Chapter 6 Modulation Techniques for Mobile Radio

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1 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Chapter 6 Modulation Techniques for Mobile Radio Text. [1] T. S. Rappaport, Wireless Communications - Principles and Practice, 2/e. Prentice-Hall, Frequency Modulation vs. Amplitude Modulation (skipped) 6.2 Amplitude Modulation (skipped) 6.3 Angle Modulation (skipped) 6.4 Digital Modulation-an overview (mostly skipped) 6.5 Line Coding (skipped) 6.6 Pulse Shaping Techniques (skipped) 6.7 Geometric Representation of Modulation Signals (skipped) 6.8 Linear Modulation Techniques (Mostly skipped) 6.9 Constant Envelope Modulation partly discussed) 6.10 Combined Linear and Constant Envelope Modulation Techniques (briefly covered) 6.11 Spread Spectrum Modulation Techniques (briefly covered) 6.12 Modulation Performance in Fading and Multipath Channels (mostly skipped) 6.x1 OFDM

2 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Digital Modulation - an Overview (mostly skipped) Factors That Influence the Choice of Digital Modulation (briefly covered) A desirable modulation scheme provides low bit error rates at low received signal-to-noise ratios, performs well in multipath and fading conditions, occupies a minimum of bandwidth, and is easy and cost-effective to implement. As existing modulation schemes do not simultaneously satisfy all of these requirements, tradeoffs are made when selecting a digital modulation, depending on the demand of the particular application. The performance of a digital modulation scheme is measured in terms of its power efficiency and bandwidth efficiency. The power efficiency (sometimes called energy efficiency) p of a modulation scheme is a measure of the tradeoff between fidelity and signal power (or energy) and is often defined as the ratio of the signal energy per bit to noise power spectral density probability of error (for example 5 10 ). N E b 0 required at the ㅇㄷ modulator input to achieve a certain

3 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 That is, p E N b. 0 BER10 5 The bandwidth efficiency B of a modulation scheme is a measure of the ability to accommodate data within a limited bandwidth and is often defined as the ratio of the throughput data rate per Hertz in a given bandwidth. That is, R B bps/hz (6.36) B where R is the data rate in bit per second and B is the bandwidth occupied by the modulated RF signal. The system capacity of a digital modulation system is directly related to the modulation scheme. Shannon s channel coding theorem states that maximum possible data rate (called channel capacity) is limited by the noise in the channel for an arbitrary small probability of error for AWGN channels [Shannon, 1948].

4 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 as From the Shannon s channel coding theorem, maximum achievable bandwidth efficiency is upper-bounded B,max C B log2 1 S N (6.37) where C is the channel capacity (in bps), and B is the RF bandwidth and S N is the signal-to-noise power ratio. Besides power efficiency and bandwidth efficiency, there are other factors which also affect the choice of a digital modulation scheme for a wireless system. A modulation which is simple to detect is preferred to minimize the cost and complexity of the subscribe receiver. A modulation scheme is required to give a good performance under various types of channel impairments such as Rayleigh and Ricean fading and multipath time dispersion, given a particular demodulator implementation.

5 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 In cellular systems where interference is a major issue, the performance of a modulation scheme in an interference environment is extremely important. Sensitivity to detection of timing jitter, which is caused by time-varying channels, is also an important consideration in choosing a modulation scheme. Ex. 6.6 DIY. Ex. 6.7 DIY.

6 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Bandwidth and Power Spectral Density of Digital Signals (briefly covered) The power spectral density (PSD) of a random signal wt ( ) is defined as [Couch, 1993] 2 WT ( f) Pw ( f) lim (6.38) T T where the bar stands for an ensemble average and WT ( f ) is the Fourier transform of wt () t which is truncated version of the signal wt ( ), defined as T T wt (), t, wt () t 2 2 0, elsewhere. (6.39) The definition of signal bandwidth varies with context. The absolute bandwidth of a signal is defined as the range of frequencies over which the signal has a nonzero power spectral density. For rectangular baseband pusses, the absolute bandwidth is infinity. The null-to-null bandwidth is equal to the width of the main spectral lobe.

7 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The half-power bandwidth (also called 3 db bandwidth) is defined as the interval between frequencies at which the PSD has dropped to half (or 3 db) of the peak power. The FCC adopted the definition of occupied bandwidth as the band which leaves exactly 0.5 % of the signal power above the upper band limit and exactly 0.5 % of the signal power below the lower band limit so that 99 % of the signal power is contained within the bandwidth.

8 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Line Coding (skipped) Digital baseband signals often use line codes to provide particular spectral characteristics of pulse train. The most common codes for wireless communication are return-to-zero (RZ), non-return-to-zero (NRZ), and Manchester codes. Figure 2.22 [B. Sklar, 2001] shows various commonly used waveforms.

9 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 2.22 Various PCM Waveforms [Sklar, Digital Communications, 2/e., Prentice-Hall, 2001].

10 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The waveform of line codes are shown in Figure (Compare some difference between two figures: Figure 6.14 in the text and Figure 2.22 in Sklars.)

11 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

12 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Their power spectral densities are shown in Figure 6.13.

13 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.13 Power spectral density of (a) unipolar NRZ.

