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Electronics Letters

Noise limits of optical spectral-encoding CDMA systems

E.D.J. Smith, P.T. Gough, Desmond P. Taylor

Published Aug 17, 1995• 70 citations
Publisher

Abstract

The performance of optical CDMA systems based on the spectral-amplitude coding of broadband sources is shown to be limited by the optical beat noise between the sources. The limits derived here are significantly lower than previous performance estimates which did not include this beat noise. Even under ideal conditions, the total throughput is approximately inversely proportional to the number of possible simultaneous users.

DOI
10.1049/el:19950993

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The performance of optical CDMA systems based on the spectral-amplitude coding of broadband sources is shown to be limited by the optical beat noise between the sources. The limits derived here are significantly lower than previous performance estimates which did not include this beat noise. Even under ideal conditions, the total throughput is approximately inversely proportional to the number of possible simultaneous users.
Enhanced security has often been cited as an important benefit of optical code-division multiple-access (O-CDMA) signaling but has seldom been analyzed in detail. This paper presents a theoretical analysis of the degree of confidentiality that can be provided by spectral-phase-encoded O-CDMA. Two eavesdropping detector structures are presented that can theoretically break the confidentiality of spectral-phase-encoded signals by detecting the code words in use by a specific user. One of them, an optical beat detector, is quantitatively analyzed to determine the probability of correctly detecting user code words. The confidentiality of user signals is shown to be vulnerable to such a detector if an eavesdropper can isolate a single user signal with a sufficiently high signal-to-noise ratio (SNR). At lower SNRs, combining multiple bits is shown to dramatically increase the probability of an eavesdropper correctly detecting user code words; even for codes long enough to strain implementation capabilities (e.g., 2048 code elements), the probability of correct detection is shown to rise from negligibly low values to virtually 100% by the combining of less than 100 transmitted bits at the eavesdropper's receiver.
Optical CDMA is being proposed as a suitable multiaccess technique to take advantage of the large bandwidth available in single-mode fiber-optic communications. In a CDMA system the communication link is shared by a number of users each of which has a unique address code, called signature. Recently an all-optical CDMA system based upon encoding and decoding coherent ultrashort pulses was introduced [l]. In the proposed optical CDMA system the transmitter consists of a bandhiited signal source, that generates a train of ultrashort light pulses. The output of the bandlimited source is multiplied by a data source that takes values 0 or 1 (ON-OFF Keying). If the data is 0, then no energy is transmitted. If the data is 1, then the ultrashort pulse is sent to the spectral-phase encoder which adds a determinate phase shift to each spectral component of the ultrashort pulse. When a pseudorandom set of spectral phase shifts is selected, spectral phase coding spreads the incident ultrashort pulse into a longer, lower intensity pseudonoise burst 111. The receiver is assumed to be a correlation receiver which is matched to the desired signal. The correlation process (optical decoder) is similar to that of the optical encoder, except that the decoder's spectral-phase code is the complex conjugate of the encoder's spectral-phase code. Thus a pulse is properly decoded when the encoding and decoding masks are a complex conjugate pair, in which case the spectral phase shifts are removed and the original pulse is recovered. On the other hand, when the encoding and decoding masks do not match, the spectral phase shifts are rearranged but not removed, and the output remains a low intensity pseudonoise burst. A threshold device is set to detect data corresponding to intense, properly decoded pulses and to reject low intensity, improperly decoded, pseudonoise bursts. An important factor in the performance of the proposed CDMA systrm is the peak intensity of the encoded signals. We consider using random signatures for the phase encoding of the phase pulses in the system and prove that they result in a fairly low peak intensity of the signals. We assume that the ultra-short light pulses are characterized by an ideal rectangular spectrum with bandwidth W. The ultrashort light pulse has peak intensity Po and duration t, $. Pulses of this form had been used in the experiments reported in [l]. The encodfng is taking place in the frequency domain. The signal
The authors obtain lower and upper bounds on the peak intensity of a spectrally phase encoded ultrashort light pulse as a function of the length of spectral phase encoding. It is shown that using random phase codes for spectral encoding of ultrashort light pulses in a coherent ultrashort light pulse code-division multiple-access (CDMA) system is almost optimal. Furthermore, simple upper bounds and an asymptotic approximation on the bit error rate (BER) for a wide class of ultrashort light pulse CDMA systems are obtained. It is shown that, in spite of being simple, these upper bounds can be used to evaluate the performance of a coherent ultrashort light pulse CDMA system.>