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In this module, we will go through some basics of modulation. As I had mentioned earlier, I am assuming that you have not done any course in communication. So, we will talk about certain basics of communication so that all of us are on the same page. We will start with analogue and digital signals. All the naturally occurring signals are analogue in nature, where the signal levels change continuously with time. These are digitized for various purposes through a process called analogue- to-digital conversion. The digitization of an analogue signal comprises of two processes: (1) sampling, and (2) quantization. Let us start with an analog signal, which is traced shown as the red line in the figure. We decide to sample this signal at specific sampling frequency (fs). The sampling frequency is decided by the bandwidth of the signal through the Nyquist criteria, which states that the sampling frequency must be at least twice the largest frequency content of the analogue signal. If the largest frequency content in the signal is at frequency fB, the signal has to be sampled with a frequency of at least 2fB. The sampling process decides the time duration between consecutive samples or the sampling duration. Thus, the sampling process discretizes the x-axis (time axis), which now consists of the sampling instants. Next, the range of the amplitude values of the signal (y-axis) is also discretized into quantization levels. Now, the values of the signal at the sampling instants NPTEL-Fiber Optic Communication Technology – Lecture3 Page 2 are assigned the value corresponding to the nearest quantization level. In this manner, the analog signal is converted to a digital signal. Let us consider the example shown here. We have considered 8-level quantization, which requires 3 bits. In general, for N-level quantization, the number of bits required is b = logଶN. Thus, each quantized level or symbol is represented using b bits. If the bandwidth of the signal is fB, the minimum sampling rate required according to Nyquist criteria is 2fB, which is equal to the symbol rate (symbols/s). Thus, the bit rate of the digital signal is given as follows. Bit rate = symbol rate × bits per symbol Bit rate = 2 × f஻ × logଶ N The optimum number of quantization levels depends on the amplitude accuracy of the quantization accuracy required in the system. Larger the number of levels, more accurate is the signal representation. But on the downside, larger the number of vertical levels, more is a number of bits required to represent the same information. That is the trade-off. For example, consider the speech signal. Human beings are more sensitive in the frequency range 2 kHz to 4 kHz. Hence, in general, the speech signal has a frequency range between 2 to 4 kHz. Now, we perform the calculation of bit rate for a speech signal. Assume that the largest frequency (fB) in the speech signal to be 4 kHz, and consider 8-bit quantization. This means that each sample is to be represented by 8 bits so that the number of quantization levels is N = 2଼ = 256. In this case, the bit rate can be computed to be 2 × 4 × 10ଷ × 8 = 64 kbps. This is the data rate of a basic telephone signal. Depending on the kind of signal to be transmitted (image, audio, video), the data content and the bandwidth may vary, which decides the number of quantization levels and the sampling rate, but the basic calculation of bit rate remains the same. This is how we move from bandwidth to bit rate in your analogue-to-digital conversion process. Now, we have sampled and quantized the analogue signal to obtain a digital signal. The next thing you want to do is modulation. The first question is why do we want to modulate? Before that, let us understand what happens during modulation. In modulation, we start with the baseband signal, which is the digital signal that we have obtained through analogue-to-digital conversion, represented by x(t). We multiply the baseband signal with a sinusoid generated from a local oscillator whose frequency is fC, which results in x(t) × cos (2πf஼t). This is the basic time-domain representation of modulation. We now visualize the same idea in the frequency-domain. The baseband signal gets multiplied by the sinusoid, and according to the laws of Fourier transform, we know that multiplication in the time domain corresponds to a convolution in the frequency domain. The spectrum of the signal x(t) is represented as X(f). When this spectrum is convolved with the spectrum of a sinusoid of NPTEL-Fiber Optic Communication Technology – Lecture3 Page 3 frequency fC, we get replicas of X(f) centred at +fC and -fC. Thus, we have moved from a baseband signal to a passband signal. The centre frequency is decided by the local oscillator frequency. Fourier transform of cos(2πf஼t) = δ(f − f஼ ) + δ(f + f஼ ) Fourier transform of x(t) cos(2πf஼t) = X(f) ∗ [δ(f − f஼ ) + δ(f + f஼ )] = X(f − f஼ ) + X(f + f஼) This