IEEE TRANSACTIONS ON BROADCASTING, VOL. 41, NO. I , M A R C H 1995
`COF'DM: AN OVERVIEW
`William Y. Zou
`Public Broadcasting Service
`1320 Braddock Place
`Alexandria, VA
`
`Yiyan Wu
`Communications Research Centre
`3701 Carling Ave. Box 11490, Station H
`Ottawa, Ontario, Canada, K2H 8S2
`
`I
`
`and monitor the development of coded OFDM (COFDM).
`Encouraged by the potential advantages of COFDM, some U. S. and
`Canadian broadcasters have decided to investigate the technology.
`Recently, several U. S . and Canadian broadcaster organizations
`formed a consortium and issued a Request for Quote to solicit
`potential bidders to build COFDM hardware for evaluation.3
`
`The debate on COFDM versus vestigial sideband (VSB) modulation
`or quadrature amplitude modulation (QAM) for terrestrial HDTV
`broadcasting has been engaged in the past and there is no sign that it
`will end soon. One reason is that neither COFDM nor VSB has a
`clear advantage in all of the performance aspects. Some differences
`may be based on specific system implementation. Another reason is
`that neither approach had been tested in the field extensively.
`Recently, the proposed 8-VSB modulation subsystem has been
`tested in Charlotte, NC by PBS, MSTV, and CableLabs. It is
`expected that the test results will provide valuable information on the
`performance of the 8-VSB system.
`
`In this paper, an overview of OFDWCOFDM research and
`is presented. The motivations of using
`development
`OFDMKOFDM and their applications are discussed. The
`principles of the technology are examined in details. Analysis is
`given on how to select key system elements. In addition, the
`performance expectations of COFDM under imperfect channel
`conditions and implementation issues are examined.
`2. OFDM History
`
`Abstract
`
`The research and development of OFDWCOFDM for digital
`television broadcasting has received considerable attention and has
`made a great deal of progress in Europe. OFDWCOFDM has
`already been implemented in digital audio broadcasting and is being
`considered for terrestrial digital television and HDTV broadcasting.
`The advantages of COFDM claimed by the advccates in Europe have
`also caught the attention of U.S. broadcasters and generated
`enthusiasm although a digital modulation technique called 8-VSB
`has been selected by the FCC Advisory Committee on Advanced
`Television Service (ACATS) for the final testing. There is
`considerable debate in the industry over the use of COFDM vs. VSB
`or QAM for terrestrial HDTV broadcasting.
`In this paper, the history of research and development on OFDM
`and COFDM is reviewed. Then, the basic principles, performance
`and implementation of OFDM and COFDM are examined. Analysis
`is given to enable the selection of key elements for meeting the
`constraints of the required applications. Based on the ATV channel
`model, performance expectation of COFDM under imperfect
`channel conditions and implementation issues are examined in
`details.
`1. Introduction
`After more than thirty years of research and development, orthogonal
`frequency division multiplexing (OFDM) has been widely
`implemented in high speed digital communications. Due to the recent
`advances of digital signal processing (DSP) and very large scale
`integrated circuit 0 technologies, the initial obstacles of OFDM
`implementation, such as massive complex computation, and high
`speed memory do not exist anymore. Meanwhile, the use of fast
`Fourier transform (FFT) algorithms eliminates arrays of sinusoidal
`generators and coherent demodulation required in parallel data
`systems and make the implementation of the technology cost
`effective. Another reason for the growing popularity of OFDM is
`that only very recently its optimal performance has been proven
`theoretically. '2
`
`The concept of using parallel data transmission and frequency
`division multiplexing was published in the mid 60s.4~5 Some early
`development can be traced back in the OS.^ A U.S. patent was filed
`and issued in January, 1970.7 The idea was to use parallel data and
`frequency division multiplexing (FDM) with overlapping
`subchannels to avoid the use of high speed equalization and to
`combat impulsive noise, and multipath distortion as well as to fully
`use the available bandwidth. The initial applications were @ military
`communications. In the telecommunication field the terms of discrete
`multi-tone (DMT), multichannel modulation, and multicarrier
`modulation (MCM) are widely used and sometimes they are
`interchangeable with OFDM. In OFDM, each carrier is orthogonal
`to the other carriers. However, this condition is not always
`maintained in MCM.
