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TELE4653 – Lecture 5: Phase Shift Keying In this lecture we’ll examine in detail Phase Shift Keying(PSK). PSK is a very popular digital modulation technique, applied in many practical systems. We’ll address each of the characteristics that make it suitable for a wide variety of applications.

1. Coherent Phase Shift Keying In M-ary Phase Shift Keying (M-PSK), the transmitted signal during a symbol period consists of the carrier with one of M possible phases, spaced equally over the interval 0 to 2π:

( ) ( ) [ ]( )mcm tftgts θπ += 2cos

where [ ]( )

⎭⎬⎫

⎩⎨⎧ −

∈M

MMMm

πππθ 12,4,2,0 K .

This can be expanded using the usual trigonometric identities, and we can easily see that M-PSK can be represented with exactly the same signal basis as we used for QASK.

( ) ( ) ( )tEatEats QgmIgmm QIψψ +=

where

( ) ( ) ( )tfEtgt cg

I πψ 2cos= and ( ) ( ) ( )tfEtgt cg

Q πψ 2sin−=

and the amplitudes of the relative phases are ( ) [ ]( ) [ ]( )( )mmmm QIaa θθ sin,cos, = .

The signal constellations for Binary PSK, 4-PSK, and 8-PSK are shown in the diagram below.

Iψ

Qψ

Iψ

Qψ

Iψ

Qψ

4-PSK:phase ambiguity = ½ nπ

2-PSK:phase ambiguity = nπ

8-PSK:phase ambiguity = ¼ nπ

The first obvious point is that the signal constellation of Binary PSK is identical to that of Binary-ASK. It is not difficult to see from this that in fact these two signalling schemes are identical. Note that the two carrier phases for binary PSK are

[ ] { }πθ ,0∈m , and the carrier amplitudes are thus, ( ) ( ) ( ){ }0,1,0,1, −+∈QI mm aa . The

transmitted signal is thus,

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( ) ( ) ( )tftgts cm π2cos±= exactly identical to bandpass binary ASK. Consequently all the results we have derived for binary ASK carry over into binary PSK, so we need not reproduce them here. The more observant will also realise that the signal constellation of 4-PSK, often called QPSK, is identical that of 4-QASK. The constellation shown above is really a rotated version of the signal constellation of 4-PSK, if one was to about the convention that the transmitted phase set is [ ] { }23,,2,0 πππθ ∈m . Rotated versions of our signal constellation are merely the result of different choices of the signal basis, and we know that the precise selection of the signal basis is irrelevant in assessing the performance of a signalling scheme. Hence, we can conclude that 4-QASK and 4-PSK are one and the same. However, for M > 4 the structure of the PSK constellations are fundamentally different from that of QASK. There are a few points to make regarding M-PSK in general. Every symbol has exactly the same transmitted energy, gE , regardless of the assigned discrete phase. This makes PSK robust to the distorting effects of non-linear amplifiers. We’ll develop this idea later when we discuss later when we address Offset-QPSK. The identification of the signal basis for PSK as that of QASK gives us the structure of a QPSK modulator and of the optimal demodulator. These are illustrated in the diagrams below.

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The decision regions can be clearly interpreted from the signal constellation. The decision regions are sectors of the plane, bisecting each pair of signal points. They are shown below for M = 8.

gE

Iψ

Qψ

2θ3θ4θ

1s

2s3s

4s

5s

6s

7s

8s

The bit error rate performance of M-PSK will be the subject of the next section.

2. Bit Error Rate Performance As discussed in the previous chapter on signal spaces it is very difficult to obtain exact expression for the BER for complex constellation like that of PSK for M > 4. Consequently we attempt to establish error bounds, in particular bounds, as performance metric. The error situation is illustrated below:

Iψ

Qψ

1s

2s3s

4s

5s

6s

7s

8s

21E

81E

4

Naturally all symbols are equivalent, in the sense that they all have the same set of distances to neighbours and the same energies, by the symmetry of the constellation. Thus we can find the average symbol error probability by considering the symbol error probability for a single symbol, say 1s ,

1ees PP = The probability of symbol 1s being in error is merely the probability that the received signal vector lies in the shaded region in the above plot. The would represent a fairly complicated two dimensional integral to compute exactly for the 2-D Gaussian noise distribution, so we can use the union bound approximation to estimate this area. The union bound approximates the probability of the symbol 1s being in error as the sum of the pair-wise probabilities of the symbol 1s being incorrectly detected as the differing symbol, ks .

