Phase-shift keying - Knowledge (XXG)

2810:) at a time to construct a QPSK symbol can allow the phase of the signal to jump by as much as 180° at a time. When the signal is low-pass filtered (as is typical in a transmitter), these phase-shifts result in large amplitude fluctuations, an undesirable quality in communication systems. By offsetting the timing of the odd and even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time. In the constellation diagram shown on the right, it can be seen that this will limit the phase-shift to no more than 90° at a time. This yields much lower amplitude fluctuations than non-offset QPSK and is sometimes preferred in practice. 3601: 132: 6632: 3203: 290: 5459: 2877: 2773: 2799: 4237: 4372: 3024: 1668: 792: 3596:{\displaystyle {\begin{aligned}p_{\theta _{r}}\left(\theta _{r}\right)&={\frac {1}{2\pi }}e^{-2\gamma _{s}\sin ^{2}\theta _{r}}\int _{0}^{\infty }Ve^{-{\frac {1}{2}}\left(V-2{\sqrt {\gamma _{s}}}\cos \theta _{r}\right)^{2}}\,dV,\\V&={\sqrt {r_{1}^{2}+r_{2}^{2}}},\\\theta _{r}&=\tan ^{-1}\left({\frac {r_{2}}{r_{1}}}\right),\\\gamma _{s}&={\frac {E_{s}}{N_{0}}}\end{aligned}}} 3763: 648:, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the phase of the received signal to a reference signal – such a system is termed coherent (and referred to as CPSK). 194: 36: 5233: 2217: 77: 2690: 2696:

quadrature component (taking the first bit as number 1). The total signal – the sum of the two components – is shown at the bottom. Jumps in phase can be seen as the PSK changes the phase on each component at the start of each bit-period. The topmost waveform alone matches the description given for BPSK above.

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The bit-error rates of DBPSK and DQPSK are compared to their non-differential counterparts in the graph to the right. The loss for using DBPSK is small enough compared to the complexity reduction that it is often used in communications systems that would otherwise use BPSK. For DQPSK though, the loss

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The modulated signal is shown below for a short segment of a random binary data-stream. Note the half symbol-period offset between the two component waves. The sudden phase-shifts occur about twice as often as for OQPSK (since the signals no longer change together), but they are less severe. In other

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CPSK requires a complicated demodulator, because it must extract the reference wave from the received signal and keep track of it, to compare each sample to. Alternatively, the phase shift of each symbol sent can be measured with respect to the phase of the previous symbol sent. Because the symbols

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Both QPSK and 8PSK are widely used in satellite broadcasting. QPSK is still widely used in the streaming of SD satellite channels and some HD channels. High definition programming is delivered almost exclusively in 8PSK due to the higher bitrates of HD video and the high cost of satellite bandwidth.

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For example, in differentially-encoded BPSK a binary "1" may be transmitted by adding 180° to the current phase and a binary "0" by adding 0° to the current phase. Another variant of DPSK is symmetric differential phase shift keying, SDPSK, where encoding would be +90° for a "1" and −90° for a "0".

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radians, hence the name) with respect to one another. Usually, either the even or odd symbols are used to select points from one of the constellations and the other symbols select points from the other constellation. This also reduces the phase-shifts from a maximum of 180°, but only to a maximum of

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These modulations carefully shape the I and Q waveforms such that they change very smoothly, and the signal stays constant-amplitude even during signal transitions. (Rather than traveling instantly from one symbol to another, or even linearly, it travels smoothly around the constant-amplitude circle

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The modulated signal is shown below for a short segment of a random binary data-stream. The two carrier waves are a cosine wave and a sine wave, as indicated by the signal-space analysis above. Here, the odd-numbered bits have been assigned to the in-phase component and the even-numbered bits to the

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Conceptual transmitter structure for QPSK. The binary data stream is split into the in-phase and quadrature-phase components. These are then separately modulated onto two orthogonal basis functions. In this implementation, two sinusoids are used. Afterwards, the two signals are superimposed, and the

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BPSK (also sometimes called PRK, phase reversal keying, or 2PSK) is the simplest form of phase shift keying (PSK). It uses two phases which are separated by 180° and so can also be termed 2-PSK. It does not particularly matter exactly where the constellation points are positioned, and in this figure

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The modulated signal is shown below for a short segment of a random binary data-stream. The construction is the same as above for ordinary QPSK. Successive symbols are taken from the two constellations shown in the diagram. Thus, the first symbol (1 1) is taken from the "blue" constellation and the

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In differentially-encoded QPSK (DQPSK), the phase-shifts are 0°, 90°, 180°, −90° corresponding to data "00", "01", "11", "10". This kind of encoding may be demodulated in the same way as for non-differential PSK but the phase ambiguities can be ignored. Thus, each received symbol is demodulated to

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Timing diagram for π/4-QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown the top and the total, combined signal at the bottom. Note that successive symbols are taken alternately from the two constellations, starting with the

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in a signal timing diagram. The topmost signal is a BPSK-modulated cosine wave that the BPSK modulator would produce. The bit-stream that causes this output is shown above the signal (the other parts of this figure are relevant only to QPSK). After modulation, the base band signal will be moved to

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One property this modulation scheme possesses is that if the modulated signal is represented in the complex domain, transitions between symbols never pass through 0. In other words, the signal does not pass through the origin. This lowers the dynamical range of fluctuations in the signal which is

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giving a prescribed (maximum) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth compared to BPSK - at the same BER. The engineering penalty that is paid is that QPSK transmitters and receivers are more complicated than the ones for

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For a signal that has been differentially encoded, there is an obvious alternative method of demodulation. Instead of demodulating as usual and ignoring carrier-phase ambiguity, the phase between two successive received symbols is compared and used to determine what the data must have been. When

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axes are termed the in-phase and quadrature axes respectively due to their 90° separation. Such a representation on perpendicular axes lends itself to straightforward implementation. The amplitude of each point along the in-phase axis is used to modulate a cosine (or sine) wave and the amplitude

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Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. With this interpretation, the even (or odd) bits are used to modulate the in-phase component of the carrier, while the odd (or even) bits are used to modulate the

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Comparing these basis functions with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals. Note that the signal-space points for BPSK do not need to split the symbol (bit) energy over the two carriers in the scheme shown in the BPSK constellation diagram.

1687:. (Although the root concepts of QPSK and 4-QAM are different, the resulting modulated radio waves are exactly the same.) QPSK uses four points on the constellation diagram, equispaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with 2534: 1909: 1926: 3031:

Any number of phases may be used to construct a PSK constellation but 8-PSK is usually the highest order PSK constellation deployed. With more than 8 phases, the error-rate becomes too high and there are better, though more complex, modulations available such as

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Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown at the top, and the total combined signal at the bottom. Note the abrupt changes in phase at some of the bit-period

4324:(AWGN). However, there will also be a physical channel between the transmitter and receiver in the communication system. This channel will, in general, introduce an unknown phase-shift to the PSK signal; in these cases the differential schemes can yield a 4750: 2825:

Timing diagram for offset-QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown the top and the total, combined signal at the bottom. Note the half-period offset between the two signal

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Differential phase shift keying (DPSK) is a common form of phase modulation that conveys data by changing the phase of the carrier wave. As mentioned for BPSK and QPSK there is an ambiguity of phase if the constellation is rotated by some effect in the

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The picture on the right shows the difference in the behavior of the phase between ordinary QPSK and OQPSK. It can be seen that in the first plot the phase can change by 180° at once, while in OQPSK the changes are never greater than 90°.

3015:- involves the polarization multiplexing of two different QPSK signals, thus improving the spectral efficiency by a factor of 2. This is a cost-effective alternative to utilizing 16-PSK, instead of QPSK to double the spectral efficiency. 976: 656:. DPSK can be significantly simpler to implement than ordinary PSK, as it is a 'non-coherent' scheme, i.e. there is no need for the demodulator to keep track of a reference wave. A trade-off is that it has more demodulation errors. 3915: 5850:

Differential schemes for other PSK modulations may be devised along similar lines. The waveforms for DPSK are the same as for differentially encoded PSK given above since the only change between the two schemes is at the receiver.

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The implementation of QPSK is more general than that of BPSK and also indicates the implementation of higher-order PSK. Writing the symbols in the constellation diagram in terms of the sine and cosine waves used to transmit them:

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differential encoding is used in this manner, the scheme is known as differential phase-shift keying (DPSK). Note that this is subtly different from just differentially encoded PSK since, upon reception, the received symbols are

765:. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the 3036:(QAM). Although any number of phases may be used, the fact that the constellation must usually deal with binary data means that the number of symbols is usually a power of 2 to allow an integer number of bits per symbol. 3684: 2333: 1243: 2319: 1574: 5139: 1335: 2987:

second symbol (0 0) is taken from the "green" constellation. Note that magnitudes of the two component waves change as they switch between constellations, but the total signal's magnitude remains constant (

2685:{\displaystyle P_{s}\approx 2Q\left({\sqrt {\frac {E_{s}}{N_{0}}}}\right)=\operatorname {erfc} \left({\sqrt {\frac {E_{s}}{2N_{0}}}}\right)=\operatorname {erfc} \left({\sqrt {\frac {E_{b}}{N_{0}}}}\right)} 2225:

encoding. These encoders can be placed before for binary data source, but have been placed after to illustrate the conceptual difference between digital and analog signals involved with digital modulation.

3753: 777:) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a 4573: 4240:

Timing diagram for DBPSK and DQPSK. The binary data stream is above the DBPSK signal. The individual bits of the DBPSK signal are grouped into pairs for the DQPSK signal, which only changes every

1747: 4123: 3208: 2338: 2105:{\displaystyle {\begin{aligned}\phi _{1}(t)&={\sqrt {\frac {2}{T_{s}}}}\cos \left(2\pi f_{c}t\right)\\\phi _{2}(t)&={\sqrt {\frac {2}{T_{s}}}}\sin \left(2\pi f_{c}t\right)\end{aligned}}} 1931: 3998: 991: 5420: 5622: 4998:{\displaystyle r_{k}r_{k-1}^{*}=E_{s}e^{j\left(\varphi _{k}-\varphi _{k-1}\right)}+{\sqrt {E_{s}}}e^{j\varphi _{k}}n_{k-1}^{*}+{\sqrt {E_{s}}}e^{-j\varphi _{k-1}}n_{k}+n_{k}n_{k-1}^{*}} 1713:

as the BER of BPSK – and believing differently is a common confusion when considering or describing QPSK. The transmitted carrier can undergo numbers of phase changes.

1427: 700:), in response to a data signal. In the case of PSK, the phase is changed to represent the data signal. There are two fundamental ways of utilizing the phase of a signal in this way: 5208:

which receives electrical binary data. For the case of BPSK, the laser transmits the field unchanged for binary '1', and with reverse polarity for '0'. The demodulator consists of a

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Receiver structure for QPSK. The matched filters can be replaced with correlators. Each detection device uses a reference threshold value to determine whether a 1 or 0 is detected.

6133: 1483: 6424:{\displaystyle Q(x)={\frac {1}{\sqrt {2\pi }}}\int _{x}^{\infty }e^{-{\frac {1}{2}}t^{2}}\,dt={\frac {1}{2}}\operatorname {erfc} \left({\frac {x}{\sqrt {2}}}\right),\ x\geq 0} 5267: 95: 6026: 6691: 5938:

required to overcome differential modulation in coded systems, however, is larger – typically about 3 dB. The performance degradation is a result of

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Any digital modulation scheme uses a finite number of distinct signals to represent digital data. PSK uses a finite number of phases, each assigned a unique pattern of

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Hill, Terrance J. (2000). "A non-proprietary, constant envelope, variant of shaped offset QPSK (SOQPSK) for improved spectral containment and detection efficiency".

