<#),$+0"$#) ?">& B"$"')+0"$#) ?">&? F. S. Blair March 24, Analog and Digital Signals

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1 S. Blair March 24, Analog and Digital Signals <#)*,$+0"$#)* B"$"')*+0"$#)* G H G? F Analog signal varies continuously with time, needs high signal-to-noise ratio Digital discrete values, binary T B bit period or time B bit rate = 1/T B bandwidth Example: ASCII code - 7 bit (0-127) a-z (65-90) A-Z (97-122) Digital modulation requires higher bandwidth than analog. A digital bit of width T, where T<T B, has a Fourier transform rect(t/t ) sinc(ft). The first zero of the sinc() function occurs when f =1/T > B. Therefore, the bandwidth required of the transmission channel is greater than the actual bit-rate. However, digital modulation results in better noise performance as nonlinearities in the channel do not degrade the signal as much. For example, laser diode modulation could produce harmonic distortion in an analog signal if the diode is not properly biased, as shown in the figure. For a nonlinear transfer function, a square wave still maps to a square wave.

2 S. Blair March 24, I5':5' :,8&( -5#.'",#+.)50&0+1)(>,#". ="0',('",#J+81".1+=&$()=&0 )#+)#)*,$+0"$#)*K++?1& ="$"')*+(&:(&0&#')'",#+.)# ',*&()'&+1)(>,#".+="0',('",#K 6#:5'+.5((&#' Analog to Digital Conversion Many signals originate in analog format (such as voice and video) and can be converted to digital. This conversion consists of three steps: 1. Sample analog signal at discrete time intervals 1/f s, with sampling frequency f s 2. Quantize sampled value into discrete set of M values 3. Digitize into binary representation of log 2 M bits Analog to digital conversion A max Analog Sampling usually by energy detected over finite window Time Sample + quantization 2ΔA ΔA Sampling frequency ƒ s > 2Δƒ = Nyquist frequency Δƒ = bandwidth Digital Sampled value 0 < A < Amax Can quantize into any number of discrete values Quantization noise is minimized by a number of discrete levels M that satisfies M = A max /A N, where A max = maximum signal amplitude A N = RMS noise amplitude of analog signal

3 S. Blair March 24, This means each quantization interval A = A N. There is no sense in having A <A N,asit provides no additional information. A max A N = amplitude dynamic range The signal-to-noise ratio is defined ( ) Pmax SNR = 10 log =10log P noise ( ) A 2 max /R =20log A 2 n/r ( Amax A N ) =20logM SNR will ultimately determine the bit-error-rate (BER). For binary modulation, the number of binary digits, or bits, needed is m =log 2 M Digital formats Binary representation Quantized value The physical digital formats used with optical pulses are pulse-position modulation, pulse duration modulation, and pulse code modulation... NN/+D:5*0&;:,0"'",# >,=5*)'",#E H G L M NB/+D:5*0&;=5()'",# >,=5*)'",#E?1&0&+0.1&>&0+)(&+#,'+ (,C50'+"#+'1&+:(&0&#.&+,-+ ="0:&(0",#+)#=O,(+P"''&( MLGH In PCM (pulse code modulation), the pulse is either present(1) or not (0). PCM is also known as on-off keyed (OOK), which is the most common modulation format in optical systems.

