Receiver Analysis for Incoherent Optical ASK Heterodyne Systems

Abstract

The present paper describes the system calculation of an optical ASK heterodyne receiver with envelope detection in detail. In particular the intermediate frequency signal and the envelope signal are derived taking account of laser phase noise, additive Gaussian noise, influence of the intermediate frequency filter on both noise terms and intersymbol interferences. Based on the derived envelope the probability density function and the bit error rate are calculated exactly and by useful approximations. In regard of a minimum bit error rate the optimum intermediate filter bandwidth is evaluated as a function of the laser linewidths of the transmitter and the local laser. To highlight typical features of incoherent ASK heterodyne systems simulated eye pattern are presented.

Comparison of Various Calculation Methods for Optical Incoherent Heterodyne Receivers

“…1). The signal of interest in this receiver is the sampled (and normalized) envelope r = a(t)cos((p(t))s(-t)dt + x [ +00 ί -00 a(t)sin(cp(t))s(-t)dt + y I-(D where a(t) denotes the transmitted information, φ (I) the laser phase noise and s(t) ο-· S(f) the time response of the baseband representation of the IF-filter S IF (f) = S(f-f IF ) + S(f+f IF ) [13,20]. The sampling values χ and y represent the inphase and the quadrature component of the additive, bandlimited Gaussian noise at the IF-filter output, caused by the shot noise of the photodiodes and the thermal noise mainly due to the front end amplifier.…”

“…To calculate the BER, the probability density function (PDF) f r (r) is required. As derived in [13,20], this PDF can be written as follows : (2) where Q(x) = 0.5 erfc(x/j/2). Assuming identical occurance probabilities for symbol "0" and "1" we obtain…”

“…(7) enables a nearly "exact" calculation of the BER given in incoherent optical ASK-heterodyne systems. The only inherent approximations are the narrowband consideration of the noisy IF-signal, the neglecting of intersymbol interference (which are considered in [13,20]) and the use of an idealized envelope detector with r(t) = |i IF (t)|.…”

“…As explained in [13,20], the main problem in solving (7) is determining the PDF f c (C) of the random envelope C. Remember that C physically represents the envelope of the IF-signal in the absence of additive Gaussian shot and thermal noise (x = y = 0). In principle it is possible to derive an analytical solution for calculating the required PDF f c (C), however, the computer numerical evaluation is very time consuming, especially for high laser linewidth to bandwidth ratios Af/Af s [13,18,20].…”

“…To begin with, Section 2 gives the basic formulas describing the main signals and the BER in an optical ASK-heterodyne receiver, summarizing the results of [13,20]. Because of the fact that incoherent FSKheterodyne receivers with dual-or single-filter detection work in nearly the same manner as incoherent ASKheterodyne receivers, in this paper we restrict our consideration to the latter receiver.…”