Chapter 2. Digital Modulation and Demodulation Techniques. 2.1 Why Digital Modulation

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1 . Digital Modulation and Demodulation Techniques Chapter Digital Modulation and Demodulation Techniques.1 Why Digital Modulation Modern wireless communication systems use digital modulation and demodulation techniques. Advantages over analogue modulation: Improved spectral efficiency Increase in capacity (higher data rates, or more users) Reduced power requirements: - reduced transmitter power - reduced antenna gain - increased path loss tolerated (range increase) Greater accuracy in transmitting and receiving messages in the presence of noise and distortion (improved tolerance to cochannel interference and multipath effects) Easier multiplexing of various forms of information (voices, data and video) Greater security Digital transmissions accommodate digital error control codes that detect and correct transmission errors. Support complex conditioning and processing techniques such as source coding encryption, and equalisation to improve performance of the overall communication link. Modulation is the process of encoding information from a message source in a manner suitable for transmission. It generally involves translating a baseband message signal to a passband signal at a much higher frequency (see Fig..1). Modulation can be done by varying the amplitude, phase or frequency of a high frequency carrier in accordance with the amplitude of the message signal. The modulating signal can be represented as a time sequence of symbols or pulses, where each symbol has m finite states. Each symbol represents n bits of information, where n=log m bits/symbol. Demodulation is the process of extracting the baseband message from the carrier so that it may be processed and interpreted by the intended receiver. Factors influence the choice of a digital modulation scheme: Provides low bit error rates at low received signal to noise ratio Performs well in multipath and fading conditions Performs well in an interference environment Occupies a minimum of bandwidth Easy and cost effective to implement Performance of a modulation scheme is often measured by: Power efficiency describes the ability of a modulation technique to preserve the fidelity of the digital message at low power levels. Bandwidth efficiency describes the ability of a modulation scheme to accommodate data within a limited bandwidth. A low bit-error-probability should be achieved in the presence of adjacent and cochannel interferences, thermal noise and other channel impairments such as fading and intersymbol interference. 1

2 . Digital Modulation and Demodulation Techniques Figure.1 (a) Baseband and (b) passband signals. In the design of a digital communication system, very often there is a trade-off between bandwidth efficiency and power efficiency. Adding error control coding to a message increases the bandwidth occupancy (and this, in turn, reduces the bandwidth efficiency), but at the same time reduces the required received power for a particular bit error rate, and hence trades bandwidth efficiency for power efficiency. When the signal passes through the channel, signal degradation by the following changes its shape (see Fig..): Distortion resulted when the signal is passed through filters having insufficient bandwidth Intersymbol interference (ISI) is the effect where one bit affects succeeding bits Delay spread is the effect when multiple delayed versions of the original signal can be received at the same time Thermal noise from within the receiver itself or from manmade or natural interference Adjacent channel interference due to other transmitters spilling over into the receiver band Cochannel interference due to distant transmitters operating at the same frequencies Table.1 covers the applications for different modulation formats in both wireless communications and video. To understand and compare different modulation format efficiencies, it is important to first understand the differences between bit rate and symbol rate. The signal bandwidth for the communications channel needed depends on the symbol rate, not on the bit rate. symbol rate = bit rate number of bits transmitted with each symbol Bit rate is the frequency of a system bit stream. Take, for example, a radio with an 8 bit sampler, sampling at 10kHz for voice. The bit rate, the basic bit stream in the radio, would be 8 bits multiplied by 10k samples per second, or 80kbits per second. The symbol rate is the bit rate divided by the number of bits that can be transmitted with each symbol. If one bit is transmitted per symbol, as with BPSK, then the symbol rate would be the same as the bit rate of 80kbits per second. If two bits are transmitted per symbol as in QPSK, then the symbol rate would be half of the bit rate or 40kbits per second. If more bits can be sent with each symbol, then the same amount of data can be sent in a narrower spectrum. This is why modulation formats that are more complex and use a higher number of states can send the same information over a narrower piece of the RF spectrum.

3 . Digital Modulation and Demodulation Techniques Figure. Waveforms in a typical digital communication system: (a) transmitted signal, (b) distorted receive signal, (c) distorted signal with noise, (d) regenerated signal (delayed). Table.1 Applications for different formats in both wireless communications and video. An example of how symbol rate influences spectrum requirements can be seen in eightstate Phase Shift Keying (8PSK). It is a variation of PSK. There are 8 possible states that the signal can transit to at any time. The phase of the signal can take any of 8 values at any symbol time. Since 3 =8, there are 3 bits per symbol. This means the symbol rate is one-third of the bit rate. This is relatively easy to decode. The symbol clock represents the frequency and exact timing of the transmission of the individual symbols. At the symbol clock transitions, the transmitted carrier is at the correct I/Q or magnitude/phase value to represent a specific symbol (a specific point in the constellation). 3