4 S. Blair March 24, Bandwidth requirements of digital PCM (OOK) The total bit rate of digital PCM is B = mf s 2 f log 2 M, which can be written in terms of the SNR as B =( f/3)snr. As an example, for SNR= 30 db, B 10 f,whichrequiresatleast a factor of 10 greater bandwidth than analog,where f is the original analog bandwidth. For a typical audio signal (i.e. telephone), f 4 khz. In order to obtain 30 db SNR, the digital bit-rate must be greater than 40 kb/sec, and is usually 64 kb/sec. In this case, the sampling frequency f s =8 khz, and each sample consists of m = 8 bits (i.e. M=256 quantized levels). For reference, AM radio has a bandwidth of 10 khz, and FM radio 200 khz. TV stations transmit with about 6 MHz of bandwidth. For real-time, uncompressed video, B 81 Mb/sec using 9-bit sampling at 9 MHz. The audio track is sampled at 30 khz with 8-bit quantization, for a total of 240 kb/s. Note that a T1 line = Mb/sec, so digital video requires at least a T3C line Mb/s. Compressed video can be transmitted at 5 Mb/s, while compressed HD requires 20 Mb/s Modulation formats The optical carrier can be represented by E(t) = 1 2 Aei(ωot+φ) + cc Any of the three major properties of the carrier can be modulated to represent data - amplitude, phase, and frequency. Analog modulation 1. amplitude (AM, change A) 2. frequency (FM, change ω = dφ/dt) 3. phase (PM, change φ) Digital modulation 1. ASK (amplitude shift keyed) 2. FSK 3. PSK For two levels, ASK is the most common, using A =0andA = A o. This is also called OOK, or on-off keyed. There are two binary OOK representations in use today in optical communications systems - return to zero (RZ), and non-return to zero (NRZ). NRZ is the current standard, but RZ will most likely dominate in future systems.

5 S. Blair March 24, !Q Detection schemes 1. Coherent 2. IM/DD intensity modulation/direct detection. Electronics determine if bit is 0 or 1. SNR determines accuracy of decision.

6 S. Blair March 24, Time-division multiplexing TDM (interleaving) is used in telephone networks to generate composite signal at high bit rate. Digitized voice at 64 kb/sec is much less than the capacity of single optical channel. Consider N independent bit streams at bit rate B. The original bit slot time of each stream is T B =1/B, whereas the new, composite, stream has a bit slot time T B =1/N B. Thisinterleavingoperation can be performed electronically up to about 10 Gb/s, using a GaAs shift register, for example. Interleaving can also be performed entirely in the optical domain, which is termed OTDM. TDM and OTDM can be done with digital signals only. TDM/OTDM Channel 1 Channel 2 Channel 3 Time MUX Electrical or optical T B T' B Digital hierarchy: DS (signaling designation), T (transmission designation). DS-0 1 voice channel 64 kb/sec DS-1 24 voice channels Mb/sec T1 line DS-2 4 DS-1 channels Mb/sec T2 DS-3 4 DS-2 channels Mb/sec T3 DS-3C 2 DS-3 channels Mb/sec T3C DS-4 6 DS-3 channels Mb/sec T4 and so on SONET SDH B(Mb/s) Voice Channels Time OC OC-3 STM ,016 OC-12 STM ,064 OC-48 STM-16 2, , s OC-192 STM-64 9, ,024 late 90s OC-768 STM , ,096 late 90s OC (optical carrier) SONET (synchronous optical network) 1980 s Now, SDH (synchronous digital hierarchy). International Standard. Defines frame structures (meanings of bits in payload header) for TDM, implemented in hardware and/or software.

7 S. Blair March 24, WDM Wavelength division multiplexing Back to the issue of channel capacity, C = f ch log 2 (1 + S/N) where f ch is the channel bandwidth, S is the average signal power, and N is the average noise power. Modulation rate f ch cannot be increased arbitrarily because of increase in noise. With shot noise, for example, N = N o f ch, where N o is the spectral density of shot noise. As f ch, C (S/N o )log 2 e S/N o,assumingthats is constant. The solution to this problem is to either increase S proportionally, or to use multiple channels (i.e. carriers) via WDM. WDM is sometimes called FDM - frequency division multiplexing. Each channel is carried a different carrier frequency, or wavelength. These channels non-overlapping in the spectral domain and can be combined or separated using spectrally-selective methods such as multiplexers and bandpass filters. G G M L M L AB/ M F %)#+C&+50&=+8"'1+C,'1+)#)*,$ T+="$"')*+D"K&K+()=",+)#=+?U C(,)=.)0'E G L WDM is the emerging technology for second generation networks. Standard channel spacings are 200, 100, and eventually, 50 GHz. Smaller spacings allow for more WDM channels, but place greater demands on component design and fabrication.

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