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Among all the modern technologies available to us, communications technology is perhaps one of the most puzzling.We use radio and television sets all the time but perhaps struggle to understand how these things work. We might also be quite puzzled when we use our mobile phones. When we make a call, messages are sent out to, say, a base station which we vaguely know. Yet there must be many other people close by who are using the mobile phone system, so that base station must be receiving a mixture of signals. How can it recover all the individual signals? A lot of us use ADSL these days to connect a computer at home to the Internet. Again, it might be hard to understand what ADSL is and how it works. Actually, communications technologies are not that hard. The first thing we have to understand is the nature of signals.We usually see a signal from the viewpoint of time, but it is important to know that a signal actually is composed of a set of cosine functions. How do we know?We know this through the use of the Fourier transform.

This transforms a signal in the time domain into the frequency domain. It is an exceedingly powerful tool. In fact, we could say that modern telecommunications would not be possible without the Fourier transform. With the Fourier transform we can view any signal from the viewpoint of its contituent frequencies. When the ordinary person talks about digital signals, he or she might not relate the pulses with frequencies. The person can easily understand the data rate of digital signals, but we will show that digital pulses are related to frequencies. Let us consider radio broadcasting, which we are all familiar with. There are many radio transmitting stations. They all broadcast either the human voice or music, or both. We must give each radio station a unique frequency to broadcast. That frequency is called the carrier frequency. Compared with the frequencies associated with voices or music, these carrier frequencies are much higher. The radio stations, through some mechanism, attach the voice or music signals to the higher carrier frequencies. This mechanism is called modulation. The air is thus filled with all kinds of signal corresponding to different frequencies.

Our radio receives some of these. Actually we tune our radio so that at a particular time it picks out one particular carrier frequency. In this way we can hear the broadcast clearly. This process in the radio is the opposite of modulation and is called demodulation. Through use of the Fourier transform, it can be shown that the human voice and music consist of relatively low frequencies. Can low-frequency signals be broadcast directly? No, because low-frequency signals have large wavelength. Unfortunately, the length of an antenna is proportional to the wavelengths of the signals it can handle. Thus, to broadcast low-frequency signals we would need a very large antenna, which is not practical. After introducing the much higher carrier frequency, we can then use reasonably sized antennas to broadcast and to receive. In the above, our modulation technique is assumed to be applied to analogue signals, so this is called analogue modulation. The carrier frequencies are often called radio frequencies (RF for short). Actually, for reasons that need not bother us here, RF today often refers to high frequencies that are no longer restricted to radio broadcasting. What about digital signals? Data are almost always represented by digital signals. Digital signals are often thought of as a sequence of pulses. We must note that, in the wireless environment, we cannot transmit pulses except in very unusual cases.

This is because, in the wireless environment, only electromagnetic waves are transmitted. What we can do is to transmit a sinusoidal signal within that short period of duration of a single pulse. This sinusoidal signal is a carrier signal and its frequency is called the carrier frequency. In this way, each user can again be uniquely identified by its carrier frequency. This kind of modulation is called digital modulation. Digital modulation is more interesting than that. We can transmit more than one bit at the same time. This will make the communication more efficient because two bits can be sent. Note that the first bit may be 1 or 0 and the second may also be 1 or 0. Thus there are four possible cases for the receiver to determine at any instant. How can the receiver do the job of distinguishing the value of the bit i (i 1; 2)? This is a very fundamental problem which we must be able to deal with. Fortunately, there is a ready-made answer. Mathematics tells us that as long as the signals are orthogonal to each other, they can be mixed and later recovered easily by using the inner-product operation. The inner-product operation is thus very important, so in this book it is introduced quite early. If two bits can be mixed together, a larger number of bits can also be mixed.

Thus the orthogonal frequency-division method (OFDM) is capable of mixing 256 bits together. In this method, each bit is represented by a cosine function with a distinct frequency. It can be easily shown that these functions are orthogonal and thus can be recovered. For OFDM systems, we shall use the discrete Fourier transform in this book, so that the transmission can be done efficiently. Our ADSL system is based on this ODFM method. In communications, it is natural to have the situation in which several users want to send signals to the same receiver simultaneously. A typical case is the mobile phone system whereby many callers around one base station are using the same base station. How can the receiver distinguish between the users? One straightforward method to distinguish data generated by different users is to use the frequency-division multiple-access (FDMA) method. We can also use the time-division multiple-access (TDMA) method, in which data are divided according to time slots. Another very interesting technique is the codedivision multiple-access (CDMA) method. In the CDMA method, different users use different codes to represent the values of bits. Each code can be considered as a function, and they can be recovered because the functions corresponding to different codes are orthogonal. A very important concept in communications is bandwidth. Consider the human voice case. Experimental results show that the human voice contains frequencies mainly from 0 to 5000 hertz (Hz), which means that the bandwidth of any system transmitting this voice signal must be larger than 5000 Hz. Let us denote the carrier frequency by fc. After analogue modulation is done, the frequencies now range from (fc  5) kHz to fc 5 kHz. We will then say that the bandwidth of the signal is 10 kHz. Unfortunately, a large bandwidth of a communication system occupies more resources and requires more sophisticated electronic circuitry.

Thus we shall often be mentioning the concept of bandwidth. Now consider a cable TV system. The cable is used to transmit a number of TV signals. Assume that there are N television stations and that the bandwidth of each TV signal is W. The bandwidth of the TV cable must therefore be larger than NW. For large N and W, the bandwidth must be quite large, and this is why we often call this kind of system a broadband system. It is easy to understand the bandwidth of analogue signals, but digital signals also have a bandwidth associated with them. Every digital signal can be seen as a sequence of pulses. Each pulse has a pulse width. When we introduce the Fourier transform, we will show that a short pulse width will occupy a wide band of frequencies. Further, a high data rate will necessarily mean a short pulse width, and consequently a large bandwidth. Thus, we may say that if we want to transmit a large number of bits in a short time, we must have a communications system with a large bandwidth. So, even when we send pure digital data, the concept of bandwidth is still important. We do not, of course, want a transmission mechanism that requires a very large bandwidth. That would be very costly. On the other hand, a very narrow bandwidth transmission has the disadvantage that it is easy for intruders to penetrate. For security reasons, sometimes we would like to widen the bandwidth. We will introduce the concept of spread spectrum technology, by which the bandwidth of a system is widened which will make it more secure. Spread spectrum technology is designed not only to make a system more secure. Frequency hopping, for instance, is a spread spectrum technology that allows a transceiver (transmitter/receiver) to communicate with many other transceivers. Imagine, for example, that we have equipment in a laboratory which are connected to many devices. Each device sends data to the equipment from time to time, and the equipment will have to send instructions to these devices very often. Frequency hopping allows this to happen. Finally, coding is something that we must understand. There are two kinds. Removing redundant data is called source coding, and adding redundant data to correct errors is called channel coding. Credits to:Communications Engineering. R.C.T. Lee, Mao-Ching Chiu and Jung-Shan Lin # 2007 John Wiley & Sons (Asia) Pte Ltd

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