4 . Digital Modulation and Demodulation Techniques. Power Spectral Density of Digital Signals With any modulation technique, the modulated bandpass signal can be expressed in the form ( ) ( ) { } j π f t c s t = Re g t e where g(t) is the complex baseband envelope, then the power spectral density of the bandpass signal S TX (f) is related to the power spectral density of the complex envelop S(f) by ( f ) [ S( f f ) + S( f )] 1 S = + TX c f c.3 Phase Modulation Digital phase modulation generally changes the phase of the carrier to a number of different phase angles. Binary phase shift keying (BPSK) carrier phase is either 0 or 180 Quadrature phase shift keying (QPSK) use one of the four different phase angles (45, 135, 45 and 135 ) to represent two bits at a time 8-PSK use eight phase angles to represent groups of three bits at a time 16-PSK use sixteen phase angles to represent groups of four bits at a time.3.1 Binary Phase Shift Keying (BPSK) Simplest form of digital phase modulation. Used in direct-sequence spread-spectrum (DSSS) transceivers, pulse compression radars and deep space telemetry. Phase of a constant amplitude carrier signal is switched between two values (0 and 180 ) according to the two possible signals corresponding to binary 1 and 0 respectively (see Fig..3). The symbol rate is one bit per second. BPSK is often referred to as an antipodal modulation, where each of the two binary waveforms is the negative of the other. The binary waveforms are the unshifted carrier or the inverted carrier (see Fig..4). This time domain response shows that the binary bit stream inverts the phase of the carrier back and forth 0 or 180. Each inversion of the carrier causes a sharp transition in the time domain response. These transitions produce a very wide transmitted spectrum. Fig..5 shows a block diagram for a typical BPSK modulator. An oscillator produces an unmodulated carrier that is fed to a double-balanced mixer. The non-return-to-zero (NRZ) data is mixed with the carrier to form the desired BPSK signal. The transmitted output spectrum is reduced by filtering the baseband modulation signal with the use of a lowpass filter between the NRZ data input and the double-balanced mixer. An amplifier is used to increase the transmitted signal level coming out of the modulator. A final filter is used to eliminate the out-of-band harmonics of the signal produced by the RF amplifier. 4

5 . Digital Modulation and Demodulation Techniques Figure.3: Phase domain of carrier for BPSK. Figure.4: BPSK time domain waveforms. 5

6 . Digital Modulation and Demodulation Techniques Figure.5: BPSK modulator. A diagram of a coherent BPSK demodulator is shown in Fig..6. The action of the demodulator is the reverse of the modulator. Coherent demodulation implies that the exact phase and frequency of the modulated signal is known at the receiver. The modulated signal is applied to a double-balanced mixer, which is mixed with a LO having the same frequency and phase as the modulated signal itself. Carrier recovery circuits are used to produce this local carrier reference. These circuits use phase or frequency information from the received signal to synchronise the local oscillator. The received modulated signal can be written as ri ( t) = B cos[ πf ct + ϕi ( t) ] where B is the amplitude of the received signal and ϕ i (t) is the phase of the transmitted signal, either 0 or 180. Multiplying the LO signal by the received signal gives s t = B cos πf t + ϕ t cos πf t i ( ) [ ( )] ( ) c i B = { cos[ 4πf ct + ϕi ( t) ] + cos[ ϕi ( t) ]} The component at twice the RF frequency is removed by filtering, leaving B si ( t) = cos[ ϕ i ( t) ] If ϕ i (t) is 0, then s i (t) is 1. If ϕ i (t) is 180, then s i (t) is 1. Thus, the original binary NRZ signal is recovered by the demodulator. c 6

7 . Digital Modulation and Demodulation Techniques Figure.6 BPSK demodulator. The NRZ data signal resembles a square wave but alternates periodically between binary 1 and 0 in a random fashion. This characteristic means that the NRZ signal power spectral density is smooth and resembles a sinx/x shape. For balanced +A and A volt NRZ signalling states, Tb Tb ( ) + A t g 1 t = 0 elsewhere Tb Tb ( ) A t g t = 0 elsewhere The Fourier transform of the g 1 (t) symbol is Similarly, S S 1 ( f ) = g( t) A = sin ( πft b ) πf The complete spectral density (neglecting the dc term and harmonics) of equiprobable p(+a)=p( A)=0.5 balanced NRZ random data is given by S A = jπf = A πf sin ( f ) = f p( 1 p) [ S ( f ) S ( f )] b e j πft Tb / Tb / ( πft ) Tb / ( f ) ( A) Tb / b j dt = j πft 1 = (0.5)(1 0.5) AT Tb e = π e ft 1 dt ( πft ) sin πftb = A Tb πftb where T b is the bit period, A is the amplitude of the signal, and f is the frequency. The PSD for the BPSK signal at RF can be evaluated by translating the baseband spectrum to the carrier frequency P BPSK ( f ) = A sin Tb π π( f f RF ) ( f f ) T RF T b b Tb / Tb / d Ae ( jπft ) b sin + π j πft sin πft dt b b π( f + f ) ( ) RF Tb f + f RF Tb 7

8 . Digital Modulation and Demodulation Techniques The PSD of an unfiltered BPSK signal is plotted in Fig..7 for a data rate of 10Mbps and a carrier frequency of 80MHz. The null-to-null bandwidth is found to be equal to twice the bit rate (BW=R b =/T b ). The first null occurs at a frequency equal to R b away from the carrier frequency and the amplitude of the first lobe is only 13dB down from its carrier value. Another important parameter of any digital modulation is how the probability of bit error, P E varies with SNR. Fig..8 shows a BPSK received signal with and without noise. The modulator decides whether the recovered signal was a 1 or 1 by sampling the waveform at the centre of the bit period. This is easy to do when there is no noise added to the signal. When noise is added to the signal, it is easy to make an error. Fig..9 shows a plot of the probability of making a bit error versus the ratio of the energy per bits over the noise power spectral density, E b /N 0. E b /N 0 is related to SNR as follows E b STb S Bn = = N 0 N / Bn N Rb where S is the average signal power of the carrier and T b is the bit period. E b /N 0 is equal to SNR when the noise bandwidth of the receiver is equal to the data rate. This is a theoretical result since the noise bandwidth of the receiver needs to be somewhat wider than the bit rate to avoid intersymbol interference in the received waveform. Binary modulation methods transmit one bit per signalling interval, with a bandwidth efficiency of 1bps/Hz. Differential Phase Shift Keying is a noncoherent form of phase shift keying which avoid the need for a coherent reference signal at the receiver. Noncoherent receivers are easy and cheap to build, and hence widely used in wireless communications. The input binary sequence is first differentially encoded and then modulated using a BPSK modulator. The received signal is compared with a delayed version of itself. Fig..10 shows both the DPSK modulator and demodulator. The data must be differentially encoded prior to modulation. If the original NRZ data stream is 0, 1, 1, 0, 1, 1, 1, 0, 0 then the encoded NRZ data signal (assuming the initial bit was a 0) is 0, 1, 0, 0, 1, 0, 1, 1, 1 From earlier equation, the delayed version of the signal can be written as ri ( t Tb ) = B cos[ πf c ( t Tb ) + ϕi ( t Tb )] Multiplying the delayed and original signals together yields ri ( t) = Acos[ πf ct + ϕi ( t) ] After some algebra and lowpass filtering, we are left with B [ ri ( t Tb ) ri ( t) ] [ ( ) ( )] LPF = cos ϕi t Tb ϕi t If the last angle and the present angle are both the same, then their difference is 0 and the filtered output is 1. If the present angle and the last angle are different, then their difference is 180, and the filtered output is 1. The differential BPSK demodulator performs a comparison detection directly on the modulated signal and thus does not require a carrier recovery circuit. Since a delayed version of the received signal, complete with added noise is used as a reference for demodulation, the P E performance for DPSK is worse than that of coherently demodulated BPSK as shown in Fig..9. While DPSK signalling has the advantage of reduced receiver complexity, its energy efficiency is inferior to that of coherent PSK by about 3dB. 8