`An example of the early OFDM applications was the AN/GSC-10
`(KATHRYN) variable rate data modem built for the high-frequency
`radio.a.9 Up to 34 parallel low rate channels using PSK modulation
`were generated by a frequency multiplexed set of subchannels.
`Orthogonal frequency assignment was used with channel spacing of
`82 Hz to provide guard time between successive signaling elements.
`OFDM was also used in other high-frequency military systems,
`such as KINEPLEX6 and ANDEFT.'O
`For a large number of subchannels, the arrays of sinusoidal
`generators and coherent demodulators required in a parallel system
`become unreasonably expensive and complex. The receiver needs
`precise phasing of the demodulating carriers and sampling times in
`order to keep crosstalk between subchannels acceptable. Weinstein
`and Ebert applied the discrete Fourier transform (DFT) to parallel
`data transmission systems as part of the modulation and
`demodulation processes.'' In addition to eliminating the banks of
`subcarrier oscillators and coherent demodulators required by FDM,
`00 18-93 16/95$04.00 0 1995 lEEE
`
`Although it has long been used for digital data transmission,
`OFDWCOFDM has been studied in Europe and elsewhere for
`potential digital X-IDTV terrestrial broadcasting. Various projects and
`prototypes of OFDWCOFDM systems have been engaged and
`demonstrated publicly. Among them are HD-DIVINE (DIgital
`VIdeo Narrowband Emission) developed by Nordic countries,
`DIAMOND developed by Thomson-CFSLER, STERNE (Systeme
`de TElevision en Radiodiffision NumeriqE) by CCETT (a joint
`venture of France Telecom and TDF), dTTt, (digital Terrestrial
`Television broadcasting) by Commission of the European
`Communities (CEC), EP-DVB (European Project on Digital Video
`Broadcasting) by European national administrations and private
`industry, SPECIRE (Special Purpose Extra Channels for Terrestrial
`Radiocommunication Enhancements) by NTL of U.K. and HDTVT
`(Hierarchical Digital TV Transmission) in Germany. COFDM
`research has also been carried out by NHK and a few Japanese
`electronic manufacturers.
`
`In North America, the FCC Advisory Committee on Advanced
`Television Service officially accepted an 8-VSB modulation
`technique developed by Zenith/the Grand Alliance for the final
`testing. However, the advisory committee indicated that it will study
`
`Petitioner Sirius XM Radio Inc. - Ex. 1023, p. 1
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`

`

`L
`a completely digital implementation could be built around special-
`purpose hardware performing the fast Fourier transform (FFT).
`Recent advances in VLSI technology make high speed large size
`FIT chips commercially affordable.12
`
`In the 1980s, OFDM had been studied for high-speed modems,
`digital mobile communications, and high density recording. Hirosaki
`explored the OFDM techniques for multiplexed QAM using
`DFT.13,I4 He also designed an 19.2 kbps voiceband data modem
`using multiplexed QAM.15 In this system a pilot tone was used for
`stabilizing carrier and clock frequency control and trellis coding was
`hnplemented to reduce the required carrier-to-noise ratio (CNR).
`Various speed modems were developed for
`telephone
`networks. 16.17.1 8.19
`
`To combat frequency selective fading, and Doppler shift in mobile
`channel, OFDM has been used to spread out a fade over many
`symbols. OFDM can effectively randomize burst errors caused by
`the Rayleigh fading, so that instead of several adjacent symbols
`being completely destroyed, many symbols are only slightly
`distorted. This allows the precise reconstruction of a majority of
`them. In addition, by using guard interval the sensitivity of the
`system to delay spread can be reduced.20
`
`In non-transmission applications, Feig et al, explored discrete multi-
`tone techniques using DFT for application in the linearized magnetic
`storage channe1.2l.22.23
`
`In the 1990s, OFDM has been exploited for wideband data
`communications over mobile radio FM channels, high-bit-rate digital
`subscriber lines (HDSL), asymmetric digital subscriber lines
`(ADSL), very high-speed digital subscriber lines (VHDSL), digital
`audio broadcasting (DAB), digital television and HDTV terrestrial
`broadcasting.55
`
`Casas et al, proposed OFDM/FM for data communication over
`
`mobile radio ~hannels.2~ It claimed that OFDM/FM systems could
`be implemented simply and inexpensively by retrofitting existing
`FM radio systems.
`
`are only slightly distorted. This allows successful reconstruction of a
`majority of them even without forward error correction (FEC).