14 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.13 Power spectral density of (b) bipolar RZ.

15 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.13 Power spectral density of (c) Manchester NRZ line codes.

16 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Pulse Shaping Techniques (briefly covered) When rectangular pulses are passed through a bandlimited channel, the pulses is spread in time, and the pulse for each symbol smears into the time intervals of succeeding symbols which causes intersymbol interference (ISI) and increases probability of error at the receiver. It is desired to have techniques to reduce the modulation bandwidth and suppress out-of-band components, while reducing intersymbol interference. Out-of-band radiation in the adjacent channel in a mobile radio system should generally be 40 to 80 db below that in the desired passband. There are various pulse shaping techniques which simultaneously reduce intersymbol interference and the spectral width of a modulated signal.

17 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Nyquist Criterion for ISI Cancellation (very briefly discussed) The effective impulse response of a communication system (which consists of the transmitter, channel, and receiver) is given by h () t ()* t p()* t h ()* t h () t (6.43) eff c r where p( t ) is the pulse shape of a symbol, h () t is the channel impulse response, and h ( t ) is the receiver impulse response. c r Nyquist found that ISI could be completely nullified if the overall response of a communication system is designed so that at every sampling instant at the receiver the response due to all symbols except the current (or desired ) symbol is equal to zero. That is, the impulse response of the overall communication system must satisfy h eff K, n 0, ( nts ) 0, otherwise, (6.42) where T s is the symbol duration, n is an integer, K is a non-zero constant.

18 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Nyquist showed that for zero ISI the transfer function of the overall communication system, H ( f ), must satisfy k Heff ( f ) constant for all f. T k s eff There are two important considerations in selecting a transfer function Heff ( f ) which satisfy (6.42). First, heff ( t ) should have a fast decay with a small magnitude near the sample values for n 0. Second, if the channel is ideal (that is, h () t () t ), then it should be possible to realize or closely c approximate shaping filters at both the transmitter and receiver to produce the desired Heff ( f ). Consider the following impulse response: h eff t sin( ) Ts () t (6.44) t T s which satisfies the Nyquist condition for ISI cancellation given in (6.42) and shown in Figure 6.15.

19 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.15 Nyquist ideal pulse shape for zero intersymbol interference.

20 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 If the overall communication system is modeled as a filter with the impulse response of (6.44), the transfer function of the filter is obtained by taking its Fourier transform, and is given by H eff 1 f ( f) rect( ) f f (6.45) s s which is a rectangular filter with absolute bandwidth f s 2, where f s is the symbol rate. While this transfer function satisfies the zero ISI criterion with a minimum of bandwidth, there are practical difficulties in implementing it, since it corresponds to a non-causal system (that is, h () t is non-zero for t 0) and is thus difficult to approximate. eff Also, the sint pulse has a waveform slope that is 1 at each zero crossing, and is zero only at exact t t multiples of T s, thus any error in the sampling time of zero-crossings will cause significant ISI due to overlapping from adjacent symbols. 1 (Note that a slope of t 2 samples.) or 3 1 t is more desirable to minimize the ISI due to timing jitter in adjacent

21 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 f 0 Nyquist also proved that any filter with a transfer function having a rectangular filter of bandwidth 1, convolved with any arbitrary even function Z( f ) with zero magnitude outside the passband of the T 2 s rectangular filter, satisfies the zero ISI condition. That is, the transfer function of the filter which satisfies the zero ISI condition is given by f Heff ( f) rect( ) Z( f) (6.46) f 0 1 where Z( f) Z( f), and Z( f ) 0 for f f0. T 2 s Expressed in terms of the impulse response, the Nyquist criterion states that any filter with an impulse response t sin( ) Ts heff () t z() t t (6.47) achieves ISI cancellation. Filters which satisfy the Nyquist criterion are called Nyquist filters (or Nyquist pulse shaping filters) (see Figure 6.16).

22 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.16 Transfer function of a Nyquist pulse-shaping filter at baseband.

23 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Assuming that the distortions introduced in the channel can be completely nullified by using an equalizer which has a transfer function that is equal to the inverse of the channel response, then the overall transfer function H ( f ) can be approximated as the product of the transfer functions of the transmitter and receiver filters. eff An effective end-to-end transfer function of H ( f ) is often achieved by using filters with transfer function Heff ( f ) at both the transmitter and receiver. eff This has the advantage of providing a matched filter response for the system, while at the same time minimizing the bandwidth and intersymbol interference.

24 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Raised Cosine Rolloff Filter (very briefly covered) The raised cosine rolloff filter is the most popular pulse shaping filter used in mobile communications which satisfies the Nyquist criterion. The transfer function of a raised cosine filter is given by (1 ) 1, 0 f, 2Ts 1 ( f 2Ts 1 ) (1 ) (1 ) HRC ( f) 1 cos[ ], f, 2 2 2Ts 2Ts (1 ) 0, f, 2Ts (6.48) where is the rolloff factor which ranges between 0 and 1. Figure 6.17 shows the transfer function of the raised cosine filter for various values of the rolloff factor.

25 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.17 Magnitude transfer function of a raised cosine filter at baseband.