9 . Digital Modulation and Demodulation Techniques Figure.7 BPSK power spectral density..3. Quadrature Phase Shift Keying (QPSK) In the case of M-ary modulation methods, more than one bit may be transmitted per signalling interval. This allows greater bit rates for the same bandwidth, at the expense of a more complex system. If we transmit M= n symbols for each signalling interval, a bandwidth efficiency of nbps/hz can be achieved. If the symbol rate is R s, then the effective is R b =nr s. If we use four states, where n= and M=4, then we transmit two bits, or four symbols for each signalling interval. This is called quadrature phase shift keying (QPSK). QPSK has twice the bandwidth efficiency of BPSK since two bits are transmitted in a single modulation symbol. The modulated signal has four distinct phase states, such as 45, 135, 45 and 135. Each value of phase corresponds to a unique pair of message bits as shown in Fig..11. QPSK is used in applications such as early telephone modems, satellite communications, global positioning system (GPS) and in some forms of code division multiple access (CDMA). For a QPSK waveform, the binary sequence is 0, 1, 1, 0, 1, 0, 0, 0 To send a stream of symbols corresponding to these bits, we first separate the bits into groups of two 01, 10, 10, 00 We can write the QPSK signal as ( ) [ ( )] ri t = Acos πf RFt + ϕi t where A is the carrier amplitude, i is an integer (0, 1,, 3) and ϕ I (t) is the instantaneous phase angle of the modulated signal with respect to the unmodulated carrier. The value ϕ i (t) can be written as π ϕi ( t) = ( i + 1) 4 9

10 . Digital Modulation and Demodulation Techniques Figure.8 Demodulated BPSK waveforms: (a) without noise, (b) with noise. 10

11 . Digital Modulation and Demodulation Techniques Figure.9 BPSK probability of bit error. Figure.10 Differentially encoded/decoded BPSK (DBPSK): (a) DBPSK transmitter, (b) DBPSK receiver. 11

12 . Digital Modulation and Demodulation Techniques Figure.11 Phase domain of carrier for QPSK (gray-coded). A more common implementation used to perform QPSK modulation is shown in Fig..1. The QPSK signal at the modulator output is normally filtered to limit the radiated spectrum, amplified and then transmitted over the transmission channel to the receiver input. The serial data stream is demultiplexed into even and odd components via the serial-parallel converter (or demultiplexer). Each data component (now at half the bit rate) is applied to a set of double-balanced modulators. Lowpass filters can be used to bandlimit the transmitted spectrum. The set of doublebalanced mixers forms a quadrature modulator which can vary both the phase and amplitude of the transmitted signal. Finally, the outputs from each double-balanced mixer are added together and fed through an amplifier to a bandpass filter to removes any harmonics of the modulated signal. QPSK can be regarded as two BPSK systems operating in quadrature. 1

13 . Digital Modulation and Demodulation Techniques Figure.1 QPSK modulator. 13

14 . Digital Modulation and Demodulation Techniques Fig..13 shows a simplified block diagram of the quadrature modulator. The inphase and quadrature components of the modulated signal can be written in their exponent forms e Q sin πf RF t = Q The output of the quadrature modulator is then Letting where we can then write s s ( t) ( t) = I 1 = I cos ( I jq) ( πf t) jπf RFt e + RF jπf RFt e + e = I RF RF ( ) j e jπf RFt = I + Q cos πf RF t + ϕ The quadrature modulator can be used to modulate both the amplitude and phase of the carrier. If I and Q are chosen to be ±1, then the amplitude of the modulated signal is a constant. Having I and Q equal to ±1, all phase angles lie along the 45 lines off the axes. We can also use the quadrature generator to perform modulations that require both amplitude and phase variation such as Quadrature Amplitude Modulation (QAM). jπf t e + Q e jπf RFt jπf jπf RFt jπf RFt jπf RFt [( I jq) e + ( I + jq) e ] = + Q e jϕ jϕ ( I + jq) = I + Q e ϕ = tan = I 1 + Q I Q I j( πf RFt+ϕ) j( πf RFt+ϕ) e + e ( ) t e j jπf RFt Fig..14 shows the time domain response for QPSK. The phase of the carrier can be changed 0, ±90 or 180 from its present value. The two bit streams in the bottom of the plot correspond to the demultiplexed I and Q data streams. The unfiltered input data bits cause abrupt changes in phase in the modulated carrier, like BPSK. If the bit rate of the input data is R b bits per second, the output symbol rate is R s = R b / symbols per second. Thus QPSK requires only half the channel bandwidth of BPSK to transmit the same data rate, and therefore has a bandwidth efficiency of bps/hz. The transmitted power spectral density of a typical QPSK signal at a carrier frequency of 80MHz and a data rate of 10Mbps is shown in Fig..15. Because the average transition between phase states is 90, the bandwidth of the QPSK spectrum is half as wide as the spectrum of a BPSK signal. 14