( ) ∑∑== ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛=≤

M

k

kM

kke N

dQPP

2 0

21

211 2

| ss

where kd1 represents the distance between 1s and ks in the signal space. However, as was discussed in the Signal Space chapter, the union bound is usually excessive, and a tighter and simpler approximate bound can be found by restricting the sum to just include nearest neighbour points. That this is still an upper bound is well illustrated in the above figure – it is equivalent to adding together the probability measure of the two half-planes, formed as the bisectors of the neighbouring points. Clearly there is a significant region of area that is double counted in sum, but at relatively high signal to noise ratios the contribution this area makes will be small.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛≤

0

218

0

212

1 22 Nd

QN

dQPe

The distance between nearest neighbour points in the signal constellation can be calculated as,

⎟⎠⎞

⎜⎝⎛=

MEd snn

πsin22..

Hence, we find the following approximate expression for the symbol error probability for M-PSK, (for M > 4)

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛≈

0

2sin22

NE

QP Mses

π

We note that the PSK constellation does lend itself readily to the application of a Gray code, as there is a clear hierarchy of distances between points in the constellation. Using the Gray code idea, we obtain the BER for M-PSK,

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⋅≈

0

22

2

sinlog2log

2NEM

QM

P Mbeb

π

The interest is then to compare the BER performance of PSK to that of QASK. Both schemes, for a given value of M have the same signal basis, and consequently can be

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assumed to occupy the same bandwidth. Thus, for a given value of M both schemes should have identical spectral efficiency. The graph below plots the BER for PSK and QASK for different values of

MK 2log= , when the SNR per bit is 10 dB. It is evident from the plots that QASK has superior BER performance. This is because, for a given energy budget, which is equivalent to fixing the average distance of signal points from the origin, QASK will achieve greater average separation between neighbouring points. Essentially, QASK is a more efficient way of packing points in a two dimensional plane than the PSK constellation, which constrains all points to lie on a circle centred at the origin.

10-5

2 3 4 5 6

10-4

10-3

10-2

10-1

MK 2log=

QASKebP

PSKebP

3. Spectral Performance It is a straightforward matter to show that the Power Spectral Density (PSD) of M-PSK is identical to that of M-QASK,

( ) ( ) ( ) ( ){ }2221

ccgsS ffGffGEERfS ++−⋅⋅=( where ( )fG is the spectrum of the shaping pulse. Here we make the usual assumption that the transmitted symbol sequence is uncorrelated. The bandwidth of a M-PSK can then be approximated as

TB γ2=

where the factor of 2 comes from the fact that the signal is in the passband, and the parameter γ is a numerical constant that is determined both by the choice of shaping pulse and precise definition of bandwidth (null to null, 99% power, 3dB, etc.) For instance, for the half-sinusoid shaping pulse, 18.1=γ , while for the Nyquist square-root Raised-cosine overall transfer function we have ( ) 21 βγ += , with roll-off factor β, when we use the 99% energy definition of bandwidth. The spectral efficiency M-PSK can then be calculated as,

6

γη

2log2 M

BRb ==

We find the same results for spectral efficiency as we saw previously for QASK. As we increase M, the spectral efficiency improves at the expense of error performance and power budget. The error performance of M-PSK is worse than that of M-QASK, however, there are a few additional features that can be introduced into M-PSK to make it an attractive choice for a modulation scheme. We’ll address these factors now.

4. Offset - QPSK This is a practical modification that can be done to a QPSK scheme to improve its robustness to distortions introduced by non-linear effects in real amplifiers. An ideal amplifier is linear in its voltage response, that is, the input voltage inv is related to the output voltage outv by,

inout Kvv = where K is the voltage gain, which may be frequency dependent but certainly not amplitude dependent. However the response of a practically implementable amplifier must look more like the diagram below – it must saturate at some finite voltage level.