`Because of dividing an entire channel bandwidth into many narrow
`subbands, the frequency response over each individual subbands is
`relatively flat. Since each subchannel covers only a small fraction of
`the original bandwidth, equalization is potentially simpler than in a
`serial system. A simple equalization algorithm can minimize mean-
`square distortion on each subchannel, and the implementation of
`differential encoding may make it possible to avoid equalization
`altogether. 11
`In a classical parallel data system, the total signal frequency band is
`divided into N non-overlapping frequency subchannels. Each
`subchannel is modulated with a separate symbol and, then, the N
`subchannels are frequency division multiplexed. There are three
`schemes that can be use to separate subbands:
`
`1. Use filters to completely separate subbands. This method was
`borrowed from the conventional FDM technology. The limitation of
`filter implementation forces the bandwidth of each subband to be
`equal to (l+a)f, , where a is the roll-off factor and f, is the Nyquist
`bandwidth. Another disadvantage is that it is difficult to assemble a
`set of matched filter when the number of carriers are large.
`2. Use staggered QAM to increase the efficiency of band usage. In
`this way the individual spectra of the modulated carriers still use a
`excess bandwidth of a , but they are overlapped at the 3-dB
`frequency. The advantage is that the composite spectrum is flat. The
`separability or orthogonality is achieved by staggering the data
`(offset the data by half a symbol). The requirement for filter design
`is less critical than that for the first scheme.
`
`3. Use the discrete Fourier transform (DFT) to modulate and
`demodulate parallel data. The individual spectra are now sinc
`functions and are not bandlimited. The FDM is achieved, not by
`bandpass filtering, but by baseband processing. Using this method,
`both transmitter and receiver can be implemented using efficient FIT
`techniques which reduce the number of operations from N2 in DFT
`down to about NlogN.
`
`Chow et al, studied the mlllti-tone modulation with discrete Fourier
`transform in transceiver design and showed that it is an excellent
`method for delivering of high speed data to customers, both in terms
`of performance and cost, for ADSL (1.536 Mbps), HDSL (1.6
`Mbps), and VHDSL (lOOMbps).25.26
`
`As is well known, orthogonal signals can be separated at the receiver
`by correlation techniques; hence, intersymbol interference among
`channels can be eliminated. This can be achieved by carefully
`selecting carrier spacing, such as letting the carrier spacing equal to
`the reciprocal of the useful symbol period.
`
`More recently, OFDM, especially COFDM, has been studied and
`implemented for digital television and HDTV terrestrial broadcasting
`as well as digital audio terrestridsatellite broadcasting.27,**.29.30,31,~
`The successful demonstrations of DAB gave researchers
`encouragement to further explore OFDM and COFDM for
`television broadcasting. The goals of using COFDM for terrestrial
`broadcasting are not only for fixed reception but also for potential
`mobile and portable receivers.32
`3. Basic Principles of OFDM
`3. I Parallel Data Transm 'ssion and MultiDle Carrie rs
`
`In a conventional serial data system, the symbols are transmitted
`sequentially, with the frequency spectrum of each data symbol
`allowed to occupy the entire available bandwidth.
`
`A parallel data transmission system offers possibilities for alleviating
`many of the problems encountered with serial systems. A parallel
`system is one in which several sequential streams of data are
`transmitted simultaneously, so that at any instant many data elements
`are being transmitted. In such a system, the spectrum of an individual
`data element normally occupies only a small part of the available
`bandwidth.
`
`A parallel approach has the advantage of spreading out a frequency
`selective fade over many symbols. This effectively randomizes burst
`errors caused by fading or impulse interference, so that, instead of
`several adjacent symbols being completely destroyed, many symbols
`
`OFDM can be simply defined as a form of multicarrier modulation
`where its carrier spacing is carefully selected so that each subcarrier
`is orthogonal to the other subcarriers.
`
`.
`
`3.2 Signal Rewesentation of OFDM Using IDFTDFT
`Consider a data sequence (4, dl , df , ... dN-l), where each d, is a
`complex number d, = a, + jb,. If a discrete Fourier transform (DFT)
`is performed, the result is a vector D = (Do, DI, ... DN.~) of N
`complex numbers,
`
`N- I
`N- 1
`D - d e-j@"'N) = d,,e-J2nfntm,
`m -
`n
`n=O
`n=O
`where fn = n/(NAt), t, = mAt and At is an arbitrarily chosen symbol
`duration of the serial data sequence d,. The real part of the vector D
`has components
`
`m = 0, 1,2, N-1
`
`(1)
`
`Y , = c (a,,cos2nf,tm + bnsin2nf,t,),
`
`N-l
`
`n=O
`
`m=O,1, ..., N-1.
