Comparison of Single-Carrier and Multitone Digital Modulation for ADSL Applications

Comparison of Single-Carrier and Multitone Digital Modulation for ADSL Applications

ABSTRACT

Single-carrier modulation such as QAM or CAP, and DMT are alternative techniques for providing digital communication in a variety of applications, in particular ADSL for communication over telephone company subscriber lines. Although theory predicts comparable performance under ideal implementations, a definitive comparison of performance over a wide range of conditions will require more experience from field trials. Similarly, accurate comparison of implementation costs must await the greater availability of commercial-grade devices. However, enough is now known about these modulation schemes to compare their inherent similarities and differences in performance and cost. Overall, a present view of single-carrier and multitone modulation indicates comparable performance with some differences depending on the type of degradation Costs should also be approximately equal, with multitone having some advantage in digital processing, but requiring greater cost in analogue circuitry.

INTRODUCTION

At the present time, there are several digital transmission systems in which multicarrier modulation implementations are contending with single-carrier techniques for adoption by standards bodies and for market acceptance:

Several versions of asymmetric digital subscriber line

Switched digital video (SDV) (fiber to the curb) access

Digital audio broadcast (DAB)

High-definition television (HDTV) broadcast

Upstream communication for interactive cable TV

These systems encompass a wide variety of channels and applications, over which the relative advantages and disadvantages of the modulation schemes differ. However, in all cases some extravagant claims have been made concerning relative performance differences. In addition, very widely varying and contradictory comparisons of the implementation complexity have been given.

The purpose of this article is to summarize, but certainly not to resolve, these issues. However, it is the author’s belief that the relative differences, in both performance and complexity, between single-carrier and multitone modulation for all applications are far less than those stated by advocates of a particular scheme. In this article we will concentrate on ADSL systems, which provide transmission of several (up to 8) megabits per second from a telephone company central office to a customer, a lower rate in the reverse direction, and a normal analog voice connection, all over a single pair of unshielded wires in the normal subscriber plant. The rates vary depending on the application and the length of the pair. The capability is provided through the use of modems at the customer premises and the central office. The first application envisioned for ADSL technology was video on demand, involving the delivery of switched compressed digital video signals such as MPEGZ. Here a very low upstream (from the customer) bit rate is needed. Required downstream (to the customer) bandwidth is relatively inflexible. Relatively high latency, or delay through the system, of up to a few hundred milliseconds can be tolerated. More recently there has been great interest in the use of ADSL for access to data networks, particularly the Internet. For efficient operation of the usual protocols, the upstream (ADSL) tions a higher upstream bit rate may be is carrying a digital voice conversation.

AN OVERVIEW OF SINGLE-CARRIER MODULATION ADSL SYSTEMS

For several decades, single-carrier quadrature amplitude modulation (QAM) has been the modulation scheme of choice for voiceband modems. In addition, QAM and its variations have been widely applied to digital transmission over many other channels. One variation of QAM is carrierless amplitude modulation-phase modulation (CAP), which eliminates the explicit modulation and demodulation in QAM.

Complexity is reduced, particularly for channels which do not introduce frequency offset or phase variation. The subscriber line is one such channel. Performance is fully equivalent to standard QAM.

Until the most recent voiceband modem standard (V.34), QAM voiceband modems used fixed transmitters (except for fallback modes) and linear equalization in the receiver. However, for channels whose loss vs. frequency characteristic and/or noise spectrum are not approximately flat, performance can be improved dramatically by the incorporation of decision feedback equalization (DFE).

In this case, the signal-to-noise ratio (SNR) at the input to the receiver’s decision device is the geometric mean of the SNR across the frequency band. This may be thought of as averaging the SNR expressed in dB, which can be far superior to averaging the reciprocal of the SNR, as occurs with linear equalization. In fact, if the channel has zero SNR at any frequency in its band, the linear equalizer fails completely, while the DFE may still provide good performance. This is true when a baseband signal is transmitted over a channel with transformer coupling, as in basic rate integrated services digital network (ISDN) access and some implementations of the high-speed digital subscriber line (HDSL). It has been shown that performance of a DFE is maximized at high SNR when the transmit power density is constant over the frequency band used [I, 2].

