HOME

TheInfoList



OR:

In
digital modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
, minimum-shift keying (MSK) is a type of continuous-phase
frequency-shift keying Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier signal. The technology is used for communication systems such as telemetry, weather ball ...
that was developed in the late 1950s by
Collins Radio Rockwell Collins was a multinational corporation headquartered in Cedar Rapids, Iowa, providing avionics and information technology systems and services to government agencies and aircraft manufacturers. It was formed when the Collins Radio Compa ...
employees Melvin L. Doelz and Earl T. Heald. Similar to OQPSK, MSK is encoded with bits alternating between
quadrature component In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (90 degrees or /2 radians). All three functions have the s ...
s, with the Q component delayed by half the
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
period. However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half
sinusoid A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ma ...
. This results in a constant-modulus signal (constant envelope signal), which reduces problems caused by non-linear distortion. In addition to being viewed as related to OQPSK, MSK can also be viewed as a continuous-phase frequency-shift keyed ( CPFSK) signal with a frequency separation of one-half the bit rate. In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. Thus, the maximum frequency deviation is where ''fm'' is the maximum modulating frequency. As a result, the modulation index ''m'' is 0.5. This is the smallest FSK
modulation index The modulation index (or modulation depth) of a modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the '' carrier signal'', with a separate signal called ...
that can be chosen such that the waveforms for 0 and 1 are orthogonal. A variant of MSK called Gaussian minimum-shift keying (GMSK) is used in the
GSM The Global System for Mobile Communications (GSM) is a standard developed by the European Telecommunications Standards Institute (ETSI) to describe the protocols for second-generation ( 2G) digital cellular networks used by mobile devices such ...
mobile phone A mobile phone, cellular phone, cell phone, cellphone, handphone, hand phone or pocket phone, sometimes shortened to simply mobile, cell, or just phone, is a portable telephone that can make and receive calls over a radio frequency link whil ...
standard.


Mathematical representation

The resulting signal is represented by the formula: : s(t) = a_(t)\cos\cos-a_(t)\sin\sin where a_(t) and a_(t) encode the even and odd information respectively with a sequence of square pulses of duration ''2T''. a_I(t) has its pulse edges on t = T, T, 3T, \ldots/math> and a_(t) on t = , 2T, 4T, \ldots/math>. The
carrier frequency In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a ...
is f_. Using the
trigonometric identity In trigonometry, trigonometric identities are Equality (mathematics), equalities that involve trigonometric functions and are true for every value of the occurring Variable (mathematics), variables for which both sides of the equality are defined. ...
, this can be rewritten in a form where the phase and frequency modulation are more obvious, : s(t) = \cos\left \pi f_c t + b_k(t) \frac + \phi_k\right/math> where ''bk(t)'' is +1 when a_I(t) = a_Q(t) and −1 if they are of opposite signs, and \phi_k is 0 if a_I(t) is 1, and \pi otherwise. Therefore, the signal is modulated in frequency and phase, and the phase changes continuously and linearly.


Properties

Since the minimum symbol distance is the same as in the
QPSK Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at ...
, the following formula can be used for the theoretical bit-error ratio bound: :P_b = Q\left(\sqrt\right) = \frac\operatorname\left(\sqrt\right) where E_b is the energy per one bit, N_0 is the noise spectral density, Q(*) denotes the Q-function and \operatorname denotes the
complementary error function In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non-elementar ...
.


Gaussian minimum-shift keying

Gaussian minimum-shift keying, or GMSK, is similar to standard minimum-shift keying (MSK); however, the digital data stream is first shaped with a
Gaussian filter In electronics and signal processing mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would have infinite impulse respons ...
before being applied to a frequency modulator, and typically has much narrower phase shift angles than most MSK modulation systems. This has the advantage of reducing
sideband In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, that are the result of the modulation process. The sidebands carry the information transmitted by the radio signal. The sidebands co ...
power, which in turn reduces out-of-band interference between signal carriers in adjacent frequency channels. However, the Gaussian filter increases the modulation memory in the system and causes
intersymbol interference In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making ...
, making it more difficult to differentiate between different transmitted data values and requiring more complex channel equalization algorithms such as an
adaptive equalizer An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation a ...
at the receiver. GMSK has high
spectral efficiency Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the information rate that can be transmitted over a given Bandwidth (signal processing), bandwidth in a specific communication system. It is a measure of how efficiently a l ...
, but it needs a higher
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
level than
QPSK Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at ...
, for instance, in order to reliably transmit the same amount of
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...
. GMSK is most notably used in the
Global System for Mobile Communications The Global System for Mobile Communications (GSM) is a standard developed by the European Telecommunications Standards Institute (ETSI) to describe the protocols for second-generation (2G) digital cellular networks used by mobile devices such as ...
(GSM), in
Bluetooth Bluetooth is a short-range wireless technology standard that is used for exchanging data between fixed and mobile devices over short distances and building personal area networks (PANs). In the most widely used mode, transmission power is limi ...
, in satellite communications,Wong, Yen F., et al. "An optimum space-to-ground communication concept for CubeSat platform utilizing NASA space network and near earth network." (2016).
/ref> and Automatic Identification System (AIS) for maritime navigation.


See also

*
Constellation diagram A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying. It displays the signal as a two-dimensional ''xy''-plane scatter diagram in the ...
used to examine the modulation in signal space (not time) *
Gaussian frequency-shift keying Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier signal. The technology is used for communication systems such as telemetry, weather ball ...


References

* Subbarayan Pasupathy, ''Minimum Shift Keying: A Spectrally Efficient Modulation'', IEEE Communications Magazine, 1979 * R. de Buda, ''Fast FSK Signals and their Demodulation'', Can. Elec. Eng. J. Vol. 1, Number 1, 1976 * F. Amoroso, ''Pulse and Spectrum Manipulation in the Minimum (Frequency) Shift Keying (MSK) Format'', IEEE Trans. * {{Cite web , url=http://www.emc.york.ac.uk/reports/linkpcp/appD.pdf , title=Appendix D – Digital Modulation and GMSK , date = 2001-03-13 , publisher =
University of Hull The University of Hull is a public research university in Kingston upon Hull, a city in the East Riding of Yorkshire, England. It was founded in 1927 as University College Hull. The main university campus is located in Hull and is home to the Hull ...
, archive-url= https://web.archive.org/web/20040924222851fw_/http://www.emc.york.ac.uk/reports/linkpcp/appF.pdf , archive-date=2004-09-24
Link Budget Analysis: Digital Modulation-Part 2-FSK (Atlanta RF)
* Elnoubi, S., Chahine, S. A., & Abdallah, H. (2004, March). BER performance of GMSK in Nakagami fading channels. In Radio Science Conference, 2004. NRSC 2004. Proceedings of the Twenty-First National (pp. C13-1). IEEE.
Feher, K. (1993, July). FQPSK: A modulation-power efficient RF amplification proposal for increased spectral efficiency and capacity GMSK and Π/4-QPSK compatible PHY standard. In IEEE 802.11 Wireless Access Methods Phys. Layer Spec. Doc.
Quantized radio modulation modes de:Minimum Shift Keying