## 1.

## Introduction

Successive 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 Scheme

The 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 Equations

In our system, we consider an incoherent, DS optical CDMA (DS-OCDMA) system. The system consists of
$N$
users, labeled by
$n$
, where
$n=1,2\dots N$
. 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 codes^{7} in this paper. It is a family of (0,1) sequences of length
$F$
and weight
$W$
that satisfy the requirement that
${\lambda}_{\mathrm{a}}$
,
${\lambda}_{\mathrm{c}}$
are equal to 1. With good auto- and cross-correlation, it enables the effective detection of the desired signal. The
$n$
’th user spreading code can be represented as

## Eq. 3

$$r\left(t\right)=\sum _{n=1}^{N}{P}_{n}{b}_{n}(t-{\tau}_{n})\sum _{i=1}^{F}{c}_{n}^{i}(t-{\tau}_{n})+n\left(t\right).$$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 $n$ ’th user’s signal on the first receiver is denoted by ${I}_{n}^{\left(1\right)}$ . We define the cross correlation between the $i$ ’th user and the $n$ ’th user as

## Eq. 5

$${I}_{n,i}\left({\tau}_{n,i}\right)=\frac{1}{T}[{\int}_{0}^{T}{c}_{n}(t-{\tau}_{n,i})\times {c}_{i}\left(t\right)\mathrm{d}t],$$Hence, the first decision variable ${Z}_{1}$ at time $T$ , can be written as

## Eq. 6

$${Z}_{1}=\frac{1}{T}{\int}_{0}^{T}r\left(t\right)\times {c}_{1}(t-{\tau}_{1})\times \mathrm{d}t$$## Eq. 7

$$=\frac{1}{T}{\int}_{0}^{T}\left[\sum _{n=1}^{N}{P}_{n}{b}_{n}(t-{\tau}_{n})\sum _{i=1}^{F}{c}_{n}^{i}(t-{\tau}_{n})\right]\sum _{i=1}^{F}{c}_{1}^{i}(t-{\tau}_{n})\times \mathrm{d}t.$$## Eq. 9

$${l}_{1}=\frac{1}{F}\sum _{n=2}^{N}{P}_{n}{b}_{n}{I}_{n,1}\left({\tau}_{n,1}\right)+n\left(t\right).$$It 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

## Eq. 11

$$=\sum _{n=2}^{N}{P}_{n}{b}_{n}(t-{\tau}_{n})\times {c}_{n}(t-{\tau}_{n})+n\left(t\right)-{l}_{1}\times {c}_{1}(t-{\tau}_{1}).$$## Eq. 13

$${l}_{2}=\frac{1}{F}[\sum _{n=3}^{N}{P}_{n}{b}_{n}{I}_{n,2}\left({\tau}_{n,2}\right)-{l}_{1}{I}_{1,2}\left({\tau}_{1,2}\right)]+n\left(t\right).$$## 4.

## SIC Interference Analysis

In 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 ${l}_{j+1}$ conditioned on ${P}_{n}$ as follows:

## Eq. 17

$${\phantom{\mid}{\sigma}_{j+1}^{2}\mid}_{-}MAI=\frac{1}{F}\{\sum _{n=j+2}^{N}{P}_{n}^{2}{b}_{n}^{2}\phantom{\rule{0.3em}{0ex}}\mathrm{var}\left[{I}_{n,j+1}\left({\tau}_{n,j+1}\right)\right]+\sum _{i=1}^{j}{\sigma}_{i}^{2}\phantom{\rule{0.3em}{0ex}}\mathrm{var}\left[{I}_{i,i+1}\left({\tau}_{i,i+1}\right)\right]\}.$$^{9, 10}Substituting 18 into 17, we get the variance of the noise in the decision variable

## Eq. 19

$${\phantom{\mid}{\sigma}_{j+1}^{2}\mid}_{-}MAI=\frac{1}{{F}^{2}}[\sum _{n=j+2}^{N}{P}_{n}^{2}+\sum _{i=1}^{j}{\sigma}_{i}^{2}].$$The responsivity of the PDs is given by $\mathfrak{R}=\eta e\u2215h{v}_{c}$ . Here, $\eta $ is the quantum efficiency, $e$ is the electron’s charge, $h$ is Plank’s constant, and ${v}_{c}$ is the central frequency of the original broadband optical pulse.

Then the signal-to-noise ratio (SNR) function of ${P}_{n}$ is

The bit error rate (BER) is given by## 5.

## Performance Results and Discussion

In 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 OOC^{11} under different powers from
$-30$
to
$-10\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$
. 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 1

Typical parameters in the system.

Parameter | Value |
---|---|

Operating frequency | $193.1\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$ |

PD quantum efficiency | 0.6 |

Receiver noise temperature | $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ |

Receiver load resistor | $1030\phantom{\rule{0.3em}{0ex}}\mathrm{\Omega}$ |

Noise-equivalent electrical bandwidth | $80\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ |

Effective received power | $-30$ to $-10\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ |

OOC | (1365,5,1,1) |

(631, 6, 1, 1) | |

(341, 5, 1, 1) | |

(63, 3, 1, 1) |

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 $-30$ to $-10\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ . It can be seen from Fig. 5 that, at an effective power of $-30\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ , the system performance with cancellation is not good; on the other hand, when the effective power is increased to $-10\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ , the system performance gives good results compared to the system without cancellation.