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The BER curve for this example is compared to ordinary BPSK on the right. As mentioned above, whilst the error rate is approximately doubled, the increase needed in

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Using DPSK avoids the need for possibly complex carrier-recovery schemes to provide an accurate phase estimate and can be an attractive alternative to ordinary PSK.

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Saeed, N.; Elzanaty, A.; Almorad, H.; Dahrouj, H.; Al-Naffouri, T.Y.; Alouini, M.S. (2020). "Cubesat communications: Recent advances and future challenges".

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Dual constellation diagram for π/4-QPSK. This shows the two separate constellations with identical Gray coding but rotated by 45° with respect to each other.

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they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are "binary phase-shift keying" (

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of its definition. The curves of mutual information saturate to the number of bits carried by each symbol in the limit of infinite signal to noise ratio

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QPSK systems can be implemented in a number of ways. An illustration of the major components of the transmitter and receiver structure are shown below.

7404: 2995: 2514:{\displaystyle {\begin{aligned}P_{s}&=1-\left(1-P_{b}\right)^{2}\\&=2Q\left({\sqrt {\frac {E_{s}}{N_{0}}}}\right)-\left^{2}.\end{aligned}}} 3609: 2324:

However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the power (since two bits are transmitted simultaneously).

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then computes the difference in phase between this received signal and the preceding one. The difference encodes the data as described above.

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Nelson, T.; Perrins, E.; Rice, M. (2005). "Common detectors for Tier 1 modulations" (Document). International Foundation for Telemetering.

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The graph on the right compares the bit-error rates of BPSK, QPSK (which are the same, as noted above), 8-PSK and 16-PSK. It is seen that

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along the quadrature axis to modulate a sine (or cosine) wave. By convention, in-phase modulates cosine and quadrature modulates sine.

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The mathematical analysis shows that QPSK can be used either to double the data rate compared with a BPSK system while maintaining the

5067: 2846:), in the sense that an integrate-and-dump offset QPSK detector produces the same output no matter which kind of transmitter is used. 1265: 7385: 7366: 7347: 7313: 7089: 6968: 6927: 6878: 1717: 460: 255: 237: 175: 113: 63: 3689: 2115:

The first basis function is used as the in-phase component of the signal and the second as the quadrature component of the signal.

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in performance compared to ordinary QPSK is larger and the system designer must balance this against the reduction in complexity.

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is a binary "1". Otherwise it remains in its previous state. This is the description of differentially encoded BPSK given above.

354: 4498: 6801: 6510: 6452: 4129: 4041: 3033: 541: 455: 427: 394: 369: 321: 2787:) is a variant of phase-shift keying modulation using four different values of the phase to transmit. It is sometimes called 1904:{\displaystyle s_{n}(t)={\sqrt {\frac {2E_{s}}{T_{s}}}}\cos \left(2\pi f_{c}t+(2n-1){\frac {\pi }{4}}\right),\quad n=1,2,3,4.} 6986:"Performance of coded offset quadrature phase-shift keying (OQPSK) and MIL-STD shaped OQPSK (SOQPSK) with iterative decoding" 558: 6644: 6436: 4462: 4321: 2977: 1702: 1498: 6953:

MILCOM 2000 Proceedings. 21st Century Military Communications. Architectures and Technologies for Information Superiority

4050: 5359:. Assume that the constellation diagram positions the symbols at ±1 (which is BPSK). The differential encoder produces: 1142:{\displaystyle s_{0}(t)={\sqrt {\frac {2E_{b}}{T_{b}}}}\cos(2\pi ft+\pi )=-{\sqrt {\frac {2E_{b}}{T_{b}}}}\cos(2\pi ft)} 807:

reaches an incorrect decision. That makes it the most robust of all the PSKs. It is, however, only able to modulate at 1

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they are shown on the real axis, at 0° and 180°. Therefore, it handles the highest noise level or distortion before the

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The modulated signal is shown below for both DBPSK and DQPSK as described above. In the figure, it is assumed that the

3950: 7240: 359: 5205: 4320:. Furthermore, this analysis (and the graphical results below) are based on a system in which the only corruption is 219: 146: 140: 2243:

quadrature-phase component of the carrier. BPSK is used on both carriers and they can be independently demodulated.

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BER comparison between DBPSK, DQPSK and their non-differential forms using Gray coding and operating in white noise

511: 331: 7105: 215: 6582:, a binary scheme, so either modulation choice in version 2 will yield a higher data rate. A similar technology, 6486: 5365: 5209: 384: 5565: 2196:{\displaystyle {\begin{pmatrix}\pm {\sqrt {\frac {E_{s}}{2}}}&\pm {\sqrt {\frac {E_{s}}{2}}}\end{pmatrix}}.} 157: 7331:

The notation and theoretical results in this article are based on material presented in the following sources:

521: 404: 6790:{\displaystyle {\textrm {MI}}\simeq \log _{2}\left({\sqrt {{\frac {4\pi }{e}}{\frac {E_{s}}{N_{0}}}}}\right).} 5939: 1386: 1343: 6612:

standard requires support for both QPSK and 8PSK. The chipsets used in new satellite set top boxes, such as

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will give the probability that a single sample taken from a random process with zero-mean and unit-variance

4200:(SDQPSK) is like DQPSK, but encoding is symmetric, using phase shift values of −135°, −45°, +45° and +135°. 4015: 418: 55: 5015: 5193: 4153: 2528:

is high (as is necessary for practical QPSK systems) the probability of symbol error may be approximated:

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The probability of error for DPSK is difficult to calculate in general, but, in the case of DBPSK it is:

6648: 5942: – in this case it refers to the fact that tracking of the phase is completely ignored. 5058:, the phase-shift between the two received signals which can be used to determine the data transmitted. 4021:

Bounds on the error rates of various digital modulation schemes can be computed with application of the

2525: 795: 754: 734: 516: 450: 7198:"Understanding the Requirements of ISO/IEC 14443 for Type B Proximity Contactless Identification Cards" 1440: 7161:

IEEE Std 802.11-1999: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications

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At intermediate values of signal to noise ratios the mutual information (MI) is well approximated by:

6693:. On the contrary, in the limit of small signal to noise ratios the mutual information approaches the 5243: 2854:: SOQPSK has the same signal constellation as QPSK, however the phase of SOQPSK is always stationary. 6579: 5144:

which, when numerically evaluated, is only slightly worse than ordinary BPSK, particularly at higher

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Analysis shows that differential encoding approximately doubles the error rate compared to ordinary

3187:{\displaystyle P_{s}=1-\int _{-\pi /M}^{\pi /M}p_{\theta _{r}}\left(\theta _{r}\right)d\theta _{r},} 1649:{\displaystyle P_{e}={\frac {1}{2}}\operatorname {erfc} \left({\sqrt {\frac {E_{b}}{N_{0}}}}\right)} 6818: 5009: 4146: 4033: 778: 399: 7273: 6631: 5988: 3944:

is used, the most probable error from one symbol to the next produces only a single bit-error and

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Mbit/s) when the link between the two devices is sufficiently robust. Bluetooth 1 modulates with

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Because of its simplicity, BPSK is appropriate for low-cost passive transmitters, and is used in

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Signal doesn't pass through the origin, because only one bit of the symbol is changed at a time.

379: 5428: 4437: 7381: 7362: 7343: 7309: 7085: 7023: 6964: 6923: 6874: 6490: 6466:, uses a variety of different PSKs depending on the data rate required. At the basic rate of 1 6463: 5326: 2994: 2988: 6985: 5786: 5726: 5693: 5633: 4714: 4654: 4384:

decoded one-by-one to constellation points but are instead compared directly to one another.

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Bit-error rate curves for BPSK, QPSK, 8-PSK and 16-PSK, additive white Gaussian noise channel

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from one symbol to the next.) SOQPSK modulation can be represented as the hybrid of QPSK and

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such as the Bell 201, 208, and 209 and the CCITT V.26, V.27, V.29, V.32, and V.34 used PSK.

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The factors of 1/2 indicate that the total power is split equally between the two carriers.

971:{\displaystyle s_{n}(t)={\sqrt {\frac {2E_{b}}{T_{b}}}}\cos(2\pi ft+\pi (1-n)),\quad n=0,1.} 746: 599: 506: 501: 326: 316: 6191: 6155: 6069: 6037: 5956: 5823: 5759: 5666: 5496: 5469: 5299: 5272: 4687: 4627: 4468: 4461:. Assume without loss of generality that the phase of the carrier wave is zero. Denote the 4410: 289: 6221: 5458: 5448: 5201: 4236: 3756: 2862: 1918: 441: 4581: 4210: 3910:{\displaystyle P_{s}\approx 2Q\left({\sqrt {2\gamma _{s}}}\sin {\frac {\pi }{M}}\right).} 811:

bit/symbol (as seen in the figure) and so is unsuitable for high data-rate applications.

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This article is about a type of digital modulation. For the PSK encryption protocol, see

6697:, which is the supremum among all possible choices of symbol statistical distributions. 5212:

which delays one bit, so two bits can be compared at one time. In further processing, a

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For the general M-PSK there is no simple expression for the symbol-error probability if

2876: 2772: 822:) is unable to tell which constellation point is which. As a result, the data is often 6440: 6272: 6254: 5493:

only changes state (from binary "0" to binary "1" or from binary "1" to binary "0") if

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into an electric current, so the information is changed back into its original state.

2976:-QPSK lends itself to easy demodulation and has been adopted for use in, for example, 640:. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the 7398: 7337: 6833: 6583: 6521: 5217: 4018:

exhibit higher error-rates; in exchange however they deliver a higher raw data-rate.

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The mutual information of PSK over the AWGN channel is generally lower than that of

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BER comparison between BPSK and differentially encoded BPSK operating in white noise

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through which the signal passes. This problem can be overcome by using the data to

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of the errors in the decoded bitstream, which is easier to implement in hardware.)

4004: 2702: 693: 669: 637: 622: 610: 546: 486: 465: 7218: 6908:"Common detectors for shaped offset QPSK (SOQPSK) and Feher-patented QPSK (FQPSK)" 5232: 652:

are encoded in the difference in phase between successive samples, this is called

6616:'s 7000 series support 8PSK and are backward compatible with the older standard. 5847:

will still be decoded correctly. Thus, the 180° phase ambiguity does not matter.

3940:-PSK can only be determined exactly once the bit-mapping is known. However, when 2884:

This variant of QPSK uses two identical constellations which are rotated by 45° (

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Mbit/s modes use OFDM with QPSK. The fastest four modes use OFDM with forms of

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and then the differential decoder reverses the encoding procedure and produces

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The even bits, highlighted here, contribute to the quadrature-phase component:

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must have a reference signal to compare the received signal's phase against; or

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error-rate than the ordinary schemes which rely on precise phase information.

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Given that radio communication channels are allocated by agencies such as the

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For determining error-rates mathematically, some definitions will be needed:

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Stüber, G.L. (August 1988). "Soft Decision Direct-Sequence DPSK Receivers".

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As a result, the probability of bit-error for QPSK is the same as for BPSK:

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Since there is only one bit per symbol, this is also the symbol error rate.

630: 614: 607: 491: 3679:{\displaystyle r_{1}\sim N\left({\sqrt {E_{s}}},{\frac {1}{2}}N_{0}\right)} 2991:). The phase-shifts are between those of the two previous timing-diagrams. 2229: 1728:

As with BPSK, there are phase ambiguity problems at the receiving end, and

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Owing to PSK's simplicity, particularly when compared with its competitor

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of M-PSK modulation schemes increases with increasing of modulation order

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but halving the bandwidth needed. In this latter case, the BER of QPSK is

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words, the magnitude of jumps is smaller in OQPSK when compared to QPSK.

