ELEC 3430 Digital Communications
PROBLEM SET 6
Problem 1: Shot Noise
Consider an intensity modulation/direct detection optical communication system. Suppose that the thermal noise and dark current are negligible at the receiver.
a) Draw the optical receiver elements if the employed modulation scheme is OOK.
b) Suppose the intensity of the laser signal at the receiver end, for bits 0 and 1, is respectively given by 0 and I1 . Suppose that the bit period is T and the quantum efficiency is 1. What is the probability mass function for the released number of photoelectrons for each bit?
c) Suppose in part (b), the average number of photons for bit 1 is given by N=1:10. Find the BER for your receiver in part (a), and plot it vs N (Do not use Gaussian approximation.)
d) Suppose we have an optical source that can generate exactly 0 and 1 photon for, respectively, modulating bits 0 and 1. What is the BER for this system if there is no loss in the channel and no noise at the receiver?
Problem 2: BER Calculation
Consider an optical communication link with the following specifications:
Modulation scheme: OOK, transmitted power for bit 1 is I1 = 1mW , and for bit 0 is I0 = 0 .
Channel: optical fibre with 0.25dB/km loss
Operating wavelength: 1550 nm
Receiver: Integrate and dump
Photodetector quantum efficiency: 0.8
Dark count rate: 1E-3/ns
Power spectral density of the thermal noise: 1E-20 A2/Hz Bits 1 and 0 are equiprobable.
a) Suppose the bit rate is 2.5Gbps. Find the minimum BER, in terms of the channel length L, using Gaussian approximation. Suppose that the optimum threshold is given by the point where the error rates for bits 0 and 1 are the same. Plot BER vs. L = 1km:120km.
b) Suppose L = 30km. Suppose that the optimum threshold is given by the point where the
error rates for bits 0 and 1 are the same. Find the minimum BER, in terms of the bit rate R, using Gaussian approximation. Plot BER vs. R = 1MHz:100GHz.