A high-speed optical data communication system is composed of a transmitter, an unamplified transmission fiber link, and a receiver. The optical transmitter generates a 10-Gb/s non-return-to-zero (NRZ) signal using a 1550-nm laser diode (linewidth=2 MHz) followed by a chirp-free Mach-Zehnder modulator. The signal has a very high extinction ratio and the fiber launch power is 0 dBm. After transmission over single-mode fiber (loss: 0.2 dB/km, chromatic dispersion: 17 ps/nm/km), the signal is detected by a PIN receiver. The responsivity of the PIN detector is 0.8 A/W and the receiver has a load resistance of 50 W. The bandwidth of the receiver is 8 GHz. Assume that the noise temperature is 300 K, and the target bit-error rate (BER) is 10^-9.
The Attempt at a Solution
First of all, even though I'm given the dispersion of 17 ps/nm/km, the "loss-limited" term refers only to the attenuation fiber loss, is this correct?
I've done the following, and I hope to know if I'm correct.
For BER of 10-9, Q-factor = 6.0.
For high extinction ratio, SNR ≈ 4Q2 = 144.
Power at transmitter, Ptrans = 0dBm = 1mW
SNR = (R2RL Prec2) / (4kBTΔf)
144 = (0.82×50×Prec2) / (4×1.38×10-23×300×8×109)
Prec = 2.44×10-5W
α = 0.2 = -(10/L)log (Prec / Ptrans)
L = 80.6 km ← loss-limited transmission distance