`
`Understanding Modern Digital Modulation Techniques
`
`Electronic Design
`Lou Frenzel
`Louis E. Frenzel
`Mon, 20120123 12:00
`
`Fundamental to all wireless communications is modulation, the process of impressing the data to be
`transmitted on the radio carrier. Most wireless transmissions today are digital, and with the limited
`spectrum available, the type of modulation is more critical than it has ever been.
`
`The main goal of modulation today is to squeeze as much data into the least amount of spectrum possible.
`That objective, known as spectral efficiency, measures how quickly data can be transmitted in an assigned
`bandwidth. The unit of measurement is bits per second per Hz (b/s/Hz). Multiple techniques have emerged
`to achieve and improve spectral efficiency.
`
`Table of Contents
`
`1. Amplitude Shift Keying (ASK) and Frequency Shift Keying (FSK)
`2. Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK)
`3. Data Rate And Baud Rate
`4. Multiple Phase Shift Keying (MPSK)
`5. Quadrature Amplitude Modulation (QAM)
`6. Amplitude Phase Shift Keying (APSK)
`7. Orthogonal Frequency Division Multiplexing
`8. Determining Spectral Efficiency
`9. Other Factors Affecting Spectral Efficiency
`10. Implementing Modulation And Demodulation
`11. The Pursuit Of Greater Spectral Efficiency
`12. Acknowledgment
`13. References
`
`Amplitude Shift Keying (ASK) and Frequency Shift Keying (FSK)
`There are three basic ways to modulate a sine wave radio carrier: modifying the amplitude, frequency, or
`phase. More sophisticated methods combine two or more of these variations to improve spectral efficiency.
`These basic modulation forms are still used today with digital signals.
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`1. Three basic digital modulation formats are still very popular with lowdatarate shortrange wireless applications: amplitude shift
`keying (a), onoff keying (b), and frequency shift keying (c). These waveforms are coherent as the binary state change occurs at carrier
`zero crossing points.
`
`Figure 1 shows a basic serial digital signal of binary zeros and ones to be transmitted and the corresponding
`AM and FM signals resulting from modulation. There are two types of AM signals: onoff keying (OOK) and
`amplitude shift keying (ASK). In Figure 1a, the carrier amplitude is shifted between two amplitude levels to
`produce ASK. In Figure 1b, the binary signal turns the carrier off and on to create OOK.
`
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`
`AM produces sidebands above and below the carrier equal to the highest frequency content of the
`modulating signal. The bandwidth required is two times the highest frequency content including any
`harmonics for binary pulse modulating signals.
`
`Frequency shift keying (FSK) shifts the carrier between two different frequencies called the mark and space
`frequencies, or fm and fs(Fig. 1c). FM produces multiple sideband frequencies above and below the carrier
`frequency. The bandwidth produced is a function of the highest modulating frequency including harmonics
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`and the modulation index, which is:
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`m = Δf(T)
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`Δf is the frequency deviation or shift between the mark and space frequencies, or:
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`Δf = fs – fm
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`T is the bit time interval of the data or the reciprocal of the data rate (1/bit/s).
`
`Smaller values of m produce fewer sidebands. A popular version of FSK called minimum shift keying (MSK)
`specifies m = 0.5. Smaller values are also used such as m = 0.3.
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`Here are two ways to further improve the spectral efficiency for both ASK and FSK. First, select data rates,
`carrier frequencies, and shift frequencies so there are no discontinuities in the sine carrier when changing
`from one binary state to another. These discontinuities produce glitches that increase the harmonic content
`and the bandwidth.
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`The idea is to synchronize the stop and start times of the binary data with when the sine carrier is
`transitioning in amplitude or frequency at the zero crossing points. This is called continuous phase or
`coherent operation. Both coherent ASK/OOK and coherent FSK have fewer harmonics and a narrower
`bandwidth than noncoherent signals.
`
`A second technique is to filter the binary data prior to modulation. This rounds the signal off, lengthening
`the rise and fall times and reducing the harmonic content. Special Gaussian and raised cosine low pass filters
`are used for this purpose. GSM cell phones widely use a popular combination, Gaussian filtered MSK
`(GMSK), which allows a data rate of 270 kbits/s in a 200kHz channel.