26 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 When 0, the raised cosine rolloff filter becomes a rectangular filter of minimum bandwidth. The impulse response of the raised cosine filter is obtained by taking the inverse Fourier transform of the transfer function, and is given by h RC t t sin( ) cos( ) Ts Ts () t. (6.49) t 4 t 2 1 ( ) 2T s Figure 6.18 shows the impulse response of the cosine rolloff filter at baseband for various values of the rolloff factor.

27 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.18 Impulse response of a raised cosine rolloff filter at baseband.

28 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, t Notice that the impulse response with 0 decays much faster at the zero-crossings (approximately as for t T ) when compared to the rectangular filter ( 0). s The rapid time rolloff allows it to be truncated in time with little deviation in performance from theory. In Figure 6.17 it is shown that as the rolloff factor increases, the bandwidth of the filter also increases, and the time sidelobe levels decrease in adjacent symbol slots. This implies that increasing decreases the sensitivity to timing jitter, but increases the occupied bandwidth. The symbol rate R s 1 T s R s that can be passed through a baseband raised cosine rolloff filter is given by 2B 1 where B is the absolute filter bandwidth. (6.50)

29 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 For RF systems, the RF passband bandwidth doubles and R s B. (6.51) 1 The cosine rolloff transfer function can be achieved by using identical H RC ( f ) filters at the transmitter and receiver, while providing a matched filter for optimum performance in a flat-fading channel. To implement the filter responses, pulse shaping filters can be used either on the baseband data or at the output of the transmitter. As a rule, pulse shaping filters are implemented in DSP in baseband. Because h () t is noncausal, it must be truncated, and pulse shaping filters are typically implemented for RC 6T s about the t 0 point for each symbol. For this reason, digital communication systems which use pulse shaping often store several symbols at a time inside the modulator, and then clock out a group of symbols by using a look-up table which represents a discrete-time waveform of the stored symbols.

30 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 As an example, assume binary baseband pulses are to be transmitted using a raised cosine rolloff filter with 1. 2 If the modulator stores three bits at a time, the there are eight possible waveform states that may be produced at random for the group. If 6T s is used to represent the timespan for each symbol (a symbol is the same as a bit in this case), then the timespan of the discrete-time waveform will be 14T s. Figure 6.19 shows the RF time waveform for the data sequence 1, 0, 1.

31 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.19 Raised cosine filtered ( 0.5 ) pulses corresponding to 1, 0, 1 data stream for a BPSK signal.

32 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The optimal bit decision points occur at 4T s, 5T s, and 6T s, and the time dispersive nature of pulse shaping can be seen. Notice that the decision points (at 4T s, 5T s, 6T s ) do not always correspond to the maximum values of the RF waveform. The spectral efficiency offered by a raised cosine filter only occurs of the exact pulse shape is preserved at the carrier. This becomes difficult if nonlinear RF amplifiers are used. Small distortions in the baseband pulse shape can dramatically change the spectral occupancy of the transmitted signal. If not properly controlled, this can cause serious adjacent channel interference in mobile communication systems. A dilemma for mobile communication designers is that the reduced bandwidth offered by Nyquist pulse shaping requires linear amplifiers which are not power efficient.

33 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 An obvious solution to this problem would be to develop linear amplifiers which use real-time feedback to offer more power efficiency, and this is currently an active research thrust for mobile communications Gaussian Pulse-Shaping Filter Unlike Nyquist filters which have zero-crossings at adjacent symbol peaks and a truncated transfer function, a Gaussian filter has a smooth transfer function with no zero-crossings. The Gaussian lowpass filter has a transfer function given by 2 2 (6.52) H ( ) exp G f f where is related to the 3-dB bandwidth of the baseband Gaussian shaping filter which is given by ln 2 2B (6.53) B As increases, the spectral occupancy of the Gaussian filter decreases and time dispersion of the output signal increases.

34 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 By taking the inverse Fourier transform of the transfer function, the impulse response of the Gaussian filter is given by 2 2 hg () t exp( t ) 2. (6.54) In Figure 6.20 the impulse response of the Gaussian filter is shown for various values of 3-dB bandwidthsymbol time product ( BT ). S

35 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

36 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The Gaussian filter has a narrow absolute bandwidth (although not as narrow as a raised cosine rolloff filter), and has sharp cut-off, low overshoot, and pulse area preservation properties which make it very attractive for use in modulation techniques that use nonlinear RF amplifiers and do not accurately preserve the transmitted pulse shape. Since Gaussian pulse-shaping filter does not satisfy the Nyquist criterion for ISI cancellation, reducing the spectral occupancy results in degradation in performance due to increased ISI. That is, a tradeoff between the desired RF bandwidth and the irreducible error due to ISI of adjacent symbols. Gaussian pulses are used when cost and power efficiency are major factors and the bit error rates due to ISI are deemed to be lower than what is nominally required. Ex. 6.8 DIY. 6.7 Geometric Representation of Modulation Signals (skipped)

37 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Linear Modulation Techniques (mostly skipped) Digital modulation techniques may be broadly classified as linear or nonlinear. In linear modulation schemes, the amplitude of the modulated signal s( t ) varies linearly with the modulating signal mt ( ). In a linear modulation scheme, the transmitted signal s( t ) is given by [Ziemer, 1992] s() t Re[ Am()exp( t j2 f t)] c A[ m ( t)cos(2 ft) m( t)sin(2 ft)] (6.65) where A is amplitude, R c I c f c is the carrier frequency, and mt () m () t jm() t is complex envelope representation of the modulation signal. R I The most popular linear modulations schemes include pulse-shaped QPSK, OQPSK, and / 4 QPSK.