1695:(BER) – sometimes misperceived as twice the BER of BPSK. 697: 278: 7109: 6899: 6473:/s, it uses DBPSK (differential BPSK). To provide the extended rate of 2 2861:. SOQPSK is one of the most spread modulation schemes in application to 7106:"Link Budget Analysis: Digital Modulation, Part 3 (www.AtlantaRF.com)" 4744:, the decision is taken on the phase of the resultant complex number: 2719:

The odd bits, highlighted here, contribute to the in-phase component:

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Hence, the signal constellation consists of the signal-space 4 points

7144: 6620: 6609: 6587: 1238:{\displaystyle s_{1}(t)={\sqrt {\frac {2E_{b}}{T_{b}}}}\cos(2\pi ft)} 762: 17: 6590:) also relies on PSK using two frequency bands: 868 MHz and 915 222:. Statements consisting only of original research should be removed. 7057: 2314:{\displaystyle P_{b}=Q\left({\sqrt {\frac {2E_{b}}{N_{0}}}}\right)} 1569:{\displaystyle P_{b}=Q\left({\sqrt {\frac {2E_{b}}{N_{0}}}}\right)} 6849: 6844: 6630: 6505:

modulation where each sub-carrier is BPSK modulated. The 12 and 18

5457: 5231: 5197: 4370: 4235: 3761: 3022: 2993: 2875: 2820: 2797: 2771: 2701: 2228: 2215: 1666: 830: 790: 758: 496: 6517: 6502: 6470: 6143: 5134:{\displaystyle P_{b}={\frac {1}{2}}e^{-{\frac {E_{b}}{N_{0}}}},} 1914:

This yields the four phases π/4, 3π/4, 5π/4 and 7π/4 as needed.

1330:{\displaystyle \phi (t)={\sqrt {\frac {2}{T_{b}}}}\cos(2\pi ft)} 626: 5200:

in a differential way. The modulation is a laser which emits a

729:

of which do not need a reference carrier (to a certain extent).

726: 7163: – the overarching IEEE 802.11 specification. 6601: 6594: 5981: 2807: 1684: 814:

In the presence of an arbitrary phase-shift introduced by the

773:) which uses two phases, and "quadrature phase-shift keying" ( 692:

All convey data by changing some aspect of a base signal, the

187: 125: 70: 29: 6912:

GLOBECOM '05. IEEE Global Telecommunications Conference, 2005

3748:{\displaystyle r_{2}\sim N\left(0,{\frac {1}{2}}N_{0}\right)} 7010:

Sahin, C.; Perrins, E. (2011). "The capacity of SOQPSK-TG".

6826: – for an overview of all modulation schemes 6443:, hence, are a good theoretical benchmark to compare with. 6439:(AWGN). These error rates are lower than those computed in 6147: 2221:

resulting signal is the QPSK signal. Note the use of polar

4568:{\displaystyle r_{k}={\sqrt {E_{s}}}e^{j\phi _{k}}+n_{k}.} 4278:-PSK but this may be overcome by only a small increase in 5627:

since binary subtraction is the same as binary addition.

1917:

This results in a two-dimensional signal space with unit

1256:

Hence, the signal space can be represented by the single

774: 719:

in the phase as conveying information –

6493:, has eight data rates: 6, 9, 12, 18, 24, 36, 48 and 54 981:

This yields two phases, 0 and π. In the specific form,

708:

itself as conveying the information, in which case the

211: 91: 2711:

The binary data that is conveyed by this waveform is:

2133: 6709: 6657: 6627:

Mutual information with additive white Gaussian noise

6548: 6485:

Mbit/s, QPSK is employed, but has to be coupled with

6284: 6257: 6224: 6194: 6158: 6104: 6072: 6040: 5991: 5959: 5902: 5860: 5826: 5789: 5762: 5729: 5696: 5669: 5636: 5568: 5529: 5499: 5472: 5431: 5368: 5329: 5302: 5275: 5246: 5150: 5070: 5018: 4753: 4717: 4690: 4657: 4630: 4610: 4584: 4501: 4471: 4440: 4413: 4393: 4341: 4284: 4264: 4213: 4178: 4053: 3953: 3926: 3841: 3796: 3776: 3692: 3612: 3206: 3079: 3050: 2954: 2919: 2890: 2537: 2336: 2255: 2127: 1929: 1750: 1582: 1510: 1443: 1389: 1346: 1268: 1157: 994: 850: 770: 733:

A convenient method to represent PSK schemes is on a

4331:

One of the most popular applications of DPSK is the

4198:

Symmetric differential quadrature phase shift keying

2842:(SOQPSK) is interoperable with Feher-patented QPSK ( 7012:

2011-MILCOM 2011 Military Communications Conference

4207:, and so there is a phase shift in both signals at 4118:{\displaystyle \rho ={\frac {\log _{2}M}{2}}\quad } 2945:desirable when engineering communications signals. 86:

