Introduction Background Digital Communication Systems Baseband Signal Representation - PDF document

Baseband Signal Representation 2Line Codes 3Passband Signal Representation 3Constellation Diagrams 4Representation of BPSK 4Generation of BPSK 5Representation and Generation of QPSK 5M-ary PSK 7 . Obviously, for binary signals, 2 and . Line Codes ned by selecting the parameters ( ( chapter, we only describe line codes that are of relevance of line codes, see Barry, Lee, and Messerschmitt ( ( ) / ) ned as: otherwise ptA()() an undesirable effect. However, the RZ format aids the The polar NRZ format has the same pulse shape as the unipolar NRZ counterpart, but it uses an alphabet {1}. Similarly, polar RZ is similar to unipolar RZ 1} for the polar case. These formats for the binary sequence 101101. Note lar case, the signal has a nonzero DC value that is usually an undesirable characteristic. A popular digital baseband , which guarantees zero DC value irrespective of the proportions of 1Õs and 0Õs in the digital signal. Manchester encoding format is also along with other binary formats. All of these baseband digital signal formats are for the binary Ñthat is, the symbol period is the same as the bit period. In general, the symbol period will be greater than or equal to the bit period. Passband Signal Representation The passband digital signal is obtained by modulating a , and the carrier wave used nication is used whereby passband signals are transmitted over the communication channel. Passband modulation is also employed whenever the communication medium is to be shared for multiple simultaneous communications over different frequency bands, as in standard commer-tion schemes are used in practice (see section 1.5 of Xiong ital transmission is digital phase modulation in which the ed according to the digital baseband signal. In the rest of the chapter, we describe and analyze various DPM schemes with a particular focus on ) and Anderson ) for details of more advanced DPM techniques. Phase shift keying is a special case of DPM in which the phase of the carrier is selected, in accordance terval. Thus, in PSK, phase discontinuities are observed ). In another type of DPM, continuous phase modulation, there are no phase discontinuities but the phase is allowed to vary throughout the symbol interval in a continuous manner. rst introduce the mathematical representation ( ture components and a carrier frequency. Mathemati-cally, we write xtxtftxtftcIcQc()()cos()sin ( ) ( is the frequency of the sinusoidal carrier. Figure 1: Digital PAM formats for unipolar NRZ, unipolar RZ, bipolar NRZ, bipolar RZ, and split-phase Manchester encoding IGITALOMMUNICATION bid44582_ch33.indd 3 bid44582_ch33.indd 3 6/28/07 6:02:41 PM 6/28/07 6:02:41 PM IGITALODULATIONEMODULATION Using the famous EulerÕs equation e j cos xtxtejft()[()] ( xtxtjxtBIQ()()() frequency and the complex envelope. We may further note (Carlson, Crilly, and Rutledge Constellation Diagrams ()cos()sintft is its reciprocal. The digital passband signal transmitted in each inter- ( ( ( ( ( ( ) chosen above are not only or- ( ) ( ) 1. To Þ nd the projection of a signal point along the ( ), we may simply use xxttdt111()() ( 1 ( ) along the basis function ( We usually show the projections along the basis func-four points in the plane of basis functions (Wikipedia 2007 GENERATION OF COHERENT SIGNALS coherent PSK signal. To this end, we Þ rst provide a math-ematical representation of the PSK signals. To develop an . Representation of which is selected for transmission in each symbol inter- xtAftxtAft()cos()cos xtAxtA()()()() ( xxttdtAxxtt111112()()()()) Similarly, the projection of ( bid44582_ch33.indd 4 bid44582_ch33.indd 4 6/28/07 6:02:42 PM 6/28/07 6:02:42 PM xxttdtAxxt221222()()()(

tdt 2 180 degrees from each other. The total number of con- transmitted energy. The average energy of all of the signal ( ) within one symbol interval is Extxtxtctdtxcc()()()() )()tdt By symmetry, the energy of the signal ( ExATc222
rst constellation point is given by Exx Finally, the transmitted energy per bit for BPSK is given xtxtxtxtcccc1222()()()() Generation of quence of 1Õs and 0Õs, and one of the two signals in BPSK constellation is assigned to each bit. For example, for the BPSK signals given in the preceding section, a 1 can be 1 2). Thus, the transmitted signals that correspond to each bit . The assignment of bit values to one of the constellation points is completely arbitrary, and the transmitter and receiver must use the same assignment. For example, for BPSK representation ) to bit value ) to bit value. Representation and Generation ever, in this case, each symbol represents two informa- xtxtftxtftcIcQc()()cos()sin To generate the QPSK signal, we need to Þ nd the in-phase ( ( Table 1 ( ) rst constellation point is ccc()cossin Figure 2: Constellation diagram for BPSKENERATION bid44582_ch33.indd 5 bid44582_ch33.indd 5 6/28/07 6:02:42 PM 6/28/07 6:02:42 PM EATATb

