Statistical analysis of fiber-optic CDMA communication systems. II. Incorporating multiple optical amplifiers

For pt. I see ibid., vol.20, no.8, p.1304-16 (2002). In this paper, we study and elaborate on the architectural consideration of using multiple optical amplifiers in an all-optical fiber-optic code-division multiple-access (FO-CDMA) network. Our study and considerations are based on obtaining the statistical characteristic functions for photon-counts of a string of output pulses that constitutes the address code in a FO-CDMA network. Optical orthogonal codes (OOCs) with minimum auto-and cross correlation are employed as the address or signature sequence codes. Our analysis is based on chip-synchronous interference only, which provides an upper bound on the system performance. Shot noise, thermal noise, and extinction ratio are considered in this analysis. Bit error rate (BER) results are obtained using two methods, namely, saddle-point and Gaussian approximations. From our BER analysis, we develop some insight into the optimum distribution of optical amplifiers and their corresponding gain setting parameter. Moreover, the effects of source power, code weight, number of users, bit rate, and amplified spontaneous emission noise are investigated.     

A new family of optical code sequences for use in spread-spectrumfiber-optic local area networks

The problem of the algebraic construction of a particular family of optical codes for use in code-division multiple-access (CDMA) fiber-optic local area networks (LANs) is treated. The conditions that the code families have to satisfy when used in such systems are reviewed. The new codes are called quadratic congruence codes, and the construction of the corresponding sequences is based on the number-theoretic concept of quadratic congruences. It is shown that p-1 codes exist for every odd prime p and can serve as many as p-1 different users in the CDMA fiber-optic system. The codes belong to the family of optical orthogonal codes, their auto- and cross-correlation properties are established, and their performance is compared to that of the previous optical codes. Examples of the codes and examples of their auto- and cross-correlation functions are given     

Statistical analysis of fiber-optic CDMA communication systems. I. Device modeling

In this paper, we present a new methodology for analysis of all-optical fiber-optic code-division multiple-access (FO-CDMA) networks. In this analysis, we propose statistical models, based on photon-counting techniques, for some basic elements of the network, such as splitters, combiners, star couplers, and FO-CDMA passive encoders/decoders. By following the statistical variation of the photon-count of the string of pulses that constitutes the address sequence in an FO-CDMA network, we will be able to reveal the quantum-limited optical signal-to-noise ratio (OSNR) required at the transmitter output to meet the performance limits. Moreover, considering receiver thermal noise and source extinction ratio, we explore the role of using an optical preamplifier before the detector and the dependence of the performance on the transmitted power and the weight of the employed optical orthogonal codes (OOCs).     

Design of a special family of optical CDMA address codes for fullyasynchronous data communications

A special family of optical address codes, called strict optical orthogonal codes (OOCs), is proposed for fiber-optic code-division multiple access (FO-CDMA) networks. Such codes can strictly guarantee both crosscorrelation and autocorrelation constraints (i.e., λ _c and λ_a) to be one in fully asynchronous data communications and ultrafast switching. Theory of strict OOCs is presented and the code design is described by using the concepts of slot distances. Moreover, the use of strict OOCs can support variable-rate and multirate data communications in an FO-CDMA network with no violation of λ_c=λ_a=1 and no increase of system complexity compared to using conventional OOCs     

Optical orthogonal codes with unequal auto- and cross-correlation constraints

An optical orthogonal code (OOC) is a collection of binary sequences with good auto- and cross-correlation properties; they were defined by Salehi and others as a means of obtaining code-division multiple access on optical networks. Up to now, all work on OOCs have assumed that the constraint placed on the autocorrelation and that placed on the cross-correlation are the same. We consider-codes for which the two constraints are not equal. Specifically we develop bounds on the size of such OOCs and demonstrate constriction techniques for building them. The results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross-correlation constraint. These results suggest that for a given performance requirement the optimal OOC may be one with unequal constraints. This paper also views OOCs with unequal auto- and cross-correlation constraints as constant-weight unequal error protection (UEP) codes with two levels of protection. The bounds derived are interpreted from this viewpoint.<>     