`
`Binary Phase Shift Keying (BPSK) And Quadrature Phase Shift Keying (QPSK)
`A very popular digital modulation scheme, binary phase shift keying (BPSK), shifts the carrier sine wave
`180° for each change in binary state (Fig. 2). BPSK is coherent as the phase transitions occur at the zero
`crossing points. The proper demodulation of BPSK requires the signal to be compared to a sine carrier of
`the same phase. This involves carrier recovery and other complex circuitry.
`
`2. In binary phase shift keying, note how a binary 0 is 0° while a binary 1 is 180°. The phase changes when the binary state switches so
`the signal is coherent.
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`A simpler version is differential BPSK or DPSK, where the received bit phase is compared to the phase of
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`the previous bit signal. BPSK is very spectrally efficient in that you can transmit at a data rate equal to the
`bandwidth or 1 bit/Hz.
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`In a popular variation of BPSK, quadrature PSK (QPSK), the modulator produces two sine carriers 90°
`apart. The binary data modulates each phase, producing four unique sine signals shifted by 45° from one
`another. The two phases are added together to produce the final signal. Each unique pair of bits generates a
`carrier with a different phase (Table 1).
`
`Figure 3a illustrates QPSK with a phasor diagram where the phasor represents the carrier sine amplitude
`peak and its position indicates the phase. A constellation diagram in Figure 3b shows the same information.
`QPSK is very spectrally efficient since each carrier phase represents two bits of data. The spectral efficiency
`is 2 bits/Hz, meaning twice the data rate can be achieved in the same bandwidth as BPSK.
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`3. Modulation can be represented without time domain waveforms. For example, QPSK can be represented with a phasor diagram (a)
`or a constellation diagram (b), both of which indicate phase and amplitude magnitudes.
`
`Data Rate And Baud Rate
`The maximum theoretical data rate or channel capacity (C) in bits/s is a function of the channel bandwidth
`(B) channel in Hz and the signaltonoise ratio (SNR):
`
`C = B log2 (1 + SNR)
`
`This is called the ShannonHartley law. The maximum data rate is directly proportional to the bandwidth
`and logarithmically proportional the SNR. Noise greatly diminishes the data rate for a given bit error rate
`(BER).
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`Another key factor is the baud rate, or the number of modulation symbols transmitted per second. The term
`symbol in modulation refers to one specific state of a sine carrier signal. It can be an amplitude, a frequency,
`a phase, or some combination of them. Basic binary transmission uses one bit per symbol.
`
`In ASK, a binary 0 is one amplitude and a binary 1 is another amplitude. In FSK, a binary 0 is one carrier
`frequency and a binary 1 is another frequency. BPSK uses a 0° shift for a binary 0 and a 180° shift for a
`binary 1. In each of these cases there is one bit per symbol.
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`Data rate in bits/s is calculated as the reciprocal of the bit time (tb):
`
`bits/s = 1/tb
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`With one symbol per bit, the baud rate is the same as the bit rate. However, if you transmit more bits per
`symbol, the baud rate is slower than the bit rate by a factor equal to the number of bits per symbol. For
`example, if 2 bits per symbol are transmitted, the baud rate is the bit rate divided by 2. For instance, with
`QPSK a 70 Mb/s data stream is transmitted at a baud rate of 35 symbols/second.
`
`Multiple Phase Shift Keying (MPSK)
`QPSK produces two bits per symbol, making it very spectrally efficient. QPSK can be referred to as 4PSK
`because there are four amplitudephase combinations. By using smaller phase shifts, more bits can be
`transmitted per symbol. Some popular variations are 8PSK and 16PSK.
`
`8PSK uses eight symbols with constant carrier amplitude 45° shifts between them, enabling three bits to be
`transmitted for each symbol. 16PSK uses 22.5° shifts of constant amplitude carrier signals. This
`arrangement results in a transmission of 4 bits per symbol.
`
`While Multiple Phase Shift Keying (MPSK) is much more spectrally efficient, the greater the number of
`smaller phase shifts, the more difficult the signal is to demodulate in the presence of noise. The benefit of
`MPSK is that the constant carrier amplitude means that more efficient nonlinear power amplification can
`be used.
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`Quadrature Amplitude Modulation (QAM)
`The creation of symbols that are some combination of amplitude and phase can carry the concept of
`transmitting more bits per symbol further. This method is called quadrature amplitude modulation (QAM).