15 . Digital Modulation and Demodulation Techniques Figure.13 Quadrature modulator. Figure.14 QPSK time domain waveforms. The QPSK demodulator is simply the reverse of the modulator. Fig..16 shows a block diagram of a typical QPSK demodulator which is simply two BPSK demodulators using mixers with quadrature LO components to recover the I and Q signals. The received signal is multiplied by cosine and sine versions of the local carrier. The carrier recovery circuitry provides a local inphase reference precisely aligned in phase to the transmitted carrier. Shifting the inphase signal by 90 generates the quadrature signal. The symbol timing recovery circuitry extracts the data clock and samples the lowpass filtered outputs at precisely the optimum position within the bit period. A data multiplexer re-interleaves the data back into the serial bit stream. 15

16 . Digital Modulation and Demodulation Techniques Figure.15 QPSK power spectral density. As before, we can write E b /N 0 as E b S B = n N 0 N Rb In QPSK, we have created two data streams, each at half the rate of the original bit stream and each having maximum amplitude of ±( S)/, this gives ( ) Eb S / Bn S Bn = = N 0 N Rb / N Rb Therefore, the BER of QPSK is the same as that of BPSK. Fig..17 shows a plot of the probability of bit error for QPSK versus E b /N 0, which is identical to BPSK. A noise spike could very easily cause the resultant vector to fall into the wrong quadrant. If we code the data properly, a symbol error will result in a single bit error and not two bit errors. Fig..18 shows the symbols on the QPSK phase plane for different assignments of bits. Because the noise is Gaussian by nature, it is much more likely that a noise spike will cause the resultant vector to fall in an adjacent quadrant, rather than the opposite quadrant. If the symbols are coded as in Fig..18(a), then falling into an adjacent quadrant could result in two bit errors. However, if we gray code the data as in Fig..18(b), then each symbol error into an adjacent quadrant causes only one bit error. This is because an error is most likely to result in a shift from the correct phase state to the immediately adjacent phase, rather than the diametrically opposite phase. A gray code is a mapping of input bits to output bits, such that only one output bit at a time changes for sequential input bit changes. This leads to improved bit error rates. 16

17 . Digital Modulation and Demodulation Techniques Figure.16 QPSK demodulator. 17

18 . Digital Modulation and Demodulation Techniques Figure.17 QPSK probability of bit error. Figure.18 Assignment of symbols for QPSK: (a) nongray-coded QPSK, (b) gray-coded QPSK. In most wireless communication systems, the QPSK spectrum would be too wide to meet regulatory requirements and would also cause unwanted interference by spilling into adjacent channels. The transmitted spectrum can be reduced by placing a very narrow bandpass filter at the output of the modulator. This is not practical since the Q of the filter would be very high as the transmitted frequency is much higher than the data rate. Such a high Q filter would be difficult to build, expensive and would cause significant distortion on the transmitted waveform due to rapid phase variations at the band edges. As there are many channels, the filter has to be tunable. 18

19 . Digital Modulation and Demodulation Techniques A better way to limit the transmitted output spectrum is by filtering the baseband I and Q modulation signals before applying those to the double-balanced modulators as shown in Fig..19. The resulting transmitted spectrum of the filtered and unfiltered QPSK is shown in Fig..0. The action of the filter greatly reduces the bandwidth of the transmitted signal. Fig..1 shows the corresponding time domain signal for a baseband filtered QPSK signal. The amplitude dips to zero every time a 180 phase change is encountered. However, a 90 phase changes result in much lower amplitude variations. In most wireless communication systems, the output of the modulator has to be amplified before applied to the antenna. To get the highest efficiency from the transmit power amplifier, it is common to run the circuit in nonlinear, Class C operation which consumes little power when no signal is applied to it. When a signal is applied to the hardlimited (compression or saturation) amplifier, most of the power is directly transferred to the load resulting in maximum efficiency. When a filtered QPSK signal is passed through a limited amplifier, much of the amplitude variations in the time envelope are reduced. Fig.. shows the spectrum of a QPSK signal that has been first filtered and then limited. The limiting action of the amplifier causes the spectral regrowth. In general, modulation schemes that have non-constant envelopes suffer from spectral regrowth when passed through a hardlimited amplifier. These types of modulations generally require linear amplifiers in the transmit path..3.3 Offset Quadrature Phase Shift Keying (OQPSK) In offset QPSK the two bit streams are staggered, so that both channels do not change simultaneously, as shown in Fig..3. The transitions do not pass through the centre of the constellation diagram, and hence the amplitude fluctuation is much reduced. Also, the transitions within the constellation diagram now occur twice as frequently. This may make symbol timing more difficult to acquire. Nevertheless, because the two channels carry orthogonal signals and still have the same baud rate as conventional QPSK, the bandwidth is not increased. OQPSK waveform is more tolerant to limiting as the phase variations are more gradual. OQPSK is identical to QPSK except that the Q data stream is offset from the I stream by delaying it by an amount equal to the incoming signal bit duration. Since the transitions of I and Q are offset, at any given time only one of the two bit streams can change values. Fig..3 shows the phase domain, I and Q data streams and corresponding phase angles for QPSK and OQPSK. The action of the one bit period delay in OQPSK causes no 180 phase transitions. OQPSK is used as a building block for other modulations such as MSK. Fig..4 shows the time domain response of OQPSK where all the phase transitions are 90. Figs..5 and.6 show the block diagrams of the OQPSK modulator and demodulator respectively. The OQPSK modulator is identical to that of QPSK with the exception that an extra bit period delay is inserted into the Q data stream. The OQPSK demodulator is very similar to that of QPSK except for the extra bit delay that is inserted into the I data stream to re-align the data. In OQPSK, the signal trajectories are modified by the symbol clock offset so that the carrier amplitude does not go through or near zero of the centre of the constellation. The spectral efficiency is the same with two I states and two Q states. The reduced amplitude variations allow a more power efficient, less linear RF power amplifier to be used. 19

