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In a digital system a photodetector in the receiver produces an output voltageproportional to the incident optical power level. This voltage is compared onceper bit time to a threshold voltage level to determine whether a pulse is presentat the photodetector in that time slot. Ideally the measured voltage wouldalways exceed the threshold voltage when a 1 is present and would be less thanthe threshold voltage when no pulse (a 0) was sent. In an actual system, vari-ous noises and interference effects cause deviations from the expected outputvoltage, which leads to errors in the interpretation of the received signal.14.1.1. Bit error rateThe most common figure of merit for digital links is the bit error rate, whichcommonly is abbreviated as BER. This is defined as the number of bit errors NEoccurring over a specific time interval, divided by the total number of bits NTsent during that interval; that is, BER ϭ NE/NT. The error rate is expressed bya number, such as 10Ϫ9, which states that on the average one error occurs forevery billion pulses sent. Typical error rates specified for optical fiber telecom-munication systems range from 10Ϫ9to 10Ϫ15. The BER also is known as theerror probability, which commonly is abbreviated as Pe.The SNR is related to the BER through the expressionBER ϭ ᎏ͙12ෆπෆᎏ ͵ϱ0expϪᎏx22ᎏdx Ϸ ᎏ͙12ෆπෆᎏ ᎏeϪQQ2/2ᎏ (14.1)where the symbol Q traditionally represents the SNR for simplicity of notation.The approximation on the right-hand side holds for BER Ͻ10Ϫ3, which meansit is accurate for all cases of interest in optical fiber communications. Figure 14.1shows how the BER or Pe varies with Q. Some commonly quoted values areQ ϭ 6 for BER ϭ 10Ϫ9, Q ϭ 7 for BER ϭ 10Ϫ12, and Q ϭ 8 for BER ϭ 10Ϫ15.The Q value is defined asQ ϭ (14.2)
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