DFE can be implemented in two different forms which are theoretically, but not practically, fully equivalent. In the standard form, a linear forward equalizer whitens the noise and produces a signal output with only lagging intersymbol interference (ISI). The feedback section removes this ISI. In the noise-predictive form, the feedforward section is a conventional linear equalizer. Its output has no ISI, but the noise in general is nonwhite, with nonzero autocorrelation among its samples. The decision feedback section reduces the power of this noise by subtracting out its predictable component. Each form has its advantages and disadvantages. It is difficult for the standard form to whiten the noise for highly irregular noise spectra such as narrowband interference.

The noise-predictive form requires a linear equalizer, which presents a problem when the sigFr I – I feedback filter Figure 1. A hybrid DFE. nal has high loss at some frequencies. A hybrid form, shown in Fig. 1, combines the best properties of both forms. A single front-end feedforward section provides most of the shaping, but need not do perfect noise whitening. A standard form feedback section removes ISI, while the noise predictive section provides the final noise whitening.

Another benefit of the hybrid form of DFE is that the total number of coefficients needed for good performance is less than that of either the standard form or the noise predictive form alone. The DFE can be adapted using either a zero forcing or least mean square (LMS) algorithm. There is essentially no difference in performance between the algorithms at high SNR. The feedforward section requires many more taps than either form of feedback section for good performance. This is further magnified by the common practice of providing more than one tap per symbol in the feedforward section, whereas such oversampling is not applicable to the feedback sections. The DFE does suffer from the problem of error propagation.

Once an error is made, incorrect decision values are fed back, leading to a higher probability of error for subsequent decisions. This effect is not very serious for uncoded systems operating at low error probability, in that the overall error probability is not greatly increased. However, the resultant burstiness of the errors can greatly reduce the effectiveness of any coding scheme, such as trellis coding or block coding. A solution to the error propagation problem is to perform part of the equalization at the transmitter, for example, by Tomlinson filtering [3]. In this approach, a full DFE is adapted in the receiver during an initial training period. The standard form feedback coefficients are reported back to the transmitter where they are used in a Tomlinson filter, and that section of the receive equalizer is disabled. Any noise predictive section in the receiver remains active. A variation of this approach is to set the Tomlinson coefficients to the convolution of the standard feedback and noise predictive filters, with either or both filters in the receiver remaining active but starting with zero coefficients. More recent transmitter techniques allow inclusion of shaping gain along with equalization and coding [4], but have not been used so far in ADSL.

AN OVERVIEW OF MULTITONE MODULATION FOR ADSL

Parallel communication, in which several carriers of different frequency each carry narrowband signals simultaneously, has been used since the distant past. In these vintage systems, some frequency guard space separated the signals, leading to significant spectral inefficiency. In the late 1960s, it was discovered that digital signals can be carried on multiple carriers whose spectra overlap, and that it is possible to separate the signals without interchannel interference [5, 6]. This form of modulation is now often referred to as orthogonal frequencydivision multiplexing (OFDM). The spacing between centers of adjacent QAM subchannels is equal to the minimum bandwidth required by each signal. Thus, except for end effects, digital data could be carried in a band equal to the overall symbol rate without extremely sharp rolloffs. The complexity of this modulation scheme was at first far too great for practical implementation.

Soon after the invention of OFDM, it was realized that modulation and demodulation could be implemented by discrete Fourier transform (DFT) techniques [7], an approach now often referred to as discrete multitone (DMT).

Fortunately, at the same time, digital signal processing devices were first becoming available. In a typical implementation [8], input data is first blocked and then converted to a set of N multibit complex symbols, ak, and an inverse DFT is then applied to the block to form a new set of N complex symbols:

As discussed later, the aks may be chosen from different size alphabets. It is well known that DFTs and their inverses can be performed quite efficiently by a technique known as the fast Fourier transform (FFT), requiring on the order of N log N multiplications.

If there is a further stage of modulation, as in most radio systems, the complex b,s can be transmitted on quadrature inputs to that modulator. In ADSL, a second stage of modulation is not used, and only real quantities can be transmitted. A usual approach is to use a sequence of 2N real numbers instead of N complex numbers, by appending the complex conjugate of the a, block to itself symmetrically before taking the inverse DFT. This results in real quantities at the output of the inverse DFT that can then be transmitted over a baseband or other one-dimensional channel. On a very basic level, the transmitted quantities are nothing more than a reversible linear transformation of the input symbols. This leads to the suspicion that system performance of DMT should not be very different from singlecarrier modulation, at least in theory. This will be confirmed later, along with many differences that arise in practical implementations. The power allocated among the subchannels would be optimum if the water pouring theorem were applied. However, at the high SNRs which are of interest here, very little performance is lost if equal power is allocated to each subchannel, over a bandwidth for which useful communication can be achieved over each subcarrier. At the same time, it is highly desirable to vary the constellation sizes among the subcarriers so that each achieves approximately the same error