20 . Digital Modulation and Demodulation Techniques Figure.19 Using premodulation lowpass filters to limit QPSK transmitted bandwidth. The spectrum of an OQPSK signal is identical to that of a QPSK signal, both signals occupy the same bandwidth. The staggered alignment of the even and odd bit streams does not change the nature of the spectrum. Due to the similarities with QPSK, both the power spectral density and the P E of OQPSK are the same as for QPSK. However, when filtered and limited, OQPSK shows much smaller spectral regrowth than QPSK as shown in Fig..7 for a plot of the time domain response of a baseband filtered OQPSK signal. The amplitude fluctuations are greatly reduced. When the signal is passed through a limiting amplifier, its spectral regrowth is much lower than that of QPSK as shown in Fig π/4 Quadrature Phase Shift Keying (π/4 QPSK) π/4 shifted QPSK modulation is a quadrature phase shift keying technique which offers a compromise between conventional QPSK and OQPSK in terms of the maximum phase variations. The maximum phase change is limited to ±135, as compared to 180 for QPSK and 90 for OQPSK. Hence, the bandlimited π/4 QPSK signal preserves the constant envelope property better than bandlimited QPSK, but is more susceptible to envelope variations than OQPSK. An extremely attractive feature of π/4 QPSK is that it can be noncoherently detected which greatly simplifies receiver design. In addition, π/4 QPSK performs better than OQPSK in the presence of multipath spread and fading. The spectral regrowth is reduced since the instantaneous phase transitions are limited to ±135. Very often, π/4 QPSK signals are differentially encoded to facilitate easier implementation of differential detection or coherent demodulation with phase ambiguity in the recovered carrier. With differentially encoded, π/4 QPSK is called π/4 DQPSK. It has been adopted for U.S. and Japanese digital cellular TDMA radio standards. In a π/4 QPSK modulator, signalling points of the modulated signal are selected from two QPSK constellations which are shifted by π/4 with respect to each other. Transitions must occur from one constellation to the other. This guarantees that there is always a change in phase at each symbol, making clock recovery easier. Fig..9 shows the two constellations along with the combined constellation where the links between two signal points indicate the possible phase transitions. Switching between two constellations, every successive bit ensures that there is at least a phase shift which is an integer multiple of π/4 radians between successive symbols. 0

21 . Digital Modulation and Demodulation Techniques Figure.0 QPSK transmit power spectral density: (a) unfiltered (10Mbps data rate, 80MHz carrier), (b) baseband filtered (10Mbps data rate, 80MHz carrier,.5mhz Gaussian lowpass premodulation filter). 1

22 . Digital Modulation and Demodulation Techniques Figure.1 Time domain waveform of baseband filtered QPSK transmit signal. A conceptual implementation block diagram of basic π/4 QPSK modulator architecture is given in Fig..30. The input bit stream is partitioned by a serial-to-parallel converter into two parallel data streams m I,k and m Q,k, each with a symbol rate equal to half that of the incoming bit rate. The k th inphase and quadrature pulses, I k and Q k, are produced at the output of the signal mapping circuit over time kt t (k+1)t and are determined by their previous values, I k 1 and Q k 1, as well as θ k. I k and Q k represent rectangular pulses over one symbol duration having amplitudes given by where I Q k k = cos θ = sin θ k k = I = I k 1 k 1 cos φ sin φ θk = θ k 1 + φ k The relationship between φ k and the input symbols is given in Table. below. Information bits m I,k and m Q,k Phase shift φ k 1 1 π/ π/ π/ π/4 k k Q + Q k 1 k 1 sin φ cos φ k k The information in a π/4 QPSK signal is completely contained in the phase difference φ k of the carrier between two adjacent symbols. It is possible to use noncoherent differential detection even in the absence of differential encoding.

23 . Digital Modulation and Demodulation Techniques Figure. QPSK transmit output spectrum with baseband filtering: (a) without limiting, (b) with limiting (amplifier 10dB into compression). 3

24 . Digital Modulation and Demodulation Techniques Figure.3 QPSK and OQPSK I/Q data waveforms with their corresponding phase angles. Figure.4 OQPSK time domain waveforms. 4

25 . Digital Modulation and Demodulation Techniques Figure.5 OQPSK modulator. 5

26 . Digital Modulation and Demodulation Techniques Figure.6 OQPSK demodulator. 6

27 . Digital Modulation and Demodulation Techniques Figure.7 Time domain waveform of baseband filtered OQPSK transmit signal. The IF differential detector shown in Fig..31 avoids the need for a local oscillator by using a delay line and two phase detectors. The received signal is converted to IF and is bandpass filtered. The bandpass filter is designed to match the transmitted pulse shape, so that the carrier phase is preserved and noise power is minimised. 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..4 Frequency Modulation In phase modulations, the phase of the carrier is abruptly changed to a new value in response to the input data signal. This can result in a wide transmitted spectrum and can also result in spectral regrowth if the signal does not have a constant envelope. Multiple phase angles are used to represent groups of bits and thus reduce the effective symbol rate at the transmitter. Smoothly changing the phase angle from one value to another will result in a transmitted signal having constant amplitude. A constant amplitude signal would be impervious to the effects of filtering/hardlimiting and spectral growth. 7

