456:, is a form of intentional ISI where a certain number of adjacent symbols interfere with each symbol in a controlled manner. A MLSE must be used to optimally demodulate any signal in the presence of ISI. Whenever the amount of ISI is known, such as with any partial-response signaling scheme, MLSE can be used to determine the exact symbol sequence (in the absence of noise). Since the optimal demodulation of full-response CPM already requires MLSE detection, using partial-response signaling requires little additional complexity, but can afford a comparatively smoother phase trajectory, and thus, even greater spectral efficiency. One extremely popular form of partial-response CPM is
31:
427:
since the derivative of the phase is not continuous. The spectral efficiency of CPM can be further improved by using a smooth phase trajectory. This is typically accomplished by filtering the phase trajectory prior to modulation, commonly using a
674:
365:
of the current symbol differs from the two message bits of the previous symbol. This discontinuity requires a relatively large percentage of the power to occur outside of the intended band (e.g., high fractional
529:
frequency components. In addition, some classes of amplifiers exhibit nonlinear behavior when driven with nearly discontinuous signals; this could have undesired effects on the shape of the transmitted signal.
394:
of CPM is complicated by the fact that the initial phase of each symbol is determined by the cumulative total phase of all previous transmitted symbols, which is known as the
743:) must be continuous; in fact, most ideal digital data waveforms contain discontinuities. However, even a discontinuous message signal will generate a proper CPFSK signal.
552:
398:. Therefore, the optimal receiver cannot make decisions on any isolated symbol without taking the entire sequence of transmitted symbols into account. This requires a
390:
Each symbol is modulated by gradually changing the phase of the carrier from the starting value to the final value, over the symbol duration. The modulation and
453:
367:
378:, i.e., the transmitted carrier power is constant. Therefore, CPM is attractive because the phase continuity yields high spectral efficiency, and the
313:
521:
As the name suggests, the phase of a CPFSK is in fact continuous; this attribute is desirable for signals that are to be transmitted over a
277:
793:
S. Cheng, R. Iyer
Sehshadri, M.C. Valenti, and D. Torrieri, The capacity of noncoherent continuous-phase frequency shift keying, in
382:
yields excellent power efficiency. The primary drawback is the high implementation complexity required for an optimal receiver.
306:
222:
716:'s argument is what gives the CPFSK signal its continuous phase; an integral over any finitely valued function (which
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201:
95:
820:
503:
282:
196:
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135:
110:
62:
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phase, as the modulated waveform cuts instantaneously between two sinusoids with different frequencies.
436:. The raised cosine filter has zero crossings offset by exactly one symbol time, and so it can yield a
252:
72:
669:{\displaystyle s(t)=A_{c}\cos \left(2\pi f_{c}t+D_{f}\int _{-\infty }^{t}m(\alpha )d\alpha \right)\,}
125:
441:
262:
145:
81:
724:) is assumed to be) will not contain any discontinuities. If the message signal is assumed to be
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52:
47:
8:
705:
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728:, then the limits on the integral change to a lower bound of zero and a higher bound of
399:
353:), with CPM the carrier phase is modulated in a continuous manner. For instance, with
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173:
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800:
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502:, encoding the information present in the data to variations in the carrier's
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the carrier instantaneously jumps from a sine to a cosine (i.e. a 90 degree
30:
499:
492:
417:(MSK) is another name for CPM with an excess bandwidth of 1/2 and a linear
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346:
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If a finitely valued digital signal to be transmitted (the message) is
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22:
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in most of the world's 2nd generation cell phones. It is also used in
402:
sequence estimator (MLSE), which is efficiently implemented using the
469:
232:
709:
526:
375:
374:. Furthermore, CPM is typically implemented as a constant-envelope
349:
phase abruptly resets to zero at the start of every symbol (e.g. M-
19:
421:. Although this linear phase trajectory is continuous, it is not
725:
713:
465:
237:
457:
354:
475:
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362:
774:"Digital and Analog Communication Systems, 6th Edition"
555:
514:). In general, a standard FSK signal does not have
506:between one of two frequencies (referred to as the
668:
525:channel, as discontinuities in a signal introduce
801:CPM minimum distance calculator (MLSE/MLSD bound)
807:
764:Notation for the CPFSK waveform was taken from:
487:(FSK), which is itself a special case of analog
686:represents the amplitude of the CPFSK signal,
472:, and many other proprietary wireless modems.