process of modulation enables the frequency-multiplexing of the data from various users. Different users can be assigned slightly different carrier frequencies, and thus all the users can transmit the data simultaneously over the same channel without the respective signals getting mixed. Apart from this, there are other reasons for the requirement of modulation. You may have learned in electromagnetics that the antenna size required to transmit a signal is decided by the frequency of operation. The size of the antenna is proportional to the wavelength. So, smaller is the frequency, larger is the wavelength, and hence, longer antennas are required. So, for a free space communication link, the practical limitations on antenna size will necessitate the need to push the signals into passbands. NPTEL-Fiber Optic Communication Technology – Lecture3 Page 4 For example, 2G or LTE signals have a certain allocated band of frequencies, and the information from different users gets modulated at slightly different fC’s in that band. This is one way of multiplexing information. Additionally, this baseband signal cannot be transmitted directly because there is a lot of environmental noise in the system at low frequencies, for example, the 50 Hz noise of the power transmission line. Baseband signals from two different sources cannot be transmitted on the same channel, because they will interfere. All these issues because of the interference and the noise can be eliminated by shifting the signal to the passband. So, that is why modulation is needed.
The important thing to be noted is the difference between bandwidth and carrier frequency. Both these terms have their own relevance. Carrier frequency indicates the frequency of the carrier signal, whereas, the bandwidth is decided by the message that is to be transmitted. We had taken the example of analogue speech signals which have a bandwidth of 4 kHz, but after analogue-to-digital conversion, the same signal corresponds to a bit rate of 64 kbps, depending upon the choice of the sampling frequency and the resolution of quantization. Now that we know that modulation is essential, we try to understand the difference between analogue modulation and digital modulation, and make a comparison between them. • Analog modulation: The picture on the top-left shows the message signal as a voltage, which is the modulating signal. For the sake of simplicity, a sinusoid is taken as the basic example of an analogue message signal. The carrier signal is considered to be a sinusoid with frequency fC. Using the modulating (message) signal, one of the properties of the carrier signal may be modulated, thus leading to the following types of modulation. o Amplitude modulation: The amplitude of the carrier signal is varied according to the modulating signal. o Frequency modulation: The carrier frequency itself is varied according to the modulating signal. o Phase modulation: The phase of the carrier signal is varied depending on the modulating signal. A phase-modulated signal may look identical to the frequency modulated signal because phase and frequency are closely related to each other: the time-derivative of phase is the instantaneous frequency. The telephone signals used in the past are examples of analogue signals. • Digital modulation: On the right, we see a digital modulating signal, which is a sequence of bits 1 and 0. Corresponding to the analogue modulation formats, digital modulation can also be categorized into 3 types of keying. o Amplitude Shift Keying (ASK): The amplitude of the carrier is modified according to the bit; for example- bit‘1’ represents high amplitude; while bit‘0’ represents low amplitude. This format is more popularly known as On-Off Keying (OOK). o Frequency shift keying (FSK) : The carrier frequency is switched between two frequencies. Note that unlike frequency modulation where the frequency is continuously varied, the carrier frequency in FSK can be in one of the 2 states - a high frequency and a low frequency. o Phase Shift Keying (PSK): The phase of the carrier signal is switched between two values, 0 and π, corresponding to the bits 1 and 0. The Fourier transform, or the frequency spectrum of a sinusoid with frequency fC is represented as two impulses (Dirac δ-function) at frequencies ±fC. When the carrier signal is modulated with a message signal, the spectrum of the carrier signal broadens, and the width of the broadened spectrum is dependent on the bandwidth of the modulating signal. It is important to have the bandwidth of the signal spectrum in mind because there are certain effects (impairments) in fiber optical communication systems, which are dependent on the bandwidth. For example, chromatic dispersion in the fiber is dependent on the signal bandwidth. Another important point to bear in mind is the distinction between bandwidth and linewidth. Signal bandwidth is a consequence of the spectral width of the modulating signal, as