28 . Digital Modulation and Demodulation Techniques Figure.8 OQPSK transmit output spectrum with baseband filtering: (a) without limiting, (b) with limiting (amplifier 10dB into compression). 8

29 . Digital Modulation and Demodulation Techniques Figure.9 Constellation diagram of a π/4 QPSK signal: (a) possible states for θ k when θ k 1 =nπ/4, (b) possible states when θ k 1 =nπ/, (c) all possible states. Figure.30 Generic π/4 QPSK transmitter. 9

30 . Digital Modulation and Demodulation Techniques Figure.31 Block diagram of an IF differential detector for π/4 QPSK. Smooth, continuous phase modulation corresponds to frequency modulation. The constant envelope family of modulations has the main advantages of employing power efficient Class C amplifiers without introducing degradation in the spectrum occupancy of the transmitted signal. In situations where bandwidth efficiency is more important than power efficiency, frequency modulation is not well-suited..4.1 Minimum Shift Keying (MSK) MSK is a binary digital FM modulation technique with a modulation index of h=0.5. It has the following fundamental properties: Constant envelope suitable for nonlinear, power efficient amplification Coherent and noncoherent detection capability Spectral main lobe is 50% wider than that of QPSK signals. First spectral null is at (f f c )T b =0.75 instead of (f f c )T b =0.5. MSK can be thought of as either a phase or frequency modulation. Fig..3 shows the phase domain plot for MSK. The carrier phase changes phase by ±90 over the course of a bit period. Note that between symbols the phase changes linearly with time, and the amplitude remains constant, so between symbols the signal moves evenly around the circle from one constellation point to another. Since a frequency shift produces an advancing or retarding phase, frequency shifts can be detected by sampling phase at each symbol period. Phase shifts of (N+1)π/ radians are easily detected with an I/Q demodulator. At even numbered symbols, the polarity of the I channel conveys the transmitted data, while at odd numbered symbols the polarity of the Q channel conveys the data. Suppose the carrier phase at the beginning of the data period is 0. If the next data bit is a 1, then the phase smoothly advances by 90 by the end of the bit period. If the data bit remains a 1, then the phase advances another 90 to 180. Instead, if the next bit were a 0, then the phase would smoothly retard by 90 to 90. Again, if the data were to remain at 0, then the phase would continue to retard itself by another

31 . Digital Modulation and Demodulation Techniques Figure.3 Phase domain of carrier for MSK. The orthogonality between I and Q simplifies detection algorithms and hence reduces power consumption in a mobile receiver. The minimum frequency shift which yields orthogonality of I and Q is that which results in a phase shift of ±π/ radians per symbol (90 per symbol). Since the phase will continue to advance or retard itself over the course of each bit period, the derivative of the phase or frequency is varied. In this way, MSK can also be considered a frequency modulation. Used in satellite communications, military tactical radio, ELF underwater communications and the GSM (Global System for Mobile Communications) cellular standards. The MSK phase trellis in Fig..33 shows the phase plotted over time. The phase angle changes smoothly by 90 over each bit period. We can write the MSK signal as t π si ( t) = Acos πf RFt + d( t) dt π = Acos πf RFt + ± 1 t + ϕ where d(t) gives rise to the ±1 term in the above equation. ( ) 0 Assume that d(t) changes from one bit period to another, the frequency will be higher in one case. And when the input changes, the frequency will be lower. We can write this as + w ϕ( t) 1 π / 1 Rb f = = = = π t π T π 4 ( ) w ϕ t 1 π / 1 Rb f = = = = π t π Tb π 4 where R b =1/T b is the bit rate and T b is the bit period. The effective frequency difference is given by b + f f = R b 31

32 . Digital Modulation and Demodulation Techniques Figure.33 MSK phase trellis. Therefore, the frequency difference in MSK corresponds to a 90 phase advance or lag over a bit period is equal to half the bit rate. The word minimum corresponds to the minimum frequency difference between the mark and space frequencies, which can be coherently demodulated. If the data stream in Fig..34 does not change, then the I and Q modulation signals are simply two sinusoids 90 out of phase with one another. Simply look at any point on the unit circle and determine what values of I and Q are required for that phase angle. If the next bit is a 1, find a point on the unit circle that corresponds to 90 more of the phase angle. This will dictate what the I and Q modulation signals should look like. As the data stream changes value, the I and Q signals will look like half-period sinusoids. This is better illustrated in the time domain waveforms in Fig..35. At the bottom of the plot, the I and Q values are shown as rectangular data pulses. After passing through special pulse-shaping filters, the I and Q signals become half-sinusoidal in nature. The corresponding output signal is indeed constant envelope, with its frequency changing from a slightly higher to a slightly lower value. A block diagram of an MSK modulator is shown in Fig..36. It is identical to an OQPSK modulator except for the special pulse-shaping filters. The input to the filter simply reverses the polarity of the output signal at the end of each symbol period. 3

33 . Digital Modulation and Demodulation Techniques Figure.34 I and Q waveforms corresponding to MSK phase trellis shown in Fig..33. Figure.35 MSK time domain waveforms. Fig..37 shows a block diagram of the MSK demodulator. It is identical to an OQPSK modulator. The lowpass filters shown are implemented as matched filters that are shaped to allow the signal itself to pass with little or no attenuation and reject all other waveforms (including noise). 33

34 . Digital Modulation and Demodulation Techniques Figure.36 MSK modulator. 34

35 . Digital Modulation and Demodulation Techniques Figure.37 MSK demodulator. 35