A DMT modem  probability, thereby maximizing total throughput for a given target of overall error probability [9]. At the receiver, data symbols are recovered by performing a DFT on each block of N received complex symbols or 2N real symbols. If there is no interference among blocks, equalization could be performed strictly in the frequency domain, and would consist simply of multiplying each complex output symbol by a complex number. These multipliers are independent, and no iterative adaptation algorithm is needed.

In typical DMT systems, all processing is confined to a single block. This is desirable in order to avoid both excess complexity and latency. In order to avoid interblock interference, a guard interval of time is inserted at the transmitter between transmitted blocks. The duration of the guard interval should be less than the dispersion of the channel. When this is not the case, as in current multitone ADSL systems, time domain equalization is required at the receiver prior to the DFT. Because of the mechanics of the DFT, the guard interval is typically filled with a “cyclic prefix”; that is, a repetition of the end of each transmitted block is appended to the beginning of the block, which is discarded at the receiver.

A block diagram of a typical DMT system is shown in Fig. 2. In order that the inefficiency due to the guard interval be kept low, the interval must be small compared with the block length. This implies that block length N must be high. A high block length also implies narrow subchannels with little variation in SNR for each one. Values of N are typically on the order of several hundred. For a transmitted sample rate equivalent to 1/T complex symbols per unit time, which is slightly higher than the original symbol rate due to the guard intervals, the block rate will be 1INT.

That rate is fixed at 4312.5 Hz in current ADSL standards, while most other parameters are variable. The transmitted signal is then equivalent to N QAM signals, each modulated by a square-wave data signal carrying one of the a,s, spaced in frequency 1INT apart. Each of the individual QAM signals therefore has a sin(kf)lf spectrum, illustrated in Fig. 3, centered on one of the frequencies kINT, with nulls at all others. As is well known, the sin(kfilffunction decays quite slowly, with sidelobes only 13.5 dB down at 1.5INT from the center; 17.9 dB 2.5lNT away, …; and asymptotic decay at a rate of f-1.

Recently, a variation of DMT, called discrete wavelet multitone (DWMT), has been introduced [10] and proposed at least for upstream cable TV. It requires multiple overlapping blocks, and therefore introduces substantial added complexity and delay. The resulting spectrum is similar to standard DMT, except that the spectrum of each subchannel decays much faster. For a transform span of six blocks, the first sidelobe is down 45 dB, with f2 decrease beyond, compared with f1 in standard DMT. In addition, no guard intervals are needed, thereby increasing spectral efficiency and obviating the need for time domain equalization.

However, interblock processing and equalization are required at the receiver.

For point-to-point applications such as ADSL, it is current practice to perform a bit allocation algorithm to achieve the criterion of approximate equal error probability among the subchannels.

An iterative measurement of performance of each subchannel is performed at the receiver, and instructions are sent back to the transmitter to change the constellation sizes. This is usually performed as part of the startup procedure. It could also take place during normal operation, in which case some receiver-to-transmitter capacity must be reserved, and great care is needed in synchronizing the algorithm.

Each subchannel is usually constrained to carry an integral number of bits, although fractional bit allocation is possible. Performance loss due to this constraint is reduced, but not eliminated, by adjusting the powers of the subchannels away from equality.

PERFORMANCE COMPARISONS

We are now ready to compare the performance of single carrier and multitone systems subjected to various impairments. The emphasis will be on impairments found on the subscriber line used for ADSL, and impairments resulting from inherent nonideal implementation.

We will assume implementations now being employed for ADSL modems, which include DFE with Tomlinson filtering in single-carrier CAP systems, and adaptive bit loading in DMT systems.

FLAT CHANNEL

In evaluating performance, flatness refers to constancy of SNR across the frequency band, rather than signal loss alone. The reasonableness of this criteria can be seen by placing a hypothetical filter at the receiver input. This changes both the signal and noise spectra, but not their ratio as a function of frequency. The flat channel is presented here as a theoretical benchmark, and in no way approximates the subscriber line. On a flat bandlimited channel, either single-carrier or multitone systems can carry slightly less than one complex symbol per Hertz. The reduction from ideal in single-carrier modulation results from finite rolloff, typically about 15 percent. For multitone, the reduction arises from the need for guard intervals and the necessity of avoiding excessive reduction of the sidelobes of subchannels near the band edge. The bandwidth efficiency increases with block size. For typical implementations with block size of a few hundred, the efficiency is approximately the same as a typical single-carrier system.