38 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Binary Phase Shift keying (BPSK) (mostly skipped) The power spectral density (PSD) of a BPSK signal in log scale is shown in Figure In Figure 6.22 it is shown that the null-to-null bandwidth is twice the bit rate, that is, BW nulltonull 2R b 1 2. T b

39 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

40 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The probability of bit error for the BPSK is given by P bqpsk, 2E Q b N 0 where E b is energy per bit and N 0 is the double-sided power spectral density of the additive white Gaussian noise (AWGN). (6.74) Differential Phase Shift keying (DPSK) (very briefly discussed) Table 6.1 illustrates the generation of a DPSK signal for a sample sequence m k which follows the relationship dk mk dk 1.

41 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The probability of bit error for the DPSK with non-coherent detection is given by P bdpsk, 1 E exp( b ) (6.75) 2 N 0 where E b is energy per bit and N 0 is the double-sided power spectral density of the additive white Gaussian noise (AWGN).

42 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Quadrature Phase Shift Keying (QPSK) (very briefly mentioned) Figure 6.26 shows QPSK signal constellation.

43 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The probability of bit error for the QPSK is given by P b, BPSK 2E Q b N 0 where E b is energy per bit and N 0 is the double-sided power spectral density of the additive white Gaussian noise (AWGN). (6.74) The bit error probability of QPSK is identical to BPSK, but twice as much data can be sent in the same bandwidth. In other words, QPSK provides twice the spectral efficiency with exactly the same energy efficiency in comparison with BPSK. The power spectral density of a QPSK signal is given by P QPSK E s sin ( f fc) T s sin ( f fc) T s 2 ( f fc) Ts ( f fc) T s 2 2 E b sin 2 ( f f ) T sin 2 ( f f ) T 2 ( f fc) Tb 2 ( f fc) T b 2 2 c b c b where T b and T s are bit duration and symbol duration, respectively, and (6.80) Eb and E s are bit energy and symbol energy, respectively.

44 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The power spectral density (PSD) of a QPSK signal is shown in Figure In Figure 6.27 it is shown that the null-to-null bandwidth is equal to the bit rate, that is, BW nulltonull R b 1 T b which is half that of the BPSK signal.

45 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

46 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Quadrature Transmission and Detection Techniques (very briefly mentioned) Figure 6.28 shows a block diagram of a typical QPSK modulator.

47 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Offset QPSK (OQPSK) (briefly covered) The amplitude of a QPSK signal is ideally constant. However, when QPSK signals are pulse shaped to reduce the spectral sidelobes, the waveform no longer has a constant envelope and the occasional phase shift of 180 o for just an instant. can cause the signal envelope to pass through zero A signal is sometimes hardlimited to remove any fluctuations in its envelope. Hardlimiting or nonlinear amplification of the zero-crossings brings back the filtered spectral sidelobes which interfere adjacent channels, since the fidelity of the signal at small voltage levels is lost in transmission. To prevent the regeneration of spectral sidelobes and spectral widening, QPSK signals must be amplified using highly linear amplifiers which are expensive and less efficient. While the bit transitions of the even and odd bit streams, mi ( t ) and mq ( t ), occur at the same time instants in QPSK signaling, the even and odd bit streams, mi ( t ) and mq ( t ), are offset in their relative alignment by one bit period (i.e., half symbol period) in offset QPSK (OQPSK or staggered QPSK (SQPSK)) signaling.

48 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 An example of the OQPSK signal is shown in Figure 6.30.

49 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

50 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 While the phase transition occurs once every T 2T with 0 o, 90 o, 180 o, or 270 o in QPSK, the phase s b transition occurs once every T b with 0 o, 90 o, or 270 o (or 90 o ) in OQPSK. By having phase transition more frequently, the OQPSK signaling eliminates 180 o phase transitions. Since 180 o envelope to go to zero. phase transitions are eliminated, bandlimiting (i.e., pulse shaping) does not cause the signal Hence, the hardlimiting or nonlinear amplification of OQPSK signals does not regenerate high frequency sidelobes as much as in QPSK and spectral occupancy of the former is significantly reduced in comparison with the latter, while permitting more efficient RF amplification. As the spectrum of an OQPSK signal is identical to that of a QPSK signal, both signals have the same bandwidth. OQPSK retains its bandlimited spectrum even after nonlinear amplification. Hence, OQPSK is attractive for wireless communication systems where bandwidth efficiency and efficient nonlinear amplifiers are crucial for low power consumption.