may be too technical for most readers to understand

7187: – the IEEE 802.11g specification. 7175: – the IEEE 802.11b specification. 6789: 6685: 6562: 6423: 6263: 6239: 6207: 6171: 6127: 6085: 6053: 6020: 5972: 5930: 5888: 5839: 5808: 5775: 5748: 5715: 5682: 5655: 5616: 5551: 5512: 5485: 5439: 5414: 5351: 5315: 5288: 5261: 5178: 5133: 5050: 4997: 4736: 4703: 4676: 4643: 4616: 4596: 4567: 4484: 4453: 4426: 4399: 4355: 4312: 4270: 4225: 4184: 4117: 3992: 3932: 3909: 3824: 3782: 3747: 3678: 3595: 3186: 3062: 2968: 2933: 2904: 2684: 2513: 2313: 2195: 2104: 1903: 1725:technology, the penalty in cost is very moderate. 1648: 1568: 1477: 1421: 1375: 1329: 1237: 1141: 970: 3993:{\displaystyle P_{b}\approx {\frac {1}{k}}P_{s}.} 644:that is represented by the particular phase. The 5196:, the data can be modulated onto the phase of a 5012:. In the absence of noise, the phase of this is 4003:(Using Gray coding allows us to approximate the 3027:Constellation diagram for 8-PSK with Gray coding 1432:This use of this basis function is shown at the 841:The general form for BPSK follows the equation: 621:inputs at a precise time. It is widely used for 613:. The modulation is accomplished by varying the 6635:Mutual information of PSK over the AWGN channel 3009:Dual-polarization quadrature phase shift keying 2857:The standard description of SOQPSK-TG involves 1675:. Each adjacent symbol only differs by one bit. 7237:"Low-Cost Satellite Set-top Box SoC — BCM7325" 6455:, it is widely used in existing technologies. 3070:. Unfortunately, it can only be obtained from 2802:Difference of the phase between QPSK and OQPSK 985:is often conveyed with the following signals: 7306:Principles and Practice of Information Theory 7296: 7294: 5236:Differential encoding/decoding system diagram 2941:-QPSK are between OQPSK and non-offset QPSK. 566: 8: 7272:. Black Box Network Services. Archived from 5896:to overcome this is small. The increase in 5523:The received signal is demodulated to yield 7156: 7154: 7045:IEEE Communications Surveys & Tutorials 5415:{\displaystyle \,e_{k}=e_{k-1}\oplus b_{k}} 757:chosen are usually positioned with uniform 64:Learn how and when to remove these messages 6906:Nelson, T.; Perrins, E.; Rice, M. (2005). 6489:. The higher-speed wireless LAN standard, 5617:{\displaystyle b_{k}=e_{k}\oplus e_{k-1},} 2913:135° and so the amplitude fluctuations of 1729: 823: 720: 573: 559: 274: 7133:IEEE Transactions on Vehicular Technology 7056: 6770: 6760: 6754: 6739: 6737: 6724: 6711: 6710: 6708: 6677: 6668: 6662: 6656: 6552: 6547: 6435:The error rates quoted here are those in 6390: 6370: 6360: 6352: 6338: 6334: 6324: 6319: 6300: 6283: 6256: 6223: 6199: 6193: 6163: 6157: 6119: 6105: 6103: 6077: 6071: 6045: 6039: 6012: 5996: 5990: 5964: 5958: 5922: 5913: 5907: 5901: 5880: 5871: 5865: 5859: 5831: 5825: 5794: 5788: 5767: 5761: 5734: 5728: 5701: 5695: 5674: 5668: 5641: 5635: 5599: 5586: 5573: 5567: 5534: 5528: 5504: 5498: 5477: 5471: 5435: 5430: 5406: 5387: 5374: 5369: 5367: 5334: 5328: 5307: 5301: 5280: 5274: 5252: 5251: 5245: 5170: 5161: 5155: 5149: 5118: 5108: 5102: 5098: 5084: 5075: 5069: 5036: 5023: 5017: 4989: 4978: 4968: 4955: 4937: 4926: 4914: 4908: 4899: 4888: 4876: 4868: 4856: 4850: 4828: 4815: 4802: 4792: 4779: 4768: 4758: 4752: 4722: 4716: 4695: 4689: 4662: 4656: 4635: 4629: 4609: 4583: 4556: 4541: 4533: 4521: 4515: 4506: 4500: 4476: 4470: 4445: 4439: 4418: 4412: 4392: 4345: 4340: 4304: 4295: 4289: 4283: 4263: 4212: 4177: 4107: 4099: 4094: 4089: 4067: 4060: 4052: 3981: 3967: 3958: 3952: 3925: 3889: 3875: 3866: 3846: 3840: 3816: 3807: 3801: 3795: 3775: 3734: 3720: 3697: 3691: 3665: 3651: 3640: 3634: 3617: 3611: 3581: 3571: 3565: 3552: 3529: 3519: 3513: 3497: 3480: 3461: 3456: 3443: 3438: 3432: 3408: 3400: 3389: 3371: 3365: 3340: 3336: 3323: 3318: 3306: 3293: 3283: 3272: 3253: 3236: 3220: 3215: 3207: 3205: 3175: 3158: 3142: 3137: 3123: 3119: 3110: 3103: 3084: 3078: 3049: 2958: 2953: 2923: 2918: 2894: 2889: 2669: 2659: 2652: 2625: 2611: 2604: 2578: 2568: 2561: 2542: 2536: 2498: 2480: 2470: 2463: 2434: 2424: 2417: 2391: 2380: 2345: 2337: 2335: 2298: 2287: 2276: 2260: 2254: 2170: 2163: 2146: 2139: 2128: 2126: 2084: 2054: 2044: 2022: 2000: 1970: 1960: 1938: 1930: 1928: 1855: 1825: 1795: 1784: 1773: 1755: 1749: 1633: 1623: 1616: 1596: 1587: 1581: 1553: 1542: 1531: 1515: 1509: 1463: 1442: 1399: 1393: 1388: 1353: 1347: 1345: 1294: 1284: 1267: 1202: 1191: 1180: 1162: 1156: 1106: 1095: 1084: 1039: 1028: 1017: 999: 993: 895: 884: 873: 855: 849: 256:Learn how and when to remove this message 238:Learn how and when to remove this message 176:Learn how and when to remove this message 114:Learn how and when to remove this message 98:, without removing the technical details. 6574:Mbit/s) and 8-DPSK at its higher rate (3 6215:, probability of symbol-error 1422:{\displaystyle -{\sqrt {E_{b}}}\phi (t)} 139:This article includes a list of general 6955:. Vol. 1. IEEE. pp. 347–352. 6861: 5269:time-slot call the bit to be modulated 4624:symbol is the phase difference between 2789:staggered quadrature phase-shift keying 1437:the high frequency band by multiplying 1376:{\displaystyle {\sqrt {E_{b}}}\phi (t)} 473: 440: 417: 339: 296: 277: 6873:. Pearson Prentice Hall. p. 283. 6477:Mbit/s, DQPSK is used. In reaching 5.5 4136:Differential phase-shift keying (DPSK) 654:differential phase-shift keying (DPSK) 7207:. ATMEL. 2005. Rev. 2056B–RFID–11/05. 6619:Historically, voice-band synchronous 6273:complementary Gaussian error function 6249:Gaussian probability density function 5756:if they are the same. Hence, if both 5051:{\displaystyle \phi _{k}-\phi _{k-1}} 4128:The same relationship holds true for 2806:Taking four values of the phase (two 96:make it understandable to non-experts 7: 7219:"How Communications Satellites Work" 5228:Example: Differentially-encoded BPSK 4363:-DQPSK and 8-DPSK were implemented. 2781:Offset quadrature phase-shift keying 1671:Constellation diagram for QPSK with 1663:Quadrature phase-shift keying (QPSK) 668:techniques used for transmission of 6128:{\displaystyle {\frac {1}{2}}N_{0}} 5323:and the resulting modulated signal 2327:The symbol error rate is given by: 1253:is the frequency of the base band. 829:BPSK is functionally equivalent to 6325: 4192:points in the constellation and a 4034:Bandwidth (or spectral) efficiency 3770:This may be approximated for high 3324: 145:it lacks sufficient corresponding 25: 7359:Digital and Analog Communications 5296:, the differentially encoded bit 1718:Federal Communications Commission 1478:{\displaystyle \cos(2\pi f_{c}t)} 664:There are three major classes of 45:This article has multiple issues. 7405:Quantized radio modulation modes 6993:Interplanetary Network Prog. Rep 6984:Li, Lifang; Simon, M.K. (2004). 6814:Binary offset carrier modulation 5262:{\displaystyle k^{\textrm {th}}} 4387:Call the received symbol in the 1732:QPSK is often used in practice. 1429:. This assignment is arbitrary. 785:Binary phase-shift keying (BPSK) 288: 192: 130: 75: 34: 6869:Stern, H.; Mahmoud, S. (2004). 6586:(the wireless standard used by 6536:, and many other applications. 6511:quadrature amplitude modulation 6453:quadrature amplitude modulation 4085: 3034:quadrature amplitude modulation 1873: 952: 737:. This shows the points in the 53:or discuss these issues on the 6481:Mbit/s and the full rate of 11 6294: 6288: 6234: 6228: 5346: 5340: 4578:The decision variable for the 4112: 4086: 3920:The bit-error probability for 2034: 2028: 1950: 1944: 1852: 1837: 1767: 1761: 1707:maintain the data-rate of BPSK 1472: 1450: 1416: 1410: 1370: 1364: 1324: 1309: 1278: 1272: 1232: 1217: 1174: 1168: 1136: 1121: 1075: 1054: 1011: 1005: 946: 943: 931: 910: 867: 861: 1: 7173:IEEE Std 802.11b-1999 (R2003) 6580:Gaussian minimum-shift keying 6437:additive white Gaussian noise 6271:. It is a scaled form of the 6028:, energy per symbol with 4463:additive white Gaussian noise 4322:additive white Gaussian noise 4205:signal starts with zero phase 4025:to the signal constellation. 1501:(AWGN) can be calculated as: 1499:additive white Gaussian noise 818:, the demodulator (see, e.g. 602:by changing (modulating) the 6251:will be greater or equal to 6021:{\displaystyle E_{s}=nE_{b}} 5008:where superscript * denotes 741:where, in this context, the 7020:10.1109/MILCOM.2011.6127730 6920:10.1109/GLOCOM.2005.1578470 6832:(PM) – the 6686:{\displaystyle E_{s}/N_{0}} 6643:of PSK can be evaluated in 6570:-DQPSK at its lower rate (2 6524:which has been adopted for 5931:{\displaystyle E_{b}/N_{0}} 5889:{\displaystyle E_{b}/N_{0}} 5552:{\displaystyle e_{k}=\pm 1} 5179:{\displaystyle E_{b}/N_{0}} 4313:{\displaystyle E_{b}/N_{0}} 3825:{\displaystyle E_{b}/N_{0}} 1721:BPSK. However, with modern 1679:Sometimes this is known as 1433: 218:the claims made and adding 7426: 7357:Couch, Leon W. II (1997). 