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1.IntroductionSuccessive interference cancellation (SIC) is a multiuser detection (MUD) technique,1 where MUD is typically employed in optical code-division multiple access (CDMA) communication systems. The problem of demodulating a specific user signal is complicated, as the other user signals exist in the same bandwidth.2 In conventional receivers, the presence of other signals is treated as noise. In MUD algorithms, this noise is usually referred to as multiple access interference (MAI), and it is shown that this type of noise limits direct sequence CDMA (DS-CDMA) system capacity. Any technique that can suppress (cancel) MAI will increase the system’s capacity. In recent years, MUD has become an attractive alternative to conventional spread spectrum detectors. It is well known that optimum MUD has a much better theoretical performance than conventional detection.3, 4 However, the majority of multiuser detectors have a very high complexity and, consequently, suboptimum structures have been presented.3 In this work, we propose and analyze a SIC scheme using an optical orthogonal code (OOC) with a different power for each user, that takes into account the impact of imperfect interference cancellation. 2.Principle of the SIC SchemeThe basic idea of this scheme is simple, it detects and demodulates the strongest user signal currently present in the overall received signal. The strongest user is not known beforehand, but it is detected from the strength of the correlations of each of the user’s chip sequences with the received signal. The correlation values can be found from the bank of the correlator. Figure 1 shows the block diagram of the SIC receiver. After this user has been detected and demodulated, its contribution to the original signal is regenerated and subtracted from the overall received signal to get a new received signal. Then we can conclude that the algorithm repeats, excluding the strongest user from the new received signal, which, composed of one user signal less, is detected, demodulated, regenerated, and subtracted.5, 6 At the end, we can say that the strongest received signals are subtracted from the original signal one by one until all users have been detected and demodulated. Figure 2 shows the flowchart of this process. In a general algorithm, the successive cancellations are carried out as follows: 3.SIC System EquationsIn our system, we consider an incoherent, DS optical CDMA (DS-OCDMA) system. The system consists of users, labeled by , where . On-off keying (OOK) modulation is used to transmit binary data via an optical channel for each user with a specific sequence code for each. In particular, OOC will be used as the signature codes7 in this paper. It is a family of (0,1) sequences of length and weight that satisfy the requirement that , are equal to 1. With good auto- and cross-correlation, it enables the effective detection of the desired signal. The ’th user spreading code can be represented as Here, , refers to the chip duration, and is the optical rectangular pulse in with unit amplitude. We consider an ideal synchronous case, that is . It has been shown in Refs. 7, 8 that the synchronous case is the worst case. Let the binary data of the ’th user be given bywhere and is the bit duration. Then we can say that the intensity signal of the ’th user is , where is the signal strength of the ’th user. Therefore, on the receiver side, we can get the signal to be the sum of the user’s signals as follows:Here, is the relative delay, and we have considered an ideal synchronous case, .In a general case, we look for the bit error probability, which can be written as follows: As we mentioned previously, the main function of this system is based on maximum cross correlation between the users, and the effect of the ’th user’s signal on the first receiver is denoted by . We define the cross correlation between the ’th user and the ’th user as where is the time delay of the ’th user relative, to the ’th user.Hence, the first decision variable at time , can be written as Then after the decoding and integration, we can get the following:where the first term refers to the desired signal term of the first user, and the second term can be defined asIt is assumed that users are detected in the order of decreasing signal strength such that user 1 will always correspond to the strongest user. Once this user has been detected and demodulated, the result is used to regenerate the user signal. Then the regenerated signal is subtracted from the original signal. The correlation value is used for cancellation Now for the second strongest user, we have interfering signals and some noise due to imperfect cancellation. In following decision statistic for user 2 after canceling user 1, after decoding and integration we gotand is defined asIn general, for the ’th, cancellations, we getHere, refers to the correlation after the ’th cancellation, then the decision variable for the ’th user is given bywhere are given byIn the above expression, the first term is MAI of the uncancelled users; second term is cumulative noise from imperfect cancellation, and the third term is the thermal noise.4.SIC Interference AnalysisIn this section, we consider the effect of both MAI and thermal noise; other sources of noise are neglected. Related to MAI, we can define the variance of conditioned on as follows: The term is a random variable that depends on the random signature sequences. Central to the analysis is the variance of this term (for the case of ). For the synchronous case, where is zero for all , the variance of cross correlation of Eq. 5 is given by9, 10 Substituting 18 into 17, we get the variance of the noise in the decision variableFurthermore, we consider the effect of thermal noisewhere is the noise-equivalent electrical bandwidth of the receiver in Hertz; is Boltzmann’s constant in joules per ; is absolute receiver noise temperature in Kelvin; and , is the receiver load resistor in ohms.The responsivity of the PDs is given by . Here, is the quantum efficiency, is the electron’s charge, is Plank’s constant, and is the central frequency of the original broadband optical pulse. Then the signal-to-noise ratio (SNR) function of is The bit error rate (BER) is given by5.Performance Results and DiscussionIn this section, we present the numerical results of SNR and BER performance of the proposed SIC scheme. The typical parameters used in the calculations are given in Table 1. In this analysis, we assume that each user had different power. Figure 3 shows the relationships between SNR and the number of users being cancelled, at various stages of cancellation using OOC11 under different powers from to . As we can see in the figure below, the SNR of the users increases at each stage of the cancellation process, and hence the SNR decreases when the number of users increased. In this analysis, we take in to account the possibilities of errors in previous cancellations. Table 1Typical parameters in the system.
Figure 4 shows a comparison of the BER under different OOC code parameters, namely different weights and lengths. We can see from the figure that an OOC with parameters (631, 6, 1, 1) gives a lower BER than that using (341, 5, 1, 1). However, when using (1365, 5, 1, 1) or (341, 5, 1, 1), we get almost the same results. We conclude from the figure that the SIC system performance depends on the code weight rather than the code length. As we can see in the figure, BER improves at each stage of the cancellation process, and we note that MAI becomes increasingly accurate as the number of users is increased. In fact, the BER performance improves as the code weight increases. In Fig. 5, we have compared the results of the system with and without cancellation for the number of active users. The BER from the obtained analysis shows that the cancellation scheme has better performance than the conventional scheme for a large number of users. However, if there is a small number of users, the system without cancellation performs better. This results from the effective power. Indeed, for the system without cancellation, the BER is independent of the effective power. However, the BER of our proposed system depends on the effective power as it is clear in Eq. 21. In our analysis, we have used different values of effective power for all users ranging from to . It can be seen from Fig. 5 that, at an effective power of , the system performance with cancellation is not good; on the other hand, when the effective power is increased to , the system performance gives good results compared to the system without cancellation. 6.ConclusionIn this paper, a new proposal for interference cancellation of MUD has been reviewed. This new method is called successive interference cancellation (SIC), and this scheme is a simple, attractive technique to improve system capacity. In this work, we have obviously analyzed the performance of SIC. It is found from the results that the proposal SIC receiver effectively suppresses MAI and significantly improves BER performance at each stage of the cancellation process. However, the major problem with the SIC scheme is the accumulated cancellation noise; therefore, interference cancellation is not a perfect solution, and the residual cancellation errors propagate because of the successive nature of the decoding. In fact, these residual errors are the principal capacity-limiting issue in SIC systems. However, the system shows much lower BER performance with SIC cancellation compared with one without cancellation. ReferencesM. B. Pearce and
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