51 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Further, OQPSK has better performance than QPSK in the presence of phase jitter due to noisy reference signals at the receiver [Chunag, 1987] /4 QPSK (briefly covered) For / 4 shifted QPSK, the maximum phase change is limited to 135 o (i.e., 135 o or 225 o ) as compared with 180 o for QPSK and 90 o (i.e., 90 o or 270 o ) for OQPSK. Hence the bandlimited / 4 QPSK signal preserves the constant envelope property better than bandlimited QPSK, but not as much as OQPSK. /4 QPSK is very attractive because it can be noncoherently detected which simplifies receiver design greatly. Further, / 4 QPSK has better performance than OQPSK in the presence of multipath spread and fading [Liu, 1989].

52 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 In / 4 QPSK modulator, signaling points of the modulated signal are selected from two QPSK constellations which are shifted by with respect to each other. 4 Figure 6.31 shows the two constellations along with the combined constellation where a link between two signal points indicates possible phase transitions.

53 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Figure 6.31 Constellation diagram of a / 4 QPSK signal; (a) possible states for k when k1 n /4.

54 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.31 Constellation diagram of a / 4 QPSK signal; (b) possible states when k1 n /2.

55 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.31 Constellation diagram of a / 4 QPSK signal; (c) all possible states.

56 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The following figure shows the transitions of / 4 QPSK signals in constellation.

57 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 [R. Peterson, R. Ziemer, and D. Both, Introduction to Spread Spectrum Communications. Prentice-Hall, 1995]

58 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Very often, differentially encoded data are / 4 QPSK modulated to facilitate the implementation of differential detection or coherent modulation with phase ambiguity in the recovered carrier. When differentially encoded, / 4 QPSK is called /4 DQPSK. /4 DQPSK is adopted in the standards such as the USDC (IS-54) and PACS in North America and the PDC (Pacific Digital Cellular) and PHS in Japan /4 QPSK Transmission Techniques The block diagram of a / 4 QPSK is shown in Figure 6.22.

59 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

60 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 In the / 4 QPSK transmitter, taking the two bit streams, m Ik, and m Qk,, for kts t ( k 1) Ts, the signal mapper produces the k-th in-phase and quadrature data, I k and Q k. I k and symbol k. Q k are determined by their previous output values k 1 I and Qk 1 as well as the phase of k -th m The phase of k -th symbol Qk,, which is given by k itself is a function of k which is a function of current input bits Ik, m and, (6.83) that is, k k1 k k k k 1.

61 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The outputs of the signal mapper is given by I and k Q k cos k cos( ) k1 k1 k k1 k k I cos Q sin (6.81) sin k sin( ) k1 k I sin Q cos. (6.82) k1 k k1 k The phase shift k is related to input bits I k and Q k as shown in Table 6.2.

62 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

63 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Then, as in a QPSK modulator, the in-phase and quadrature bit streams I k and Q k are separately modulated by two carriers cos and sin c t to produce the / 4 QPSK signal which is given by c t s /4 QPSK() t I()cos t ct Q()sin t ct (6.84) where and N 1 Ts It () Ipt k ( kts ) 2 k0 N 1 Ts cos kpt ( kts ) (6.85) 2 k0 N 1 Ts Qt () Qpt k ( kts ) 2 k0 N 1 Ts sin kpt ( kts ) (6.86) 2 k0 where the function p( t ) corresponds to the pulse shape and T s is the symbol period. Usually both I k and reduce the bandwidth occupancy. Q k are passed through the raised cosine pulse shaping filters before modulation to Pulse shaping also reduces the spectral restoration problem which may be significant in fully saturated, nonlinear amplifiers.

64 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Note that the peak amplitudes of the modulated waveforms I ( t ) and Qt ( ) can take values of 0, 1, 1, 1 2, and 1. 2 As the information in a / 4 QPSK signal is completely contained in the phase difference k of the carrier between two adjacent symbol (that is, k k k 1 ), it is possible to apply noncoherent differential detection even in the absence of differential encoding. Ex. 6.9 DIY.

65 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, /4 QPSK Detection Techniques (very briefly covered) Differential detection is often used to demodulate / 4 QPSK signals due to its easy hardware implementation. Differentially detected / 4 QPSK has error performance 3 db inferior to QPSK in an AWGN channel, while coherently detected / 4 QPSK has the same error performance as QPSK. In low bit-rate, fast Rayleigh fading channels, differential detection for / 4 QPSK offers a lower error floor, since it does not rely on phase synchronization [Feher, 1991]. Various types of detection techniques are used for / 4 QPSK such as baseband differential detection, IF differential detection, and FM discriminator detection. Baseband Differential Detection Figure 6.33 shows the block diagram of a baseband differential detector.

66 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

67 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The incoming / 4 QPSK signal is quadrature demodulated using two local oscillator signals having the same frequency as the carrier at the transmitter, but not necessarily the same phase. 1 Qk Let k tan denote the phase of the carrier due to the k-th data bit, the outputs from the lowpass Ik filters in the in-phase and quadrature branches are given by and w cos( ) (6.87) k k z sin( ), (6.88) k k respectively, where the is a phase shift due to noise, propagation delay, and interference. Assume that the phase changes much slower than k so that the former is essentially a constant. Taking the output sequences from the LPFs, the differential decoders in the in-phase and quadrature branches give outputs given by and x ww zz (6.89) k k k1 k k1 y z w w z, (6.90) k k k1 k k1 respectively.