Input voltage, inv

Output voltage, outv

The point is that a real amplifier will not amplify the low amplitude parts of the signal the same as the high voltage parts, which will alter the balance of the signal and possibly distort its information content. Not only do amplifiers suffer from voltage non-linearities like this, so do antennae, waveguides, and other electrical comments and sub-systems in our communication link. Offset QPSK is a clever way making the signal robust to such non-linear effects in the channel and the communication system in general. To understand this, let’s write the PSK signal as

( ) ( ) [ ]( )nmcn

tfnTtgts θπ +−= ∑∞

−∞=

2cos2

7

where [ ]{ }∞−∞=nnmθ is the sequence of transmitted phases. The signal power as a

function of time is found by squaring the signal,

( ) ( ) [ ]( )nmcn

tfnTtgts θπ +−= ∑∞

−∞=

2cos2 222

since, neglecting ISI introduced by the channel, the shaping pulses sent at different symbol intervals should be disjoint. We find the power profile by averaging out the rapidly varying carrier terms,

( ) ( )∑∞

−∞=

−=n

nTtgtP 2

The shaping pulse is in general not constant over a symbol interval, and hence the power profile of the transmitted signal will fluctuate at the symbol rate TR 1= . This is shown in the diagram below. The exception to this is naturally the unit rectangular shaping pulse, ( ) ( )tutg T= , however this pulse has very poor bandwidth efficiency and as such is not popular in practise. For any other type of shaping pulse the power profile will vary with time, and the signal is thus susceptible to distortions caused by non-linear amplifiers.

)(tg

tT0

)(tP

t0

Offset QPSK is a simple technique to obtain a more constant power profile by offsetting the in-phase and quadrature data streams by half a symbol period. Denoting

bTT 2= , where bT is the bit period (or time to send one bit, knowing that for QPSK we are transmitting two bits per symbol), we write the O-QPSK signal as

( )[ ]

( ) ( )[ ]

( )( ) ( )[ ]∑∞

−∞=

+−−−=n

cbQcbI tfTntgatfnTtgatsnmnm

ππ 2sin122cos22

The power profile for this signal is,

( ) ( ) ( )( )∑∑∞

−∞=

∞

−∞=

+−+−=n

bn

b TntgnTtgtP 122 22

The offsetted Q-phase power profile fills in the gaps of the I-phase power profile, to produce an overall smoother power profile. This is illustrated in the diagram below.

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For the case when the shaping pulse is a half-sinusoid,

( ) ( ) ⎟⎠⎞

⎜⎝⎛=

Tttutg Tπsin

the power spectrum of the O-QPSK signal is constant.

( ) ( ) ( )( )

( ) ( )

[ ]∑

∑

∑

∞

∞=

∞

−∞=

∞

−∞=

=

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ +−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

-n

22

22

1

22

cos2

2sin

212

sin2

2sin

n b

b

b

b

n b

b

b

b

TnTt

TnTt

TTnt

TnTt

tP

ππ

ππ

The half-sinusoid also has excellent spectral efficiency, so O-QPSK with this shaping pulse is a popular solution in communication systems.

5. Non-coherent detection of PSK We’ll address the general problem of non-coherent detection in the following chapter. Non-coherent detection refers to detection in the case where the receiver cannot obtain a synchronised version of the carrier, as this may be too costly, or alternatively the designer may choose to disregard the phase information at the expense of some degradation in noise performance. Particularly for narrowband wireless communication systems, the carrier phase can be very difficult to recover, as there can be transmission over a multitude of paths of different and variable lengths, and rapidly varying delays in the propagating medium from transmitter to receiver may cause the received phase to vary in a way that it is hard for the receiver to follow. The first component of a non-coherent PSK system is differential encoding. Differential encoding makes the transmitted signal dependent not on the precise carrier phase, but instead the information is encapsulated in the changes in carrier phase. Differential encoding of PSK, known as DPSK, can be achieved by encoding the transmitted phases as

[ ] [ ] [ ]M

nmnmnmπθθ 2

1 += −

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where [ ]1−nmθ represents the carrier phase at the last transmitted symbol, and [ ] { }1,1,0 −∈ Mnm K is the message to be transmitted at the nth symbol.