discussed above, whereas linewidth is the property of the carrier signal. Due to certain imperfections (phase noise) in the laser source generating the carrier signal, its spectrum may not be an ideal δ- function; it may have a finite width, which is better known as linewidth. The chromatic dispersion is dependent on the bandwidth, rather than the linewidth. Conventionally, optical communication is carried out predominantly with digital modulation. Recently, we have realized that analogue modulation may be better for certain specific applications, which we will deal with when we talk about networks. But predominantly, optical communication systems deal with digital modulation. Let us have a look at the advantages of digital modulation. • Ease of storage: It is convenient to store data in digital format, in the form of bits, using registers/buffers and digital memory devices. Storing and retrieving data in analogue forms is relatively complicated (magnetic tapes and memories) and inefficient. • Signaling/multiplexing: Since the signal consists of only discrete amplitude levels, signalling (encoding and decoding) is relatively simpler, compared to analogue signals, where there are continuous (infinite) amplitude levels. Due to the discrete nature of the signal, it is easier to multiplex/demultiplex data from multiple sources on the same channel. • Robust to distortion: Since the signal consists of discrete values, even if the signal gets distorted in the link, a simple thresholding and level detection to retrieve high and low levels (1 and 0 bits) maybe sufficient for successful detection (at an appropriate sampling instant). Such robustness to distortion is not possible with analogue modulation. • Digital signal processing: One of the key benefits in case of the digital signal is the possibility of signal processing, which means that the signal can be collected, and samples can be retrieved at an optimum sampling instant through offline processing. Once the samples are recovered, certain operations such as filtering, averaging, low-pass/high-pass filtering can be carried out in the digital domain to do the data recovery from the samples. Correspondingly, analogue processing is also possible, but it requires a complicated design of electronics. In case of digital signals, the samples can be put through the traditional digital signal processors to perform such operations, so as to improve the quality of the recovered data. Thus, the possibility of digital signal processing is probably the biggest advantage of digital signals. • Error correction codes: The possibility of error correction codes is another advantage, which is implemented by building in redundancy in the transmitted bit sequence, so that, even if some bits are lost in the transmission, the original bit sequence can still be worked out with the received bits. For example, instead of sending 100 information bits, we may send 110 bits or 120 bits using some kind of redundancy. There are various schemes for adding redundancy, which is typically referred to as Error Correction Codes. Using this redundancy and a relevant digital processing algorithm, the original bit sequence can be recovered even when the signal to noise ratio of the received signal is poor. Such an error correction is not possible in case of analogue processing. There are a few drawbacks for digital modulation as well. • Increased bandwidth: The analogue-to-digital conversion process increases the signal bandwidth from fB to 2 × ffBB × log2 NN, and hence a digital signal requires a larger bandwidth for transmission compared to the original message signal. • Increases processing and latency: The data recovery process, especially using the error correction codes require additional overhead and complexities due to signal processing. Also, the latency in storage, buffering, and processing algorithms contribute to a delay between the reception of signal and recovery of data. However, the advantages of the digital modulation far outweigh the disadvantages, which is why predominantly digital signals are used for optical communication. We now talk about the carrier frequencies used in digital communication, on what basis are they chosen, and what are the factors to be considered to decide the carrier frequency. Depending on the carrier frequency chosen, we need to have an appropriate source and detector. 