68 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The differential detector is implemented using a delay line and two mixers. By plugging (6.87) and (6.88) into (6.89) and (6.90), respectively, the output of the differential detector is given by and x cos( )cos( ) sin( )sin( ) k k k1 k k1 cos( ) (6.91) k k 1 y sin( )cos( ) cos( )sin( ) k k k1 k k1 sin( ). (6.92) k k 1 Taking the outputs from the differential decoders, the decision devices in the in-phase and quadrature branches produce outputs given by S and S I Q 1, 0 xk, (6.93) 0, xk 0, 1, 0 yk, (6.94) 0, yk 0, respectively. (Check this with Table 6.2)

69 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Ensure that the frequency of the local oscillator is the same as the transmitter carrier frequency and it does not drift. Any drift in the local oscillator frequency causes a drift in output phase which results in degradation in BER. Ex DIY. IF Differential Detector (skipped) Figure 6.34 shows the block diagram of an IF differential detector.

70 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

71 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The IF differential detector avoids the need of a local oscillator by using a delay line and two phase detectors. The received signal is downconverted to IF and passes through bandpass filter which is matched to the transmitted pulse shape so that the carrier phase is preserved and noise power is minimized. To minimize the effect of ISI and noise the bandwidth of the filters are chosen to be 0.57 T s [Liu 1991]. In each branch the received IF signal is differentially decoded using a delay line and two mixers. The bandwidth of the signal at the output of the differential detector is twice that of the baseband signal at the transmitter end, as symbols duration the former is half of that of the latter.

72 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 FM Discriminator (skipped) Figure 6.35 shows the block diagram of an FM discriminator detector for / 4 QPSK.

73 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The received signal passes through the bandpass filter matched to the transmitted pulse shape and then hardlimited to remove any envelope fluctuations. The FM discriminator extracts the instantaneous frequency deviation of the received signal. The instantaneous frequency deviation is integrated over each symbol period to give the phase difference between sampling instants. Phase difference can be detected using a modulo- 2 phase detector.

74 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Constant Envelope Modulation Constant envelope modulation is nonlinear modulation where the amplitude of the carrier is constant regardless of the variation in the modulating signal. Constant envelope modulations have advantages as follows [Young, 1979]. Power efficient Class C amplifiers can be used without causing degradation in the bandwidth occupancy of the transmitted signal. Low out-of-band radiation can be achieved to the order of 60 to 70 db. Limiter-discriminator detection can be used which simplifies receiver design and provides high immunity against FM noise and signal fluctuation due to Rayleigh fading. Constant envelope modulations have disadvantages as follows. They occupy a larger bandwidth than linear modulation schemes.

75 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Hence, in applications where bandwidth efficiency is more important than power efficiency, constant envelope modulation is not suitable. BFSK, MSK and GMSK are considered, as examples of constant envelope modulations Binary Frequency Shift Keying (BFSK) (skipped) A binary frequency shift keying (BFSK) signal has constant envelope and has either a discontinuous phase or constant phase, depending on how the frequency variations according to data symbols are imparted into the transmitted waveform. In general, a BFSK signal is given by s FSK 2Eb vh( t) cos(2 fc 2 f) t, if m( t) 1, Tb () t 2Eb vl( t) cos(2 fc 2 f) t, if m( t) 1(or 0), Tb (6.95) for 0 t T, where 2 f is a constant offset from the nominal carrier frequency and mt ( ) is the modulating signal. b

76 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 For a BFSK signal to be continuous, it is required that ft ( f) T 2fT n for some integer n. b b b One method to generate an FSK signal is to switch between two independent oscillators according to whether the data is 0 or 1. FSK. As the resulted waveform is discontinuous at the switching times, this type of FSK is called discontinuous A discontinuous BFSK signal is given by s FSK 2Eb vh() t cos(2 fht1), if m() t 1, Tb () t 2Eb vl() t cos(2 flt2), if m() t 1(or 0), Tb for 0 t T. b (6.96) Since the phase discontinuities cause several problems such as spectral spreading and spurious transmissions, this type of FSK is generally not used in highly regulated wireless systems. The more common method to generate an FSK signal is to frequency modulate a single carrier oscillator using the message waveform.

77 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 This type of modulation is similar to analog FM generation, except that the modulating signal mt ( ) is a binary waveform. Hence, the BFSK signal is represented as 2Eb sfsk () t cos[2 fct ()] t T b 2E T b b t cos 2 fct 2 kf m( ) d. (6.97) Even though the modulating signal mt ( ) is discontinuous at bit transitions, the phase function ( t) is proportional to the integral of mt ( ) and is continuous. Spectrum and Bandwidth of BFSK Signals As the complex envelope of an FSK signal is a nonlinear function of the modulating signal mt ( ), its evaluation is quite involved and is usually performed using actual time-averaged measurements. The power spectral density of a binary FSK signal consists of discrete frequency components at f c,