7239:. Broadcom. Archived from 7067:10.1109/COMST.2020.2990499 7014:. IEEE. pp. 555–560. 6961:10.1109/MILCOM.2000.904973 4144: 2865:satellite communications. 1340:where 1 is represented by 482:Capacity-approaching codes 267: 7336:Proakis, John G. (1995). 7263:"Local and Remote Modems" 6487:complementary code keying 5440:{\displaystyle \oplus {}} 5216:is used to transform the 5210:delay line interferometer 4454:{\displaystyle \phi _{k}} 5980:, energy per 5940:noncoherent transmission 5352:{\displaystyle m_{k}(t)} 4016:higher-order modulations 1383:and 0 is represented by 688:Phase-shift keying (PSK) 6645:additive Gaussian noise 6528:, credit cards such as 5809:{\displaystyle e_{k-1}} 5749:{\displaystyle b_{k}=0} 5716:{\displaystyle e_{k-1}} 5656:{\displaystyle b_{k}=1} 4737:{\displaystyle r_{k-1}} 4677:{\displaystyle r_{k-1}} 1434:end of the next section 419:Hierarchical modulation 160:more precise citations. 7378:Digital Communications 7376:Haykin, Simon (1988). 7339:Digital Communications 7084:. Wiley. p. 368. 6871:Communications Systems 6791: 6687: 6636: 6564: 6563:{\displaystyle \pi /4} 6425: 6265: 6241: 6209: 6173: 6140:power spectral density 6129: 6087: 6055: 6022: 5974: 5932: 5890: 5841: 5810: 5777: 5750: 5717: 5684: 5657: 5618: 5553: 5514: 5487: 5463: 5441: 5416: 5353: 5317: 5290: 5263: 5237: 5206:Mach–Zehnder modulator 5194:optical communications 5180: 5135: 5052: 4999: 4738: 4705: 4678: 4645: 4618: 4598: 4569: 4486: 4455: 4434:and let it have phase 4428: 4401: 4376: 4357: 4356:{\displaystyle \pi /4} 4314: 4272: 4255: 4227: 4186: 4154:communications channel 4119: 4040:(unlike, for example, 3994: 3934: 3911: 3826: 3784: 3767: 3749: 3680: 3597: 3188: 3064: 3063:{\displaystyle M>4} 3028: 3013:dual-polarization QPSK 3000: 2970: 2969:{\displaystyle \pi /4} 2935: 2934:{\displaystyle \pi /4} 2906: 2905:{\displaystyle \pi /4} 2881: 2827: 2803: 2777: 2708: 2686: 2515: 2315: 2234: 2226: 2197: 2106: 1905: 1730:differentially encoded 1676: 1650: 1570: 1479: 1423: 1377: 1331: 1239: 1143: 972: 824:differentially encoded 816:communications channel 799: 683:Frequency-shift keying 677:Amplitude-shift keying 598:process which conveys 7243:on September 15, 2015 7185:IEEE Std 802.11g-2003 7082:Communication Systems 6792: 6695:AWGN channel capacity 6688: 6649:numerical integration 6634: 6565: 6426: 6266: 6242: 6210: 6208:{\displaystyle P_{s}} 6174: 6172:{\displaystyle P_{b}} 6130: 6088: 6086:{\displaystyle T_{s}} 6056: 6054:{\displaystyle T_{b}} 6023: 5975: 5973:{\displaystyle E_{b}} 5933: 5891: 5842: 5840:{\displaystyle b_{k}} 5811: 5778: 5776:{\displaystyle e_{k}} 5751: 5718: 5685: 5683:{\displaystyle e_{k}} 5658: 5619: 5554: 5515: 5513:{\displaystyle b_{k}} 5488: 5486:{\displaystyle e_{k}} 5461: 5442: 5417: 5354: 5318: 5316:{\displaystyle e_{k}} 5291: 5289:{\displaystyle b_{k}} 5264: 5235: 5181: 5136: 5053: 5000: 4739: 4706: 4704:{\displaystyle r_{k}} 4679: 4646: 4644:{\displaystyle r_{k}} 4619: 4599: 4570: 4487: 4485:{\displaystyle n_{k}} 4456: 4429: 4427:{\displaystyle r_{k}} 4402: 4374: 4358: 4315: 4273: 4239: 4228: 4187: 4141:Differential encoding 4120: 4007:of the errors as the 3995: 3935: 3912: 3827: 3785: 3765: 3750: 3681: 3598: 3189: 3065: 3026: 2997: 2971: 2936: 2907: 2879: 2824: 2801: 2775: 2705: 2687: 2526:signal-to-noise ratio 2516: 2316: 2232: 2219: 2198: 2107: 1906: 1705:of the signal, or to 1670: 1651: 1571: 1480: 1424: 1378: 1332: 1240: 1144: 973: 826:prior to modulation. 796:Constellation diagram 794: 735:constellation diagram 27:Type of data encoding 7279:on December 22, 2015 7112:on February 10, 2020 6804:modulation formats. 6707: 6655: 6597:with BPSK and at 2.4 6546: 6282: 6255: 6240:{\displaystyle Q(x)} 6222: 6192: 6156: 6102: 6070: 6038: 5989: 5957: 5900: 5858: 5824: 5787: 5760: 5727: 5694: 5667: 5634: 5566: 5527: 5497: 5470: 5429: 5366: 5327: 5300: 5273: 5244: 5148: 5068: 5016: 4751: 4715: 4688: 4655: 4628: 4608: 4582: 4499: 4469: 4438: 4411: 4391: 4339: 4282: 4262: 4211: 4176: 4051: 3951: 3924: 3839: 3794: 3774: 3690: 3610: 3204: 3077: 3048: 2952: 2917: 2888: 2535: 2334: 2253: 2238:Probability of error 2125: 1927: 1748: 1580: 1508: 1497:(BER) of BPSK under 1441: 1387: 1344: 1266: 1155: 992: 848: 755:constellation points 7080:Haykin, S. (2001). 6819:Differential coding 6526:biometric passports 6497:Mbit/s. The 6 and 9 6329: 5010:complex conjugation 4994: 4904: 4784: 4597:{\displaystyle k-1} 4226:{\displaystyle t=0} 4147:differential coding 4029:Spectral efficiency 3466: 3448: 3328: 3132: 2948:On the other hand, 2768:Offset QPSK (OQPSK) 7308:. Addison Wesley. 6787: 6683: 6641:mutual information 6637: 6560: 6520:standards such as 6421: 6315: 6261: 6237: 6205: 6169: 6125: 6083: 6051: 6018: 5970: 5928: 5886: 5837: 5806: 5773: 5746: 5713: 5680: 5653: 5614: 5549: 5510: 5483: 5464: 5437: 5412: 5349: 5313: 5286: 5259: 5238: 5176: 5131: 5048: 4995: 4974: 4884: 4764: 4734: 4711:is projected onto 4701: 4674: 4641: 4614: 4594: 4565: 4482: 4451: 4424: 4397: 4377: 4353: 4333:Bluetooth standard 4310: 4268: 4256: 4223: 4182: 4115: 3990: 3930: 3907: 3822: 3780: 3768: 3755:are each Gaussian 3745: 3676: 3593: 3591: 3452: 3434: 3314: 3184: 3099: 3060: 3029: 3001: 2981:cellular telephone 2966: 2931: 2902: 2882: 2828: 2804: 2778: 2709: 2682: 2511: 2509: 2311: 2235: 2227: 2223:non-return-to-zero 2193: 2184: 2102: 2100: 1901: 1677: 1646: 1566: 1475: 1419: 1373: 1327: 1235: 1139: 968: 800: 672:represented data: 666:digital modulation 596:digital modulation 588:Phase-shift keying 341:Digital modulation 203:possibly contains 7410:Data transmission 7361:. Prentice-Hall. 7029:978-1-4673-0081-0 6914:. pp. 5 pp. 6836:equivalent of PSK 6778: 6776: 6752: 6714: 6501:Mbit/s modes use 6491:IEEE 802.11g-2003 6464:IEEE 802.11b-1999 6411: 6400: 6399: 6378: 6346: 6313: 6312: 6264:{\displaystyle x} 6113: 5255: 5124: 5092: 4920: 4862: 4617:{\displaystyle k} 4527: 4400:{\displaystyle k} 4271:{\displaystyle M} 4185:{\displaystyle M} 4110: 4102: 4092: 4083: 3975: 3933:{\displaystyle M} 3897: 3881: 3783:{\displaystyle M} 3728: 3659: 3646: 3587: 3535: 3467: 3377: 3348: 3266: 2989:constant envelope 2835:The license-free 2676: 2675: 2633: 2632: 2585: 2584: 2487: 2486: 2441: 2440: 2305: 2304: 2180: 2179: 2156: 2155: 2061: 2060: 1977: 1976: 1863: 1802: 1801: 1640: 1639: 1604: 1560: 1559: 1405: 1359: 1301: 1300: 1209: 1208: 1113: 1112: 1046: 1045: 902: 901: 761:spacing around a 583: 582: 298:Analog modulation 266: 265: 258: 248: 247: 240: 205:original research 186: 185: 178: 124: 123: 116: 68: 16:(Redirected from 7417: 7391: 7372: 7353: 7320: 7319: 7298: 7289: 7288: 7286: 7284: 7278: 7267: 7259: 7253: 7252: 7250: 7248: 7233: 7227: 7226: 7215: 7209: 7208: 7205:Application Note 7202: 7194: 7188: 7182: 7176: 7170: 7164: 7158: 7149: 7148: 7145:10.1109/25.16541 7128: 7122: 7121: 7119: 7117: 7108:. Archived from 7102: 7096: 7095: 7077: 7071: 7070: 7060: 7040: 7034: 7033: 7007: 7001: 7000: 6990: 6981: 6975: 6974: 6948: 6942: 6941: 6903: 6891: 6885: 6884: 6866: 6840:Polar modulation 6830:Phase modulation 6796: 6794: 6793: 6788: 6783: 6779: 6777: 6775: 6774: 6765: 6764: 6755: 6753: 6748: 6740: 6738: 6729: 6728: 6716: 6715: 6712: 6692: 6690: 6689: 6684: 6682: 6681: 6672: 6667: 6666: 6600: 6593: 6577: 6573: 6569: 6567: 6566: 6561: 6556: 6530:American Express 6508: 6500: 6496: 6484: 6480: 6476: 6469: 6430: 6428: 6427: 6422: 6409: 6405: 6401: 6395: 6391: 6379: 6371: 6359: 6358: 6357: 6356: 6347: 6339: 6328: 6323: 6314: 6305: 6301: 6270: 6268: 6267: 6262: 6246: 6244: 6243: 6238: 6214: 6212: 6211: 6206: 6204: 6203: 6178: 6176: 6175: 6170: 6168: 6167: 6134: 6132: 6131: 6126: 6124: 6123: 6114: 6106: 6092: 6090: 6089: 6084: 6082: 6081: 6060: 6058: 6057: 6052: 6050: 6049: 6027: 6025: 6024: 6019: 6017: 6016: 6001: 6000: 5979: 5977: 5976: 5971: 5969: 5968: 5937: 5935: 5934: 5929: 5927: 5926: 5917: 5912: 5911: 5895: 5893: 5892: 5887: 5885: 5884: 5875: 5870: 5869: 5846: 5844: 5843: 5838: 5836: 5835: 5815: 5813: 5812: 5807: 5805: 5804: 5782: 5780: 5779: 5774: 5772: 5771: 5755: 5753: 5752: 5747: 5739: 5738: 5722: 5720: 5719: 5714: 5712: 5711: 5689: 5687: 5686: 5681: 5679: 5678: 5662: 5660: 5659: 5654: 5646: 5645: 5623: 5621: 5620: 5615: 5610: 5609: 5591: 5590: 5578: 5577: 5558: 5556: 5555: 5550: 5539: 5538: 5519: 5517: 5516: 5511: 5509: 5508: 5492: 5490: 5489: 5484: 5482: 5481: 5446: 5444: 5443: 5438: 5436: 5421: 5419: 5418: 5413: 5411: 5410: 5398: 5397: 5379: 5378: 5358: 5356: 5355: 5350: 5339: 5338: 5322: 5320: 5319: 5314: 5312: 5311: 5295: 5293: 5292: 5287: 5285: 5284: 5268: 5266: 5265: 5260: 5258: 5257: 5256: 5253: 5185: 5183: 5182: 5177: 5175: 5174: 5165: 5160: 5159: 5140: 5138: 5137: 