## 6.

## Conclusion

In 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.

## References

**,” IEEE Trans. Commun., 42 (2/3/4), 1801 –1810 (1994). https://doi.org/10.1109/TCOMM.1994.582889 0090-6778 Google Scholar**

*Multiuser detection for optical code division multiple access systems***,” J. Lightwave Technol., 23 (12), 3959 –3965 (2005). https://doi.org/10.1109/JLT.2005.858232 0733-8724 Google Scholar**

*Design and analysis of a dynamic code division multiple access communication system based on tunable optical filter***,” Wireless Networks, 4 447 –452 1998). Google Scholar**

*Implementation aspects for successive interference cancellation in DS/CDMA systems***,” 299 –303 (2006). Google Scholar**

*A novel successive interference cancellation scheme in OCDMA system***,” IEEE J. Sel. Areas Commun., 12 (5), 796 –807 (1994). https://doi.org/10.1109/49.298053 0733-8716 Google Scholar**

*Analysis of a simple successive interference cancellation scheme in a DS/CDMA system***,” (1993) Google Scholar**

*Analysis of a simple successive interference cancellation scheme in DS/CDMA system using correlations***,” IEEE Trans. Commun., 37 (8), 824 –842 (1989). https://doi.org/10.1109/26.31181 0090-6778 Google Scholar**

*Code division multiple-access techniques in optical fiber networks—Part I***,” IEEE Trans. Commun., 37 (8), 834 –842 (1989). https://doi.org/10.1109/26.31182 0090-6778 Google Scholar**

*Code division multiple-access techniques in optical fiber networks—Part II: Systems performance analysis***,” 47 –53 (1999). Google Scholar**

*Analysis of a successive interference canceler with multiple antennas for DS/CDMA on multipath fading channels***,” IEEE Trans. Inf. Theory, 35 595 –604 (1989). https://doi.org/10.1109/18.30982 0018-9448 Google Scholar**

*Optical orthogonal codes: Design, analysis, and applications*## Biography

**Tawfig Eltaif** received his BS in communication engineering, from A1-Fateh University, Tripoli, Libya, in 2003, and his MS in microelectronics engineering, from Universiti Kebangsaan Malaysia, Bangi, Malaysia, in 2005. He is currently working toward his PhD at the Institute of Micro-Engineering & Nanoelectronics, University Kebangsaan Malaysia, Bangi, Malaysia. His current research interests include optical CDMA and spread-spectrum communications.

**Hossam M. H. Shalaby** received his BS and MS degrees from the University of Alexandria, Egypt, in 1983 and 1986, respectively, and his PhD from the University of Maryland, College Park, Maryland, in 1991, all in electrical engineering. In 1991, he joined the Department of Electrical Engineering, University of Alexandria, Egypt, as an assistant professor. He was promoted to the position of associate professor in 1996 and then to professor (current position) in 2001. From December 2000 to 2004, he was an adjunct professor with Department of Electrical and Information Engineering, Faculty of Sciences and Engineering, Laval University, Quebec, Canada. From March to April 1996, he was a visiting professor at the Electrical Engineering Department, Beirut Arab University, Lebanon. From September 1996 to January 1998, he was an associate professor with the Electrical and Computer Engineering Department, International Islamic University Malaysia. From February 1998 to December 1998, he was with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, where he was a senior lecturer and, from January 1999 to February 2001, an associate professor. His research interests include optical communications, optical CDMA, spread-spectrum communications, and information theory. Dr. Shalaby received the SRC fellowship from 1987 to 1991 (Systems Research Center, Maryland), Shoman Prize for Young Arab Researchers in 2002 (the Abdul Hameed Shoman Foundation, Amman, Jordan), the State Award twice in 1995 and 2001 (Academy of Scientific Research and Technology, Egypt), the University Award in 1996 (University of Alexandria, Egypt), and Soliman Abd-El-Hay Award in 1995 (Academy of Scientific Research and Technology, Egypt). He has served as a student branch counselor (Alexandria University), IEEE Alexandria and North Delta Subsection, from 2002 to 2006, and served as a chairman of the Student Activities Committee of IEEE Alexandria Subsection from 1995 to 1996.

**Sahbudin Shaari** received his MS in quantum electronics from University of Essex, United Kingdom, in 1980, and PhD in microelectronics from University of Wales, United Kingdom, in 1989. He joined the faculty of the Department of Electrical, Electronics, and System Engineering, Universiti Kebangsaan, Malaysia, in 1978. He is currently a principal research fellow and professor in the Institute of Micro-Engineering and Nanoelectronics at the same university. His current research interests are nanophotonics and optical communications.

**Mohammad M. N. Hamarsheh** received his BS in electrical engineering from An-najah National University, Nablus, Palestine, in 1999, and his MS and PhD degrees in computer and communication engineering and communications and network engineering, in 2002 and 2006, respectively from University Putra Malaysia, Serdang, Malaysia. He worked with Photronix, Cyberjaya, Malaysia (2002 to 2005) as a research engineer. He was involved in fiber Bragg grating research and development. Currently, he is a lecturer on the faculty of information science and technology, Multimedia University. His research interests include optical code division multiple access systems, fiber Bragg gratings, dense wavelength division multiplexing, and polarization effect on optical fiber communication.