On this idealized channel, each multitone subchannel should carry the same size constellation, which in turn is what a single-carrier system should carry for the same total transmitted power and the same error probability. Not surprisingly, the systems are fully equivalent under these ideal conditions. As will be described later, if the power constraint is changed from average power to peak power, multitone systems are at a distinct disadvantage. Another reasonable constraint is on power spectral density rather than total average power. Indeed, many requirements impose a mask below which the signal spectrum must lie at all frequencies. If the mask is flat over the band used, the multitone system is at a slight disadvantage in that reallocating power among subchannels is not a viable means of improving performance as it would be under an average power constraint.

NONFLAT CHANNELS

The subscriber line is an extremely nonflat channel. Not only does the signal loss increase with frequency, but the noise, which is primarily due to crosstalk from other signals in the cable, typically also increases with frequency. The noise is generally modeled as Gaussian but nonwhite. Implementation imperfections, such as quantization noise and residual echo, are modeled as an additional Gaussian white noise floor. It has been shown that over a nonflat channel, a single-carrier system using an ideal DFE achieves the same performance as a multitone system with ideal bit allocation, at high SNR where ADSL systems operate [ll]. However, practical implementation issues cause both systems to deviate from ideal. For the single-carrier system, use of a DFE is essential. If any form of coding is employed, as is typical in a highperformance system, error propagation could become a serious problem. This is fully solved by the use of transmitter functionality, the simplest of which is the Tomlinson filter. A new problem of enabling continuous adaptation arises unless some reverse transmission capacity is dedicated. The hybrid form of DFE provides another solution to this as well as other problems. Here good performance is achieved without a full-time reverse adaptation channel, by continually adapting the forward section and the initially zeroed feedback coefficients in the receiver, while leaving the Tomlinson filter fixed. In most multitone systems, the number of bits per subchannel is restricted to an integral number. Fractional rates per subchannel are possible, but the bit allocation procedure becomes much more complex. After bit allocation to integral quantities is completed, a power adjustment among the subchannels reduces this performance loss to approximately 0.5 dB, assuming an average power rather than a spectral density constraint. Continual adaptation is difficult, in that not only is a reverse communication channel required, but synchronization between the transmitter and receiver is critical in order for both to assume the same constellation set at every instant. A further loss results from a practical limit on individual constellation size. Ideal performance requires that the constellation size of subchannels in the high SNR region be quite high, while implementation issues such as bits of precision and irreducible imperfections limit the maximum constellation size. It is interesting to compare bandwidth utilization for the two systems. Unlike a radio or voiceband channel, the wirepair channel does not have a clearcut bandwidth. Since both the theoretical capacity and the actual performance of highquality modems depend primarily on the SNR, a good definition of bandwidth is the frequency range over which the SNR is above some value. For a typical wire-pair channel with crosstalk as the dominant noise, approximately 96 percent of the ideal capacity is achieved if the band is restricted to that for which the SNR is greater than 0 dB. Empirical optimization of a single-channel system, varying the symbol rate and constellation size to maximize bit rate for a given error probability, usually leads to use of approximately such a bandwidth. A typical multitone system, on the other hand, does not use any spectrum which cannot support a fourpoint QAM constellation. This requires an SNR of 10-15 dB, depending on the required performance and the presence of coding. The bandwidth used is therefore less than that of a single-carrier system. Under an average power constraint, not using some bandwidth may entail little or no performance loss because the power is distributed over the narrower band. However, this is not the case under a power spectral density constraint.

TIME-VARYING CHANNELS

The frequency domain equalizer in a multitone system is particularly well suited for tracking time-varying loss and phase vs. frequency functions as are present in radio environments. Fortunately, the subscriber line’s transmission characteristics remain largely constant over time. The only significant variation is a slow one as temperature changes. The relatively slow equalizer convergence in a single-carrier system is more than adequate for adaptation. However, the noise in a subscriber line channel may be more time-varying than the transmission characteristics, because offending crosstalk signals and other interferers may come and go during the course of a communication session. The DFE, which remains active in the receiver in a single-carrier system, will adapt to changing noise and interference, albeit slowly. On the other hand, continuous adaptation of the multitone bit allocation algorithm may be difficult to implement.