36 . Digital Modulation and Demodulation Techniques We can produce an MSK signal via standard FM circuitry. In Fig..38, the bit stream is fed directly into the modulation input of a VCO. The modulation index for an FM signal is given by f h β = f m where the variable h is more commonly used as the index of modulation for digital signals and β is the more familiar FM (analogue) index of modulation. f is the total frequency difference and f m is the modulation frequency. For MSK, we set the level of the modulating signal into the VCO to produce a modulation index, h, of 0.5. Fig..39 shows the time domain response of MSK with the modulated carrier being shown at the top of the plot. The phase changes linearly 90 over the course of a bit period and this is shown in the second trace. The relative slope is the same for a logic 0 as it is for a logic 1, only with a negative slope. The input data stream is shown at the lower portion of the plot. A plot of the power spectral density of an MSK signal compared to that of an unfiltered QPSK signal is shown in Fig..40 for a carrier frequency of 80MHz and a data rate of 10Mbps. The MSK spectrum falls off much more rapidly than the QPSK spectrum due to the fact that the MSK signal is continuous inphase. Although the phase is continuous in MSK, the frequency is not. It is this discontinuous frequency that results in a wider power spectral density with sharp nulls. Fig..41 shows a plot of bit error probability versus E b /N 0. The curve is the same as that of BPSK and QPSK as MSK can be viewed as QPSK with special pulse-shaping filters acting over two bit periods. Fig..4 shows a plot of an MSK signal in the time domain which shows that MSK is a true constant envelope modulation with no amplitude fluctuations. This is a desirable characteristic for improving the power efficiency of transmitters. Amplitude variations can exercise nonlinearities in an amplifier s amplitude transfer function, generating spectral regrowth, a component of adjacent channel power. Fig..43 shows a plot of the MSK signal before and after hardlimiting. There is essentially no spectra regrowth and this makes MSK very attractive in applications where saturated power amplifiers are employed..4. Gaussian Minimum Shift Keying (GMSK) GMSK has a very narrow transmitted spectrum, yet exhibits very little intersymbol interference and is tolerant to hardlimiting. It is a derivative of MSK where the bandwidth required is further reduced by passing the modulating waveform through a Gaussian filter. The Gaussian filter minimises the instantaneous frequency variations over time. GMSK is a spectrally efficient modulation scheme and is particularly useful in mobile radio systems. It has a constant envelope, spectral efficiency, good BER performance and is self synchronising. 36

37 . Digital Modulation and Demodulation Techniques Figure.38 Using a voltage-controlled oscillator (VCO) as an MSK modulator. Figure.39 Time domain waveforms from VCO-based MSK modulator. 37

38 . Digital Modulation and Demodulation Techniques Figure.40 MSK versus QPSK power spectral density. Figure.41 MSK probability of bit error. 38

39 . Digital Modulation and Demodulation Techniques Figure.4 Time domain waveform of baseband filtered MSK transmit signal (using 5MHz Gaussian lowpass filter). To retain a constant envelope, coherent and noncoherent detection capability and increase the spectral efficiency, the transmitted spectrum of MSK is narrowed by filtering the modulation signal through a lowpass filter, before applying it to the VCO. The lowpass filter must have a well-behaved time domain response such as the Gaussian filters. The frequency response of a Gaussian lowpass filter is Gaussian in nature and follows the following relation ( τω) ( ) H ω = τ π e where ω is the frequency in rad/sec and τ is a constant. 1 The time domain response of a Gaussian filter is Gaussian as well. Taking the inverse Fourier transform of the spectrum h 1 jωt 1 = = π e dt π ( t) H( ω) = e 1 t τ τ π e 1 ( τω) e jωt dt Fig..44 shows the plots of both the time domain and frequency responses of a Gaussian lowpass filter. Both curves have the same bell-shaped response. Fig..45(a) shows a block diagram of a GMSK modulator. It is identical to the VCObased version of the MSK modulator except for the lowpass modulation filter. The relative bandwidth, BT of the filter is BW 3dB BT = = BW 3dB Tb R b 39

40 . Digital Modulation and Demodulation Techniques Figure.43 MSK transmit output spectrum with baseband filtering: (a) without limiting, (b) with limiting (amplifier 10dB into compression). 40

41 . Digital Modulation and Demodulation Techniques Figure.44 Gaussian lowpass filter waveforms: (a) impulse response, (b) frequency response. 41