`
`(2)
`
`If these components are applied to a low-pass filter at time intervals
`At, a signal is obtained that closely approximates the frequency
`division multiplexed signal
`
`N- I
`y(t) =
`n=O
`
`(a, cos2nfnt + b,sin2afnt),
`
`0 S t I NAt.
`
`(3)
`
`Petitioner Sirius XM Radio Inc. - Ex. 1023, p. 2
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`

`

`3
`
`Fig. 1 m-based OFDM System
`
`Fig. 1 illustrates the process of a typical FFT-based OFDM system.
`The incoming serial data is fmt converted from serial to parallel and
`grouped into x bits each to form a complex number. The number x
`determines the signal constellation of the corresponding subcarrier,
`such as 16 QAM or 32 QAM. The complex numbers are modulated
`in a baseband fashion by the inverse FlT
`and converted back
`to serial data for transmission. A guard interval is inserted between
`symbols to avoid intersymbol interference (ISI) caused by multipath
`distortion. The discrete symbols are converted to analog and low-
`pass filtered for RF upconversion. The receiver performs the inverse
`process of the transmitter. An one-tap equalizer is used to correct
`channel distortion. The tap coefficients of the filter are calculated
`based on channel information.
`Fig. 2(a) shows the spectrum of an OFDM subchannel and Fig. 2(b)
`presents an OFDM spectrum. By carefully selecting the carrier
`spacing, the OFDM signal spectrum can be made flat and the
`orthogonality among the subchannels can be guaranteed.
`
`Fig. 2(a) Spectrum of An OFDM Subchannel
`
`Fig. 2(b) OFDM Spectrum
`
`3.3 Guard Interval and Its Implementation
`The orthogonality of subchannels in OFDM can be maintained and
`individual subchannels can be completely separated by the FW at
`the receiver when there are no intersymbol interference (ISI) and
`intercarrier interference (ICI) introduced by transmission channel
`distortion. In practice these conditions can not be obtained. Since the
`spectra of an OFDM signal is not strictly band limited (sinc(f)
`function), linear distortions such as multipath cause each subchannel
`to spread energy into the adjacent channels and consequently cause
`ISI. A simple solution is to increase the symbol duration or the
`number of carriers so that the distortion becomes insignificant.
`However, this method may be difficult to implement in terms of
`carrier stability, Doppler shift, FFT size and latency.
`One way to prevent IS1 is to create a cyclically extended guard
`interval,2 where each OFDM symbol is preceded by a periodic
`extension of the signal itself. The total symbol duration is T t d = Tg
`+ T, where T, is the guard interval and T is the useful symbol
`duration. When the guard interval is longer than the channel impulse
`response, or the multipath delay, the IS1 can be eliminated. However,
`the ICI, or in-band fading, still exists. The ratio of the guard interval
`to useful symbol duration is application-dependent. Since the
`insertion of ward interval will reduce data t h r o ~ e h ~ ~ t . T. is usuallv
`less than T / Z ~
`The reasons to use a cyclic prefix for the guard interval are:
`
`1) to maintain the receiver carrier synchronization; some signal
`instead of a long silence must always be transmiw,
`2) cyclic convolution can still be. applied between the OFDM signal
`and the channel response to model the transmission system.2.@
`Fig. 3 gives the time and frequency representation of OFDM using
`guard interval. With the two-dimensional signal representation, the
`symbols are overlapped in the frequency domain and are separated
`by the guard interval in the time domain. This arrangement also
`matches the television channel characteristics well (e.g. in the
`television channel the time dispersion is large and frequency
`dispersion is less critical).
`3.4 Choice of kev Elements
`After settling the channel bandwidth, guard interval, and data
`throughput, a few key elements can be determined.