DPSK lends itself to recovery with a very simple and elegant receiver structure. The receiver for DPSK is shown in the diagram below. How this receiver differs from receiver structures that we have previously considered is that it has memory, in the sense that the decisions are made using the previous received signal values, not solely on a symbol by symbol basis. Our current communication model assumed both the data signal and the channel to memory-less, and consequently the transmission and detection of a particular symbol was not at all effected by what was transmitted or received before. Thus, our optimal receiver has always been implemented in a symbol by symbol manner. In DPSK, we have introduced a dependence of the current transmitted symbol on the previous symbol, and consequently the form of optimal receiver must change.

)(tr

phase Shift, 90º

∫T

g

dtEtg

0

)()(

local oscillator

( )φπ +tfc2cos2

( )φπ +− tfc2sin2

∫T

g

dtEtg

0

)()(

delay][nrI ]1[ −nrI

mixer

delay][nrQ ]1[ −nrQ

phase detectorIr

Qr

The feature of this receiver is that it will successfully recover the transmitted symbol regardless of the phase error of the local oscillator, φ , by comparing the previous symbol to current symbol and in doing so, removing the dependence of the received symbol on φ . The receiver recovers two amplitudes, by correlating the received symbol with both phases of the local oscillator,

[ ] [ ]( ) [ ]nnEnr InmsI +−= φθcos

[ ] [ ]( ) [ ]nnEnr QnmsQ +−= φθsin The noise terms, [ ]nnI and [ ]nnQ , are two samples from independent and identically distributed Gaussian white noise processes. The mixer then combines these received amplitudes with those of the previous symbol as follows:

[ ] [ ] [ ] [ ]11 −+−= nrnrnrnrr QQIII [ ] [ ] [ ] [ ]11 −−−= nrnrnrnrr QIIQQ

One can easily show that these amplitudes are completely independent of the local oscillator phase,

[ ] [ ]( ) InmnmsI nEr ′+−= −1cos θθ

[ ] [ ]( ) QnmnmsQ nEr ′+−= −1sin θθ

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Since, for DPSK, our information is associated with the difference in carrier phase, the decision rule is same then as for M-PSK, on the recovered amplitude pair ( )QI rr , . The decision rule is to choose the transmitted message m that is closest to the received amplitude signal vector,

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−=

′

222sin2cosminargM

mErM

mErm sQsIm

ππ

The decision regions are identical to those of M-PSK.

gE

Iψ

Qψ

1sΔ

2sΔ3sΔ

4sΔ

5sΔ

6sΔ

7sΔ

8sΔ

y

decision thresholds

The noise performance of this non-coherent DPSK receiver is in general more complicated than for coherent DPSK, as the noise variables affecting the recovered amplitudes, In′ and Qn′ are proportional to the product of Gaussian random variables, and as such are not Gaussian distributed. For the binary case an exact expression for the BER is easily able to found. In the next chapter we’ll look at the error performance of the optimal non-coherent demodulator for binary orthogonal signal. The BER we’ll obtain is,

0221 NE

ebbeP −=

The point here is that we can visualise binary-DPSK as a binary orthogonal system lasting T2 . The last symbol acts like us transmitting a phase reference, so in effect our symbols are one of either

( ) ( ) ( ) ( ) ( )θπθπ ++↔ tftgtftgts cc 2cos2,2cos21

( ) ( ) ( ) ( ) ( )θπθπ +−+↔ tftgtftgts cc 2cos2,2cos22 Note that each new symbol is transmitted every T seconds, with the previous symbol becoming the phase reference. These symbols are equivalent to the pair of orthogonal vectors ( ) ( ){ }1,1,1,1 −+++ . Using that each bit effectively takes two symbols to transmit (since we must transmit the phase reference too), we find the expression for the BER of non-coherent detection of DPSK,

0/21DPSK-n.c NE

ebbeP −=

It is instructive to compare this result to that obtained for coherent BPSK, and also DPSK when coherent detection is used. Note that DPSK can also be recovered with the coherent BPSK receiver, with the additional complication that the recovered

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message is obtained by taking the difference of the received symbol with the previous received symbol. The BER of DPSK with coherent detection is twice that of non-differentially encoded BPSK, since for differential encoding any error will affect two recovered symbols – the current and the next.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

0

BPSK 2NE

QP beb

⎟⎟⎠

⎞⎜⎜⎝

⎛=

0

DPSK-c 22

NE

QP beb

The three cases are compared in the diagram below. The important result is that DPSK-n.cDPSK-cBPSK

ebebeb PPP << meaning that differential encoding a cost in error performance in making transmitted symbols dependent, while the non-coherent detector a further cost in error performance by doubling the number of correlators required, creating more sources of noise on our recovered signal.