`For example, 8QAM uses four carrier phases plus two amplitude levels to transmit 3 bits per symbol. Other
`popular variations are 16QAM, 64QAM, and 256QAM, which transmit 4, 6, and 8 bits per symbol
`respectively (Fig. 4).
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`4. 16QAM uses a mix of amplitudes and phases to achieve 4 bits/Hz. In this example, there are three amplitudes and 12 phase shifts.
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`While QAM is enormously efficient of spectrum, it is more difficult to demodulate in the presence of noise,
`which is mostly random amplitude variations. Linear power amplification is also required. QAM is very
`widely used in cable TV, WiFi wireless localarea networks (LANs), satellites, and cellular telephone
`systems to produce maximum data rate in limited bandwidths.
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`Amplitude Phase Shift Keying (APSK)
`Amplitude phase shift keying (APSK), a variation of both MPSK and QAM, was created in response to the
`need for an improved QAM. Higher levels of QAM such as 16QAM and above have many different amplitude
`levels as well as phase shifts. These amplitude levels are more susceptible to noise.
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`Furthermore, these multiple levels require linear power amplifiers (PAs) that are less efficient than
`nonlinear (e.g., class C). The fewer the number of amplitude levels or the smaller the difference between the
`amplitude levels, the greater the chance to operate in the nonlinear region of the PA to boost power level.
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`APSK uses fewer amplitude levels. It essentially arranges the symbols into two or more concentric rings with
`a constant phase offset θ. For example, 16APSK uses a doublering PSK format (Fig. 5). This is called 412
`16APSK with four symbols in the center ring and 12 in the outer ring.
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`5. 16APSK uses two amplitude levels, A1 and A2, plus 16 different phase positions with an offset of θ. This technique is widely used in
`satellites.
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`Two close amplitude levels allow the amplifier to operate closer to the nonlinear region, improving
`efficiency as well as power output. APSK is used primarily in satellites since it is a good fit with the popular
`traveling wave tube (TWT) PAs.
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`Orthogonal Frequency Division Multiplexing (OFDM)
`Orthogonal frequency division multiplexing (OFDM) combines modulation and multiplexing techniques to
`improve spectral efficiency. A transmission channel is divided into many smaller subchannels or subcarriers.
`The subcarrier frequencies and spacings are chosen so they’re orthogonal to one another. Their spectra
`won’t interfere with one another, then, so no guard bands are required (Fig. 6).
`
`6. In the OFDM signal for the IEEE 802.11n WiFi standard, 56 subcarriers are spaced 312.5 kHz in a 20MHz channel. Data rates to
`300 Mbits/s can be achieved with 64QAM.
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`The serial digital data to be transmitted is subdivided into parallel slower data rate channels. These lower
`data rate signals are then used to modulate each subcarrier. The most common forms of modulation are
`BPSK, QPSK, and several levels of QAM. BPSK, QPSK, 16QAM, and 64QAM are defined with 802.11n. Data
`rates up to about 300 Mbits/s are possible with 64QAM.
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`The complex modulation process is only produced by digital signal processing (DSP) techniques. An inverse
`fast Fourier transform (IFFT) generates the signal to be transmitted. An FFT process recovers the signal at
`the receiver.
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`OFDM is very spectrally efficient. That efficiency level depends on the number of subcarriers and the type of
`modulation, but it can be as high as 30 bits/s/Hz. Because of the wide bandwidth it usually occupies and the
`large number of subcarriers, it also is less prone to signal loss due to fading, multipath reflections, and
`similar effects common in UHF and microwave radio signal propagation.
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`Currently, OFDM is the most popular form of digital modulation. It is used in WiFi LANs, WiMAX
`broadband wireless, Long Term Evolution (LTE) 4G cellular systems, digital subscriber line (DSL) systems,
`and in most powerline communications (PLC) applications. For more, see “Orthogonal FrequencyDivision
`Multiplexing (OFDM): FAQ Tutorial.”
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`Determining Spectral Efficiency
`Again, spectral efficiency is a measure of how quickly data can be transmitted in an assigned bandwidth, and
`the unit of measurement is bits/s/Hz (b/s/Hz). Each type of modulation has a maximum theoretical spectral
`efficiency measure (Table 2).
`
`SNR is another important factor that influences spectral efficiency. It also can be expressed as the carrier to
`noise power ratio (CNR). The measure is the BER for a given CNR value. BER is the percentage of errors
`that occur in a given number of bits transmitted. As the noise becomes larger compared to the signal level,
`more errors occur.
