Trellis ternary line coding scheme for asynchronous optical CDMA systems
Introduction
An optical code division multiple access (CDMA) technique has been proposed for high-speed fiber-optic networks [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. One of the most deteriorating factors in optical CDMA systems is multiple access interference (MAI), which may lead to an asymptotic error floor and thus limit the number of simultaneous active users. To mitigate the adverse impact of MAI and enhance the throughput of networks, many schemes and architectures have been discussed [1], [2], [3], [4], [5], [6].
In commercial wireless spread spectrum communications, direct sequence spread spectrum (DSSS) and frequency hopping spread spectrum (FHSS) are the most promising techniques. Although hybrid systems (e.g. DSSS+FHSS) can further reduce MAI and strengthen network security, the system complexity and the enhancement of some core techniques (say, acquisition and tracking) are the inevitable costs. The data rate in optical CDMA systems is much higher than that in wireless spread spectrum communication systems; hence, this leads to stringent requirements of realizing optical CDMA systems for commercial applications. Therefore, the system complexity and some core techniques must be reasonable for implementation.
Conventionally, a sparse code is utilized as a signature sequence in direct-detection optical CDMA systems, for it can reduce the cross-correlation between different users. Optical orthogonal codes (OOCs) and prime sequences are often employed as signature sequences in asynchronous optical CDMA systems [1], [2], [3]. Such coding architectures have tunable encoders/decoders with fast reconfiguration time [8], [9] and an effective interference reduction mechanism [5]; furthermore, the synchronization of signature sequence has also been discussed [12], [13], [14].
For “asynchronous” optical CDMA systems, each user transmits data asynchronously with each other; thus network synchronization is unnecessary [1], [2], [3]. However, the transmitter and intended receiver should be in exact synchronism; otherwise, timing error will lead to impairment of system performance. To eliminate timing error, a precise synchronization scheme is necessary at the receiver. Traditionally, the self-synchronization technique is often used for a synchronization subsystem in terms of benefits of bandwidth, transmitted power, and system complexity. Such a scheme acquires symbol synchronization (i.e. clock recovery) directly from the received signal, which must contain adequate timing information to allow for proper operation of clock recovery circuitry. Transmitted signals without sufficient level transitions (say, a long sequence with consecutive null symbols) will cause severe timing jitter or even transient loss of lock in baseband synchronization, and also foils adaptive equalization and echo cancellation [15], [16]. In conventional optical CDMA systems [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], to overcome the problem mentioned above, scrambling and bit-stuffing techniques have been employed. Of course, the additional complexity is inevitable. Alternatively, the line coding technique is an effective way to overcome the problem described above. In the literature, some line coding techniques had also been discussed for applications in optical communication systems [17], [18], [19].
The trellis-coded scheme for applications in baseband systems was first discussed by Wolf and Ungerboeck [20]. Applying Ungerboeck's trellis-coded scheme [21], a ternary line coding technique is proposed in [22]. In [10], [11], the OOC and prime sequence have been studied for an equal-weight orthogonal (EWO) signaling scheme. The EWO scheme requires two mutually orthogonal signature sequences to represent binary “+1” and “−1”. It has been found that the EWO signaling scheme has some superior merits over on–off keying (OOK). First of all, an OOK signaling scheme requires a dynamically adjustable receiving threshold. The optimal threshold for optical CDMA systems varies with the number of active users, and the use of a nonoptimal threshold may degrade the bit error rate (BER) by several orders of magnitude [10], [11], [23]. Receivers with dynamic thresholding schemes will increase the system complexity, and will even be intractable especially in high-speed transmission and bursty traffic situations. Secondly, when the lasers are power-limited, the EWO signaling scheme is preferable to the OOK signaling scheme because it utilizes twice the amount of average signal energy in transmission [10], [24], [25], [26], [27]. Besides, the OOK optical CDMA is more vulnerable than EWO in terms of network security [28]. In this paper, we utilize a ternary {+1, 0, −1} symbol set based on the EWO scheme [10], [11], and also use the line coding method [22] to further improve system performance.
Avalanche photodiode (APD) is employed for photodetection. We apply Gaussian approximation [10] to analyze the bit error probability (BEP). Moreover, instead of OOC, the prime sequence is utilized as a signature sequence in our proposed scheme for two reasons. In the first place, for a large number of users and large received optical power, using a prime sequence can yield better performance than using OOC under the EWO scheme [10], [11]. In addition, efficient and less complex encoders for prime codes have been proposed which have fast reconfiguration time [8], [9]; thus it is suitable for ultrafast optical CDMA networking because of the all-optical architecture used.
This paper is organized as follows. In Section 2, systems using ternary codes and trellis-coding schemes for asynchronous optical CDMA systems are described. System performance analysis of the proposed scheme is given in Section 3. Section 4 presents some numerical results. Finally, conclusions are drawn in Section 5.
Section snippets
System description
In this paper, the prime sequence is employed as a signature sequence. The prime code can be constructed from the Galois field GF(p)={0, 1, …, j,…, p−1}, where p is a prime number [1], [2]. There are p codewords each with weight p, and length p2. The cross-correlation value is no greater than 2, and the cardinality is p.
In [10], [11], the EWO scheme was proposed that used two mutually orthogonal signature sequences a and to represent binary “+1” and “−1”, respectively. Here is generated from
System performance analysis
At the receiver, the upper and lower correlators correlate the received multiple access signal individually, and then the correlated optical signals are incident upon APDs for photodetection. The received optical signal intensity over a chip interval Tc can be modeled as a Poisson point process. The average number of absorbed photons is λsTc, where λs is the average arrival rate of incident photons during a chip “1” (weight of signature sequence) transmission in the signature sequence, which
Numerical results
In this section, the typical APD parameters used here are the same as those in [10] and listed in Table 1.
We employ the prime sequence as the signature sequence; thus the bandwidth expansion factor (i.e. spreading factor) is F=p2, where p is prime. Fig. 3, Fig. 4 show BEP comparisons under bit rate Rb=10 Mbps for the EWO scheme [10] and the proposed TTC scheme. Here the number of active users K=10 and p=11, 13, 17, and 19. The asymptotic error floors appear due to multiple access interference.
Concluding remarks
In this paper, we apply the TTC scheme for asynchronous optical CDMA systems, which is based on the EWO scheme [10], [11] and line coding technique [22]. Such arrangements not only can considerably improve system performance but also allow for proper operation of timing extraction circuitry because sufficient clock information is embedded in the transmitted signal.
The prime sequence is used as signature sequence, because for a large number of users and large received optical power systems,
Acknowledgment
This work was supported in part by the National Science Council, under Grant NSC 96-2218-E-197-001, NSC 94-2213-E-002-061, NSC 96-2628-E-002-252-MY3 and National Taiwan University Aim for Top University Program.
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