307:
546:), then the corresponding CPFSK signal is
314:
300:
665:
795:Proc. Conf. on Info. Sci. and Sys (CISS)
483:(CPFSK) is a commonly used variation of
341:. In contrast to other coherent digital
481:Continuous-phase frequency-shift keying
476:Continuous-phase frequency-shift keying
447:
808:
452:Partial-response signaling, such as
409:
13:
735:Note that this does not mean that
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361:) whenever one of the two message
14:
832:
704:is a parameter that controls the
491:. FSK is a method of modulating
29:
385:
651:
645:
565:
559:
1:
797:, (Baltimore, MD), Mar. 2007.
759:
708:of the modulated signal. The
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746:
440:CPM waveform that prevents
327:Continuous phase modulation
10:
837:
223:Capacity-approaching codes
779:Prentice-Hall, Inc., 2001
533:
337:of data commonly used in
442:intersymbol interference
504:instantaneous frequency
160:Hierarchical modulation
821:Radio modulation modes
712:located inside of the
670:
485:frequency-shift keying
671:
345:techniques where the
753:Minimum-shift keying
553:
489:frequency modulation
454:duo-binary signaling
448:Partial response CPM
415:Minimum-shift keying
816:Wireless networking
706:frequency deviation
641:
460:, which is used by
372:spectral efficiency
370:), leading to poor
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624:
400:maximum-likelihood
333:) is a method for
82:Digital modulation
695:carrier frequency
404:Viterbi algorithm
380:constant envelope
368:out-of-band power
324:
323:
39:Analog modulation
828:
769:Leon W. Couch II
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419:phase trajectory
410:Phase trajectory
343:phase modulation
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508:space frequency
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434:Gaussian filter
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339:wireless modems
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183:Spread spectrum
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729:
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693:is the base
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500:carrier wave
493:digital data
480:
479:
451:
437:
422:
418:
413:
396:phase memory
395:
392:demodulation
389:
386:Phase memory
330:
326:
325:
288:Multiplexing
228:Demodulation
100:
523:bandlimited
359:phase shift
233:Line coding
810:Categories
760:References
516:continuous
497:sinusoidal
335:modulation
23:modulation
658:α
649:α
633:∞
630:−
626:∫
596:π
585:
470:Bluetooth
747:See also
710:integral
527:wideband
376:waveform
215:See also
20:Passband
495:onto a
444:(ISI).
347:carrier
785:
726:causal
714:cosine
697:, and
679:where
534:Theory
468:FHSS,
466:802.11
424:smooth
141:SC-FDE
755:(MSK)
432:or a
238:Modem
783:ISBN
510:and
458:GMSK
363:bits
355:QPSK
278:OFDM
207:THSS
202:FHSS
197:DSSS
111:MFSK
96:APSK
582:cos
462:GSM
351:PSK
331:CPM
283:FDM
273:ΔΣM
268:PWM
263:PDM
258:PCM
253:PAM
248:PoM
243:AnM
192:CSS
174:WDM
169:QAM
151:WDM
146:TCM
136:QAM
131:PSK
126:PPM
121:OOK
116:MSK
106:FSK
101:CPM
91:ASK
73:SSB
63:QAM
812::
781:.
777:,
771:,
732:.
406:.
68:SM
58:PM
53:FM
48:AM
741:t
739:(
737:m
730:t
722:t
720:(
718:m
701:f
699:D
690:c
688:f
683:c
681:A
662:)
655:d
652:)
646:(
643:m
638:t
620:f
616:D
612:+
609:t
604:c
600:f
593:2
589:(
577:c
573:A
569:=
566:)
563:t
560:(
557:s
544:t
542:(
540:m
329:(
315:e
308:t
301:v
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