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`Some modulation methods are more immune to noise than others. Amplitude modulation methods like
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`ASK/OOK and QAM are far more susceptible to noise so they have a higher BER for a given modulation.
`Phase and frequency modulation (BPSK, FSK, etc.) fare better in a noisy environment so they require less
`signal power for a given noise level (Fig. 7).
`
`7. This is a comparison of several popular modulation methods and their spectral efficiency expressed in terms of BER versus CNR.
`Note that for a given BER, a greater CNR is needed for the higher QAM levels.
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`Other Factors Affecting Spectral Efficiency
`While modulation plays a key role in the spectral efficiency you can expect, other aspects in wireless design
`influence it as well. For example, the use of forward error correction (FEC) techniques can greatly improve
`the BER. Such coding methods add extra bits so errors can be detected and corrected.
`
`These extra coding bits add overhead to the signal, reducing the net bit rate of the data, but that’s usually an
`acceptable tradeoff for the singledigit dB improvement in CNR. Such coding gain is common to almost all
`wireless systems today.
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`Digital compression is another useful technique. The digital data to be sent is subjected to a compression
`algorithm that greatly reduces the amount of information. This allows digital signals to be reduced in
`content so they can be transmitted as shorter, slower data streams.
`
`For example, voice signals are compressed for digital cell phones and voice over Internet protocol (VoIP)
`phones. Music is compressed in MP3 or AAC files for faster transmission and less storage. Video is
`compressed so highresolution images can be transmitted faster or in bandwidthlimited systems.
`
`Another factor affecting spectral efficiency is the use of multipleinput multipleoutput (MIMO), which is
`the use of multiple antennas and transceivers to transmit two or more bit streams. A single highrate stream
`is divided into two parallel streams and transmitted in the same bandwidth simultaneously.
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`By coding the streams and their unique path characteristics, the receiver can identify and demodulate each
`stream and reassemble it into the original stream. MIMO, therefore, improves data rate, noise
`performance, and spectral efficiency. Newer wireless LAN (WLAN) standards like 802.11n and 802.11ac/ad
`and cellular standards like LTE and WiMAX use MIMO. For more, see “How MIMO Works.”
`
`Implementing Modulation And Demodulation
`In the past, unique circuits implemented modulation and demodulation. Today, most modern radios are
`softwaredefined radios (SDR) where functions like modulation and demodulation are handled in software.
`DSP algorithms do the job previously assigned to modulator and demodulator circuits.
`
`The modulation process begins with the data to be transmitted being fed to a DSP device that generates two
`digital outputs, which are needed to define the amplitude and phase information required at the receiver to
`recover the data. The DSP produces two baseband streams that are sent to digitaltoanalog converters
`(DACs) that produce the analog equivalents.
`
`These modulation signals feed the mixers along with the carrier. There is a 90° shift between the carrier
`signals to the mixers. The resulting quadrature output signals from the mixers are summed to produce the
`signal to be transmitted. If the carrier signal is at the final transmission frequency, the composite signal is
`ready to be amplified and sent to the antenna. This is called direct conversion. Alternately, the carrier signal
`may be at a lower intermediate frequency (IF). The IF signal is upconverted to the final carrier frequency by
`another mixer before being applied to the transmitter PA.
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`At the receiver, the signal from the antenna is amplified and downconverted to IF or directly to the original
`baseband signals. The amplified signal from the antenna is applied to mixers along with the carrier signal.
`Again, there is a 90° shift between the carrier signals applied to the mixers.
`
`The mixers produce the original baseband analog signals, which are then digitized in a pair of analogto
`digital converters (ADCs) and sent to the DSP circuitry where demodulation algorithms recover the original
`digital data.
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`There are three important points to consider. First, the modulation and demodulation processes use two
`signals in quadrature with one another. The DSP calculations call for two quadrature signals if the phase and
`amplitude are to be preserved and captured during modulation or demodulation.
`
`Second, the DSP circuitry may be a conventional programmable DSP chip or may be implemented by fixed
`digital logic implementing the algorithm. Fixed logic circuits are smaller and faster and are preferred for
`their low latency in the modulation or demodulation process.