Optical orthogonal codes: design, analysis and applications

An optical orthogonal code (OOC) is a family of (0,1) sequences with good auto- and cross-correlation properties, i.e the autocorrelation of each sequence exhibits the `thumbtack' shape and the cross correlation between any two sequences remains low throughout. The use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably. The thumbtack-shaped autocorrelation facilitates the detection of the desired signal, and low-profile cross correlation reduces interference from unwanted signals. Theoretical upper and lower bounds on the maximum possible size of OOCs are derived. Methods for the design and analysis of OOCs, using tools from projective geometry, the greedy algorithm, iterative constructions, algebraic coding theory, block design, and various other combinational disciplines, are discussed     

Code division multiple-access techniques in optical fiber networks.II. Systems performance analysis

For pt.I see ibid., vol.37, no.8, p.824-33 (1989). In Part I a technique based on optical orthogonal codes was presented to establish a fiber-optic code-division multiple-access (FO-CDMA) communications system. The results are used to derive the bit error rate of the proposed FO-CDMA system as a function of data rate, code length, code weight, number of users, and receiver threshold. The performance characteristics for a variety of system parameters are discussed. A means of reducing the effective multiple-access interference signal by placing an optical hard-limiter at the front end of the desired optical correlator is presented. Performance calculations are shown for the FO-CDMA with an ideal optical hard-limiter, and it is shown that using an optical hard-limiter would, in general, improve system performance     

Optical orthogonal codes with nonideal cross correlation

For optical code division multiple access (OCDMA) networks, many optical orthogonal codes (OOCs) with ideal auto- and cross-correlation properties had been studied widely. In this paper, we relax the cross-correlation constraint slightly and propose a new code family based on perfect difference codes. Given the same code weight and code length, the size of new codes may increase 10 times more than that of ideal OOCs. Although the maximum cross correlation of new codes is larger than one, the cross correlation is less than or equal to one, for the most part. Consequently, the performance of new codes approaches that of ideal OOCs. Numerical results show that the performance of proposed codes was almost the same as that of conventional OOCs under the same code length and code weight     

Two-dimensional spatial signature patterns

An optical orthogonal signature pattern code (OOSPC) is a collection of (0,1) two-dimensional (2-D) patterns with good correlation properties (i.e., high autocorrelation peaks with low sidelobes, and low cross-correlation functions). Such codes find applications, for example, to parallelly transmit and access images in “multicore-fiber” code-division multiple-access (CDMA) networks. Up to now all work on OOSPCs has been based on an assumption that at most one pulse per column or one pulse per row and column is allowed in each two-dimensional pattern. However, this restriction may not be required in such multiple-access networks if timing information can be extracted from other means, rather than from the autocorrelation function. A new class of OOSPCs is constructed without the restriction. The relationships between two-dimensional binary discrete auto- and cross-correlation arrays and their corresponding “sets” for OOSPCs are first developed. In addition, new bounds on the size of this special class of OOSPCs are derived. Afterwards, four algebraic techniques for constructing these new codes are investigated. Among these constructions, some of them achieve the upper bounds with equality and are thus optimal. Finally, the codes generated from some constructions satisfy the restriction of at most one pulse per row or column and hence can be used in applications requiring, for example, frequency-hopping patterns     

Performance bounds for DS/SSMA communications with complexsignature sequences

A unified performance analysis of direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with deterministic complex signature sequences is presented. The probability density function (PDF) of the multiple-user interference is determined. Using a round-down and round-up procedure on the PDF, arbitrarily tight lower and upper bounds on the probability of bit error (PBE) are obtained. Results based on the Gaussian approximation method are also presented. It is shown that complex sequences can yield better PBE performance than binary sequences. Using complex sequences, the number of signature sequences that have good auto- and cross-correlation properties is greatly enlarged. New users employing complex or binary signature sequences can be added to existing systems with graceful performance degradation     

Asynchronous fast frequency-hopping CDMA cellular systems

We address the problem of constructing frequency-hopping codes for use in a fast frequency-hopping code-division multiple-access cellular system with a K-cell frequency-reuse scheme. Different hopping codes are used in different cochannel cells to reduce the cochannel interference. The frequency-hopping patterns possess ideal auto- and cross-correlation properties for use in the intracells and ideal autocorrelation and nearly ideal cross-correlation properties in the cochannel intercells. Additionally the cardinalities (the number of patterns) of the codes for use in the intracells meets the bound and hence are optimal. The maximum number of users which can be accommodated by using the proposed scheme is 20% more than the scheme using the same frequency-hopping code in all cells under a carrier-to-interference ratio of -15 dB     

