DCSK2 can be seen in the higher SNR region. The reason for the superiority of CI-4DCSK2 is that IM provides a new domain to carry information, and in the high SNR region, the probability of the correct decision for the state of index carrier increases, which gives rise to improving the error performance. Second, if or , CI-MDCSK2 has better SE, while MC-MDCSK has better BER performance. The performance of CI-MDCSK2 in the above cases ( or ) can be considered as sacrificing BER performance for SE. Figure 9Open in figure viewerPowerPoint Performance comparisons between MC-MDCSK and CI-MDCSK2 over the AWGN channel with the same number of carriers and constellation size 5.3.3 CI-MDCDK compares with DCSK. As shown in Figs. 8 and 9, where the constellation is not 8, both schemes outperform the traditional DCSK. The reason is that the Euclidean distance of MDCSK becomes smaller with the constellation increasing, which is bad for the BER performance. Besides, it is well known that DCSK transmits one bits by two carriers. Hence, compared with SE for CI-MDCSK schemes shown in Tables 1 and 2, the SE of DCSK is lower than that of CI-MDCSK2 cases, but higher than most CI-MDCSK1 cases. 6 Conclusion In this paper, two new high-data-rate and spectrum-efficient CI-MDCSK schemes are presented. Based on two different index selectors and detectors, the two schemes transmit the information bits not only by MDCSK modulation but also by the index of the carrier, which significantly increase the data rates and SEs of the systems compared with CI-DCSK. Analytical BER expressions of the proposed schemes over AWGN channel and multipath Rayleigh fading channel are derived. By simulating the BER performance with different numbers of carriers and constellation sizes, it is observed that setting the constellation of CI-MDCSK schemes as 4 achieves better BER performance. Compared with MC-MDCSK of the same number of carriers and constellation size, CI-MDCSK1 has better BER performance but sacrifices SE, and CI-MDCSK2 has better SE or BER performance in some cases, especially for the case of , CI-MDCSK2 has better BER performance and SE. The superiority of CI-4MDCSK2 is attributed to IM for providing a new domain to carry information. 7 Acknowledgments This work was supported in part by the National Natural Science Foundation (NSF) of China under grant no. 61671395 and in part by the Hong Kong GRF under Grant CityU 11208515. References 1Mesleh R.Y., Haas H., Sinanovic S.et al.: 'Spatial modulation', IEEE Trans. Veh. Technol., 2008, 57, (4), pp. 2228– 2241 2Tsonev D., Sinanovic S., Haas H.: ' Enhanced subcarrier index modulation (SIM) OFDM'. Proc. 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Publication Year: 2018
Publication Date: 2018-03-09
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 26
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