0 2 4 6 8 10(dB) N0bE

eP

-110

-310

-510

-610

-410

-210

Figure: Comparison of the BER for (i) binary PSK with coherent detection (lower curve); (ii) binary DPSK with coherent detection (middle curve); and (iii) binary

DPSK with non-coherent detection (upper curve). The BER for higher M-PSK with non-coherent detection is fairly complicated to calculate, but as expected the demodulator’s lack of phase knowledge always costs in energy efficiency. Fundamentally this is because in DPSK detection two noise vectors influence the recovery of the phase difference however exact results are difficult as products of Gaussian variables means chi-squared statistics. The comparative performance of non-coherent detection as a function of M for M-DPSK is shown in the figure below. Due to the poor energy efficiency of non-coherent M-DPSK for

8>M , particularly when compared to their coherent counterpart, these are rarely used in practise.

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6. Optimal Linear Receiver Revisited At this point it is worth revisiting our discussion of the optimal linear receiver. As we saw in the above section, when we introduce correlation between the symbols transmitted at different symbols our optimal receiver is no longer a symbol-by-symbol detector, and must instead involve some memory. The other source of correlation between different symbols at the receiver is of course the channel, by such effects as multi-pathing, culminating in Intersymbol Interference (ISI). It is natural then to ask: what is the optimal form of the receiver when ISI is present? Earlier, we determined the form of the receiver that was optimal when we considered the effect of noise alone – our matched filter. The received signal is, taking the case simple baseband ASK system,

( ) ( )tnkTtgatrk

k +−′= ∑)(

where ( ) ( )( )tghtg ∗=′ is the form of the pulse after it has been passed through the channel with impulse response ( )th . The linear receiver we can then think of a filter with impulse response ( )tc . We pass the received signal through this filter and sample the output at time instants kTt = (or equivalently realise this receiver with a correlator). The recovered symbols are

( ) kk nkTy += ξ

13

where ( ) ( ) τττξ dnTkTgcan

nk ∫∑∞

∞−

−−′= is the received signal amplitude and kn is

the noise at the output. We desire naturally that for perfect operation that we have ( ) kakTy = . The deviation of our obtained output from that desired is, known as our error,

kkkk ane −+= ξ For the Gaussian distributed noise samples, our optimal receiver is obtained by designing it to minimise the mean square of this error,

[ ]221

keEJ = The factor of one half is introduced for convenience. This is

[ ] [ ] [ ] [ ] [ ] [ ]kkkkkkkkk naEaEnEaEnEEJ −−+++= ξξξ 2212

212

21

The from the independence of the noise from our signal we have,

[ ] [ ] 0== kkkk naEnE ξ The other expectation values in the above mean squared error must be directly calculated. Firstly,

[ ] [ ] ( ) ( ) ( ) ( ) 2121212 ττττττξ ddkTglTgccaaEE

l kklk −′−′= ∫ ∫∑∑

∞

∞−

∞

∞−

We’ll consider that the transmitted symbol sequence is uncorrelated, so [ ] [ ]lkaaE lk −= δ , and treat when the transmitted symbols are correlated separately,

as we did for DPSK above, and will again for Continuous Phase Modulation(CPM) in the next chapter. Thus,