CLIPPING

Practical modems have limits on the extremes of signal amplitude they can handle, because of transmit amplifier saturation and digital-to-analog (D/A) and A/D range limits. Because performance in the presence of noise depends on average transmit power, sensitivity of a modulation system to clipping depends on the peak-to-average power ratio (PAR), the ratio of the system’s peak power excursion to its average power. It may be noted that the PAR is the square of the crest factor, which is the ratio of peak to root mean square (rms) voltage. For a large one-dimensional alphabet or a square two dimensional constellation, the inherent peak power is up to three times or 4.8 dB greater than the average. If the constellation is shaped to be closer to circular than square, as is usual in high-performance voiceband modems, the PAR can be reduced by up to 2 dB. This latter reduction is usually not applicable when Tomlinson filtering is employed. Although it is possible to provide constellation shaping, the simplest and usual Tomlinson filter leads to a square constellation. The above quantities apply only at the sampling instants. Sharp rolloff systems produce significant overshoot between samples. For 15 percent rolloff, the maximum overshoot is 6 dB. Adding another 3 dB for the PAR of the sinusoidal carrier, whether actual or implicit, a final PAR of approximately 14 dB results for the above assumptions, including a square constellation. In a multitone system the absolute PAR can be extremely large. If the information is such that all N subcarriers line up in phase, the amplitude will be N times that of each subchannel, so the peak total power will be hR times the peak subchannel power. The absolute PAR, therefore, is proportional to N, and becomes extremely large for block sizes on the order of hundreds. However, absolute PAR is not a reasonable measure, because with well scrambled data extreme peaks will occur with very low probability. A more reasonable approach is to recognize that rare clipping can be tolerated if it occurs seldom enough to have an insignificant effect on the error probability. When the number of subchannels is greater than about 32, the central limit theorem holds for probabilities of interest, say above 10-8, and the amplitude distribution is well approximated by a normal one with variance equal to the average power. Notice that for typical block sizes this probability distribution is independent of block size, and only depends on the total power. For example, the amplitude will exceed five times its rms value with probability 1.2 x 10-6. It makes sense to define the crest factor according to some such probability, rather than the absolute peak. The effect of clipping can be treated as an added noise equal to the clipped portion of the signal. Some recent analysis examines the average power of this clipping noise and reaches very optimistic conclusions about its effects, because the signal-to-clipping-noise ratio will be high due to the rare occurrence of clips. However, the clipping noise is highly impulsive in nature, and is far more likely to produce error than Gaussian noise of the same average power. A mild clip will produce a relatively small impulse that may not lead to error, particularly if the constellation size is not very large, so the clipping probability could be greater than the resulting error probability. A clipping level of five times the rms signal amplitude (14 dB) is needed to guarantee an error probability below le8 due to clipping alone in a typical system. Adding 3 dB for modulation, the effective PAR for this condition is 17 dB, or 3 dB greater than the absolute PAR of a typical singlecarrier system. Some standards specifications require a clipping probability below which adds approximately an additional 1 dB to the above multitone PAR.

