9.6.1 Spectral Efficiency

An important issue is related to the enhancement of spectral efficiency of dense WDM systems as much as possible. As discussed in Section 9.1.1, the spectral efficiency is defined as η_s = B/Δv_ch, where B is the single-channel bit rate and Δv_ch is the channel spacing. Most commercial WDM systems in 2004 were operating with η_s ≤ 0.2 (b/s)/Hz, as they were designed to transmit 10-Gb/s channels with a spacing of 50 GHz or more. Many laboratory experiments have shown that WDM systems whose channels operate at 40 Gb/s with a spacing of 100 GHz can be designed to realize system capacities of more than 2 Tb/s with a spectral efficiency of 0.4 (b/s)/Hz. Such a 50-channel system occupies a bandwidth of 5 THz (around 40 nm near 1.55 µm) that covers the entire C band. Any increase in the capacity requires either the use of both the C and L bands or a reduction in channel spacing. For this reason, several experiments transmitted 40-Gb/s channels with a spacing of 50 GHz, resulting in a spectral efficiency of 0.8 (b/s)/Hz. Such WDM systems either employ modulation formats that are different than the standard RZ and NRZ formats or prefilter the optical signal at the transmitter end using an optical filter [135]-[142].

The idea behind prefiltering is simple. An optical bit stream generated by modulating an optical carrier has a symmetric spectrum with multiple peaks separated by a frequency equal to the bit rate. Since the left and right sidebands contain redundant information, one can borrow a technique from the microwave technology known as vestigial sideband (VSB) transmission, and launch only one of the sidebands into the fiber link. This technique has been used for NRZ-format WDM systems by filtering the signal spectrum with an optical filter that is detuned from the center by an optimum amount [141]. Figure 9.27(a) shows the location of filter passband (dashed curve) superimposed on the the spectrum of a 40-Gb/s NRZ bit stream. The penalty curve and the eye patterns for several detunings show that the optimum detuning is around 20 GHz for a 30-GHz bandwidth filter.

It turns out that the suppressed sideband can be reconstructed partially during transmission by the nonlinear effects occurring within the fiber link. An alternative scheme transmits the whole spectrum but employs an optical filter at the receiver end to select only one sideband. The spectral efficiency is enhanced in this scheme by using a channel allocation pattern as shown in Figure 9.27(b). Rather than using a constant channel spacing, it is alternated between 50 and 75 GHz for successive 40-Gb/s channels, resulting in a spectral efficiency of 0.64 (b/s)/Hz. At the receiver end, channels are selected with a 30-GHz filter that is detuned by 20 GHz or so toward the 75 GHz-spaced neighboring channel. With this arrangement, one always selects the sideband experiencing the smallest overlap with adjacent channels. This scheme was used as early as 2000 to transmit 128 channels at 40 Gb/s over 300 km, resulting in a system capacity of 5.12 Tb/s [141]. In later experiments, link length could be increased to around 1,500 km with the use of FEC, even though the effective bit rate of each channel increased to 42.7 Gb/s.

Figure 9.27: (a) Measured power penalty (thick solid curve) as a function of filter detuning (top inset) and eye diagrams at four values of detuning, (b) Measured spectra of filtered channels at the receiver end when channels are alternatively spaced by 50 and 75 GHz. (After Ref. [141]; ©2004 IEEE.)

In a 2001 experiment, the same scheme was used to realize a record capacity of 10.2 Tb/s by transmitting 256 channels at 40 Gb/s over 100 km [141]. This experiment employed the technique of PDM by transmitting two orthogonally polarized channels at each wavelength, and thus realized a spectral efficiency of 1.28 (b/s)/Hz. The PDM technique should be distinguished from polarization interleaving (see Section 9.5.3) in which neighboring channels are orthogonally polarized. In the case of PDM, the bit rate is effectively doubled as two orthogonally polarized bit streams are launched at each channel wavelength. Such a scheme suffers the most from the PMD problem. In a 2002 experiment, the distance could be increased to 300 km at 10.2 Tb/s by shifting the wavelengths slightly for the two orthogonally polarized bit streams.

In the case of RZ format, the channel bandwidth can be reduced to some extent by employing the CSRZ format (see Section 2.3.3) in which phases of the neighboring pulses in an optical bit stream differ by π. The carrier is suppressed for such a bit stream, and the two dominant spectral peaks are located at v₀± B/2, rather than at v₀± B, where v₀ is the carrier frequency and B is the channel bit rate. This feature allows considerable filtering of the signal before it is launched into the optical filter, while still retaining both sidebands. Figure 9.28 shows in several situations the effects of filtering on the spectrum of a 40-Gb/s channel modulated with the CSRZ format [142]. The eye diagrams recorded under back-to-back conditions (no fiber) are also shown. When the filter passband was centered at the carrier frequency (symmetric filtering), even a 68-GHz filter produced an almost 3-dB penalty in the measured Q factor. In contrast, the penalty was below 1.5 dB even for a 35-GHz filter, detuned off-center by an optimum amount (asymmetric filtering). In a 2002 experiment, a spectral efficiency of 1 (b/s)/Hz was realized with asymmetric filtering by transmitting 25 channels at 40 Gb/s, resulting in a capacity of 1 Tb/s. By 2003, a 5.12-Tb/s WDM signal (128 channels at 40 Gb/s per channel) was transmitted over 1,280 km by filtering each 42.7-Gb/s CSRZ bit stream (with 7% FEC overhead) with a 50-GHz optical filter [137]. Each channel was launched with -4 dBm of average power, and neighboring channels were orthogonally polarized to reduce interchannel crosstalk.