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`Third, the PA in the transmitter needs to be a linear amplifier if the modulation is QPSK or QAM to
`faithfully reproduce the amplitude and phase information. For ASK, FSK, and BPSK, a more efficient non
`linear amplifier may be used.
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`The Pursuit Of Greater Spectral Efficiency
`With spectrum being a finite entity, it is always in short supply. The Federal Communications Commission
`(FCC) and other government bodies have assigned most of the electromagnetic frequency spectrum over the
`years, and most of that is actively used.
`
`Shortages now exist in the cellular and land mobile radio sectors, inhibiting the expansion of services such
`as high data speeds as well as the addition of new subscribers. One approach to the problem is to improve
`the efficiency of usage by squeezing more users into the same or less spectrum and achieving higher data
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`rates. Improved modulation and access methods can help.
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`One of the most crowded areas of spectrum is the land mobile radio (LMR) and private mobile radio (PMR)
`spectrum used by the federal government, state governments, and local public safety agencies like fire and
`police departments. Currently they’re assigned spectrum by FCC license in the 150 to 174MHz VHF
`spectrum and the 421 to 512MHz UHF spectrum.
`
`Most radio systems and handsets use FM analog modulation that occupies a 25kHz channel. Recently the
`FCC has required all such radios to switch over to 12.5kHz channels. This conversion, known as
`narrowbanding, doubles the number available channels.
`
`Narrowbanding is expected to improve a radio’s ability to get access to a channel. It also means that more
`radios can be added to the system. This conversion must take place before January 1, 2013. Otherwise, an
`agency or business could lose its license or be fined. This switchover will be expensive as new radio systems
`and handsets are required.
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`In the future, the FCC is expected to mandate a further change from the 12.5kHz channels to 6.25kHz
`channels, again doubling capacity without increasing the amount of spectrum assigned. No date for that
`change has been assigned.
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`The new equipment can use either analog or digital modulation. It is possible to put standard analog FM in a
`12.5kHz channel by adjusting the modulation index and using other bandwidthnarrowing techniques.
`However, analog FM in a 6.25kHz channel is unworkable, so a digital technique must be used.
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`Digital methods digitize the voice signal and use compression techniques to produce a very lowrate serial
`digital signal that can be modulated into a narrow band. Such digital modulation techniques are expected to
`meet the narrowbanding goal and provide some additional performance advantages.
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`New modulation techniques and protocols—including P25, TETRA, DMR, dPMR, and NXDN—have been
`developed to meet this need. All of these new methods must meet the requirements of the FCC’s Part 90
`regulations and/or the regulations of the European Telecommunications Standards Institute (ETSI)
`standards such as TS102 490 and TS102658 for LMR.
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`The most popular digital LMR technology, P25, is already in wide use in the U.S. with 12.5kHz channels. Its
`frequency division multiple access (FDMA) method divides the assigned spectrum into 6.25kHz or 12.5kHz
`channels.
`
`Phase I of the P25 project uses a foursymbol FSK (4FSK) modulation. Standard FSK, covered earlier, uses
`two frequencies or “tones” to achieve 1bit/Hz. However, 4FSK is a variant that uses four frequencies to
`provide 2bits/Hz efficiency. With this scheme the standard achieves a 9600bit/s data rate in a 12.5KHz
`channel. With 4FSK, the carrier frequency is shifted by ±1.8 kHz or ±600 Hz to achieve the four symbols.
`
`In Phase 2, a compatible QPSK modulation scheme is used to achieve a similar data rate in a 6.25kHz
`channel. The phase is shifted either ±45° or ±135° to get the four symbols. A unique demodulator has been
`developed to detect either the 4FSK or QPSK signal to recover the digital voice. Only different modulators
`on the transmit end are needed to make the transition from Phase 1 to Phase 2.
`
`The most widespread digital LMR technology outside of the U.S. is TETRA, or Terrestrial Trunked Radio.
`This ETSI standard is universally used in Europe as well as in Africa, Asia, and Latin America. Its time
`division multiple access (TDMA) approach multiplexes four digital voice or data signals into a 25kHz
`channel.
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`A single channel is used to support a digital stream of four time slots for the digital data for each subscriber.
`This is equivalent to four independent signals in adjacent 6.25kHz channels. The modulation is π/4
`DQPSK, and the data rate is 7.2 kbits/s per time slot.
`
`Another ETSI standard, digital mobile radio (DMR), uses a 4FSK modulation scheme in a 12.5kHz channel.