78 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 fc n f, and fc n f, where n is an integer. It can be shown that the PSD of a continuous phase FSK ultimately falls off as the inverse fourth power of the frequency offset from f c. However, if phase discontinuities exist, the PSD falls of as the inverse square of the frequency offset from f c [Couch 1993]. From (6.95) it can be derived that the minimum frequency spacing which allows two FSK signals to be coherently orthogonal is 1 fh fl 2f. 2T b This allows orthogonal detection [Sklar, Digital Communications: Fundamentals and Applications. Prentice Hall, 2001]. By Carson s rule the transmission bandwidth of a BFSK signal is given by B 2f 2B (6.98) T where B is the bandwidth of the baseband binary signal. Assuming that the first null-to-null bandwidth, the bandwidth of the baseband of rectangular pulses is given

79 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 by B R. Hence the FSK transmission bandwidth becomes B 2( f R). (6.99) T If a raised cosine pulse-shaping filter is used, then the transmission bandwidth reduces to B 2 f (1 ) R (6.100) T where is the rolloff factor of the filter. Coherent Detection of BFSK Figure 6.36 shows the block diagram of a coherent FSK receiver.

80 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The probability of error for coherent detection of BFSK (or coherent BFSK) is given by E. (6.101) b PeFSK, Q N 0

81 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Noncoherent Detection of BFSK Figure 6.37 shows the block diagram of a noncoherent FSK receiver.

82 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The probability of error for noncoherent detection of BFSK (or noncoherent BFSK) is given by P efsk,, NC 1 1 exp 2 2 E N b 0. (6.102)

83 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Minimum Shift Keying (MSK) (briefly covered) Minimum shift keying (MSK) is a type of continuous phase-frequency shift keying (CPFSK) of which peak frequency deviation is equal to 1 4 the bit rate. In other words, MSK is continuous phase FSK (CPFSK) with a modulation index of 0.5. The modulation index of continuous phase FSK is similar to the FM modulation, and is defined as k FSK where 2f R b f is the peak RF frequency deviation and R b is the bit rate. The modulation index of 0.5 corresponds to the minimum frequency spacing which allows two FSK signals to be coherently orthogonal, that is, T vh() t vl() t dt 0 (6.103) 0 for two FSK signals vh ( t ) and vl( t ). This allows orthogonal detection.

84 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The name minimum shift keying implies the minimum frequency separation (i.e., bandwidth). MSK is sometimes referred to as fast FSK, as the frequency spacing used is only half as much as that used in conventional noncoherent FSK [Xiong, 1994]. MSK is attractive in wireless communication systems, as it is a spectrally efficient modulation. MSK has properties such as constant envelope, spectral efficiency, good BER performance, and selfsynchronizing capability. The MSK signal can be regarded as a special form of an OQPSK signal where the baseband rectangular pulses are replaced by half-sinusoidal pulses [Pasupathy, 1979]. Consider the OQPSK signal with the bit streams offset as shown in Figure The MSK signal for an N -bit stream is given by MSK N 1 S () t m () t p( t 2 it )cos2 f t i0 N 1 i0 I b c mq() t p( t2 itb Tb)sin2 fct (6.104)

85 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 where the baseband pulse shaping function is given by t cos( ), Tb t Tb, pt () 2Tb 0, elsewhere, (6.105) and mi ( t ) and mq ( t ) are the odd and even bits of the data stream, mi ( t ), mq ( t ) { 1, 1}, which are fed into the in-phase and quadrature branches of the modulator at the rate of R b. 2 Although there are a number of variations of MSK in the literature, all of them are continuous phase FSK (CPFSK) employing different techniques to achieve spectral efficiency [Sundberg 1986]. The MSK signal can be regarded as a special form of a continuous phase FSK (CPFSK) signal if (6.97) is rewritten as 2E 1 b SMSK () t cos2 ( fc mi () t mq ()) t tk Tb 4Tb 0, if mi ( t) 1, where k, if mi ( t) 1. (6.106) From (6.106) it is deduced that an MSK signal has a constant envelope.

86 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Phase continuity at bit transition periods is ensured by choosing the carrier frequency f c such that 1 fc n for some integer n. (Verify it. DIY.) 4 Tb f c Comparing (6.106) with (6.97), it is concluded that the MSK signal is a FSK signal with binary frequencies 1 and 4T b f c 1. 4T b The minimum frequency separation is given by ( fc ) ( fc ). 4T 4T 2T b b b Further, from (6.105) it can be shown that the phase of the MSK signal varies linearly during each bit period.

87 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 MSK Power Spectrum (The power spectral density of the bandpass signal wt ( ) is given by 1 Ps ( f) [ Pg( f fc) Pg( f fc)] (6.41) 4 where Pg ( f ) is the power spectral density of gt ( ) which is the baseband complex envelope of wt ( ).) From (6.41) and (6.105) the normalized power spectral density for MSK is given by P MSK ( f) 2 2 E b 16 cos2 ( f fc) T 16 cos2 ( f fc) T (6.108) 2 116f T 116f T Figure 6.38 shows the power spectral density for MSK along with QPSK and OQPSK.