122224 Now that we have expressions for each signal point in the stellation point represents two signal bits and, as in the case of BPSK, every possible pair of bits needs to be mapped onto one of the constellation points. Because there are four possible combinations a bit pair may takeÑ00, 01, 10, and 11Ñwe have just enough constellation points to map these bit pairs. Once again, the mapping is arbitrary as long as a single bit pair maps onto a single constellation point. Next, we note from Table ponent pairs can be generated by mixing two polar NRZ BPSK signals. Thus, the QPSK signal can be generated by . To generate the two BPSK signals, we split the polar NRZ encoded information bits into even and odd M-ary bits transmitted in each symbol. signals. Theoretically, one signal point on the M-ary cally, every possible log Figure 6: Constellation diagram for QPSK Table 1: In-Phase and Quadrature Components of a QPSK SignalConstellation point signal In-phase component, ) Quadrature component, A2 A2 xc2(t) A2 A2 xc3(t) A2 A2 xc4(t) A2 A2 Figure 7: Generation of QPSK signal from polar NRZ signalsENERATION bid44582_ch33.indd 7 bid44582_ch33.indd 7 6/28/07 6:02:44 PM 6/28/07 6:02:44 PM IGITALODULATIONEMODULATION in the symbol interval. To generate the signal correspond- t and sin 2 t , respectively. DEMODULATION OF COHERENT SIGNALS quency. To this end, the coherent receiver tracks the carrier by using a carrier recovery circuit. We will brie” y describe zation and its effects on the performance of PSK signals. and phase. We will also assume that the transmitted sig-channel. In real communications, however, the received what was sent from the transmitter. For an understanding imperfections and later evaluate the effects of noise once ( ) is the received signal. Ignor- xtAftxtAft()cos()cos 1 ( 2 ( ( rtaptnTft()()cos
 ( ) ( – ) ( ) ()()coscosrtftdttnT ftftdt
cos cosAaftdt ftdt(cos) fkTfkT[sin()sin()] kkfkTfT242cossin In the above expression, the second term is approximately Tger multiple of 1/T. Thus, the input to the decision device, , is approximately (or ). The 1 was sent from the trans-mitter if the input to the decision device is greater than 1 was sent otherwise. Thus, in the absence of noise, one can completely and perfectly recover the transmitted signal using the above demodulation scheme. The presence of noise in the signal would cause the input to the decision device to be different from , depending on the magnitude of the noise, and may lead to occasional errors in inferring what was sent from the transmitter. Figure 8: Constellation diagram for M-ary PSK Figure 9: bid44582_ch33.indd 8 bid44582_ch33.indd 8 6/28/07 6:02:45 PM 6/28/07 6:02:45 PM SPECTRAL CHARACTERISTICS OF SIGNALS ciency of the a signal that has narrower PSD. We will provide expres- 2 (BPSK) and (QPSK). To simplify things, we use the fact that for pass- xtaptnTft()()cos
 NRZ signal: xtaptnTtnT()()

 ( ( )  ) (  ( ) ( – ) )  ( ) ( ) ( ) ( PSDof/sincsincxtSfTATfT()()()222 Finally, the baseband-shifted PSD of BPSK signal is given . Thus, ShiftedPSDofBPSK/sincSfTATfT()()AfTsinc It can be seen that the PSD of a polar NRZ signal falls off rst null at 1/T. Thus, the PSD of a BPSK signal will also fall off with squared frequency, will be centered at rst null at anAtT2() ( ) above. However, the QPSK is generated by summing up Figure 10: Power spectral density of BPSK bid44582_ch33.indd 9 bid44582_ch33.indd 9 6/28/07 6:02:46 PM 6/28/07 6:02:46 PM REFERENCES Anderson E. W. , Barry . New York Springer Carlson P. B. Crilly . New York Couch L. W. Upper Saddle River, NJ Prentice-Hall Haykin New York John Wiley & Sons Proakis New York Rappaport T. S. Wireless communications: Prin-Upper Saddle River, NJ Prentice-Hall Simon W. C. Lindsey Upper Saddle River, NJ Wikipedia Wilson Saddle River, NJ Xiong Artech House Publishers bid44582_ch33.indd 13 bid44582_ch33.indd 13 6/28/07 6:02:48 PM 6/28/07 6:02:48 PM