5132: 5127: 5126: 5125: 5123: 5122: 5113: 5112: 5103: 5093: 5085: 5080: 5079: 5057: 5055: 5054: 5049: 5047: 5046: 5028: 5027: 5004: 5002: 5001: 4996: 4993: 4988: 4973: 4972: 4960: 4959: 4950: 4949: 4948: 4947: 4921: 4919: 4918: 4909: 4903: 4898: 4883: 4882: 4881: 4880: 4863: 4861: 4860: 4851: 4846: 4845: 4844: 4840: 4839: 4838: 4820: 4819: 4797: 4796: 4783: 4778: 4763: 4762: 4743: 4741: 4740: 4735: 4733: 4732: 4710: 4708: 4707: 4702: 4700: 4699: 4683: 4681: 4680: 4675: 4673: 4672: 4650: 4648: 4647: 4642: 4640: 4639: 4623: 4621: 4620: 4615: 4603: 4601: 4600: 4595: 4574: 4572: 4571: 4566: 4561: 4560: 4548: 4547: 4546: 4545: 4528: 4526: 4525: 4516: 4511: 4510: 4491: 4489: 4488: 4483: 4481: 4480: 4460: 4458: 4457: 4452: 4450: 4449: 4433: 4431: 4430: 4425: 4423: 4422: 4406: 4404: 4403: 4398: 4362: 4360: 4359: 4354: 4349: 4319: 4317: 4316: 4311: 4309: 4308: 4299: 4294: 4293: 4277: 4275: 4274: 4269: 4232: 4230: 4229: 4224: 4191: 4189: 4188: 4183: 4124: 4122: 4121: 4116: 4111: 4108: 4103: 4100: 4098: 4093: 4090: 4084: 4079: 4072: 4071: 4061: 4009:Hamming distance 3999: 3997: 3996: 3991: 3986: 3985: 3976: 3968: 3963: 3962: 3939: 3937: 3936: 3931: 3916: 3914: 3913: 3908: 3903: 3899: 3898: 3890: 3882: 3880: 3879: 3867: 3851: 3850: 3831: 3829: 3828: 3823: 3821: 3820: 3811: 3806: 3805: 3789: 3787: 3786: 3781: 3757:random variables 3754: 3752: 3751: 3746: 3744: 3740: 3739: 3738: 3729: 3721: 3702: 3701: 3685: 3683: 3682: 3677: 3675: 3671: 3670: 3669: 3660: 3652: 3647: 3645: 3644: 3635: 3622: 3621: 3602: 3600: 3599: 3594: 3592: 3588: 3586: 3585: 3576: 3575: 3566: 3557: 3556: 3540: 3536: 3534: 3533: 3524: 3523: 3514: 3505: 3504: 3485: 3484: 3468: 3465: 3460: 3447: 3442: 3433: 3407: 3406: 3405: 3404: 3399: 3395: 3394: 3393: 3378: 3376: 3375: 3366: 3349: 3341: 3327: 3322: 3313: 3312: 3311: 3310: 3298: 3297: 3288: 3287: 3267: 3265: 3254: 3245: 3241: 3240: 3227: 3226: 3225: 3224: 3193: 3191: 3190: 3185: 3180: 3179: 3167: 3163: 3162: 3149: 3148: 3147: 3146: 3131: 3127: 3118: 3114: 3089: 3088: 3069: 3067: 3066: 3061: 3019:Higher-order PSK 2975: 2973: 2972: 2967: 2962: 2940: 2938: 2937: 2932: 2927: 2911: 2909: 2908: 2903: 2898: 2758: 2757: 2753: 2749: 2745: 2737: 2735: 2731: 2727: 2723: 2714: 2691: 2689: 2688: 2683: 2681: 2677: 2674: 2673: 2664: 2663: 2654: 2653: 2638: 2634: 2631: 2630: 2629: 2616: 2615: 2606: 2605: 2590: 2586: 2583: 2582: 2573: 2572: 2563: 2562: 2547: 2546: 2520: 2518: 2517: 2512: 2510: 2503: 2502: 2497: 2493: 2492: 2488: 2485: 2484: 2475: 2474: 2465: 2464: 2446: 2442: 2439: 2438: 2429: 2428: 2419: 2418: 2400: 2396: 2395: 2390: 2386: 2385: 2384: 2350: 2349: 2320: 2318: 2317: 2312: 2310: 2306: 2303: 2302: 2293: 2292: 2291: 2278: 2277: 2265: 2264: 2202: 2200: 2199: 2194: 2189: 2188: 2181: 2175: 2174: 2165: 2164: 2157: 2151: 2150: 2141: 2140: 2111: 2109: 2108: 2103: 2101: 2097: 2093: 2089: 2088: 2062: 2059: 2058: 2046: 2045: 2027: 2026: 2013: 2009: 2005: 2004: 1978: 1975: 1974: 1962: 1961: 1943: 1942: 1910: 1908: 1907: 1902: 1869: 1865: 1864: 1856: 1830: 1829: 1803: 1800: 1799: 1790: 1789: 1788: 1775: 1774: 1760: 1759: 1711:exactly the same 1691:to minimize the 1655: 1653: 1652: 1647: 1645: 1641: 1638: 1637: 1628: 1627: 1618: 1617: 1605: 1597: 1592: 1591: 1575: 1573: 1572: 1567: 1565: 1561: 1558: 1557: 1548: 1547: 1546: 1533: 1532: 1520: 1519: 1484: 1482: 1481: 1476: 1468: 1467: 1428: 1426: 1425: 1420: 1406: 1404: 1403: 1394: 1382: 1380: 1379: 1374: 1360: 1358: 1357: 1348: 1336: 1334: 1333: 1328: 1302: 1299: 1298: 1286: 1285: 1244: 1242: 1241: 1236: 1210: 1207: 1206: 1197: 1196: 1195: 1182: 1181: 1167: 1166: 1148: 1146: 1145: 1140: 1114: 1111: 1110: 1101: 1100: 1099: 1086: 1085: 1047: 1044: 1043: 1034: 1033: 1032: 1019: 1018: 1004: 1003: 977: 975: 974: 969: 903: 900: 899: 890: 889: 888: 875: 874: 860: 859: 810: 798:example for BPSK 575: 568: 561: 292: 275: 261: 254: 243: 236: 232: 229: 223: 220:inline citations 196: 195: 188: 181: 174: 170: 167: 161: 156:this article by 147:inline citations 134: 133: 126: 119: 112: 108: 105: 99: 79: 78: 71: 60: 38: 37: 30: 21: 7425: 7424: 7420: 7419: 7418: 7416: 7415: 7414: 7395: 7394: 7388: 7375: 7369: 7356: 7350: 7342:. McGraw Hill. 7335: 7329: 7324: 7323: 7316: 7300: 7299: 7292: 7282: 7280: 7276: 7265: 7261: 7260: 7256: 7246: 7244: 7235: 7234: 7230: 7217: 7216: 7212: 7200: 7196: 7195: 7191: 7183: 7179: 7171: 7167: 7159: 7152: 7130: 7129: 7125: 7115: 7113: 7104: 7103: 7099: 7092: 7079: 7078: 7074: 7042: 7041: 7037: 7030: 7009: 7008: 7004: 6988: 6983: 6982: 6978: 6971: 6950: 6949: 6945: 6930: 6905: 6904: 6893: 6892: 6888: 6881: 6868: 6867: 6863: 6858: 6810: 6766: 6756: 6741: 6733: 6720: 6705: 6704: 6673: 6658: 6653: 6652: 6629: 6598: 6591: 6575: 6571: 6544: 6543: 6506: 6498: 6494: 6482: 6478: 6474: 6467: 6449: 6441:fading channels 6386: 6348: 6330: 6280: 6279: 6253: 6252: 6220: 6219: 6195: 6190: 6189: 6159: 6154: 6153: 6115: 6100: 6099: 6095:symbol duration 6073: 6068: 6067: 6041: 6036: 6035: 6008: 5992: 5987: 5986: 5960: 5955: 5954: 5948: 5918: 5903: 5898: 5897: 5876: 5861: 5856: 5855: 5827: 5822: 5821: 5790: 5785: 5784: 5763: 5758: 5757: 5730: 5725: 5724: 5697: 5692: 5691: 5670: 5665: 5664: 5637: 5632: 5631: 5595: 5582: 5569: 5564: 5563: 5530: 5525: 5524: 5500: 5495: 5494: 5473: 5468: 5467: 5427: 5426: 5402: 5383: 5370: 5364: 5363: 5330: 5325: 5324: 5303: 5298: 5297: 5276: 5271: 5270: 5247: 5242: 5241: 5230: 5202:continuous wave 5166: 5151: 5146: 5145: 5114: 5104: 5094: 5071: 5066: 5065: 5032: 5019: 5014: 5013: 4964: 4951: 4933: 4922: 4910: 4872: 4864: 4852: 4824: 4811: 4810: 4806: 4798: 4788: 4754: 4749: 4748: 4718: 4713: 4712: 4691: 4686: 4685: 4658: 4653: 4652: 4631: 4626: 4625: 4606: 4605: 4604:symbol and the 4580: 4579: 4552: 4537: 4529: 4517: 4502: 4497: 4496: 4472: 4467: 4466: 4465:(AWGN) term as 4441: 4436: 4435: 4414: 4409: 4408: 4389: 4388: 4369: 4337: 4336: 4300: 4285: 4280: 4279: 4260: 4259: 4252: 4245: 4209: 4208: 4174: 4173: 4149: 4143: 4138: 4063: 4062: 4049: 4048: 4031: 3977: 3954: 3949: 3948: 3922: 3921: 3871: 3865: 3861: 3842: 3837: 3836: 3812: 3797: 3792: 3791: 3772: 3771: 3730: 3713: 3709: 3693: 3688: 3687: 3661: 3636: 3633: 3629: 3613: 3608: 3607: 3590: 3589: 3577: 3567: 3558: 3548: 3545: 3544: 3525: 3515: 3509: 3493: 3486: 3476: 3473: 3472: 3425: 3419: 3418: 3385: 3367: 3355: 3351: 3350: 3332: 3302: 3289: 3279: 3268: 3258: 3246: 3232: 3228: 3216: 3211: 3202: 3201: 3171: 3154: 3150: 3138: 3133: 3080: 3075: 3074: 3046: 3045: 3042: 3021: 3006: 2950: 2949: 2915: 2914: 2886: 2885: 2874: 2859:ternary symbols 2833: 2770: 2765: 2755: 2751: 2747: 2743: 2741: 2733: 2729: 2725: 2721: 2720: 2712: 2699: 2665: 2655: 2648: 2621: 2617: 2607: 2600: 2574: 2564: 2557: 2538: 2533: 2532: 2508: 2507: 2476: 2466: 2459: 2455: 2451: 2450: 2430: 2420: 2413: 2398: 2397: 2376: 2369: 2365: 2364: 2351: 2341: 2332: 2331: 2294: 2283: 2279: 2272: 2256: 2251: 2250: 2240: 2183: 2182: 2166: 2158: 2142: 2129: 2123: 2122: 2099: 2098: 2080: 2073: 2069: 2050: 2037: 2018: 2015: 2014: 1996: 1989: 1985: 1966: 1953: 1934: 1925: 1924: 1919:basis functions 1821: 1814: 1810: 1791: 1780: 1776: 1751: 1746: 1745: 1738: 1681:quadriphase PSK 1665: 1629: 1619: 1612: 1583: 1578: 1577: 1549: 1538: 1534: 1527: 1511: 1506: 1505: 1491: 1459: 1439: 1438: 1395: 1385: 1384: 1349: 1342: 1341: 1290: 1264: 1263: 1198: 1187: 1183: 1158: 1153: 1152: 1102: 1091: 1087: 1035: 1024: 1020: 995: 990: 989: 891: 880: 876: 851: 846: 845: 839: 808: 787: 767:complex numbers 715:By viewing the 704:By viewing the 662: 633:communication. 579: 442:Spread spectrum 273: 262: 251: 250: 249: 244: 233: 227: 224: 209: 197: 193: 182: 171: 165: 162: 152:Please help to 151: 135: 131: 120: 109: 103: 100: 92:help improve it 89: 80: 76: 39: 35: 28: 23: 22: 15: 12: 11: 5: 7423: 7421: 7413: 7412: 7407: 7397: 7396: 7393: 7392: 7386: 7373: 7367: 7354: 7348: 7328: 7325: 7322: 7321: 7314: 7290: 7254: 7228: 7210: 7189: 7177: 7165: 7150: 7139:(3): 151–157. 7123: 7097: 7090: 7072: 7051:(3): 1839–62. 