OTHER NONLINEARITIES

Power law nonlinearities, which generate spurious signals at various sum and difference frequencies of combinations of signal components, are not a major problem on subscriber lines. However, minimizing such nonlinearities in a transmitter’s analog circuitry can pose a difficult design problem. For usual DMT implementations, these spurious components will fall directly on other channels, and the results will not be too serious. The degradation will be about the same as for a single-carrier system. However, if a second modulation stage is used whose frequency is not at an integral multiple of the block rate, the spurious components may interfere with several subchannels in a noncoherent manner, leading to substantially poorer performance. FREQUENCY OFFSET AND PHASE NOISE Frequency offset, such as that introduced by Doppler shift in a mobile radio environment, can greatly degrade multitone performance due to interference among subchannels. However, this should not be a problem in the ADSL environment. In typical implementations, one of the subchannels is devoted to synchronization, and the receiver derives required frequencies from that signal. For a large number of subchannels, the loss in efficiency is small. It is essential that the recovered frequencies be very free of phase noise for good performance. Frequencies for demodulation in a single-carrier system are almost always derived from the information-bearing signal itself. This leads to higher phase noise, but the system is less sensitive to such phase noise. In any case, this should not be a problem in any well designed system of either type. TIMING JIITER The problem of timing jitter is similar to that of phase noise. A multitone system typically carries timing information by sending a known sequence on its synchronization subchannel, while a single-carrier system typically extracts timing from the information signal itself. Inherent jitter in recovered timing will inherently be higher when timing is recovered from the information signal. But again, the multitone system is more susceptible to timing jitter, particularly for the higher-frequency subchannels and those that carry large constellations [12]. It is well recognized for both modulation schemes that low jitter timing recovery is essential. This invariably requires the use of a phase-locked loop with extremely narrow bandwidth. IMPULSE NOISE It is well recognized that impulse noise is one of the most severe degradations in systems for high-speed transmission over the subscriber loop plant. Although numerous measurement programs and studies have been performed throughout the world, the nature of impulse noise is still not fully understood, nor does a realistic model exist. It is generally believed, however, that such noise arises due to switching transients coupled to many pairs in the central office, and to various electrical devices on the customers’ premises. Inability to characterize impulse noise renders the problem of comparing the sensitivity of different modulation systems difficult if not impossible. Because of the importance of this problem, standards bodies have proposed models which may not well approximate most actual cases of impulse noise, because some repeatable means of comparative testing is believed to be essential. The simplest, but not very realistic, model of impulse noise consists of isolated narrow pulses of varying amplitude. For such interference, uncoded single-tone systems will begin to make errors at impulse amplitudes which will not affect multitone, unless the multitone system contains extremely large constellations on any of its subchannels. The multitone receiver will spread the energy of the impulse over many subchannels, thereby reducing its effect; or equivalently, that receiver processes each symbol over a long period of time, namely the block duration, minimizing the effect of a short-duration impulse. As the strength of the impulse increases further, however, it will affect a major portion of a block in multitone, while still only affecting a few symbols in a single-carrier system. Any subsequent coding, such as a Reed-Solomon code, will therefore be more effective in a single-carrier system, in that a multitone system may require an excessive amount of interleaving. For a given requirement on latency which in effect restricts interleaving depth, the relative advantage of multitone over single-carrier vanishes when a powerful code such as Reed-Solomon is used in both cases. If the impulses occur in bursts, as is frequently the case, rather than as single isolated pulses, the relative susceptibility of multitone increases. The same is true when the duration of the impulses is long.

NARROWBAND INTERFERENCE

Because of the wide band used by advanced ADSL systems, over 1 MHz., narrow band interferers become another important source of degradation. Such interference may result, for example, from pickup of a nearby AM radio station in uncontrolled wiring on customers’ premises or in the final drop to the customer. For multitone systems, it was thought at first that adaptive 118 IEEE Communications Magazine November 1998 bit loading provided a good solution to the problem. The idea was to reduce the constellation size, possibly to zero, on those subchannels affected by the interferer. However, because of the sin(b)/x spectrum of each subchannel, the receiver will pass the interferer into many subchannels, even if the interferer is narrow compared with a subchannel (Fig. 3). Because the signal power on a subchannel is only 1/N of the total signal power, susceptibility to an interferer with energy concentrated in frequency is particularly acute. Large constellation size on an affected subchannel further aggravates the problem. Coding across the frequency subchannels, rather than over time, can provide some improvement. It was primarily for this problem that DWMT was proposed. Because of the restricted spectrum of each subchannel in this modulation scheme, eliminating or reducing the constellation on the few affected subchannels becomes effective. However, at this time DWMT is only being proposed for the upstream cable TV channel, where the problem is particularly serious, and not for ADSL. It has long been recognized that a mean square algorithm in a single-carrier equalizer can reduce the effect of a narrowband interferer by creating a notch in the receiver’s response at the offending frequency. In many cases this is done at the expense of poorer IS1 correction. However, a noise predictive DFE, or that component of a hybrid DFE, is particularly effective in reducing a narrowband interferer without affecting ISI. This has been extensively verified experimentally. In addition, a single-carrier system is inherently less susceptible to narrowband interference. THE COST OF IMPLEMENTATION Any comparison of the costs of different modulation systems is certain to be highly controversial. Apparent complexity of required functionality does not necessarily translate into a measure of cost, such as chip area. Clever system, circuit, and algorithmic design often produces unexpected cost-saving shortcuts. With this caveat in mind, we will try to identify differences between single-carrier and multitone system that lead to higher cost for one of them, under the constraint of approximately equal performance. Of necessity, comparisons will have to be qualitative. One component of cost which should not be overlooked is that of power drain, particularly in the central office modem. The cost of power, and its associated heat removal, is substantially higher in that environment than in most customer premises environments. However, power consumption, and therefore temperature rise, can be a significant issue on customers’ premises where the ambient temperature is not controlled.