Demonstration of over 128-gb/s-capacity (12-User/spl times/10.71-gb/s/user) asynchronous OCDMA using FEC and AWG-based multiport optical encoder/decoders

For the first time, an arrayed-waveguide-grating (AWG)-based multiport optical encoder/decoder (E/D) and forward-error-correction (FEC) technique are applied in an optical code-division multiple-access (OCDMA) system. The AWG-based OCDMA E/D with high power contrast ratio between auto-/cross-correlation can significantly suppress the interference noises in an asynchronous OCDMA system without using ultralong optical codes and optical thresholder. A 12-user 10.71-Gb/s asynchronous OCDMA experiment has been successfully demonstrated to transmit ITU-T G.709 OTN frames including FEC.     

A note on the equivalence between strict optical orthogonal codes and difference triangle sets

Zhang (see IEEE Trans. Commun., vol.47, p.967-973, July 1999) proposed a special family of optical address codes, called strict optical orthogonal codes (S-OOCs), was proposed for fiber-optic code-division multiple-access (FO-CDMA) networks. Such codes can strictly guarantee both cross-correlation and autocorrelation functions constrained to have the value one in fully asynchronous data communications and ultra fast switching. In Zhang's work the theory and designs of S-OOC, plus several examples, comparison tables, and performance analyses were presented. In this article, we set up the equivalence between S-OOC and so-called difference triangle sets (DTS), which have been extensively studied previously. Thus, all the known constructions, bounds, and analyses for DTS can be directly applied to S-OOC.     

Code-division multiple-access techniques in optical fiber networks - part III: optical AND logic gate receiver structure with generalized optical orthogonal codes

In this paper, we present a deep insight into the behavior of optical code-division multiple-access (OCDMA) systems based on an incoherent, intensity encoding/decoding technique using a well-known class of codes, namely, optical orthogonal codes (OOCs). As opposed to parts I and II of this paper, where OOCs with cross-correlation /spl lambda/=1 were considered, we consider generalized OOCs with 1/spl les//spl lambda//spl les/w, where w is the weight of the corresponding codes. To enhance the performance of such systems, we propose the use of an optical and logic gate receiver, which, in an ideal case, e.g., in the absence of any noise source, except the optical multiple-access interference, is optimum. Using some basic laws on probability, we present direct and exact solutions for OOCs with /spl lambda/=1,2,3,...,w, with the optical and logic gate as receiver. Using the exact solution, we obtain empirical solutions that can be easily used in optimizing the design criteria of such systems. From our optimization scheme, we obtain some fresh insight into the performance of OOCs with /spl lambda//spl ges/1. In particular, we can obtain some simple relations between P/sub emin/ (minimum error rate), L/sub min/ (minimum required OOC length), and N/sub max/ (maximum number of interfering users to be supported), which are the most desired parameters for any OCDMA system design. Furthermore, we show that in most practical cases, OOCs with /spl lambda/=2,3 perform better than OOCs with /spl lambda/=1, while having a much bigger cardinality. Finally, we show that an upper bound on the maximum weight of OOCs are on the order of /spl radic/2/spl lambda/L where L is the length of the OOCs.     

Channel interference reduction using random Manchester codes forboth synchronous and asynchronous fiber-optic CDMA systems

We propose the random Manchester codes (RMC) to improve the bit error probability (BEP) performance in both synchronous and asynchronous fiber-optic code-division multiple-access (CDMA) systems. The spreading sequences used in the synchronous and asynchronous systems are modified prime sequence codes and optical orthogonal codes (OOCs), respectively. Thermal noise, shot noise, and avalanche photodiode (APD) bulk and surface leakage currents are taken into consideration in the BEP analyzes. The results show that the proposed systems can support a larger number of simultaneous users than other systems with similar system complexity under the same bit-error probability constraint     

Polyphase codes for uplink OFDM-CDMA systems

We propose a OFDM-CDMA system that employs polyphase codes to support variable spreading factors. A systematic approach for constructing the polyphase code sequences of variable spreading factors is developed. Polyphase codes exhibit better auto- and cross-correlation properties than Hadamard codes. When employed in OFDM-CDMA systems, polyphase codes result in certain structured multiple-access interference (MAI) caused by multipath. Analytical and numerical results show that OFDM-CDMA systems employing polyphase codes have better PAPR performance than those using Hadamard codes. The BER performance of the OFDM-CDMA system using polyphase codes is evaluated by numerical results and compared to that of the OFDM-CDMA system using Hadamard codes with and without clipping.     