Figure 9.28: Effect of optical filtering on channel spectra and eye patterns: (a) unfiltered case; (b) symmetric 68-GHz filter; (c) symmetric 35-GHz filter; (d) asymmetric 68-GHz filter; (e) asymmetric 35-GHz filter. (After Ref. [142]; ©2004 IEEE.)

In the case of the CSRZ format, phases of neighboring pulses differ by π, but information is coded through ASK or on-off keying. In the case of the RZ-DPSK format, information is coded in the optical phase but a pulse is present in all bit slots. One can even employ the CSRZ format in which an additional phase shift of π is added to alternate pulses, in addition to the phase shift required for DPSK coding. This type of DPSK coding has proven to be quite useful for enhancing the performance of high-capacity WDM systems. In a 2003 experiment, 89 channels, each operating at 42.7 Gb/s (because of 7% FEC overhead), were transmitted over 4,000 km using the CSRZ-DPSK format, while employing Raman amplification with 100-km spacing between pump stations [131]. The channel spacing was 100 GHz in this experiment.

Several experiments have used the DPSK format for transmitting 40-Gb/s channels with 50-GHz channel spacing to realize a spectral efficiency of 0.8 (b/s)/Hz. In one experiment, 160 channels at 42.7 Gb/s (capacity 6.4 Tb/s) were transmitted over 3200 km of fiber [138]. Figure 9.29 shows the experimental setup schematically. Each 100-km section had a dispersion of 7.5 ps/(nm-km) and a dispersion slope of 0.039 ps/(nm²-km). Its loss was compensated through Raman amplification, while its accumulated dispersion was compensated using a DCF such that residual dispersion after one round trip in a 400-km recirculating loop was below 0.03 ps/(nm-km) for all channels. Two dynamic gain equalizers were used to maintain nearly equal power for all channels after each round trip inside the loop. It was necessary to employ FEC coding to ensure a corrected BER of less than 10^-12 after 3,200 km. The capacity-distance product exceeded 20 (Pb/s)-km for this experiment.

Figure 9.29: Experimental setup for the CSRZ-DPSK system with a 6.4-Tb/s capacity. PC: polarization controller; GE: gain-equalizing filter; RP: Raman pump; MZDI: Mach-Zehnder delay interferometer; WGR: waveguide grating router. (After Ref. [138]; ©2004 IEEE.)

One may wonder whether it is possible to realize a spectral efficiency of > 1 (b/s)/Hz, and if the answer is yes, how large it can be made. This question has attracted considerable attention in recent years as it is related to the ultimate capacity of a communication system operating over a finite channel bandwidth [143]-[148]. The issue of channel capacity was first studied by Shannon [149], who showed that for a finite-bandwidth signal, the maximum capacity C_ch of a linear channel of bandwidth Δf_ch in the presence of Gaussian noise is given by

where SNR is the signal-to-noise ratio at the receiver. If we assume that Δf_ch is nearly equal to the bit rate B and define the capacity per unit bandwidth as

we find that η_c for a linear channel can be increased beyond 1 (b/s)/Hz without an upper bound, as long as SNR is made large enough, even though η_s = B/Δv_ch remains below 1 (b/s)/Hz. Sometimes, η_c is referred to as the spectral efficiency [148], and η_s is called the bandwidth utilization factor.

Figure 9.30: Spectral efficiency as a function of input power density. Solid lines show the limitation set by XPM or FWM; dashed lines are obtained in the absence of nonlinear effects. Information is coded in both the intensity and phase for the curves marked unconstrained. (After Ref. [148]; ©2004 IEEE.)

As we have seen, optical fibers do not constitute a linear channel, and the preceding equation cannot be applied to them. The degradation caused by the nonlinear effects eventually limits η_c to a maximum value. Figure 9.30 shows η_c as a function of input power density (defined as the average input power per unit bandwidth) when information is recovered using a coherent detection scheme. The intensity of the channel is kept constant for the lower curve but both the phase and intensity are modulated for the curve marked unconstrained. These results are obtained for a dense WDM system (101 channels at 40 Gb/s spaced 50 GHz apart), designed with fiber parameters α = 0.2 dB/km, D = 17 ps/(km-nm), and γ = 1.24 W^-1/km. Fiber loss and dispersion are assumed to be compensated every 80 km. It is evident from Figure 9.30 that the nonlinear effects limit the maximum spectral efficiency to below 5 (b/s)/Hz even when information is coded in both the phase and amplitude of each channel.

In practice, a spectral efficiency of at most 1 (b/s)/Hz can be realized when a binary modulation scheme is employed. The use of polarization multiplexing can increase this value, but the enhancement is limited because of the difficulty in recovering a polarization-coded bit stream at the receiver end. Nevertheless, a value of 1.28 (b/s)/Hz has been realized with polarization multiplexing [141]. Larger values of η_c are possible if multilevel signaling is employed. A spectral efficiency of 1.6 (b/s)/Hz was realized in a 2003 experiment in which a format known as differential quadrature PSK (or DQPSK) was employed in combination with polarization multiplexing [150].