Continuous Phase Modulation (CPM)

• CPM– Carrier phase varies in a continuous manner– Constant envelope

• An infinite variety of CPM signals can be generated by adjusting– Frequency pulse shaping functions– Modulation index h– Modulation alphabet size M– Pulse duration L

• Phase transition diagram

• Spectra of CPM signals– Compact PSD: narrow main lobe and fast sidelobe roll-off

Continuous Phase Modulation

• Sidebands produced by modulation schemes like FSK and PSK can interfere with nearby channels (adjacent channel interference) or with other communications systems (co–channel interference). It is important that modulation used to transmit information over the radio channels of a cellular phone network be bandwidth efficient so that more subscribers can be served in a given frequency band.

• In addition, modulation schemes that introduce phase discontinuities will tend to introduce undesirable frequencysidelobes when amplified through a non–linear ampli-fier. However, linear amplifiers are less power efficient(transmitted power versus power supplied) than non–linear (Class C) amplifiers.

Continuous Phase Modulation• By imposing, within a modulation scheme, that the phase

of a carrier be continuous from one symbol to the next,the level of sidebands of the transmitted signal can bereduced. In conventional FSK or PSK the phase of thecarrier may change at the beginning of each symbol.

• Some improvement in the case of QPSK modulation isintroduced by a variation called offset QPSK (OQPSK),which limits the range of possible phase variations. Con tinuous phase is effectively achieved with CPFSK (continuous phase frequency shift keying) schemes like minimum shift keying (MSK).

Variations on CPM

• Minimum Shift Keying (MSK)

– Special form of CPFSK– Minimum spacing that allows two frequencies states to be orthogonal– spectral efficient, easily generated

• Gaussian Minimum Shift Keying (GMSK)

– MSK + premodulation Gaussian lowpass filter– Increase spectral efficiency with sharper cutoff,excellent power efficiency due to constant envelope– Used extensively in 2nd-generation digital and cordless

telephone applications

CPM• g(t) is a pulse, e.g., rectangular, RC,…

If g(t)=0 , t>Ts ► Full-response CPM

If g(t) ≠0, t > Ts ► Partial-response CPM

• Different CPM signals can be generated by

varying M, {h}, and g(t)

• If q(t) is rectangular pulse, the CPM is

continuous-Phase FSK (CPFSK)

• Furthermore, if h = ½ ► CPFSK is called

Minimum Shift Keying (MSK)

Minimum shift keying (MSK)

• Goal: avoid sudden change.

• Two frequencies are used, f2 =2f1.

• Separate into even and odd bits.

• The duration of each bit is doubled.

– A higher frequency is chosen if even and odd bits are equal.

– The signal is inverted if the odd bit equals 0.

Example of MSK

MSKSimilarly to OQPSK, MSK is encoded with bits alternating between quarternary components, with the Q component delayed by half a bit period. However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid. This results in a constant-modulus signal, which reduces problems caused by non-linear distortion.

MSK• The spacing between the two carrier

frequencies is the minimum: Δf = 1/2Ts

Hence, it is called minimum shift keying

Minimum shift keying

Proper utilization of phase during detection, for improving noise performance

Complexity increasesCPFSK (Continuous-phase frequency-shift keying)

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Signal Space Characterization of MSK

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MSK Transmitter

MSK receiver

Q-channel

PSD of MSK• The PSD is given by:

P(∆f) = 16 / π2[cos(2 π ∆fT) / 1.16fT]• MSK has a wider first null than QPSK

but lower 99%-power BW

PSD of MSK

Problem:

Sketch the waveform of the MSK signal for the sequence for the 101101.Assume that the carrier frequencya) Is 1.25 times the bit rate. b) Equal to the bit

Solution (a) fc =(f1+f2)/2 =1.25/ Tb OR f1+f2=2.5/Tb

Also f1-f2=1/(2Tb)

Solving f1=1.5/Tb f2=1/Tb

(b) fc=1/Tb f1+f2=2/Tb f1-f2=1/(2Tb)\

Solving f1=1.25/Tb f2=0.75/Tb

GMSK• GMSK is similar to MSK except it incorporates a premodulation

Gaussian LPF

• Achieves smooth phase transitions between signal states which can significantly reduce bandwidth requirements

• There are no well-defined phase transitions to detect for bit synchronization at the receiving end.

• With smoother phase transitions, there is an increased chance in intersymbol interference which increases the complexity of the receiver.

• Used extensively in 2nd generation digital cellular and cordless telephone apps. such as GSM

Gaussian MSK (GMSK)• A derivative of MSK that uses a Gaussian pulse

shaping filter to filter the NRZ binary

modulating waveform

hG(t) = √π / α exp(- π2t2 / α2)

• This converts the signal from full-response CPM to a partial-response CPM signal

Gaussian Pulse

GMSKThe Gaussian pulse-shaping filter reduces the levelsof side-lobes of the GMSK spectrum compared toMSKIt can be coherently detected (as MSK) or noncoherently detected (as FSK)

Block diagram of a GMSK transmitter using MSK modulator

GMSK• GMSK is characterized by its BT product:

- B is the 3-dB BW of the Gaussian filter- T is the symbol duration

• B = 0.5887/alpha, alpha is the filter parameter• As alpha increases B decreases

- Sidelobes power decreases- More spectral efficiency- But more ISI because pulse is wider

• MSK corresponds to alpha = 0• In GSM, GMSK is used with BT=0.3

GMSK BT 90% BW 99% BW 99.9% BW 99.99% BW0.2 0.52 0.79 0.99 1.22

0.25 0.57 0.86 1.09 1.37

0.5 0.69 1.04 1.33 2.08

MSK 0.78 1.2 2.76 6.00

RF Bandwidth as a fraction of Rb

Probability of Error• Is defined as the probability of detecting a

received observations as one signal given theother signal was transmitted

• It is a function of:- Distances between signals in the constellation (a function of the SNR)- Noise distribution (Usually Gaussian – AWGN)- Rx signal level distribution (in case of fading)

• The closer the signals in constellation, thehigher the error probability

GMSK Performance• The GMSK filtering can cause ISI if the BT is

too small (too narrow filter and wide pulse)

• The GMSK error rate is given by:

• Pe = Q( √2δEb / No)

where δ = 0.68 for BT = 0.25

δ = 0.85 for BT = ∞

Performance Over Rayleigh Channels

•The performance is usually 20 to 40 dB worse than the AWGN case (no fading) for reasonable BER•This is mostly due to deep fades which occur often because of the Rayleigh distribution•For a Ricean or Nakagami fading distributions with large K-factor , or m, the error probability is smaller•This is because the probability of deep fade is smallerMitigation:-Diversity, Channel Coding, Adaptive modulation