7035: 7028: 7002: 6976: 6969: 6943: 6928: 6886: 6879: 6860: 6859: 6857: 6854: 6853: 6852: 6847: 6842: 6837: 6827: 6821: 6816: 6809: 6806: 6798: 6797: 6786: 6782: 6773: 6769: 6763: 6759: 6751: 6747: 6744: 6736: 6732: 6727: 6723: 6719: 6680: 6676: 6671: 6665: 6661: 6628: 6625: 6559: 6555: 6551: 6448: 6445: 6433: 6432: 6420: 6417: 6414: 6408: 6404: 6398: 6394: 6389: 6385: 6382: 6377: 6374: 6369: 6366: 6363: 6355: 6351: 6345: 6342: 6337: 6333: 6327: 6322: 6318: 6311: 6308: 6304: 6299: 6296: 6293: 6290: 6287: 6260: 6236: 6233: 6230: 6227: 6217: 6216: 6202: 6198: 6187: 6166: 6162: 6151: 6122: 6118: 6112: 6109: 6097: 6080: 6076: 6065: 6048: 6044: 6033: 6015: 6011: 6007: 6004: 5999: 5995: 5984: 5967: 5963: 5947: 5944: 5925: 5921: 5916: 5910: 5906: 5883: 5879: 5874: 5868: 5864: 5834: 5830: 5803: 5800: 5797: 5793: 5770: 5766: 5745: 5742: 5737: 5733: 5710: 5707: 5704: 5700: 5677: 5673: 5652: 5649: 5644: 5640: 5625: 5624: 5613: 5608: 5605: 5602: 5598: 5594: 5589: 5585: 5581: 5576: 5572: 5548: 5545: 5542: 5537: 5533: 5507: 5503: 5480: 5476: 5434: 5423: 5422: 5409: 5405: 5401: 5396: 5393: 5390: 5386: 5382: 5377: 5373: 5348: 5345: 5342: 5337: 5333: 5310: 5306: 5283: 5279: 5250: 5229: 5226: 5173: 5169: 5164: 5158: 5154: 5142: 5141: 5130: 5121: 5117: 5111: 5107: 5101: 5097: 5091: 5088: 5083: 5078: 5074: 5045: 5042: 5039: 5035: 5031: 5026: 5022: 5006: 5005: 4992: 4987: 4984: 4981: 4977: 4971: 4967: 4963: 4958: 4954: 4946: 4943: 4940: 4936: 4932: 4929: 4925: 4917: 4913: 4907: 4902: 4897: 4894: 4891: 4887: 4879: 4875: 4871: 4867: 4859: 4855: 4849: 4843: 4837: 4834: 4831: 4827: 4823: 4818: 4814: 4809: 4805: 4801: 4795: 4791: 4787: 4782: 4777: 4774: 4771: 4767: 4761: 4757: 4731: 4728: 4725: 4721: 4698: 4694: 4684:. That is, if 4671: 4668: 4665: 4661: 4638: 4634: 4613: 4593: 4590: 4587: 4576: 4575: 4564: 4559: 4555: 4551: 4544: 4540: 4536: 4532: 4524: 4520: 4514: 4509: 4505: 4479: 4475: 4448: 4444: 4421: 4417: 4396: 4368: 4365: 4352: 4348: 4344: 4307: 4303: 4298: 4292: 4288: 4267: 4250: 4243: 4222: 4219: 4216: 4181: 4145:Main article: 4142: 4139: 4137: 4134: 4126: 4125: 4114: 4106: 4097: 4088: 4082: 4078: 4075: 4070: 4066: 4059: 4056: 4030: 4027: 4001: 4000: 3989: 3984: 3980: 3974: 3971: 3966: 3961: 3957: 3929: 3918: 3917: 3906: 3902: 3896: 3893: 3888: 3885: 3878: 3874: 3870: 3864: 3860: 3857: 3854: 3849: 3845: 3819: 3815: 3810: 3804: 3800: 3779: 3743: 3737: 3733: 3727: 3724: 3719: 3716: 3712: 3708: 3705: 3700: 3696: 3674: 3668: 3664: 3658: 3655: 3650: 3643: 3639: 3632: 3628: 3625: 3620: 3616: 3604: 3603: 3584: 3580: 3574: 3570: 3564: 3561: 3559: 3555: 3551: 3547: 3546: 3543: 3539: 3532: 3528: 3522: 3518: 3512: 3508: 3503: 3500: 3496: 3492: 3489: 3487: 3483: 3479: 3475: 3474: 3471: 3464: 3459: 3455: 3451: 3446: 3441: 3437: 3431: 3428: 3426: 3424: 3421: 3420: 3417: 3414: 3411: 3403: 3398: 3392: 3388: 3384: 3381: 3374: 3370: 3364: 3361: 3358: 3354: 3347: 3344: 3339: 3335: 3331: 3326: 3321: 3317: 3309: 3305: 3301: 3296: 3292: 3286: 3282: 3278: 3275: 3271: 3264: 3261: 3257: 3252: 3249: 3247: 3244: 3239: 3235: 3231: 3223: 3219: 3214: 3210: 3209: 3195: 3194: 3183: 3178: 3174: 3170: 3166: 3161: 3157: 3153: 3145: 3141: 3136: 3130: 3126: 3122: 3117: 3113: 3109: 3106: 3102: 3098: 3095: 3092: 3087: 3083: 3059: 3056: 3053: 3041: 3040:Bit error rate 3038: 3020: 3017: 3005: 3002: 2965: 2961: 2957: 2930: 2926: 2922: 2901: 2897: 2893: 2873: 2867: 2832: 2829: 2769: 2766: 2764: 2761: 2760: 2759: 2738: 2693: 2692: 2680: 2672: 2668: 2662: 2658: 2651: 2647: 2644: 2641: 2637: 2628: 2624: 2620: 2614: 2610: 2603: 2599: 2596: 2593: 2589: 2581: 2577: 2571: 2567: 2560: 2556: 2553: 2550: 2545: 2541: 2522: 2521: 2506: 2501: 2496: 2491: 2483: 2479: 2473: 2469: 2462: 2458: 2454: 2449: 2445: 2437: 2433: 2427: 2423: 2416: 2412: 2409: 2406: 2403: 2401: 2399: 2394: 2389: 2383: 2379: 2375: 2372: 2368: 2363: 2360: 2357: 2354: 2352: 2348: 2344: 2340: 2339: 2322: 2321: 2309: 2301: 2297: 2290: 2286: 2282: 2275: 2271: 2268: 2263: 2259: 2239: 2236: 2204: 2203: 2192: 2187: 2178: 2173: 2169: 2162: 2159: 2154: 2149: 2145: 2138: 2135: 2134: 2132: 2113: 2112: 2096: 2092: 2087: 2083: 2079: 2076: 2072: 2068: 2065: 2057: 2053: 2049: 2043: 2040: 2038: 2036: 2033: 2030: 2025: 2021: 2017: 2016: 2012: 2008: 2003: 1999: 1995: 1992: 1988: 1984: 1981: 1973: 1969: 1965: 1959: 1956: 1954: 1952: 1949: 1946: 1941: 1937: 1933: 1932: 1912: 1911: 1900: 1897: 1894: 1891: 1888: 1885: 1882: 1879: 1876: 1872: 1868: 1862: 1859: 1854: 1851: 1848: 1845: 1842: 1839: 1836: 1833: 1828: 1824: 1820: 1817: 1813: 1809: 1806: 1798: 1794: 1787: 1783: 1779: 1772: 1769: 1766: 1763: 1758: 1754: 1737: 1736:Implementation 1734: 1693:bit error rate 1683:, 4-PSK, or 4- 1664: 1661: 1657: 1656: 1644: 1636: 1632: 1626: 1622: 1615: 1611: 1608: 1603: 1600: 1595: 1590: 1586: 1564: 1556: 1552: 1545: 1541: 1537: 1530: 1526: 1523: 1518: 1514: 1495:bit error rate 1490: 1489:Bit error rate 1487: 1474: 1471: 1466: 1462: 1458: 1455: 1452: 1449: 1446: 1418: 1415: 1412: 1409: 1402: 1398: 1392: 1372: 1369: 1366: 1363: 1356: 1352: 1338: 1337: 1326: 1323: 1320: 1317: 1314: 1311: 1308: 1305: 1297: 1293: 1289: 1283: 1280: 1277: 1274: 1271: 1258:basis function 1247: 1246: 1245:for binary "1" 1234: 1231: 1228: 1225: 1222: 1219: 1216: 1213: 1205: 1201: 1194: 1190: 1186: 1179: 1176: 1173: 1170: 1165: 1161: 1150: 1149:for binary "0" 1138: 1135: 1132: 1129: 1126: 1123: 1120: 1117: 1109: 1105: 1098: 1094: 1090: 1083: 1080: 1077: 1074: 1071: 1068: 1065: 1062: 1059: 1056: 1053: 1050: 1042: 1038: 1031: 1027: 1023: 1016: 1013: 1010: 1007: 1002: 998: 979: 978: 967: 964: 961: 958: 955: 951: 948: 945: 942: 939: 936: 933: 930: 927: 924: 921: 918: 915: 912: 909: 906: 898: 894: 887: 883: 879: 872: 869: 866: 863: 858: 854: 838: 837:Implementation 835: 786: 783: 731: 730: 713: 690: 689: 686: 680: 661: 658: 606:of a constant 581: 580: 578: 577: 570: 563: 555: 552: 551: 550: 549: 544: 539: 534: 529: 524: 519: 514: 509: 504: 499: 494: 489: 484: 476: 475: 471: 470: 469: 468: 463: 458: 453: 445: 444: 438: 437: 436: 435: 430: 422: 421: 415: 414: 413: 412: 407: 402: 397: 392: 387: 382: 377: 372: 367: 362: 357: 352: 344: 343: 337: 336: 335: 334: 329: 324: 319: 314: 309: 301: 300: 294: 293: 285: 284: 270:Pre-shared key 264: 263: 246: 245: 200: 198: 191: 184: 183: 138: 136: 129: 122: 121: 83: 81: 74: 69: 43: 42: 40: 33: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 7422: 7411: 7408: 7406: 7403: 7402: 7400: 7389: 7387:0-471-62947-2 7383: 7379: 7374: 7370: 7368:0-13-081223-4 7364: 7360: 7355: 7351: 7349:0-07-113814-5 7345: 7341: 7340: 7334: 7333: 7332: 7326: 7317: 7315:0-201-10709-0 7311: 7307: 7303: 7302:Blahut, R. E. 7297: 7295: 7291: 7275: 7271: 7264: 7258: 7255: 7242: 7238: 7232: 7229: 7224: 7220: 7214: 7211: 7206: 7199: 7193: 7190: 7186: 7181: 7178: 7174: 7169: 7166: 7162: 7157: 7155: 7151: 7146: 7142: 7138: 7134: 7127: 7124: 7111: 7107: 7101: 7098: 7093: 7091:0-471-17869-1 7087: 7083: 7076: 7073: 7068: 7064: 7059: 7054: 7050: 7046: 7039: 7036: 7031: 7025: 7021: 7017: 7013: 7006: 7003: 6998: 6994: 6987: 6980: 6977: 6972: 6970:0-7803-6521-6 6966: 6962: 6958: 6954: 6947: 6944: 6939: 6935: 6931: 6929:0-7803-9414-3 6925: 6921: 6917: 6913: 6909: 6901: 6897: 6890: 6887: 6882: 6880:0-13-121929-4 6876: 6872: 6865: 6862: 6855: 6851: 6848: 6846: 6843: 6841: 6838: 6835: 6831: 6828: 6825: 6822: 6820: 6817: 6815: 6812: 6811: 6807: 6805: 6803: 6784: 6780: 6771: 6767: 6761: 6757: 6749: 6745: 6742: 6734: 6730: 6725: 6721: 6717: 6703: 6702: 6701: 6698: 6696: 6678: 6674: 6669: 6663: 6659: 6650: 6646: 6642: 6633: 6626: 6624: 6622: 6617: 6615: 6611: 6605: 6603: 6596: 6589: 6585: 6584:IEEE 802.15.4 6581: 6557: 6553: 6549: 6541: 6537: 6535: 6531: 6527: 6523: 6522:ISO/IEC 14443 6519: 6514: 6512: 6504: 6492: 6488: 6472: 6465: 6461: 6456: 6454: 6446: 6444: 6442: 6438: 6418: 6415: 6412: 6406: 6402: 6396: 6392: 6387: 6383: 6380: 6375: 6372: 6367: 6364: 6361: 6353: 6349: 6343: 6340: 6335: 6331: 6320: 6316: 6309: 6306: 6302: 6297: 6291: 6285: 6278: 6277: 6276: 6274: 6258: 6250: 6231: 6225: 6200: 6196: 6188: 6186: 6182: 6179:, 6164: 6160: 6152: 6149: 6145: 6141: 6138: 6120: 6116: 6110: 6107: 6098: 6096: 6093:, 6078: 6074: 6066: 6064: 6061:, 6046: 6042: 6034: 6031: 6013: 6009: 6005: 6002: 5997: 5993: 5985: 5983: 5965: 5961: 5953: 5952: 5951: 5945: 5943: 5941: 5923: 5919: 5914: 5908: 5904: 5881: 5877: 5872: 5866: 5862: 5852: 5848: 5832: 5828: 5819: 5801: 5798: 5795: 5791: 5768: 5764: 5743: 5740: 5735: 5731: 5708: 5705: 5702: 5698: 5675: 5671: 5650: 5647: 5642: 5638: 5628: 5611: 5606: 5603: 5600: 5596: 5592: 5587: 5583: 5579: 5574: 5570: 5562: 5561: 5560: 5546: 5543: 5540: 5535: 5531: 5521: 5505: 5501: 5478: 5474: 5460: 5456: 5454: 5450: 5432: 5407: 5403: 5399: 5394: 5391: 5388: 5384: 5380: 5375: 5371: 5362: 5361: 5360: 5343: 5335: 5331: 5308: 5304: 5281: 5277: 5248: 5234: 5227: 5225: 5221: 5219: 5218:optical field 5215: 5211: 5207: 5203: 5199: 5195: 5190: 5187: 5171: 5167: 5162: 5156: 5152: 5128: 5119: 5115: 5109: 5105: 5099: 5095: 5089: 5086: 5081: 5076: 5072: 5064: 5063: 5062: 5059: 5043: 5040: 5037: 5033: 5029: 5024: 5020: 5011: 4990: 4985: 4982: 4979: 4975: 4969: 4965: 4961: 4956: 4952: 4944: 4941: 4938: 4934: 4930: 4927: 4923: 4915: 4911: 4905: 4900: 4895: 4892: 4889: 4885: 4877: 4873: 4869: 4865: 4857: 4853: 4847: 4841: 4835: 4832: 4829: 4825: 4821: 4816: 4812: 4807: 4803: 4799: 4793: 4789: 4785: 4780: 4775: 4772: 4769: 4765: 4759: 4755: 4747: 4746: 4745: 4729: 4726: 4723: 4719: 4696: 4692: 4669: 4666: 4663: 4659: 4636: 4632: 4611: 4591: 4588: 4585: 4562: 4557: 4553: 4549: 4542: 4538: 4534: 4530: 