88 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

89 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 In Figure 6.38 it is shown that MSK has lower spectral sidelobes than QPSK and OQPSK % of the MSK power spectrum is contained within a bandwidth B 99%, while for QPSK and T 8 OQPSK, 99 % bandwidth is given by B99% for QPSK and OQPSK. T b b The faster rolloff of the MSK spectrum is due to its smoother pulse shaping function. However, in Figure 6.38 it is shown that the main lobe of MSK is wider than QPSK and OQPSK, and hence the null-to-null bandwidth B null-to-null of the former is larger than the latter. That is, in terms of null-to-null bandwidth, MSK is less spectrally efficient than QPSK and OQPSK. Bandlimiting a MSK signal to meet required out-of-band specifications does not cause the signal envelope to go through zero, since there is no abrupt change in phase at bit transition periods. Since the amplitude of MSK signals is kept constant, it can be amplified using efficient nonlinear amplifiers without generating undesired spectral sidelobes.

90 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The following figure shows a MSK waveform [R. Ziemer and R. Peterson, Digital Communications and Spread Spectrum Systems. Macmillan, 1985].

91 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

92 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The following figure shows the trellis diagram for the type-i MSK [R. Peterson, R. Ziemer, and D. Borth, Introduction to Spread Spectrum Communications. Prentice-Hall, 1995].

93 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

94 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The continuous phase property makes MSK desirable for highly reactive loads. Also MSK has simple modulation and synchronization circuits. MSK Transmitter and Receiver Figure 6.39 shows the block diagram of an MSK modulator.

95 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

96 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.40 shows the block diagram of an MSK demodulator.

97 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, Gaussian Minimum Shift Keying (GMSK) GMSK can be regarded as a variation of MSK. In GMSK, the sidelobes of the power spectrum are further reduced by passing the modulating NRZ data waveform through a premodulation Gaussian pulse-shaping filter. Baseband Gaussian pulse shaping smoothens the phase trajectory of the MSK signal over time and hence stabilized the instantaneous frequency variations. By this, the sidelobe levels are reduced considerably in the transmitted spectrum. The impulse response of the GMSK premodulation filter, which is a Gaussian lowpass filter, is given by 2 2 hg () t exp t 2 (6.54) (6.109) where is a parameter related to B which is 3 db baseband bandwidth of the filter given by ln2 2B (6.53)(6.111) B

98 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Figure 6.22 show the impulse response h () t of the Gaussian filter. G

99 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

100 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 The has a transfer function of the GMSK premodulation filter, which is a Gaussian lowpass filter, given by H f f. (6.52)(6.110) 2 2 G( ) exp( ) As the result of GMSK filtering is completely described by the baseband bandwidth B and the baseband symbol duration T, it is customary to define GMSK by its B T product. Figure 6.41 shows power spectrum of the GMSK signal for various values of BT.

101 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

102 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 Note that the power spectral density of MSK is equivalent to that of GMSK with BT. In Figure 6.41 it is shown that as the BT product decreases, the sidelobe levels fall off very fast. For example, the peak of the second lobe is 30 db below the main lobe for GMSK with BT 0.5, while the peak of the second lobe is 20 db below the main lobe for GMSK with BT (that is, MSK). However, reducing BT increases the irreducible bit error rate produced by the lowpass filter due to ISI. As to be shown in Section 6.11 mobile radio channels induce an irreducible error rate due to MS velocity. As long as the GMSK irreducible error rate is less than that produced by the mobile channel, there is no penalty in using GMSK. Table 6.3 shows occupied bandwidth containing a given percentage of power in a GMSK signal as a function of the BT product [Murota, 1981].

103 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

104 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 While the GMSK spectrum becomes more compact with decreasing BT value, the degradation due to ISI increases. It was shown that the BER degradation due to ISI caused by Gaussian filtering is minimum at BT , where the degradation in the required E b N 0 is only 0.14 db from the case of no ISI [Ishizuka 1980]. GMSK Bit Error Rate The BER of GMSK is a function of BT, since pulse shaping impacts ISI. The bit error probability of GMSK is given by P e 2 E b Q N 0 where is a constant related to BT by 0.68 for GMSK with BT 0.25, 0.85 for simple MSK ( BT ). (6.112a) (6.112b) It is shown that the GMSK with BT 0.25 offers BER performance within 1 db of optimum MSK for AWGN.

105 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 GMSK Transmitter and Receiver A GMSK signal is generated by passing a NRZ message bit stream through the Gaussian filter having an impulse response given in (6.109), followed by the FM modulator as shown in Figure The transmitter may also be implemented digitally using a standard I / Q modulator. A GMSK signal can be detected using orthogonal coherent detectors as shown in Figure 6.43.

106 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010

107 Chapter 6. Modulation Techniques for Mobile Radio nd Semester, 2010 GMSK is used in the standards such as the CDPD and DCS-1900 in North America and the GSM and DCS in Europe. Ex DIY Combined Linear and Constant Envelope Modulation Techniques (briefly covered) Modern modulation techniques exploit the fact that digital baseband data may be sent by varying both the envelope and phase (or frequency) of an RF carrier. Because the envelope and phase offer two degrees of freedom, such modulation techniques map baseband data into four or more possible RF carrier signals. Such modulation techniques are called M -ary modulation, since they can represent more signals than if just the amplitude or phase were varied alone. In an M -ary signaling scheme, two or more bits are grouped together to form symbols and one of M possible signals, s1(), t s2(), t, sm () t is transmitted during each symbol period of duration T s.

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