`It can achieve a 6.25kHz channel equivalent in a 12.5kHz channel by using twoslot TDMA. The voice is
`digitally coded with error correction, and the basic rate is 3.6 kbits/s. The data rate in the 12.5kHz band is
`9600 kbits/s.
`
`A similar technology is dPMR, or digital private mobile radio standard. This ETSI standard also uses a 4FSK
`modulation scheme, but the access is FDMA in 6.25kHz channels. The voice coding rate is also 3.6 kbits/s
`with error correction.
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`LMR manufacturers Icom and Kenwood have developed NXDN, another standard for LMR. It is designed to
`operate in either 12.5 or 6.25kHz channels using digital voice compression and a foursymbol FSK system.
`A channel may be selected to carry voice or data.
`
`The basic data rate is 4800 bits/s. The access method is FDMA. NXDN and dPMR are similar, as they both
`use 4FSK and FDMA in 6.25kHz channels. The two methods are not compatible, though, as the data
`protocols and other features are not the same.
`
`Because all of these digital techniques are similar and operate in standard frequency ranges, Freescale
`Semiconductor was able to make a singlechip digital radio that includes the RF transceiver plus an ARM9
`processor that can be programmed to handle any of the digital standards. The MC13260 systemonachip
`(SoC) can form the basis of a handset radio for any one if not multiple protocols. For more, see “Chip Makes
`TwoWay Radio Easy.”
`
`Another example of modulation techniques improving spectral efficiency and increasing data throughput in
`a given channel is a new technique from NovelSat called NS3 modulation. Satellites are positioned in an
`orbit around the equator about 22,300 miles from earth. This is called the geostationary orbit, and
`satellites in it rotate in synchronization with the earth so they appear fixed in place, making them a good
`signal relay platform from one place to another on earth.
`
`Satellites carry several transponders that pick up the weak uplink signal from earth and retransmit it on a
`different frequency. These transponders are linear and have a fixed bandwidth, typically 36 MHz. Some of
`the newer satellites have 72MHz channel transponders. With a fixed bandwidth, the data rate is somewhat
`fixed as determined by the modulation scheme and access methods.
`
`The question is how one deals with the need to increase the data rate in a remote satellite as required by the
`ever increasing demand for more traffic capacity. The answer lies in simply creating and implementing a
`more spectrally efficient modulation method. That’s what NovelSat did. Its NS3 modulation method
`increases bandwidth capacity up to 78%.
`
`That level of improvement comes from a revised version of APSK modulation covered earlier. One
`commonly used satellite transmission standard, DVBS2, is a single carrier (typically Lband, 950 to 1750
`MHz) that can use QPSK, 8PSK, 16APSK, and 32APSK modulation with different forward error correction
`(FEC) schemes. The most common application is video transmission.
`
`NS3 improves on DVBS2 by offering 64APSK with multiple amplitude and phase symbols to improve
`efficiency. Also included is low density parity check (LDPC) coding. This combination provides a maximum
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`data rate of 358 Mbits/s in a 72MHz transponder. Because the modulation is APSK, the TWT PAs don’t
`have to be backed off to preserve perfect linearity. As a result, they can operate at a higher power level and
`achieve the higher data rate with a lower CNR than DVBS2. NovelSat offers its NS1000 modulator and
`NS2000 demodulator units to upgrade satellite systems to NS3. In most applications, NS3 provides a data
`rate boost over DVBS2 for a given CNR.
`
`Acknowledgment
`Special thanks to marketing director Debbie Greenstreet and technical marketing manager Zhihong Lin at
`Texas Instruments as well as David Furstenberg, chairman of NovelSat, for their help with this article.
`
`References
`
`1. De Gaudenzi, Riccardo, et al, European Space Agency, American Institute of Aeronautics and
`Astronautics paper, 2002.
`2. Frenzel, Louis E., Principles of Electronics Communication Systems, 3rd edition, McGraw Hill, 2008.
`3. Kolimbiris, Haorld, Digital Communications Systems, Prentice Hall, 2000.
`4. Young, Paul H., Electronic Communications Techniques, 5th edition, Prentice Hall, 2004.
`5. Company briefings: Texas Instruments, Freescale and NovelSat
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`Source URL: http://electronicdesign.com/communications/understandingmoderndigitalmodulation
`techniques
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