`a. Useful Symbol DuratiQg
`The useful symbol duration T affects the carrier spacing and coding
`latency. To maintain the data throughput, a longer usdful symbol
`duration results in an increase of the number of carriers and the size
`of FFT (assuming that the signal constellation is fixed). In practice,
`
`Petitioner Sirius XM Radio Inc. - Ex. 1023, p. 3
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`

`

`4
`
`Subchannels
`
`GuardIntervals
`
`FL
`
`,/d
`
`Symbols
`
`J
`
`Fig. 3 Time and Frequency Representation of OFDM Using Guard Interval
`
`carrier offset and phase stability may affect how close two carriers
`can be placed. If the application is for the mobile reception, the
`carrier spacing must be large enough to make the Doppler shift
`negligible. Generally, the useful symbol duration should be chosen
`so that the channel is stable for the duration of a symbol.
`
`b. Number of Carriers
`
`The number of subcarriers can be determined based on the channel
`bandwidth, data throughput and useful symbol duration. The carriers
`are spaced by the reciprocal of the useful symbol duration. The
`number of carriers corresponds to the number of complex points
`being processed in FFT. In HDTV applications, the number of
`subcarriers are in the range of several thousands so as to
`accommodate the data rate and guard interval requirement.
`
`F. Modulation Scheme
`
`The modulation scheme used in an OFDM system can be selected
`based on the requirement of power or spectrum efficiency. The type
`of modulation can be specified by the complex number d, = a,, + b,
`defined in section 3.1. The symbols a, and b, take on values of +1,
`+3, ... depending on the number of signal points in the signal
`constellations. For example, a, and b, can be selected to (&I, 53) for
`16 QAM and +1 for QPSK. In general, the selection of modulation
`scheme applying to each subchannel depends solely on the
`compromise between the data rate requirement and transmission
`robustness. Another advantage of OFDM is that different
`modulation schemes can be used on different subchannels for
`layered services.
`3.5 Coded OFDM
`
`By using time and frequency diversity OFDM provides a means to
`transmit data in a frequency selective channel. However, it does not
`suppress fading itself. Depending on their position in the frequency
`domain, individual subchannels could be affected by fading. This
`requires the use of channel coding to further protect transmitted data.
`Among those channel coding techniques, trellis coded modulation
`(TCM)45 combined with frequency and time interleaving is
`considered the most effective means for a frequency selective fading
`channel.
`
`TCM combines coding and modulation to achieve high coding gain
`without affecting the bandwidth of the signal. In a TCM encoder,
`each symbol of n bits is mapped into a constellation of n+l bits,
`using a set-partitioning rule.45 This process increases the
`constellation size and effectively adds additional redundancy to
`trellis-code the signal. A TCM code can be decoded with a soft
`decision Viterbi decoding algorithm,46 which exploits the soft
`decision nature of the received signal. The coding gain for a two-
`dimensional TCM code over a Gaussian channel is about 3 dB for a
`bit error rate (BER) of IO-'.
`
`It should be mentioned that one of the advantages of OFDM is that it
`can convert a wideband frequency selective fading channel into a
`series of narrowband and frequency non-selective fading
`subchannels by using parallel and multicarrier transmission. Coding
`OFDM subcarriers sequentially by using specially designed TCM
`codes for frequency non-selective fading channel is the major reason
`for using COFDM for terrestrial broadcasting. However, the
`searching of the best TCM code is still on going.
`
`Although trellis codes produce improvements in the signal-to-noise
`ratio ( S N ) , they do not perform well with impulsive or burst noise.
`Besides electromechanical sources of burst noise, burst noise is also
`caused by NTSC co-channel interference and phase noise which can
`cause data-dependent crosstalk. In general, transmission errors have
`a strong time/frequency correlation. Interleaving plays an essential
`role in channel coding by providing diversity in the time domain.
`Interleaving breaks the correlation and enables the decoder to
`eliminate or reduce local fading throughout the band and over the
`whole depth of the time interleaving. Interleaving depth should be
`large enough to break long straight errors.
`4. COFDM Performance Expectation
`In this section the performance expectation of COFDM in terrestrial
`digital television broadcasting is examined.
`
`4.1 ATV Channel Model
`
`It should be noted that for the additive white Gaussian noise channel.
`COFDM and single carrier modulation have comparable
`performance.55.56 However, the broadcasting channels for HDTV
`
`Petitioner Sirius XM Radio Inc. - Ex. 1023, p. 4
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`

`

`consist of various other impairments. The signals arriving at the
`receiver are impacted by random noise, impulse noise, multipath
`distortion, fading, and interference. Through theoretical analyses and
`field measurements, HDTV transmission channel models have been
`
`e s t a b l i ~ h e d . ~ ~ , ~ ~ , ~ ~ It is well known and proven that digital
`transmission offers better performance than its analog counterpart in
`terms of random noise and interference.36 However, other
`impairments such as multipath distortion and fading are considered
`very challenging to the success of digital television terrestrial
`broadcast.
