3/18/10 1 MS in Telecommunications TCOM 500: Modern Telecommunications Dr. Bernd-Peter Paris George Mason University Spring 2009 MS in Telecommunications Outline • Line codes are used to transmit digital information over guided media. • E.g., cables and wires • Properties of line codes relevant for transmission in practice. • Mainly bandwidth and synchronization considerations. • Some line codes used in practice. Paris 2 TCOM 500: Modern Telecommunications3/18/10 2 MS in Telecommunications Reminder • Purpose of a digital communication system: • Replicate digital information available at the transmitter’s location at the receiver’s location. • Generally this implies connecting spatially separate locations. • Same principle applies for communicating over time – storage of information. • The communications channel models the link connecting transmitter and receiver. • Channel models the degradation that the transmitted signal experiences. Paris 3 TCOM 500: Modern Telecommunications Transmitter Channel Receiver bits signal signal bits MS in Telecommunications Transmitter • The transmitter maps a sequence of bits to an analog signal. • The transmitted signal must be continuous in time for transmission through a physical link. • The mapping performed by the transmitter is also called modulation. • A large number of options exists for this mapping. • Choice of mapping depends mainly on the characteristics of the channel. • E.g., radio communications requires signals that occupy only a given portion of the radio frequency spectrum. Paris 4 TCOM 500: Modern Telecommunications Transmitter bits signal …0110… … …3/18/10 3 MS in Telecommunications BASEBAND AND PASSBAND COMMUNICATIONS Paris 5 TCOM 500: Modern Telecommunications MS in Telecommunications Baseband and Passband • Transmitted signals occupy a portion of the frequency spectrum. • Baseband signals occupy spectrum near zero Hz (DC). • Passband signals occupy a portion of the spectrum centered at a carrier frequency fc. Paris 6 TCOM 500: Modern Telecommunications f f fc Baseband Passband3/18/10 4 MS in Telecommunications Baseband Signals • Baseband signals use (baseband) pulses to construct the transmitted waveform. • The canonical example of such a pulse is a rectangular pulse. • We will take a close look at practical choices and trade-offs for constructing baseband signals. • This process is often called line-coding. Paris 7 TCOM 500: Modern Telecommunications T Pulse Transmitted Signal MS in Telecommunications Spectrum of Baseband Signals • It can be shown that the spectrum of a baseband signal with rectangular pulses of duration T, has the following (power) spectrum: • For other pulse-shapes, different spectra are obtained. • However, the shape of the spectra for different pulses have strong similarities. • =>Focus on rectangular pulse. Paris 8 TCOM 500: Modern Telecommunications € S( f ) = T2sin(πfT)πfT⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 23/18/10 5 MS in Telecommunications Spectrum of Baseband Signals 0 1/T 2/T 3/T 4/T 5/T T^2 FrequencySpectrum• Bandwidth of the signal is often defined as the location of the first zero. • Occurs at 1/T. • Note that spectrum is not strictly zero outside the bandwidth. Paris 9 TCOM 500: Modern Telecommunications B = 1/T MS in Telecommunications Another Common Baseband Pulse • A different pulse that we will see in our discussion has a transition in the middle of the symbol period. • We will see, that such pulses offer advantages in the ability to synchronize with the received signal. • Manchester encoding. Paris 10 TCOM 500: Modern Telecommunications Pulse Transmitted Signal T T 2T 3T3/18/10 6 MS in Telecommunications 0 1/T 2/T 3/T 4/T 5/T T^2 FrequencySpectrumSpectrum of Baseband Signals • With this pulse, bandwidth is 2/T. • This is related to the fact that signal remains constant for only T/2. • At frequency zero, spectrum is zero. • No DC component. Paris 11 TCOM 500: Modern Telecommunications B = 2/T MS in Telecommunications Passband Signals • Will look more closely at passband signals in a later class. • Passband signals can be created from baseband signals and vice versa. • The respective conversions are called up-conversion and down-conversion. Paris 12 TCOM 500: Modern Telecommunications Baseband signal Passband signal cos(2πfct) Up-conversion: Passband signal Baseband signal cos(2πfct) Down-conversion: Lowpass Filter3/18/10 7 MS in Telecommunications PROPERTIES OF LINE CODES Paris 13 TCOM 500: Modern Telecommunications MS in Telecommunications Line codes • Line codes are used whenever information is transmitted through guided media. • Cables or optical fibers. • The principles also apply for example with bar codes or IR remote controls. • We will first state a number of desirable properties of line codes. • Then, present some specific line codes found in practice. Paris 14 TCOM 500: Modern Telecommunications3/18/10 8 MS in Telecommunications Comparison of Line Codes • The following characteristics will be used to compare line codes: • Bandwidth – in relation to the data rate. • Can code lead to long runs of constant signal? • This is undesirable for synchronization or for multi-level codes. • Does code have built-in error correction? • If not, can always have error coding before line coding. • Does code have a DC component? • Some channels cannot carry DC, e.g., telephone lines. Paris 15 TCOM 500: Modern Telecommunications MS in Telecommunications Bit Rate and Bandwidth • Digital communication systems are expected to transport bits at a constant rate. • To do so, the transmitted signals occupy a portion of the spectrum – bandwidth. • The relationship hinges on three factors: • More than one bit may be transmitted at a time. • This leads to the notion of baud rate. • The bandwidth of the pulse being used. • Specifically, does the pulse have a transition in the middle or not. • We saw earlier, that pulses with a transition require twice the bandwidth. • With error correction coding, the overhead from coding increases the bandwidth. • Proportional to ratio of coded bits and uncoded bits. Paris 16 TCOM 500: Modern