1. Bandwidth: The first factor to be considered is the bandwidth of the signal that needs to be transmitted. Consider a baseband message signal of bandwidth B, such that its power spectral density S(f) spans from frequency –B to B. Upon modulation, this spectrum gets translated to the carrier frequency fC, so that the spectrum of the modulated signal spans from fC –B to fC+B. Given this carrier frequency, if the signal bandwidth is increased, there may arise a situation where the modulated signal spectrum crosses zero frequency and folds over, which is undesirable. Thus, for a given carrier frequency, the signal bandwidth cannot be chosen arbitrarily. As a rule of thumb, the signal bandwidth must be limited to 10% of the carrier frequency. For instance, if the carrier frequency is 1 GHz, the signal bandwidth should typically be limited to 100 MHz. Of course, this number is dependent on the kind of modulation scheme used, sampling rate, quantization levels, but as a thumb rule, the signal bandwidth should not be very close to fC. Consider internet, with such a large volume of videos being streamed or downloaded at the same time, the signal bandwidth is huge, so it requires a suitably large carrier frequency as well, which is the first point of concern from a designer’s viewpoint. For example, if the signal bandwidth is 1 MHz, a~THz carrier frequency may not be necessary. On the other hand,if the data rate required is Terabit per second (Tbps), which corresponds to THz of bandwidth, obviously a radio frequency of 2.5 GHz as carrier frequency would not be sufficient. 2. Attenuation: The communication channel may have a different attenuation at different carrier frequency; it may support the transmission of some frequencies, while completely suppressing others. The atmosphere, for instance, has different attenuation for different carrier frequencies. So, in case of a free space communication link, one should check the attenuation spectrum (attenuation as a function of frequency) and choose the frequency which has the lowest attenuation, so that the power required in transporting the information is minimum. 3. Topology: The topology of the link is another design concern. Depending on the the requirement, one may set up a point-to-point link, or a multicasting link. 4. Ease of deployment/cost: This is one of the most important constraints for the design of a link. To understand the challenges in deployment, consider a point-to-point link in a hilly terrain, where laying optical fiber can be challenging. A line-of-sight microwave link would be much more practical. Availability of components and their cost is another related concern. One may come up with a novel channel with low attenuation at a particular carrier frequency, but the sources and detectors for that frequency may not be available at a low cost, which would make the solution impractical. 5. Security: Data security is also an important concern since through internet, we regularly share some sensitive information (passwords, credit card details and so on.). It may be possible to tap the transmitted information from an insecure channel. For example, a coaxial line start to radiate at higher frequencies, which means that an antenna placed nearby can pick up the data being transported, which may not be acceptable.There may be some cases where this kind of channel security may not be a concern. For example, in the case of FM radio, the information is broadcasted, and it is meant to be received by anyone having a suitable receiver. But the same may not be the case for, say, a link connecting one bank to the other. The International Telecommunication Union – Telecommunication Standardization Sector (ITU- T) has recommended the range of carrier frequencies, ranging from 1 kHz to 1000 THz, for various applications. Please take note that these are not to be confused with the signal bandwidth, these are the carrier frequencies, which can be adopted depending upon the application. For example, telegraph and submarine cables operate with carrier frequencies in the range ~kHz,while the short wave radio applications (FM radio, TV, cellular) operate in the MHz-GHz range. Microwave applications use GHz range of frequencies. Then there is a gap in the frequencies in the THz range, beyond which there are the optical frequencies in 100s of THz range. We can do small exercise here. The wavelength of visible light ranges from 400-800 nm. We take the example of green colour, which has a wavelength of 532 nm (approximately 500 nm). The carrier frequency for green colour is calculated as follows. cc = ffff ⇒ ff = cc λλ = 3×10^8 500×10−9 = 600 THz. Green, or blue-green, is one of the favorite wavelengths for underwater communication, where submarines communicate with a buoy, or among each other. This is because the channel attenuation is minimum for the frequency corresponding to that color. But in an optical fiber, green has a very large attenuation. Here, we have represented the carrier frequencies also in terms of the corresponding wavelengths. The visible optical frequencies correspond to wavelengths of 100s of nm, while for microwave signals, wavelength is in cms. There is another class of carrier frequency called millimeter waves, which is gaining popularity because the upcoming 5G standards in wireless communication are interested in using millimeter waves as the carrier frequencies. Currently the cellular services use 2.5 GHz / 2.8 GHz as the carrier frequency, but the next generation wireless communication systems are talking