THE NEED FOR AND BENEFITS OF ECHO CANCELING

Before examining relative costs, it is necessary to address an architectural issue which has a substantial effect on both cost and performance, which is whether or not to implement echo cancellation in an ADSL system. For a system with simultaneous symmetric data rates in both directions over a wire pair, such as ISDN access or HDSL, there is little question that echo cancellation is the preferred way of providing the required separation. Either frequency or time separation involves a bandwidth penalty greater than a factor of two, which is intolerable. In ADSL, when the ratio of upstream to downstream bandwidth is low, it is questionable whether the relatively small benefit in bandwidth utilization is worth the many problems and high cost that are present in systems with echo cancellation. In current single-carrier ADSL designs, echo canceling is not used. Instead, a relatively narrow low-frequency upstream band is separated in frequency from a wider downstream band that is higher in frequency, by a pair of sharp active analog filters. In a recent high-performance system, the upstream spectrum is confined to the band 35-191 kHz, while the downstream signal spectrum begins at 240 kHz and may extend as far as 1491 kHz. The separation filters therefore have the range between 191 and 240 kHz to transition from high to low attenuation. Normal equalization can handle the distortion introduced by the filter with little increase in the already large number of taps. It would certainly be possible to save up to 205 kHz in total bandwidth by using echo cancellation and allowing the upstream and downstream bands to overlap. Performance of the downstream channel would improve by having its upper frequency reduced out of the region of poor SNR. If this were done, however, all the problems described below would be present. In the multitone system, echo cancellation is essentially required, and in fact is present in such existing systems. If, instead, a multitone system depended on frequency separation, the phase distortion of the separation filters, and the elimination of sidelobes of some of the subchannels, would introduce time dispersion substantially greater than the guard interval. This in turn would require enough time domain equalization prior to the receiver DFT to obviate one of the prime advantages of multitone. The use of an echo cancellation architecture, with overlapping spectra, introduces the problem of near-end crosstalk, which is the dominant impairment in ISDN access and HDSL. The problem exists particularly at the central office, which is most likely to have many collocated ADSL systems, and where the received upstream channel may be subjected to full overlap of its spectrum by the offending downstream channels. The problem is somewhat mitigated by the lower crosstalk coupling present at these lower frequencies. Many of the subsequent issues are dependent on the presence or absence of echo cancellation. They are applicable to comparison of the two modulation schemes only to the extent that, at least in current implementations, one scheme uses echo cancellation while the other does not, for the reasons given above.

COMPUTATIONAL COMPLEXITY

Computational complexity is translated into cost, and also power drain, through the required number or size of digital signal processing (DSP) devices, program memory, and temporary memory. Again, one must be careful to look beyond apparent conceptual complexity to estimate approximate cost. Because of the efficiency of FFT algorithms in a multitone implementation, and the large number of taps required for satisfactory equalization in a single-carrier system, the number of multiplications and additions per unit of time is typically larger in the single-carrier system. This is at least partially compensated for by the smoother control flow in time domain equalization as compared with FFT processing. The inherent complexity of the bit allocation procedure in a high-performance multitone system leads to the need for large program storage. Overall, the DSP hardware required for basic modulation and demodulation should not be radically different for the two high-performance modulation schemes. It is interesting to note that less digital processing is required for the transmitter function in the single-carrier system because the Tomlinson filter requires few taps compared to the feedforward filter in the receiver’s equalizer. This may be significant in reducing the relative cost of the central office modem where the high-speed transmitter is located. Echo cancellation typically requires about as much or more IEEE Communications Magazine November 1998 119 I I W Table 1. Relative advantages of single-cam’er and multitone modulation for ADSL. X denotes the system with betterperformance or lower cost. processing than equalization. Here a multitone system using a frequency domain algorithm for echo cancellation can save cost because the frequency overlap of the desired and interfering spectra is only partial. The large number of coefficients in the single-carrier time domain equalizer requires that each of those coefficients must be represented with a large number of bits in order to reduce quantization error and to allow adaptation with the necessarily small step size. The required small step size also leads to long adaptation time. The frequency domain equalizer in the multitone system does not have these problems, even though the number of multipliers is also large. In this case, there is no interaction among the multipliers, so adaptation is very quick, and quantization errors due to multiplier roundoff do not add.