42 . Digital Modulation and Demodulation Techniques Fig..45(b) shows a simple noncoherent demodulator for demodulating GMSK. Applications for GMSK include the Global System for Mobile communication (GSM) with BT=0.3, and the Digital European Cordless Telephone (DECT) with BT=0.5. The time domain response of GMSK with BT=0.5 is shown in Fig..46. The top trace shows the modulated signal. As in the case of MSK, GMSK is a constant envelope modulation. In contrast to MSK, the second trace shows that the phase has a smooth slope due to the action of the Gaussian lowpass filter. The filter also smoothes out the input bit stream, removing the sharp transitions in the data. The action of the filter has a radical effect on the transmitted spectrum. Fig..47 shows a plot of the power spectral density for various GMSK signals having different relative filter bandwidths. If no filter is use as in MSK, then BT=infinity. The figure shows that a filter having a bandwidth equal to half the data rate (i.e. BT=0.5) rolls off much faster in frequency than MSK. Using filters with smaller relative bandwidths causes even faster roll-off. As the relative filter bandwidth is lowered, more and more intersymbol interference (ISI) is imparted to the waveform. The eye diagram gives a qualitative indication of the amount of ISI on the waveform. As noise or ISI increases, the eye begins to close, increasing P E. Fig..48(a) shows the time domain response of a GMSK modulation signal with a BT=0.5 filter. The amplitude of the modulation waveform is equivalent to the instantaneous frequency deviation of the carrier. Fig..48(b) shows an eye diagram of this same signal taken over many more bit periods. Very little ISI is seen in the waveform for a filter having a bandwidth of half the bit period (BT=0.5). Fig..49(a) shows the time domain response for a BT=0.5 filter (quarter of the bit rate). The alternating strings of 0s and 1s result in waveforms that are nowhere near the full value of the original, unfiltered signal. The eye diagram shows this effect much more clearly. At the sampling instant (near t=0), the eye is almost closed. It is easy to see that very little noise will cause a bit error in this case. The output of the noncoherently demodulated GMSK signal is equivalent to the instantaneous frequency deviation of the signal. For low values of BT, the eye is almost closed. Therefore, a relatively high SNR must be maintained if bit errors are to be kept low. Fig..50 shows a block diagram of a coherent GMSK demodulator that is identical to that of MSK. A predetection Gaussian bandpass filter is used at the input of the demodulator. The lowpass filters can be implemented as matched filters for better performance. Fig..51 show a plot of the amount of degradation in performance of a GMSK signal for different values of BT. We need to increase E b /N 0 by only 1dB over that of coherently demodulated MSK to maintain the same P E performance when BT=0.15. The reason for this result is that when we coherently demodulate the GMSK signal, we are looking at the phase of the signal over two or more bit periods. Fig..5 shows the eye diagrams for both the I and Q portions of a coherently demodulated GMSK signal for BT=0.5. The eye diagrams are relatively open. If we reduce BT to 0.5, there is some closing of the eye as shown in Fig..53, but the waveforms are remarkably good as compared to that for noncoherent demodulation. This is the reason in Fig..51 shows little degradation over coherent MSK, even for low values of BT. 4

43 . Digital Modulation and Demodulation Techniques Figure.45 Gaussian lowpass filtered MSK (GMSK): (a) GMSK modulator (noncoherent), (b) GMSK demodulator (noncoherent). 43

44 . Digital Modulation and Demodulation Techniques Figure.46 GMSK time domain waveforms. Figure.47 GMSK power spectral density for different relative filter bandwidths (BT). 44

45 . Digital Modulation and Demodulation Techniques Figure.48 GMSK demodulated waveforms (noncoherent): (a) recovered bit stream (BT=0.5), (b) eye diagram (BT=0.5). 45

46 . Digital Modulation and Demodulation Techniques Figure.49 GMSK demodulated waveforms (noncoherent): (a) recovered bit stream (BT=0.5), (b) eye diagram (BT=0.5). 46

47 . Digital Modulation and Demodulation Techniques Figure.50 Coherent GMSK demodulator. 47

48 . Digital Modulation and Demodulation Techniques Figure.51 Theoretical E b /N 0 degradation of GMSK as a function of BT compared to ideal coherent demodulation. Figure.5 Eye diagrams for coherently demodulated GMSK (BT=0.5): (a) I-channel, (b) Q-channel. 48

49 . Digital Modulation and Demodulation Techniques Figure.5 (continued). Figure.53 Eye diagrams for coherently demodulated GMSK (BT=0.5): (a) I-channel, (b) Q-channel. 49

50 . Digital Modulation and Demodulation Techniques Figure.53 (continued)..5 Viewing a Digitally Modulated Signal.5.1 Time and Frequency View There are a number of different ways to view a signal. This simplified example is an RF pager signal at a centre frequency of MHz. This pager uses two-level FSK and the carrier shifts back and forth between two frequency that are 8kHz apart ( and MHz). This frequency spacing is small in proportion to the centre frequency of MHz. This is shown in Fig..54(a). The difference in period between a signal at 930MHz and one at 930MHz plus 8kHz is very small. Even a high performance oscilloscope, using the latest in high-speed digital techniques, the change in period cannot be observed or measured. In a pager receiver, the signals are first down-converted to an IF or baseband frequency. In this example, the MHz FSK-modulated signal is mixed with another signal at MHz. The FSK modulation causes the transmitted signal to switch between and MHz. The result is a baseband signal that alternates between two frequencies, khz and +6kHz. The demodulated signal shifts between khz and +6kHz. The difference can be easily detected. This is sometimes referred to as zoom time or IF time. To be more specific, it is a bandconverted signal at IF or baseband. IF time is important as it is how the signal looks in the IF portion of a receiver. This is how the IF of the radio detects the different bits that are present. The frequency domain representation is shown in Fig..54(c). 50

51 . Digital Modulation and Demodulation Techniques Figure.54 Time and frequency domain view. Most pagers use a two-level FSK scheme. FSK is used in this instance because it is less affected by multipath propagation, attenuation and interference, common in urban environments. It is possible to demodulate it even deep inside modern steel/concrete buildings, where attenuation, noise and interference would otherwise make reliable demodulation difficult..5. Power and Frequency View There are many different ways of looking at a digitally modulated signal. To examine how transmitters turn on and off, a power-versus-time measurement (as shown in Fig..55) is very useful for examining the power level changes involved in pulsed or bursted carriers. For example, very fast power changes will result in frequency spreading or spectral regrowth. Very slow power changes waste valuable transmit time, as the transmitter cannot send data when it is not fully on. Turning on too slowly can also cause high bit error rates at the beginning of the burst. In addition, peak and average power levels must be well understood, since asking for excessive power from an amplifier can lead to compression. These phenomena distort the modulated signal and usually lead to spectral regrowth as well..5.3 Constellation Diagrams The rectangular I/Q diagram is a polar diagram of magnitude and phase. A twodimensional diagram of the carrier magnitude and phase can be represented differently by superimposing rectangular axes on the same data and interpreting the carrier in terms of inphase (I) and quadrature-phase (Q) components. It would be possible to perform AM and PM on a carrier at the same time and send data this way. It is easier for circuit design and signal processing to generate and detect a rectangular, linear set of values (one set for I and an independent set for Q). 51