about using higher carrier frequencies, such as 26 or 28 GHz, depending on the country, and these come under the class of millimeter waves. Microwaves are conventionally used for military communication, and short/long wave are used for radio communications. Longwave is used for submarine communication. This table from ITU-T enlists the carrier frequencies to be used to ensure compatibility between various applications. RF is classified as frequency range between 3 Hz and 3 GHz, which includes brands such as UHF, VHF, MF, HF etc. Microwave frequencies, used for satellite and radar systems, range from 3 GHz to 3 THz actually. The range 3 – 30 GHz is quite interesting since most of the radars operating today, such as atmospheric/weather radars, synthetic aperture radars, military communication operate in this range. They operate under S, C, X, Ku, K, Ka, bands. Optical frequencies start beyond 3 THz which are again specified in terms of bands as per ITU standards. These bands as specified in terms of wavelength instead of frequencies, because the frequency values are quite large in this range, and it is more convenient to express them as wavelengths. The wavelength range 1260-1360 nm is the original communication band known as O-band, followed by the E-band. The most conventional band is C-band, spanning from 1530 to 1565 nm, which corresponds to a carrier frequency of~200 THz for optical communication, which results in a large allowed bandwidth. Long bands (L-band) in the range 1565 to 1625 nm are also being used, but the Ultra-long band (U-band) is currently not used. Recently, the capacity in optical fiber link has also been saturating, so the current ongoing trend is to explore the other bands in optical communication, and to find out the cost-effective sources and detectors for these wavelengths. The choice of the carrier frequency depends on the channel attenuation. Let us look at the variation of atmospheric attenuation in the range 1-350 GHz, as shown by the red line. The y- axis is marked as specific attenuation, which means attenuation per unit length in dB/km. It is minimal, in fact less than .01 dB/km up to 10 GHz - which means atmospheric loss is really low from 1 GHz to ~8-9 GHz. This is why conventional cellular bands operate in the range of 3- 3.5 GHz, and are now scaling to 6 GHz in case of 5G standards. The orange trace represents the absorption of water vapor due to molecular resonances. When excited with frequencies close to the resonance, the channel exhibits absorption, which limits the range of carrier frequencies. Similarly, the blue trace represents the absorption spectrum of oxygen. Such absorption peaks restrict the range of carrier frequencies for free-space radio communication, which in turn limits the bandwidth as well. Considering the cellular operating frequency of 3.5 GHz, the largest allowed bandwidth would be 300 MHz, but typically,20-30 MHz is used for seamless error-free operation in the cellular band. In order to carry larger bandwidth, the carrier frequency needs to be increased, which is not possible with free-space, so copper cables are used. The plot shows the attenuation characteristics of various types of copper cables. In case of a conventional coaxial line, the attenuation varies from~100 to ~1000 dB/km for the frequency of operation varying from 100 kHz to 100 MHz, which causes a very large change in the magnitude of the signal strength. For transmitting such large carrier frequencies, special waveguides have to be designed with specific materials, dielectrics, and specific dimensions for a particular range of frequencies. Examples of such waveguides are WG 16, WG 10. For further increasing the bandwidths, we need to use optical bands as carrier frequencies and optical fibers as the channel. In the case of optical fibers, this plot has to be interpreted differently. The frequency ranges now represent the signal bandwidth and not the carrier frequencies. Obviously, a 10 MHz baseband signal cannot be transmitted in an optical fiber, since it would not be guided in the fiber. Thus the carrier signal corresponds to the optical bands (~1550 nm). The attenuation of the optical fiber remains the same, irrespective of whether the signal bandwidth is 100 kHz or 10 GHz. Thus, unlike copper cables, the bandwidth in case of optical fibers is not limited because of the transmission line losses. There may be other factors that limit the bandwidth of an optical fiber, which we will deal with later. Although the optical fiber can support a carrier frequency of 200 THz, it is still not feasible to successfully transmit ~200 GHz bandwidths in an optical fiber. But the challenge is not because of the fiber characteristics, it is because of the limitations of the transmitter and the receiver, about which we will learn later. It is critical to understand these limitations to choose a suitable transmitter and receiver while designing a fiber optic communication link.