`
`Due to the multipath propagation, the cancellation of different paths
`creates a field of moderate peaks separated by holes of various
`depths (fading) ranging from a few dB to more than 50 dB deep. As
`indicated by the FCC, the majority of ATV channels will be allocated
`in the UHF bands. At the high end of the UHF band, the
`wavelengths are very short (around 0.5 m). The characteristics of
`these holes and peaks can be modeled by a statistical distribution
`known as a Rayleigh distribution.&
`
`4.2 MdtiDath/fading
`
`It is believed that with properly designed guard interval, interleaving
`and channel coding, COFDM is capable of handling very strong
`echoes.% The BER improvement resulted from multiple echoes was
`indicated by
`the computer simulations and
`laboratory
`demon~trations.3~~53 With the assumption of withstanding strong
`multipath propagation, COFDM might allow the use d om&
`directional antenna in urban areas and mobile reception where UN is
`sufficiently high.
`
`In addition to channel fading, time-variant signals caused by
`transmitter tower swaying, airplane flut&ring and even tree swaying
`generate dynamic ghosts and consequently produce errors in digital
`transmission. With its parallel transmission structure as well as the
`use of trellis coding, COFDM systems might present advantages in
`fading and time-variant channel envimmnt.53
`
`4.3 Phase Noise and Jitt er
`
`A COFDM system is much more affected by carrier frequency
`errors.38 A small frequency offset at receiver compromises the
`orthogonality between the subchannels, giving a degradation in
`system performance that increases rapidly with fresuency offset and
`with the number of subcarriers. Phase noise and jitter can be
`influenced by transmitter up-converter, receiver downconverter, and
`tuner. A possible solution is the use of pilots which can be used to
`track phase noise in the demodulation. However, this is done under
`the penalty of reducing the payload data throughput.
`4.4 Carrier Recovem@yahz.a ’ tion
`In the severe channel conditions, such as low C/N, strong
`interference and fading, COFDM signal must be designed to provide
`robust carrier recovery. Carrier frequency detection could be one of
`the biggest limitations in COFDM design. The use of pilots and
`reference symbols are efficient methods for carrier recovery and
`subchannel equalization. A pilot can be a sine wave or a known
`binary sequence. A reference symbol can be a chirp or a pseudo-
`random sequence.
`
`The two-dimensional signal feature in COFDM makes pilot and
`reference symbol insertion very flexible. Pilots can be inserted in the
`frequency domain (fured carriers) and reference symbols in the time
`domain (fixed data packets). Because they are transmitted at the
`predetermined positions in the signal frame structure, it can be
`captured at the receiver whenever the frame synchronization is
`recovered. In a frequency-selective channel, high correlation between
`the complex fading envelopes of the pilots and data must be ensured.
`The appropriate complex correction can be obtained by interpolating
`among the pilots. Cimini reported that interpolation in real and
`imaginary parts of the complex fading envelopes outperformed the
`interpolation in amplitude and phase.”
`
`For single carrier systems, equalization is done in the time domain.
`For a QAM system with a N-tap equalizer, there are about N
`
`5
`complex multiplication, or 4N real multiplication-mumulatiom per
`input symbol. For a VSB system, its symbol rate needs to be twice
`that of a QAM system for the same data throughput. Assuming the
`same echo range as for the QAM system, an 2N-tap real q u a k e r is
`required, which has a computational complexity of about 2N
`multiplication-accumulations per input symbol.
`
`For a COFDM system, assuming multipath delay is less than the
`guard interval, a frequency domain one-tap equalizer could be used
`for each subchannel to correct the amplitude and phase distortions.
`This corresponds to four real multiplication-accumulations per data
`symbol. Additionally, the FlT operation requires a computational
`complexity that is proportional to C*logzM, where M is the size of
`the FFT and C is a constant between 1.5 to 4 depending on the FFT
`implementation.