Optimum code structures for positive optical CDMA using normalized divergence maximization criterion

In this letter we consider optimum code structure for positive optical code division multiple-access (optical CDMA) systems. Positive systems are a class of systems that operate with positive real numbers only. We consider the effect of multipleaccess interference in our model and show that code design for both On-Off Keying (OOK) and Binary PPM optical CDMA systems results in the same solutions. Furthermore, we show that a class of codes known as optical orthogonal codes (OOCs) are the best possible positive codes. In obtaining the results we define normalized divergence based on signal-to-multipleaccess interference ratio (SIR) for a multiple-access system in a useful manner and use it as our criterion to maximize the multiple-access capability of the codes. Finally, we demonstrate that BPPM/OOC can be considered as the closest counterpart of ±1 pseudorandom sequence in radio CDMA communication systems.     

Multimedia transmission in fiber-optic LANs using optical CDMA

In this paper, we address the problem of multimedia transmission in fiber-optic networks. We apply the code-division multiple-access (CDMA) technique for such a network. The necessary conditions for successful operation of the network are given. It is shown that for successful operation, new families of optical orthogonal codes (OOCs) are needed which will have not only good correlation properties within one code family, but also between families of different code lengths. Some possible constructions of multimedia OOCs and the corresponding basic structure of the receiver for the multimedia network are given. Specific examples of OOCs for the case of users with two different data rates are given, and the probability of error (using the Gaussian approximation) as a function of the number of low and high rate users is calculated     

Novel optical fiber code-division multiple access networkssupporting real-time multichannel variable-bit-rate (VBR) videodistributions

we design novel code-division multiple access (CDMA) networks which use strict optical orthogonal codes (OOCs) and incoherent optical processing for multichannel variable-bit-rate (VBR) video broadcasting. The proposed techniques possess the characteristics of fast access tunability and bit-rate flexibility. This in turn can facilitate real-time VBR video distributions for entertainment HDTV applications. Compared with conventional OOCs, the use of strict OOCs can ensure both auto- and cross-correlation constraints to be minimum (i.e., “1”) for multichannel VBR video broadcasting and high-speed photonic switching applications. A parallel-serial hybrid architecture for all-optical tunable decoders (or encoders) is also presented to strict OOCs, which has a fast reconfiguration time to support real-time video applications in high-speed optical fiber CDMA networks     

Two-dimensional optical orthogonal codes for fiber-optic CDMA networks

Several constructions of two-dimensional (2-D) codes have been proposed to overcome the drawbacks of nonlinear effects in large spread sequences of one-dimensional (1-D) unipolar codes in fiber-optic code-division multiple-access (FO-CDMA) networks. Wavelength-time (W/T) encoding of the 2-D codes is practical in FO-CDMA networks. W/T codes reported so far can be classified mainly into two types: 1) hybrid codes, where one type of sequence is crossed with another to improve the cardinality and correlation properties and 2) conversion of 1-D sequences to 2-D codes to reduce the "timelike" property. This paper describes the basic principles of a new family of wavelength/time multiple-pulses-per-row (W/T MPR) codes, for incoherent FO-CDMA networks, which have good cardinality, spectral efficiency, and minimal cross correlation values. In addition, an expression for the upper bound on the cardinality of W/T MPR codes is derived. Another feature of the W/T MPR codes is that the aspect ratio can be varied by a tradeoff between wavelength and temporal lengths. The correlation properties of W/T MPR codes are verified by simulation using Matlab. For given wavelength /spl times/ time dimensions, various W/T codes, whose cardinalities are known, are compared, and it is shown that the W/T MPR family of codes have better cardinality and spectral efficiency than the other W/T codes. Performance analysis of the W/T MPR codes and their limiting cases is carried out for various parameter variations such as the dimensions of wavelength, time, and weight of the code.