4522: 4518: 4512: 4507: 4503: 4495: 4494: 4493: 4477: 4473: 4464: 4446: 4442: 4419: 4415: 4394: 4385: 4383: 4373: 4366: 4364: 4350: 4346: 4342: 4334: 4329: 4327: 4323: 4305: 4301: 4296: 4290: 4286: 4265: 4253: 4246: 4238: 4234: 4220: 4217: 4214: 4206: 4201: 4199: 4195: 4179: 4169: 4165: 4163: 4159: 4155: 4148: 4140: 4135: 4133: 4131: 4104: 4095: 4080: 4076: 4073: 4068: 4064: 4057: 4054: 4047: 4046: 4045: 4043: 4039: 4035: 4028: 4026: 4024: 4019: 4017: 4012: 4010: 4006: 3987: 3982: 3978: 3972: 3969: 3964: 3959: 3955: 3947: 3946: 3945: 3943: 3927: 3904: 3900: 3894: 3891: 3886: 3883: 3876: 3872: 3868: 3862: 3858: 3855: 3852: 3847: 3843: 3835: 3834: 3833: 3817: 3813: 3808: 3802: 3798: 3777: 3764: 3760: 3758: 3741: 3735: 3731: 3725: 3722: 3717: 3714: 3710: 3706: 3703: 3698: 3694: 3672: 3666: 3662: 3656: 3653: 3648: 3641: 3637: 3630: 3626: 3623: 3618: 3614: 3582: 3578: 3572: 3568: 3562: 3560: 3553: 3549: 3541: 3537: 3530: 3526: 3520: 3516: 3510: 3506: 3501: 3498: 3494: 3490: 3488: 3481: 3477: 3469: 3462: 3457: 3453: 3449: 3444: 3439: 3435: 3429: 3427: 3422: 3415: 3412: 3409: 3401: 3396: 3390: 3386: 3382: 3379: 3372: 3368: 3362: 3359: 3356: 3352: 3345: 3342: 3337: 3333: 3329: 3319: 3315: 3307: 3303: 3299: 3294: 3290: 3284: 3280: 3276: 3273: 3269: 3262: 3259: 3255: 3250: 3248: 3242: 3237: 3233: 3229: 3221: 3217: 3212: 3200: 3199: 3198: 3181: 3176: 3172: 3168: 3164: 3159: 3155: 3151: 3143: 3139: 3134: 3128: 3124: 3120: 3115: 3111: 3107: 3104: 3100: 3096: 3093: 3090: 3085: 3081: 3073: 3072: 3071: 3057: 3054: 3051: 3039: 3037: 3035: 3025: 3018: 3016: 3014: 3010: 3003: 2996: 2992: 2990: 2984: 2982: 2979: 2963: 2959: 2955: 2946: 2942: 2928: 2924: 2920: 2899: 2895: 2891: 2878: 2871: 2868: 2866: 2864: 2860: 2855: 2853: 2847: 2845: 2841: 2839: 2830: 2823: 2819: 2815: 2811: 2809: 2800: 2796: 2794: 2790: 2786: 2782: 2774: 2767: 2762: 2739: 2718: 2717: 2716: 2704: 2700: 2697: 2678: 2670: 2666: 2660: 2656: 2649: 2645: 2642: 2639: 2635: 2626: 2622: 2618: 2612: 2608: 2601: 2597: 2594: 2591: 2587: 2579: 2575: 2569: 2565: 2558: 2554: 2551: 2548: 2543: 2539: 2531: 2530: 2529: 2527: 2504: 2499: 2494: 2489: 2481: 2477: 2471: 2467: 2460: 2456: 2452: 2447: 2443: 2435: 2431: 2425: 2421: 2414: 2410: 2407: 2404: 2402: 2392: 2387: 2381: 2377: 2373: 2370: 2366: 2361: 2358: 2355: 2353: 2346: 2342: 2330: 2329: 2328: 2325: 2307: 2299: 2295: 2288: 2284: 2280: 2273: 2269: 2266: 2261: 2257: 2249: 2248: 2247: 2244: 2237: 2231: 2224: 2218: 2214: 2211: 2207: 2190: 2185: 2176: 2171: 2167: 2160: 2152: 2147: 2143: 2136: 2130: 2121: 2120: 2119: 2116: 2094: 2090: 2085: 2081: 2077: 2074: 2070: 2066: 2063: 2055: 2051: 2047: 2041: 2039: 2031: 2023: 2019: 2010: 2006: 2001: 1997: 1993: 1990: 1986: 1982: 1979: 1971: 1967: 1963: 1957: 1955: 1947: 1939: 1935: 1923: 1922: 1921: 1920: 1915: 1898: 1895: 1892: 1889: 1886: 1883: 1880: 1877: 1874: 1870: 1866: 1860: 1857: 1849: 1846: 1843: 1840: 1834: 1831: 1826: 1822: 1818: 1815: 1811: 1807: 1804: 1796: 1792: 1785: 1781: 1777: 1770: 1764: 1756: 1752: 1744: 1743: 1742: 1735: 1733: 1731: 1726: 1724: 1719: 1714: 1712: 1708: 1704: 1701: 1696: 1694: 1690: 1686: 1682: 1674: 1669: 1662: 1660: 1642: 1634: 1630: 1624: 1620: 1613: 1609: 1606: 1601: 1598: 1593: 1588: 1584: 1562: 1554: 1550: 1543: 1539: 1535: 1528: 1524: 1521: 1516: 1512: 1504: 1503: 1502: 1500: 1496: 1488: 1486: 1469: 1464: 1460: 1456: 1453: 1447: 1444: 1435: 1430: 1413: 1407: 1400: 1396: 1390: 1367: 1361: 1354: 1350: 1321: 1318: 1315: 1312: 1306: 1303: 1295: 1291: 1287: 1281: 1275: 1269: 1262: 1261: 1260: 1259: 1254: 1252: 1229: 1226: 1223: 1220: 1214: 1211: 1203: 1199: 1192: 1188: 1184: 1177: 1171: 1163: 1159: 1151: 1133: 1130: 1127: 1124: 1118: 1115: 1107: 1103: 1096: 1092: 1088: 1081: 1078: 1072: 1069: 1066: 1063: 1060: 1057: 1051: 1048: 1040: 1036: 1029: 1025: 1021: 1014: 1008: 1000: 996: 988: 987: 986: 984: 965: 962: 959: 956: 953: 949: 940: 937: 934: 928: 925: 922: 919: 916: 913: 907: 904: 896: 892: 885: 881: 877: 870: 864: 856: 852: 844: 843: 842: 836: 834: 832: 827: 825: 821: 817: 812: 806: 797: 793: 789: 784: 782: 780: 776: 772: 768: 764: 760: 756: 751: 748: 744: 740: 739:complex plane 736: 728: 724: 723: 718: 714: 711: 707: 703: 702: 701: 699: 695: 687: 684: 681: 678: 675: 674: 673: 671: 667: 659: 657: 655: 649: 647: 643: 639: 638:binary digits 634: 632: 628: 624: 623:wireless LANs 620: 616: 612: 609: 605: 601: 597: 593: 589: 585: 576: 571: 569: 564: 562: 557: 556: 554: 553: 548: 545: 543: 540: 538: 535: 533: 530: 528: 525: 523: 520: 518: 515: 513: 510: 508: 505: 503: 500: 498: 495: 493: 490: 488: 485: 483: 480: 479: 478: 477: 472: 467: 464: 462: 459: 457: 454: 452: 449: 448: 447: 446: 443: 439: 434: 431: 429: 426: 425: 424: 423: 420: 416: 411: 408: 406: 403: 401: 398: 396: 393: 391: 388: 386: 383: 381: 378: 376: 373: 371: 368: 366: 363: 361: 358: 356: 353: 351: 348: 347: 346: 345: 342: 338: 333: 330: 328: 325: 323: 320: 318: 315: 313: 310: 308: 305: 304: 303: 302: 299: 295: 291: 287: 286: 283: 280: 276: 271: 260: 257: 242: 239: 231: 221: 217: 213: 207: 206: 201:This article 199: 190: 189: 180: 177: 169: 159: 155: 149: 148: 142: 137: 128: 127: 118: 115: 107: 97: 93: 87: 84:This article 82: 73: 72: 67: 65: 58: 57: 52: 51: 46: 41: 32: 31: 19: 7377: 7358: 7338: 7330: 7305: 7283:December 20, 7281:. Retrieved 7274:the original 7269: 7257: 7247:September 8, 7245:. Retrieved 7241:the original 7231: 7222: 7213: 7204: 7192: 7180: 7168: 7136: 7132: 7126: 7114:. Retrieved 7110:the original 7100: 7081: 7075: 7048: 7044: 7038: 7011: 7005: 6996: 6992: 6979: 6952: 6946: 6911: 6900:10150/604890 6889: 6870: 6864: 6799: 6699: 6638: 6618: 6606: 6604:with OQPSK. 6538: 6515: 6460:wireless LAN 6457: 6450: 6447:Applications 6434: 6218: 6184: 6063:bit duration 6029: 5949: 5853: 5849: 5817: 5629: 5626: 5522: 5465: 5424: 5239: 5222: 5191: 5188: 5143: 5060: 5007: 4577: 4386: 4381: 4378: 4367:Demodulation 4330: 4325: 4257: 4248: 4241: 4204: 4202: 4197: 4170: 4166: 4161: 4160:rather than 4157: 4150: 4127: 4037: 4032: 4020: 4013: 4005:Lee distance 4002: 3919: 3769: 3605: 3196: 3043: 3030: 3012: 3011:(DPQPSK) or 3008: 3007: 2985: 2947: 2943: 2883: 2869: 2856: 2848: 2843: 2840:-offset QPSK 2836: 2834: 2816: 2812: 2805: 2792: 2788: 2784: 2780: 2779: 2710: 2698: 2694: 2523: 2326: 2323: 2245: 2241: 2212: 2208: 2205: 2117: 2114: 1916: 1913: 1739: 1727: 1715: 1710: 1706: 1699: 1697: 1680: 1678: 1658: 1492: 1431: 1339: 1255: 1250: 1248: 980: 840: 833:modulation. 828: 813: 801: 788: 753:In PSK, the 752: 732: 722:differential 721: 716: 694:carrier wave 691: 663: 660:Introduction 653: 650: 635: 611:carrier wave 591: 587: 586: 584: 547:Multiplexing 487:Demodulation 389: 252: 234: 225: 202: 172: 166:October 2022 163: 144: 110: 104:October 2022 101: 85: 61: 54: 48: 47:Please help 44: 6181:probability 5946:Definitions 5723:differ and 5630:Therefore, 4172:one of the 4164:the phase. 4023:union bound 3942:Gray coding 2999:"blue" one. 2826:components. 2707:boundaries. 1723:electronics 1689:Gray coding 1673:Gray coding 983:binary data 820:Costas loop 805:demodulator 710:demodulator 696:(usually a 646:demodulator 492:Line coding 158:introducing 7399:Categories 7327:References 7223:Planet Fox 7058:1908.09501 6824:Modulation 6534:ExpressPay 6462:standard, 5455:addition. 5447:indicates 5214:photodiode 4194:comparator 282:modulation 228:March 2024 212:improve it 141:references 50:improve it 7380:. Wiley. 7270:Black Box 6746:π 6731:⁡ 6718:≃ 6550:π 6540:Bluetooth 6416:≥ 6384:⁡ 6336:− 6326:∞ 6317:∫ 6310:π 6185:bit-error 5799:− 5706:− 5604:− 5593:⊕ 5544:± 5433:⊕ 5400:⊕ 5392:− 5100:− 5041:− 5034:ϕ 5030:− 5021:ϕ 4991:∗ 4983:− 4942:− 4935:φ 4928:− 4901:∗ 4893:− 4874:φ 4833:− 4826:φ 4822:− 4813:φ 4781:∗ 4773:− 4727:− 4667:− 4589:− 4539:ϕ 4443:ϕ 4407:timeslot 4343:π 4105:⋅ 4074:⁡ 4055:ρ 3965:≈ 3892:π 3887:⁡ 3873:γ 3853:≈ 3790:and high 3704:∼ 3624:∼ 3550:γ 3507:⁡ 3499:− 3478:θ 3387:θ 3383:⁡ 3369:γ 3360:− 3338:− 3325:∞ 3316:∫ 3304:θ 3300:⁡ 3281:γ 3274:− 3263:π 3234:θ 3218:θ 3173:θ 3156:θ 3140:θ 3121:π 3108:π 3105:− 3101:∫ 3097:− 2983:systems. 2956:π 2921:π 2892:π 2646:⁡ 2598:⁡ 2549:≈ 2448:− 2374:− 2362:− 2161:± 2137:± 2078:π 2067:⁡ 2020:ϕ 1994:π 1983:⁡ 1936:ϕ 1858:π 1847:− 1819:π 1808:⁡ 1703:bandwidth 1610:⁡ 1457:π 1448:⁡ 1408:ϕ 1391:− 1362:ϕ 1316:π 1307:⁡ 1270:ϕ 1224:π 1215:⁡ 1128:π 1119:⁡ 1082:− 1073:π 1061:π 1052:⁡ 938:− 929:π 917:π 908:⁡ 747:imaginary 725:schemes, 670:digitally 631:Bluetooth 608:frequency 216:verifying 56:talk page 7304:(1988). 7116:July 15, 6938:11020777 6834:analogue 6808:See also 6614:Broadcom 5818:inverted 5453:modulo-2 5204:, and a 5186:values. 2763:Variants 2713:11000110 781:of two. 698:sinusoid 474:See also 279:Passband 7225:. 2014. 6542:2 uses 5240:At the 4492:. 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