`
`The number of pilots and reference symbols used in a COFDM
`system determine the trade-off between payload capacity and
`transmission robustness. Simulation results indicated that an OFDM
`system with equalization performed better than that of a single carrier
`system with a linear equalizer.%
`4.5NTscInterference
`For digital television and HDTV broadcasting, the potential
`interference to and from the conventional NTSC needs to be
`considered. For a COFDM system, the robustness to NTSC
`interference depends on the degree of the error correction coding
`implemented and the amount of interleaving applied.55 To further
`reduce the impact of interference from NTSC, one can also explore
`the unique NTSC signal spectrum. The NTSC spectrum consists of
`a visual carrier, a color subcarrier and an aural carrier. Each of the
`visual and color signals is made up of the discrete components
`spaced by the line frequency of 15,750 kHz. The visual and color
`parts are offset relative to one another by half the line frequency.
`Based on this knowledge of the NTSC spectrum, COFDM carrier
`spacing can be chosen and offset between the NTSC frequency
`components, such as 7.875*n IrHz, where n is a positive nonzero
`integer. However, this concept needs to be proven.
`
`Another approach to combat NTSC interference is using spectrum
`shaping. This can be achieved by not using the COFDM carriers in
`certain spectra regions (the corresponding values in the FlT data
`array are set to zero) where strong NTSC signal energy are expected,
`such as the visual, color and aural carriers. Combined with error
`pmtection, spectrum shaping can tolerate significantly high levels of
`interference.47 Obviously, the gain is obtained at the expense of data
`throughput. The data throughput can be increased using larger
`constellation with higher transmission power. Recently, Trellis
`coding and Viterbi decoding are considered as a better way to deal
`with interference.3159
`
`For interference from COFDM into NTSC, spectrum shaping has
`few advantages. Removing those Carriers relating to the NTSC Visual,
`color and audio carriers does not affect much about the desired
`NTSC signal since those are the most robust part of NTSC signal.
`Subjective test results also indicated that there is almost no impact on
`NTSC over the OFDM parameters such as spec-
`shaping, and
`the behavior of the OFDM signal interference is similar to that of
`random n ~ i s e . ~ ~ . ~
`
`
`
`4.6 I m ~ u l ~ e Interference
`
`COFDM is more immune to impulse noise than a single carrier
`system because a COFDM signal is integrated over a long symbol
`period and the impact of impulse noise is much less than that for
`single carrier systems. As a matter of fact, the i”unity of impulse
`noise was one of the original mtivatiom for MCM. Test reported to
`the CCI’lT showed that the threshold level for impulse noise at
`which errors occur can be as much as 11 dB higher for MCM than
`that of a single carrier system40 Meanwhile, studies indicated that the
`best approach of impulse noise reduction for OFDM involves a
`combination of soft and hard error protection.4’
`
`Petitioner Sirius XM Radio Inc. - Ex. 1023, p. 5
`
`

`

`6
`
`4.7 Peak-to-averape Power Ratio
`
`The peak-to-average power ratio for a single carrier system depends
`on the signal constellation and the roll-off factor ct of pulse shaping
`filter (Gibbs' phenomenon). For the Grand Alliance 8-VSB system,
`a = 1 1.5%. The corresponding peak-to-average power ratio is about
`7 dB for 99.99% of the time.
`
`Theoretically, the difference of the peak-to-average power ratio
`between a multicarrier system and a single carrier system is a
`Fnction of the number of carriers as:
`
`A (dB) = IOlogloN
`
`where N is the number of carriers. When N = 1000, the difference
`could be 30 dB. However, this theoretical value can rarely occur.
`Since the input data is well scrambled, the chances of reaching its
`maximum value are very low, especially when the signal constellation
`size is large.
`
`Since COFDM signal can be treated as a series of independent and
`identically distributed carriers, the Central Limit theorem implies that
`the COFDM signal distribution should tend to be Gaussian when
`the number of carriers, N, is large. Generally, when N > 20, which is
`the case for most of the COFDM systems, the distribution is very
`close to Gaussian. Its probability of above three times (9.6 dB peak-
`to-average power ratio) of its variance, or average power, is about
`0.1%. For four times of variance, or 12 dB peak-to-average power
`ratio, it is less than 0.01%.4*,56
`
`It should be pointed out that, for each COFDM subchannel, there is
`usually no pulse shaping implemented. The peak-to-average power
`ratio for each subchannel depends only on the signal constellation.
`
`In common practice, signals could be clipped because of limited
`quantization levels, rounding and truncation during the FFT
`computation as well as other distributed parameters after D