[ ] ( ) ( ) ( ) 2121212 , ττττττξ ddccRE gk ∫ ∫

∞

∞−

∞

∞−′=

where ( ) ( ) ( )2121 , ττττ −′−′= ∑′ kTglTgRk

g in some way captures the ISI introduced

by the channel. Similarly, one easily finds that

[ ] ( ) ( ) τττξ dgcaE kk −′= ∫∞

∞−

[ ] ( ) ( ) ( ) 21212102

2ττττττδ ddcc

NnE k ∫ ∫

∞

∞−

∞

∞−

−=

Substituting these into the form of the mean squared error,

( ) ( ) ( ) ( ) ( ) ( )dttgtcddtctctN

tRJ g −′−⎟⎠⎞

⎜⎝⎛ −+−+= ∫∫ ∫

∞

∞−

∞

∞−

∞

∞−′ τττδτ

20

21

21

To minimise this mean square error, with the best choice of receiver, we use the calculus of variations methods to define the functional choice of the receiver filter ( )tc to minimise the above expression. The result is the equation

( ) ( ) ( ) ( )tgdctN

tRg −′=⎟⎠⎞

⎜⎝⎛ −+−∫

∞

∞−′ τττδτ

20

14

Note for the previous case, when we neglected ISI, so ( ) ( )τδτ −=− ′′ tEtR gg , we get the matched filter result, ( ) ( )tgtc −′≡ . Expressed in the frequency domain, the general form of the optimal filter is,

( ) ( )

∑ ⎟⎠⎞

⎜⎝⎛ +′+

′=

∗

k TkfG

TN

fGfC 20 1

2

Note the similarity of the above expression that of an IIR filter,

( )∑=

−+= N

k

kk zc

czC

1

0

1.

This is important, as we can realise this optimal linear filter as a matched filter, followed by a tapped delay line digital filter, as shown below. This form of receiver is known as a linear equaliser. It is usually required to make this receiver filter adaptive, to account for the changing channel characteristics. The principles of adaptive equalisation will be covered in other courses.

This type of receiver, which we will explore again when we consider partial response signalling, is know as the Maximum Likelihood Sequence Estimator (MLSE).

7. Case Study – IS-95 CDMA IS-95 CDMA, short for Interim Standard-95 Code Division Multiple Access, was the 2G mobile phone system used in the USA, Japan, and Korea, and formed the basis for the current 3G mobile networks that are in the process of being rolled out and implemented. The modulation technique chosen for this standard was π/4-ODQPSK, or π/4 – Offset Differential Quadrature Phase Shift Keying. The only feature of this modulation scheme that we have not yet discussed is the π/4 aspect. This is the idea to make the phase shifts introduced into the transmitted carrier wave are multiples of π/4. That is, each input symbol introduces a change in carrier phase as described in the following table:

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Input Bit Pair Phase change of carrier 00 π/4 01 3π/4 11 -3π/4 10 -π/4

The motivation for this that every symbol will cause a change in the phase of the carrier, making symbol synchronisation easier. The principles of symbol synchronisation, where the receiver must determine when transmitted symbols begin and end will be covered in a later chapter. Symbol synchronisation is an important and critical issue in Direct Sequence Spread Spectrum Multiple Access techniques, however discussion of the principles of CDMA is left for later courses. Note that for DQPSK, the phase changes of the carrier are one of { }2,,2,0 πππ − , and thus the transmitted carrier phase over any symbol must be one of { }2,,2,0 πππ − , and we see that the signal constellation of DQPSK is the same as that of QPSK. However, for π/4-DQPSK there are two alternative signal constellations: if we call the initial carrier phase state as θ = 0, then for all even symbols, the carrier phase is one of { }2,,2,0 πππ − , while for all odd numbered symbols the carrier phase state is one of { }4,4/3,43,4/ ππππ −− . This alternating signal constellation is shown in the diagram below.

The key parameters of the IS-95 CDMA system are listed below. Uplink Frequency Band: 824-849 MHz Downlink Frequency Band: 869-894 MHz Number of carriers/band: 20 Bandwidth per carrier: 1.25 MHz Number of users per carrier: 60 Chip rate: 1.2288 Mcps Pulse-shaping: Overall Nyquist Square-root Raised Cosine Channel Coding: convolutional encoding, Uplink (3,1,9), Downlink (2,1,9) Modulation (Uplink): 64-ary orthogonal Hadamard, with π/4-ODQPSK for spreading.

(non-coherent detection) Modulation (Downlink): BPSK for data with π/4-ODQPSK for spreading (coherent

detection) Speech Data rate: 9600, 4800, 2400, 1200 bps Speech coding: Variable rate Code-Excited Linear Prediction (CELP)

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