D/A AND A/D CONVERSION

A major component of the cost and power drain of any modem is the D/A converter in the transmitter and the A/D converter in the receiver. For a given speed of operation, the cost increases rapidly with the number of bits of conversion. The effect of finite precision is to introduce a white quantization noise at the converter output. The converters must handle the full signal amplitude range with no (or negligible) clipping, and also produce quantization noise sufficiently below the signal power to have negligible effect on the error probability. The required number of bits therefore depends on both the PAR and the required SNR at all frequencies. Even neglecting problems associated with echo cancellation, multitone systems will require more bits in the D/A and A/D converters. First, the PAR is higher, as described previously. Second, the use of large constellation sizes on some subcarriers leads to greater sensitivity to quantization noise. The use of echo cancellation further increases the required number of bits. Because of the high loss to which the received signal may be subjected and the difficulty of providing more than moderate trans-hybrid loss, the echo of the transmitted signal may be substantially stronger than the desired received signal. The effect is stronger at the central office modem, where the transmitted downstream power is much higher than the upstream power at the customer’s end. The result is a need for additional bits in the receiver’s A/D converter to avoid clipping of the echo and still keep quantization noise well below the receive level. Performance of an echo canceller is particularly sensitive to clipping. In any case, high precision is needed due to the need for high echo reduction. For a multitone signal, the echo has the same PAR problems as those of the signal itself, therefore magnifying the problem.

ANALOG FRONT-END CIRCUITRY

As improvements in the density of digital circuitry continue, the fractional cost of the irreducible analog circuitry (including the D/A and A/D converters) becomes larger and even dominant because of the much slower pace of cost reduction for these types of circuitry. The components include analog filters in the transmitter and receiver, the transmitter line driver, receiver input amplifier, and hybrid circuit. These components also account for a major part of the modem power drain. These components are a possible source of the nonlinearities which must be avoided in any modulation system. Nonlinearities can be particularly serious in an echo cancellation architecture. This can be inferred by the use of nonlinear echo cancellers in some ISDN access modems, and the absence of nonlinear equalization in any known modem. A particularly critical analog component is the transmitter line driver, particularly the downstream driver at the central office which delivers the wider band and higher power channel. This component must deliver approximately 100 mW average signal power into a low impedance with high linearity and low probability of clipping. The line driver is therefore a major source of cost and the largest consumer of power in the environment where power consumption is most critical. Its requirements are more severe for high PAR signals such as multitone. The receiver input amplifier must linearly amplify a potentially weak signal without contributing enough internal noise or other degradation to substantially decrease the received SNR. The requirements become much more severe in an echo cancellation architecture. However, in this environment the requirements of the analog filters are substantially eased, since they need perform little or no separation of the two directions of transmission.

BIT RATE ADAPTATION

In the most current version of ADSL, intended primarily for applications such as access to the Internet, it is intended that the bit rate, particularly in the downstream direction, be automatically adjustable in order to provide acceptable performance over a wide variety of subscriber lines. The applications can tolerate the variable bit rate, and it is further desirable that different versions of modems need not be provided to account for lines of different length, noise level, and so on. The capability of providing the maximum bit rate that a particular line can support is inherent in the multitone bit allocation algorithm. It is intended in such systems to be able to vary the bit rate in steps of 32 kbis. A rate adjustment procedure will be needed in the single-carrier system. The procedure will most likely involve changing both constellation size and symbol rate, as is common procedure in voiceband modems.

CONCLUTION

On a fundamental level, there is little difference in performance between single-carrier and multicarrier systems, because the multicarrier modulation can be seen to be just a linear reversible transformation of a single-carrier signal. However, many practical differences lead to advantages of one system over the other, in terms of both performance and cost of implementation, depending on the degradations present in the channel and on the application. Table 1 presents a current view of which modulation system has the relative advantage, if any, for various performance and cost issues. This article presents the author’s observations concerning probable differences between the modulation systems. More definitive comparisons must await availability of final production devices, particularly for multitone. Examination of cost and performance in a large and diversified set of field trials should clarify the relative advantages and disadvantages of the modulation systems.